From 13f7d144ea868547b7f21000f1fddd836f8b38e9 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Thu, 15 Nov 2012 16:31:17 -0500
Subject: fields definitions are placed

---
 .../realistic_Rb_and_fields.xmds                   | 641 +++++++++++++++++++++
 1 file changed, 641 insertions(+)
 create mode 100644 xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
new file mode 100644
index 0000000..bfed139
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
@@ -0,0 +1,641 @@
+<?xml version="1.0"?>
+<simulation xmds-version="2">
+	<testing>
+		<arguments> --Ndens=1e15 --Lcell=10.0e-2  --Temperature=1e-3  --Pwidth=0.4e-6  --delta1=0 --delta2=0 --delta3=0  --E1o=0 --E2o=1e2 --E3o=0 --E4o=0</arguments>
+		<xsil_file name="realistic_Rb.xsil" expected="realistic_Rb_expected.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5">
+			<moment_group number="0" absolute_tolerance="1e-7" relative_tolerance="1e-6" />
+		</xsil_file>
+	</testing>
+
+	<name>realistic_Rb_and_fields</name>
+
+	<author>Eugeniy Mikhailov</author>
+	<description>
+		License GPL.
+
+		Solving simplified Rb atom model
+		with fields propagation along spatial axis Z
+		with Doppler broadening.
+
+
+		We assume four-wave mixing condition when w3-w4=w2-w1 i.e. fields E3 and E4 drive the same
+		resonance as fields E2 and E1.
+
+
+		*              --------------- | F=1, 2P_3/2 >
+		*                \        \    
+		*                 \ E3_r   \    -------- | F=2, 2P_+1/2 >
+		*                  \   E4_r \   /    \
+		*                   \        \ / E2_l \ 
+		*                    \        /        \ E1_l
+		*   | F=2, 2S_1/2 > --------------      \
+		*                               \        \
+		*                                \        \
+		*                               ------------- | F=1, 2S_1/2 >
+		*            
+
+
+		We are solving 
+			dE/dz+(1/c)*dE/dt=i*eta*rho_ij,  where j level is higher than i.
+			Note that E is actually a Rabi frequency of electromagnetic field not the EM field
+		in xmds terms it looks like
+			dE_dz = i*eta*rhoij - 1/c*L[E], here we moved t dependence to Fourier space
+
+		VERY IMPORTANT: all Rabi frequency should be given in [1/s], if you want to
+		normalize it to something else look drho/dt equation.
+		No need to renormalizes eta as long as its express through
+		the upper level decay rate in the same units as Rabi frequency.
+	</description>
+
+	<features>
+		<globals>
+			<![CDATA[
+				// Some numerical constants
+				const double pi = M_PI; 
+
+				// atom related constants
+				//read from Mathematica generated Constants.txt
+//---------------- Constants.txt starts ------------------
+const double ha0 = 2.1471788680034824e10;
+const double ha1 = 2.558764384495815e9;
+const double g1 = 3.612847284945266e7;
+const double ha2 = 5.323020344462938e8;
+const double hb2 = 7.85178251911697e7;
+const double g2 = 3.8117309832741246e7;
+const double lambda1 = 7.949788511562656e-7;
+const double lambda2 = 7.802412096860509e-7;
+const double eta1 = 5.450949336831401e-6;
+const double eta2 = 5.5397657647874e-6;
+const double rt6 = 2.449489742783178;
+const double rt3 = 1.7320508075688772;
+const double rt2 = 1.4142135623730951;
+//---------------- Constants.txt ends   ------------------
+
+				const double c=3.e8;
+				const double k_boltzmann= 1.3806505e-23; // Boltzmann knostant in [J/K]
+				const double lambda=794.7e-9; //wavelength in m
+				// Fields k-vector
+				const double Kvec = 2*M_PI/lambda;  
+				// Simplified k-vectors
+				const double Kvec1 = Kvec, Kvec2=Kvec, Kvec3=Kvec;
+
+				//  ---------  Atom and cell properties -------------------------
+				// range of Maxwell distribution atomic velocities
+				const double mass = (86.909180527 * 1.660538921e-27); // atom mass in [kg] 
+				// above mass expression is written as (expression is isotopic_mass * atomic_mass_unit)
+
+				// Average sqrt(v^2) in Maxwell distribution for one dimension
+				// Maxwell related parameters will be calculated in <arguments> section
+				double v_thermal_averaged=0;
+				// Maxwell distribution velocities range to take in account in [m/s]
+				double V_maxwell_min = 0, V_maxwell_max = 0;
+
+				// repopulation rate (atoms flying in/out the laser beam)  in [1/s]
+				const double gt=0.01 *(2*M_PI*1e6);
+
+				// Larmor frequency 
+				double WL=0;
+
+
+				// inner use variables 
+				double probability_v; // will be used as p(v) in Maxwell distribution
+
+			]]>
+		</globals>
+		<validation kind="run-time"/> <!--allows to put ranges as variables-->
+		<benchmark />
+    <arguments>
+			<!-- Rabi frequency divided by 2 in [1/s] -->
+			<!--
+				Had to be very verbal with fields names, since otherwise short options name
+				algorithm runs out of choices
+			-->
+      <argument name="Ep1o_field" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+      <argument name="Em1o_field" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+      <argument name="Ep2o_field" type="real" default_value="0.05*(2*M_PI*1e6)" />
+      <argument name="Em2o_field" type="real" default_value="0.05*(2*M_PI*1e6)" />
+      <argument name="Ep3o_field" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+      <argument name="Em3o_field" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+      <argument name="Ep4o_field" type="real" default_value=".01*(2*M_PI*1e6)" />
+      <argument name="Em4o_field" type="real" default_value=".01*(2*M_PI*1e6)" />
+			<!-- Fields detuning in [1/s] -->
+      <argument name="delta1"  type="real" default_value="0.0" />
+      <argument name="delta2"  type="real" default_value="0.0" />
+      <argument name="delta3"  type="real" default_value="0.0" />
+			<!--Pulse duration/width [s] -->
+			<argument name="Pwidth"  type="real" default_value="0.1e-6" />
+			<!--  Atom and cell properties -->
+			<!--Cell length [m] -->
+			<argument name="Lcell"  type="real" default_value="1.5e-2" />
+			<!--Density of atoms [1/m^3] -->
+			<argument name="Ndens"  type="real" default_value="1e15" />
+			<!--Atoms temperature [K] -->
+			<!--TODO: looks like Temperature > 10 K knocks solver, 
+					 I am guessing detunings are too large and thus it became a stiff equation-->
+			<!--! make sure it is not equal to zero!-->
+			<argument name="Temperature"  type="real" default_value="5" />
+			<!-- This will be executed after arguments/parameters are parsed -->
+			<!-- Read the code Luke: took me a while of reading the xmds2 sources to find it -->
+			<![CDATA[
+				// Average sqrt(v^2) in Maxwell distribution for one dimension
+				if (Temperature == 0)
+					_LOG(_ERROR_LOG_LEVEL, "ERROR: Temperature should be >0 to provide range for Maxwell velocity distribution\n");
+				v_thermal_averaged=sqrt(k_boltzmann*Temperature/mass); 
+				// Maxwell distribution velocities range to take in account in [m/s]
+				// there is almost zero probability for higher velocity p(4*v_av) = 3.3e-04 * p(0)
+				V_maxwell_min = -4*v_thermal_averaged; V_maxwell_max = -V_maxwell_min; 
+			]]>
+    </arguments>
+		<bing />
+		<diagnostics /> 
+		<fftw plan="estimate" threads="1" />
+		<!--<fftw plan="patient" threads="1" />-->
+		<!-- I don't see any speed up on 6 core CPU even if use threads="6" -->
+		<!--<openmp />-->
+		<auto_vectorise />
+		<halt_non_finite />
+	</features>
+
+	<!-- 'z', 't', and 'v'  to have dimensions [m], [s], and [m/s]   -->
+	<geometry>
+		<propagation_dimension> z </propagation_dimension>
+		<transverse_dimensions>
+			<!-- IMPORTANT: looks like having a lot of points in time helps with convergence.
+					 I suspect that time spacing should be small enough to catch
+					 all pulse harmonics and more importantly 1/dt should be larger than
+					 the largest detuning (including Doppler shifts).
+					 Unfortunately calculation time is proportional to lattice size
+					 so we cannot just blindly increase it.
+					 Some rules of thumb:  
+						* lattice="1000"   domain="(-1e-6, 1e-6)" 
+							was good enough detunings up to 155 MHz (980 rad/s) notice that 1/dt=500 MHz
+						* lattice="10000"   domain="(-1e-6, 1e-6)" 
+							works for Doppler averaging in up to 400K for Rb when lasers are zero detuned
+			 -->
+			<dimension name="t"   lattice="10000"   domain="(-1e-6, 1e-6)" />
+			<dimension name="v"   lattice="2"   domain="(V_maxwell_min, V_maxwell_max)" />
+		</transverse_dimensions>
+	</geometry>
+
+	<!-- Rabi frequency --> 
+	<vector name="E_field" type="complex" initial_space="t">
+		 <!--plus/minus circular polarization components-->
+		<components>Ep1 Em1 Ep2 Em2 Ep3 Em3 Ep4 Em4</components>
+		<initialisation>
+			<![CDATA[
+			// Initial (at starting 'z' position) electromagnetic field does not depend on detuning
+			// as well as time
+			Ep1=Ep1o_field;
+			Em1=Em1o_field;
+			Ep2=Ep2o_field*exp(-pow( ((t-0.0)/Pwidth),2) );
+			Em2=Em2o_field*exp(-pow( ((t-0.0)/Pwidth),2) );
+			Ep3=Ep3o_field;
+			Em3=Em3o_field;
+			Ep4=Ep4o_field;
+			Em4=Em4o_field;
+			]]>
+		</initialisation>
+	</vector>
+
+	<!--Maxwell distribution probability p(v)-->
+	<computed_vector name="Maxwell_distribution_probabilities" dimensions="v" type="real">
+		<components>probability_v</components>
+		<evaluation>
+			<![CDATA[
+			// TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during  the script lifetime since 'v' is fixed.
+			probability_v=1.0/(v_thermal_averaged*sqrt(2*M_PI)) * exp( - mod2(v/v_thermal_averaged)/2.0 ); 
+			]]>
+		</evaluation>
+	</computed_vector>
+
+	<!--Maxwell distribution norm sum(p(v))
+			 Needed since we sum over the grid instead of true integral,
+			 we also have finite cut off velocities-->
+	<computed_vector name="Maxwell_distribution_probabilities_norm" dimensions="" type="real">
+		<components>probability_v_norm</components>
+		<evaluation>
+			<dependencies basis="v">Maxwell_distribution_probabilities</dependencies>
+			<![CDATA[
+			// TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during  the script lifetime since 'v' is fixed.
+			probability_v_norm=probability_v;
+			]]>
+		</evaluation>
+	</computed_vector>
+
+
+	<!-- Averaged across Maxwell distribution fields amplitudes -->
+	<computed_vector name="E_field_avgd" dimensions="t" type="complex">
+		<components>Ep1a Em1a Ep2a Em2a Ep3a Em3a Ep4a Em4a</components>
+		<evaluation>
+			<dependencies basis="v">E_field Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm</dependencies>
+			<![CDATA[
+			double prob_v_normalized=probability_v/probability_v_norm;
+			Ep1a=Ep1*prob_v_normalized;
+			Em1a=Em1*prob_v_normalized;
+			Ep2a=Ep2*prob_v_normalized;
+			Em2a=Em2*prob_v_normalized;
+			Ep3a=Ep3*prob_v_normalized;
+			Em3a=Em3*prob_v_normalized;
+			Ep4a=Ep4*prob_v_normalized;
+			Em4a=Em4*prob_v_normalized;
+			]]>
+		</evaluation>
+	</computed_vector>
+
+	<vector name="density_matrix" type="complex" initial_space="t">
+		<components>
+			<!-- read from Mathematica generated RbChosenRho.txt -->
+<!-- ############### RbChosenRho.txt starts ################ -->
+r0101 r0113 r0202 r0214 r0303 r0309 r0315 r0404 r0410 r0416 r0505 r0511 r0602 r0606 r0614 r0703 r0707 r0709 r0715 r0804 r0808 r0810 r0816 r0909 r0915 r1010 r1016 r1111 r1313 r1414 r1515 r1616 
+<!-- ############### RbChosenRho.txt ends  ################# -->
+		</components>
+		<initialisation>
+			<!--This sets boundary condition at all times and left border of z (i.e. z=0)-->
+			<![CDATA[
+			// Note: 
+			// convergence is really slow if all populations concentrated at the bottom level |1>
+			// this is because if r11=1, everything else is 0 and then every small increment 
+			// seems to be huge and adaptive solver makes smaller and smaller steps.
+			// As quick and dirty fix I reshuffle initial population  
+			// so some of the population sits at the  second ground level |2>
+			// TODO: Fix above. Make the equation of motion for r11 
+			//       and express other level, let's say r44
+			//       through population normalization
+
+			//read from Mathematica generated RbInits.txt
+//---------------- RbInits.txt starts ------------------
+r0101 = 0.125;
+r0109 = 0;
+r0110 = 0;
+r0111 = 0;
+r0112 = 0;
+r0113 = 0;
+r0114 = 0;
+r0115 = 0;
+r0116 = 0;
+r0201 = 0;
+r0202 = 0.125;
+r0209 = 0;
+r0210 = 0;
+r0211 = 0;
+r0212 = 0;
+r0213 = 0;
+r0214 = 0;
+r0215 = 0;
+r0216 = 0;
+r0301 = 0;
+r0302 = 0;
+r0303 = 0.125;
+r0309 = 0;
+r0310 = 0;
+r0311 = 0;
+r0312 = 0;
+r0313 = 0;
+r0314 = 0;
+r0315 = 0;
+r0316 = 0;
+r0401 = 0;
+r0402 = 0;
+r0403 = 0;
+r0404 = 0.125;
+r0409 = 0;
+r0410 = 0;
+r0411 = 0;
+r0412 = 0;
+r0413 = 0;
+r0414 = 0;
+r0415 = 0;
+r0416 = 0;
+r0501 = 0;
+r0502 = 0;
+r0503 = 0;
+r0504 = 0;
+r0505 = 0.125;
+r0509 = 0;
+r0510 = 0;
+r0511 = 0;
+r0512 = 0;
+r0513 = 0;
+r0514 = 0;
+r0515 = 0;
+r0516 = 0;
+r0601 = 0;
+r0602 = 0;
+r0603 = 0;
+r0604 = 0;
+r0605 = 0;
+r0606 = 0.125;
+r0609 = 0;
+r0610 = 0;
+r0611 = 0;
+r0612 = 0;
+r0613 = 0;
+r0614 = 0;
+r0615 = 0;
+r0616 = 0;
+r0701 = 0;
+r0702 = 0;
+r0703 = 0;
+r0704 = 0;
+r0705 = 0;
+r0706 = 0;
+r0707 = 0.125;
+r0709 = 0;
+r0710 = 0;
+r0711 = 0;
+r0712 = 0;
+r0713 = 0;
+r0714 = 0;
+r0715 = 0;
+r0716 = 0;
+r0801 = 0;
+r0802 = 0;
+r0803 = 0;
+r0804 = 0;
+r0805 = 0;
+r0806 = 0;
+r0807 = 0;
+r0808 = 0.125;
+r0809 = 0;
+r0810 = 0;
+r0811 = 0;
+r0812 = 0;
+r0813 = 0;
+r0814 = 0;
+r0815 = 0;
+r0816 = 0;
+r0909 = 0;
+r0912 = 0;
+r0913 = 0;
+r0914 = 0;
+r0915 = 0;
+r0916 = 0;
+r1009 = 0;
+r1010 = 0;
+r1012 = 0;
+r1013 = 0;
+r1014 = 0;
+r1015 = 0;
+r1016 = 0;
+r1109 = 0;
+r1110 = 0;
+r1111 = 0;
+r1112 = 0;
+r1113 = 0;
+r1114 = 0;
+r1115 = 0;
+r1116 = 0;
+r1212 = 0;
+r1312 = 0;
+r1313 = 0;
+r1412 = 0;
+r1413 = 0;
+r1414 = 0;
+r1512 = 0;
+r1513 = 0;
+r1514 = 0;
+r1515 = 0;
+r1612 = 0;
+r1613 = 0;
+r1614 = 0;
+r1615 = 0;
+r1616 = 0;
+//---------------- RbInits.txt ends  ------------------
+			]]>
+		</initialisation>
+	</vector>
+
+	<sequence>
+		<!--For this set of conditions ARK45 is faster than ARK89-->
+		<!--ARK45 is good for small detuning when all frequency like term are close to zero-->
+		<integrate algorithm="ARK45" tolerance="1e-5" interval="Lcell"> 
+		<!--<integrate algorithm="SI" steps="200" interval="Lcell"> -->
+		<!--RK4 is good for large detunings when frequency like term are big, it does not try to be too smart about adaptive step which ARK seems to make too small-->
+		<!--When ARK45 works it about 3 times faster than RK4 with 1000 steps-->
+		<!--<integrate algorithm="RK4" steps="100" interval="1.5e-2">-->
+		<!--SIC algorithm seems to be much slower and needs fine 'z'  step tuning and much finer time grid-->
+		<!--For example I had to quadruple the time grid from 1000 to 4000 when increased z distance from 0.02 to 0.04-->
+
+		<!--<integrate algorithm="SIC" interval="4e-2" steps="200">-->
+
+			<samples>100</samples>
+			<!--<samples>100 100</samples>-->
+			<!--Use the next line for debuging to see velocity dependence. Uncomment/switch on output groups 3,4-->
+			<!--<samples>100 100 100 100</samples>--> 
+			<operators>
+        <operator kind="cross_propagation" algorithm="SI" propagation_dimension="t">
+					<integration_vectors>density_matrix</integration_vectors>
+          <dependencies>E_field_avgd</dependencies>
+          <boundary_condition kind="left">
+						<!--This set boundary condition at all 'z'  and left border of 't' (i.e. min(t))-->
+						<!--
+            <![CDATA[
+							r11 = 0; r22 = 1; r33 = 0; r44 = 0;
+							r12 = 0; r13 = 0; r14 = 0;
+							r23 = 0; r24 = 0;
+							r34 = 0;
+							printf("z= %g, t= %g\n", z, t);
+            ]]>
+						-->
+          </boundary_condition>
+					<![CDATA[
+						// Equations of motions according to Simon's mathematica code
+						//read from Mathematica generated RbEquations.txt
+//---------------- RbEquations.txt starts ------------------
+dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1212)/3. + (g2*r1313)/6. - i*((conj(Em1a)*conj(r0109))/4. - (conj(Em4a)*conj(r0113))/(4.*rt6) - (Em1a*r0109)/4. + (Em4a*r0113)/(4.*rt6) + r0201*(WLx/2. - (i*WLy)/2.) - conj(r0201)*(WLx/2. + (i*WLy)/2.));
+dr0109_dt = (-(gt*r0109) - (gt + g1)*r0109)/2. - i*(-(conj(Ep1a)*conj(r0301))/(4.*rt6) + (conj(Ep2a)*conj(r0701))/(4.*rt6) - (conj(Em4a)*conj(r0913))/(4.*rt6) - (conj(Em1a)*r0101)/4. + (conj(Em1a)*r0909)/4. + r0209*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-delta1 - v*Kvec1 - WLz/6.) + r0109*WLz);
+dr0110_dt = (-(gt*r0110) - (gt + g1)*r0110)/2. - i*(-(conj(Em1a)*conj(r0201))/(4.*rt2) - (conj(Ep1a)*conj(r0401))/(4.*rt2) - (conj(Em2a)*conj(r0601))/(4.*rt6) + (conj(Ep2a)*conj(r0801))/(4.*rt6) + (conj(Em1a)*conj(r1009))/4. - (conj(Em4a)*conj(r1013))/(4.*rt6) + (delta1 + v*Kvec1)*r0110 + r0210*(WLx/2. - (i*WLy)/2.) - r0111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0110*WLz);
+dr0111_dt = (-(gt*r0111) - (gt + g1)*r0111)/2. - i*(-(conj(Em1a)*conj(r0301))/(4.*rt6) - (conj(Ep1a)*conj(r0501))/4. - (conj(Em2a)*conj(r0701))/(4.*rt6) + (conj(Em1a)*conj(r1109))/4. - (conj(Em4a)*conj(r1113))/(4.*rt6) + r0211*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0111*(-delta1 - v*Kvec1 + WLz/6.) + r0111*WLz);
+dr0112_dt = (-(gt*r0112) - (gt + g2)*r0112)/2. - i*(-(conj(Ep4a)*conj(r0201))/(4.*rt6) - (conj(Ep3a)*conj(r0601))/(4.*rt2) + (conj(Em1a)*r0912)/4. - (conj(Em4a)*r1312)/(4.*rt6) + r0212*(WLx/2. - (i*WLy)/2.) - r0113*((2*WLx)/3. + (2*i*WLy)/3.) + r0112*WLz - r0112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0113_dt = (-(gt*r0113) - (gt + g2)*r0113)/2. - i*(-(conj(Ep4a)*conj(r0301))/8. - (conj(Ep3a)*conj(r0701))/8. + (conj(Em4a)*r0101)/(4.*rt6) + (conj(Em1a)*r0913)/4. - (conj(Em4a)*r1313)/(4.*rt6) - r0112*((2*WLx)/3. - (2*i*WLy)/3.) + r0213*(WLx/2. - (i*WLy)/2.) - r0114*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r0113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + r0113*WLz);
+dr0114_dt = (-(gt*r0114) - (gt + g2)*r0114)/2. - i*((conj(Em4a)*conj(r0201))/8. - (conj(Ep4a)*conj(r0401))/8. - (conj(Em3a)*conj(r0601))/(8.*rt3) - (conj(Ep3a)*conj(r0801))/(8.*rt3) - (conj(Em4a)*conj(r1413))/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0114 + (conj(Em1a)*r0914)/4. + r0214*(WLx/2. - (i*WLy)/2.) - r0113*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0115*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0114*WLz);
+dr0115_dt = (-(gt*r0115) - (gt + g2)*r0115)/2. - i*((conj(Em4a)*conj(r0301))/8. - (conj(Ep4a)*conj(r0501))/(4.*rt6) - (conj(Em3a)*conj(r0701))/8. - (conj(Em4a)*conj(r1513))/(4.*rt6) + (conj(Em1a)*r0915)/4. + r0215*(WLx/2. - (i*WLy)/2.) - r0116*((2*WLx)/3. + (2*i*WLy)/3.) - r0114*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0115*WLz);
+dr0116_dt = (-(gt*r0116) - (gt + g2)*r0116)/2. - i*((conj(Em4a)*conj(r0401))/(4.*rt6) - (conj(Em3a)*conj(r0801))/(4.*rt2) - (conj(Em4a)*conj(r1613))/(4.*rt6) + (conj(Em1a)*r0916)/4. - r0115*((2*WLx)/3. - (2*i*WLy)/3.) + r0216*(WLx/2. - (i*WLy)/2.) - r0116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0116*WLz);
+dr0201_dt = -(gt*r0201) + (g1*r1009)/(2.*rt2) + (g2*r1312)/6. + (g2*r1413)/(2.*rt6) - i*((conj(Em1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0112))/(4.*rt6) - (conj(Em4a)*conj(r0114))/8. - (Em1a*r0209)/4. + (Em4a*r0213)/(4.*rt6) + r0101*(WLx/2. + (i*WLy)/2.) - r0202*(WLx/2. + (i*WLy)/2.) + r0301*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - (r0201*WLz)/2.);
+dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1212)/6. + (g2*r1313)/12. + (g2*r1414)/4. - i*((conj(Em1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Em4a)*conj(r0214))/8. - (Em1a*r0210)/(4.*rt2) - (Ep4a*r0212)/(4.*rt6) + (Em4a*r0214)/8. - r0201*(WLx/2. - (i*WLy)/2.) + conj(r0201)*(WLx/2. + (i*WLy)/2.) + r0302*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - conj(r0302)*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.));
+dr0209_dt = (-(gt*r0209) - (gt + g1)*r0209)/2. - i*(-(conj(Ep1a)*conj(r0302))/(4.*rt6) + (conj(Ep2a)*conj(r0702))/(4.*rt6) + (conj(Ep4a)*conj(r0912))/(4.*rt6) - (conj(Em4a)*conj(r0914))/8. - (conj(Em1a)*r0201)/4. + (conj(Em1a)*r1009)/(4.*rt2) + r0109*(WLx/2. + (i*WLy)/2.) + r0309*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-delta1 - v*Kvec1 - WLz/6.) + (r0209*WLz)/2.);
+dr0210_dt = (-(gt*r0210) - (gt + g1)*r0210)/2. - i*(-(conj(Ep1a)*conj(r0402))/(4.*rt2) - (conj(Em2a)*conj(r0602))/(4.*rt6) + (conj(Ep2a)*conj(r0802))/(4.*rt6) + (conj(Ep4a)*conj(r1012))/(4.*rt6) - (conj(Em4a)*conj(r1014))/8. - (conj(Em1a)*r0202)/(4.*rt2) + (delta1 + v*Kvec1)*r0210 + (conj(Em1a)*r1010)/(4.*rt2) + r0110*(WLx/2. + (i*WLy)/2.) + r0310*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0211*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + (r0210*WLz)/2.);
+dr0211_dt = (-(gt*r0211) - (gt + g1)*r0211)/2. - i*(-(conj(Em1a)*conj(r0302))/(4.*rt6) - (conj(Ep1a)*conj(r0502))/4. - (conj(Em2a)*conj(r0702))/(4.*rt6) + (conj(Em1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1112))/(4.*rt6) - (conj(Em4a)*conj(r1114))/8. + r0111*(WLx/2. + (i*WLy)/2.) + r0311*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0211*(-delta1 - v*Kvec1 + WLz/6.) + (r0211*WLz)/2.);
+dr0212_dt = (-(gt*r0212) - (gt + g2)*r0212)/2. - i*(-(conj(Ep3a)*conj(r0602))/(4.*rt2) - (conj(Ep4a)*r0202)/(4.*rt6) + (conj(Em1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1212)/(4.*rt6) - (conj(Em4a)*r1412)/8. + r0112*(WLx/2. + (i*WLy)/2.) - r0213*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + (r0212*WLz)/2. - r0212*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0213_dt = (-(gt*r0213) - (gt + g2)*r0213)/2. - i*(-(conj(Ep4a)*conj(r0302))/8. - (conj(Ep3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1312))/(4.*rt6) + (conj(Em4a)*r0201)/(4.*rt6) + (conj(Em1a)*r1013)/(4.*rt2) - (conj(Em4a)*r1413)/8. - r0212*((2*WLx)/3. - (2*i*WLy)/3.) + r0113*(WLx/2. + (i*WLy)/2.) - r0214*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0313*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0213*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + (r0213*WLz)/2.);
+dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*(-(conj(Ep4a)*conj(r0402))/8. - (conj(Em3a)*conj(r0602))/(8.*rt3) - (conj(Ep3a)*conj(r0802))/(8.*rt3) + (conj(Ep4a)*conj(r1412))/(4.*rt6) + (conj(Em4a)*r0202)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 + (conj(Em1a)*r1014)/(4.*rt2) - (conj(Em4a)*r1414)/8. + r0114*(WLx/2. + (i*WLy)/2.) - r0213*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0215*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0314*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + (r0214*WLz)/2.);
+dr0215_dt = (-(gt*r0215) - (gt + g2)*r0215)/2. - i*((conj(Em4a)*conj(r0302))/8. - (conj(Ep4a)*conj(r0502))/(4.*rt6) - (conj(Em3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1512))/(4.*rt6) - (conj(Em4a)*conj(r1514))/8. + (conj(Em1a)*r1015)/(4.*rt2) + r0115*(WLx/2. + (i*WLy)/2.) - r0216*((2*WLx)/3. + (2*i*WLy)/3.) - r0214*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0315*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0215*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + (r0215*WLz)/2.);
+dr0216_dt = (-(gt*r0216) - (gt + g2)*r0216)/2. - i*((conj(Em4a)*conj(r0402))/(4.*rt6) - (conj(Em3a)*conj(r0802))/(4.*rt2) + (conj(Ep4a)*conj(r1612))/(4.*rt6) - (conj(Em4a)*conj(r1614))/8. + (conj(Em1a)*r1016)/(4.*rt2) - r0215*((2*WLx)/3. - (2*i*WLy)/3.) + r0116*(WLx/2. + (i*WLy)/2.) + r0316*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0216*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + (r0216*WLz)/2.);
+dr0301_dt = -(gt*r0301) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0109))/(4.*rt6) + (conj(Em1a)*conj(r0111))/(4.*rt6) + (conj(Ep4a)*conj(r0113))/8. - (conj(Em4a)*conj(r0115))/8. - (Em1a*r0309)/4. + (Em4a*r0313)/(4.*rt6) - r0302*(WLx/2. + (i*WLy)/2.) + r0401*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0201*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0301*WLz);
+dr0302_dt = -(gt*r0302) + (g1*r1009)/(2.*rt3) + (g1*r1110)/(4.*rt3) + (g2*r1312)/(2.*rt6) + (g2*r1514)/4. - i*((conj(Ep1a)*conj(r0209))/(4.*rt6) + (conj(Em1a)*conj(r0211))/(4.*rt6) + (conj(Ep4a)*conj(r0213))/8. - (conj(Em4a)*conj(r0215))/8. - (Em1a*r0310)/(4.*rt2) - (Ep4a*r0312)/(4.*rt6) + (Em4a*r0314)/8. - r0301*(WLx/2. - (i*WLy)/2.) + r0402*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0202*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0303*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (r0302*WLz)/2.);
+dr0303_dt = gt/8. - gt*r0303 + (g1*r0909)/12. + (g1*r1010)/3. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1515)/4. - i*((conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Em1a)*conj(r0311))/(4.*rt6) + (conj(Ep4a)*conj(r0313))/8. - (conj(Em4a)*conj(r0315))/8. - (Ep1a*r0309)/(4.*rt6) - (Em1a*r0311)/(4.*rt6) - (Ep4a*r0313)/8. + (Em4a*r0315)/8. - r0302*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0403*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + conj(r0302)*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - conj(r0403)*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.));
+dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*((conj(Ep2a)*conj(r0703))/(4.*rt6) + (conj(Ep4a)*conj(r0913))/8. - (conj(Em4a)*conj(r0915))/8. - (conj(Em1a)*r0301)/4. - (conj(Ep1a)*r0303)/(4.*rt6) + (conj(Ep1a)*r0909)/(4.*rt6) + (conj(Em1a)*r1109)/(4.*rt6) + r0409*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0209*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-delta1 - v*Kvec1 - WLz/6.));
+dr0310_dt = (-(gt*r0310) - (gt + g1)*r0310)/2. - i*(-(conj(Ep1a)*conj(r0403))/(4.*rt2) - (conj(Em2a)*conj(r0603))/(4.*rt6) + (conj(Ep2a)*conj(r0803))/(4.*rt6) + (conj(Ep1a)*conj(r1009))/(4.*rt6) + (conj(Ep4a)*conj(r1013))/8. - (conj(Em4a)*conj(r1015))/8. - (conj(Em1a)*r0302)/(4.*rt2) + (delta1 + v*Kvec1)*r0310 + (conj(Em1a)*r1110)/(4.*rt6) + r0410*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0210*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0311*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr0311_dt = (-(gt*r0311) - (gt + g1)*r0311)/2. - i*(-(conj(Ep1a)*conj(r0503))/4. - (conj(Em2a)*conj(r0703))/(4.*rt6) + (conj(Ep1a)*conj(r1109))/(4.*rt6) + (conj(Ep4a)*conj(r1113))/8. - (conj(Em4a)*conj(r1115))/8. - (conj(Em1a)*r0303)/(4.*rt6) + (conj(Em1a)*r1111)/(4.*rt6) + r0411*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0211*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0311*(-delta1 - v*Kvec1 + WLz/6.));
+dr0312_dt = (-(gt*r0312) - (gt + g2)*r0312)/2. - i*(-(conj(Ep3a)*conj(r0603))/(4.*rt2) - (conj(Ep4a)*r0302)/(4.*rt6) + (conj(Ep1a)*r0912)/(4.*rt6) + (conj(Em1a)*r1112)/(4.*rt6) + (conj(Ep4a)*r1312)/8. - (conj(Em4a)*r1512)/8. - r0313*((2*WLx)/3. + (2*i*WLy)/3.) + r0412*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0212*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0313_dt = (-(gt*r0313) - (gt + g2)*r0313)/2. - i*(-(conj(Ep3a)*conj(r0703))/8. + (conj(Em4a)*r0301)/(4.*rt6) - (conj(Ep4a)*r0303)/8. + (conj(Ep1a)*r0913)/(4.*rt6) + (conj(Em1a)*r1113)/(4.*rt6) + (conj(Ep4a)*r1313)/8. - (conj(Em4a)*r1513)/8. - r0312*((2*WLx)/3. - (2*i*WLy)/3.) - r0314*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0413*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0213*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0313*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0314_dt = (-(gt*r0314) - (gt + g2)*r0314)/2. - i*(-(conj(Ep4a)*conj(r0403))/8. - (conj(Em3a)*conj(r0603))/(8.*rt3) - (conj(Ep3a)*conj(r0803))/(8.*rt3) + (conj(Ep4a)*conj(r1413))/8. + (conj(Em4a)*r0302)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0314 + (conj(Ep1a)*r0914)/(4.*rt6) + (conj(Em1a)*r1114)/(4.*rt6) - (conj(Em4a)*r1514)/8. - r0313*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0315*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0414*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0214*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.));
+dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(conj(Ep4a)*conj(r0503))/(4.*rt6) - (conj(Em3a)*conj(r0703))/8. + (conj(Ep4a)*conj(r1513))/8. + (conj(Em4a)*r0303)/8. + (conj(Ep1a)*r0915)/(4.*rt6) + (conj(Em1a)*r1115)/(4.*rt6) - (conj(Em4a)*r1515)/8. - r0316*((2*WLx)/3. + (2*i*WLy)/3.) - r0314*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0415*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0215*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0315*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0316_dt = (-(gt*r0316) - (gt + g2)*r0316)/2. - i*((conj(Em4a)*conj(r0403))/(4.*rt6) - (conj(Em3a)*conj(r0803))/(4.*rt2) + (conj(Ep4a)*conj(r1613))/8. - (conj(Em4a)*conj(r1615))/8. + (conj(Ep1a)*r0916)/(4.*rt6) + (conj(Em1a)*r1116)/(4.*rt6) - r0315*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0216*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0316*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr0401_dt = -(gt*r0401) - (g2*r1512)/6. + (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0114))/8. - (conj(Em4a)*conj(r0116))/(4.*rt6) - (Em1a*r0409)/4. + (Em4a*r0413)/(4.*rt6) + r0501*(WLx/2. - (i*WLy)/2.) - r0402*(WLx/2. + (i*WLy)/2.) + r0301*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (3*r0401*WLz)/2.);
+dr0402_dt = -(gt*r0402) + (g1*r1109)/4. + (g2*r1412)/(2.*rt6) - (g2*r1513)/12. + (g2*r1614)/(2.*rt6) - i*((conj(Ep1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0214))/8. - (conj(Em4a)*conj(r0216))/(4.*rt6) - (Em1a*r0410)/(4.*rt2) - (Ep4a*r0412)/(4.*rt6) + (Em4a*r0414)/8. - r0401*(WLx/2. - (i*WLy)/2.) + r0502*(WLx/2. - (i*WLy)/2.) + r0302*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0403*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0402*WLz);
+dr0403_dt = -(gt*r0403) + (g1*r1009)/(4.*rt3) + (g1*r1110)/(2.*rt3) + (g2*r1413)/4. + (g2*r1615)/(2.*rt6) - i*((conj(Ep1a)*conj(r0310))/(4.*rt2) + (conj(Ep4a)*conj(r0314))/8. - (conj(Em4a)*conj(r0316))/(4.*rt6) - (Ep1a*r0409)/(4.*rt6) - (Em1a*r0411)/(4.*rt6) - (Ep4a*r0413)/8. + (Em4a*r0415)/8. + r0503*(WLx/2. - (i*WLy)/2.) - r0402*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0303*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0404*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (r0403*WLz)/2.);
+dr0404_dt = gt/8. - gt*r0404 + (g1*r1010)/4. + (g1*r1111)/4. + (g2*r1414)/4. + (g2*r1515)/12. + (g2*r1616)/6. - i*((conj(Ep1a)*conj(r0410))/(4.*rt2) + (conj(Ep4a)*conj(r0414))/8. - (conj(Em4a)*conj(r0416))/(4.*rt6) - (Ep1a*r0410)/(4.*rt2) - (Ep4a*r0414)/8. + (Em4a*r0416)/(4.*rt6) + r0504*(WLx/2. - (i*WLy)/2.) - conj(r0504)*(WLx/2. + (i*WLy)/2.) - r0403*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + conj(r0403)*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.));
+dr0409_dt = (-(gt*r0409) - (gt + g1)*r0409)/2. - i*((conj(Ep2a)*conj(r0704))/(4.*rt6) + (conj(Ep4a)*conj(r0914))/8. - (conj(Em4a)*conj(r0916))/(4.*rt6) - (conj(Em1a)*r0401)/4. - (conj(Ep1a)*r0403)/(4.*rt6) + (conj(Ep1a)*r1009)/(4.*rt2) + r0509*(WLx/2. - (i*WLy)/2.) + r0309*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-delta1 - v*Kvec1 - WLz/6.) - (r0409*WLz)/2.);
+dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(conj(Em2a)*conj(r0604))/(4.*rt6) + (conj(Ep2a)*conj(r0804))/(4.*rt6) + (conj(Ep4a)*conj(r1014))/8. - (conj(Em4a)*conj(r1016))/(4.*rt6) - (conj(Em1a)*r0402)/(4.*rt2) - (conj(Ep1a)*r0404)/(4.*rt2) + (delta1 + v*Kvec1)*r0410 + (conj(Ep1a)*r1010)/(4.*rt2) + r0510*(WLx/2. - (i*WLy)/2.) + r0310*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0411*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - (r0410*WLz)/2.);
+dr0411_dt = (-(gt*r0411) - (gt + g1)*r0411)/2. - i*(-(conj(Ep1a)*conj(r0504))/4. - (conj(Em2a)*conj(r0704))/(4.*rt6) + (conj(Ep1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1114))/8. - (conj(Em4a)*conj(r1116))/(4.*rt6) - (conj(Em1a)*r0403)/(4.*rt6) + r0511*(WLx/2. - (i*WLy)/2.) + r0311*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0411*(-delta1 - v*Kvec1 + WLz/6.) - (r0411*WLz)/2.);
+dr0412_dt = (-(gt*r0412) - (gt + g2)*r0412)/2. - i*(-(conj(Ep3a)*conj(r0604))/(4.*rt2) - (conj(Ep4a)*r0402)/(4.*rt6) + (conj(Ep1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1412)/8. - (conj(Em4a)*r1612)/(4.*rt6) + r0512*(WLx/2. - (i*WLy)/2.) - r0413*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (r0412*WLz)/2. - r0412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0413_dt = (-(gt*r0413) - (gt + g2)*r0413)/2. - i*(-(conj(Ep3a)*conj(r0704))/8. + (conj(Em4a)*r0401)/(4.*rt6) - (conj(Ep4a)*r0403)/8. + (conj(Ep1a)*r1013)/(4.*rt2) + (conj(Ep4a)*r1413)/8. - (conj(Em4a)*r1613)/(4.*rt6) - r0412*((2*WLx)/3. - (2*i*WLy)/3.) + r0513*(WLx/2. - (i*WLy)/2.) - r0414*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0313*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - (r0413*WLz)/2.);
+dr0414_dt = (-(gt*r0414) - (gt + g2)*r0414)/2. - i*(-(conj(Em3a)*conj(r0604))/(8.*rt3) - (conj(Ep3a)*conj(r0804))/(8.*rt3) + (conj(Em4a)*r0402)/8. - (conj(Ep4a)*r0404)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0414 + (conj(Ep1a)*r1014)/(4.*rt2) + (conj(Ep4a)*r1414)/8. - (conj(Em4a)*r1614)/(4.*rt6) + r0514*(WLx/2. - (i*WLy)/2.) - r0413*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0415*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0314*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (r0414*WLz)/2.);
+dr0415_dt = (-(gt*r0415) - (gt + g2)*r0415)/2. - i*(-(conj(Ep4a)*conj(r0504))/(4.*rt6) - (conj(Em3a)*conj(r0704))/8. + (conj(Ep4a)*conj(r1514))/8. + (conj(Em4a)*r0403)/8. + (conj(Ep1a)*r1015)/(4.*rt2) - (conj(Em4a)*r1615)/(4.*rt6) + r0515*(WLx/2. - (i*WLy)/2.) - r0416*((2*WLx)/3. + (2*i*WLy)/3.) - r0414*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0315*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0415*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - (r0415*WLz)/2.);
+dr0416_dt = (-(gt*r0416) - (gt + g2)*r0416)/2. - i*(-(conj(Em3a)*conj(r0804))/(4.*rt2) + (conj(Ep4a)*conj(r1614))/8. + (conj(Em4a)*r0404)/(4.*rt6) + (conj(Ep1a)*r1016)/(4.*rt2) - (conj(Em4a)*r1616)/(4.*rt6) - r0415*((2*WLx)/3. - (2*i*WLy)/3.) + r0516*(WLx/2. - (i*WLy)/2.) + r0316*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0416*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - (r0416*WLz)/2.);
+dr0501_dt = -(gt*r0501) - (g2*r1612)/3. - i*((conj(Ep1a)*conj(r0111))/4. + (conj(Ep4a)*conj(r0115))/(4.*rt6) - (Em1a*r0509)/4. + (Em4a*r0513)/(4.*rt6) + r0401*(WLx/2. + (i*WLy)/2.) - r0502*(WLx/2. + (i*WLy)/2.) - 2*r0501*WLz);
+dr0502_dt = -(gt*r0502) + (g2*r1512)/6. - (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0211))/4. + (conj(Ep4a)*conj(r0215))/(4.*rt6) - (Em1a*r0510)/(4.*rt2) - (Ep4a*r0512)/(4.*rt6) + (Em4a*r0514)/8. - r0501*(WLx/2. - (i*WLy)/2.) + r0402*(WLx/2. + (i*WLy)/2.) - r0503*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (3*r0502*WLz)/2.);
+dr0503_dt = -(gt*r0503) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0311))/4. + (conj(Ep4a)*conj(r0315))/(4.*rt6) - (Ep1a*r0509)/(4.*rt6) - (Em1a*r0511)/(4.*rt6) - (Ep4a*r0513)/8. + (Em4a*r0515)/8. + r0403*(WLx/2. + (i*WLy)/2.) - r0502*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0504*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0503*WLz);
+dr0504_dt = -(gt*r0504) + (g1*r1110)/(2.*rt2) + (g2*r1514)/(2.*rt6) + (g2*r1615)/6. - i*((conj(Ep1a)*conj(r0411))/4. + (conj(Ep4a)*conj(r0415))/(4.*rt6) - (Ep1a*r0510)/(4.*rt2) - (Ep4a*r0514)/8. + (Em4a*r0516)/(4.*rt6) + r0404*(WLx/2. + (i*WLy)/2.) - r0505*(WLx/2. + (i*WLy)/2.) - r0503*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - (r0504*WLz)/2.);
+dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((conj(Ep1a)*conj(r0511))/4. + (conj(Ep4a)*conj(r0515))/(4.*rt6) - (Ep1a*r0511)/4. - (Ep4a*r0515)/(4.*rt6) - r0504*(WLx/2. - (i*WLy)/2.) + conj(r0504)*(WLx/2. + (i*WLy)/2.));
+dr0509_dt = (-(gt*r0509) - (gt + g1)*r0509)/2. - i*((conj(Ep2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r0915))/(4.*rt6) - (conj(Em1a)*r0501)/4. - (conj(Ep1a)*r0503)/(4.*rt6) + (conj(Ep1a)*r1109)/4. + r0409*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-delta1 - v*Kvec1 - WLz/6.) - r0509*WLz);
+dr0510_dt = (-(gt*r0510) - (gt + g1)*r0510)/2. - i*(-(conj(Em2a)*conj(r0605))/(4.*rt6) + (conj(Ep2a)*conj(r0805))/(4.*rt6) + (conj(Ep4a)*conj(r1015))/(4.*rt6) - (conj(Em1a)*r0502)/(4.*rt2) - (conj(Ep1a)*r0504)/(4.*rt2) + (delta1 + v*Kvec1)*r0510 + (conj(Ep1a)*r1110)/4. + r0410*(WLx/2. + (i*WLy)/2.) - r0511*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0510*WLz);
+dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(conj(Em2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r1115))/(4.*rt6) - (conj(Em1a)*r0503)/(4.*rt6) - (conj(Ep1a)*r0505)/4. + (conj(Ep1a)*r1111)/4. + r0411*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0511*(-delta1 - v*Kvec1 + WLz/6.) - r0511*WLz);
+dr0512_dt = (-(gt*r0512) - (gt + g2)*r0512)/2. - i*(-(conj(Ep3a)*conj(r0605))/(4.*rt2) - (conj(Ep4a)*r0502)/(4.*rt6) + (conj(Ep1a)*r1112)/4. + (conj(Ep4a)*r1512)/(4.*rt6) + r0412*(WLx/2. + (i*WLy)/2.) - r0513*((2*WLx)/3. + (2*i*WLy)/3.) - r0512*WLz - r0512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0513_dt = (-(gt*r0513) - (gt + g2)*r0513)/2. - i*(-(conj(Ep3a)*conj(r0705))/8. + (conj(Em4a)*r0501)/(4.*rt6) - (conj(Ep4a)*r0503)/8. + (conj(Ep1a)*r1113)/4. + (conj(Ep4a)*r1513)/(4.*rt6) - r0512*((2*WLx)/3. - (2*i*WLy)/3.) + r0413*(WLx/2. + (i*WLy)/2.) - r0514*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r0513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r0513*WLz);
+dr0514_dt = (-(gt*r0514) - (gt + g2)*r0514)/2. - i*(-(conj(Em3a)*conj(r0605))/(8.*rt3) - (conj(Ep3a)*conj(r0805))/(8.*rt3) + (conj(Em4a)*r0502)/8. - (conj(Ep4a)*r0504)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0514 + (conj(Ep1a)*r1114)/4. + (conj(Ep4a)*r1514)/(4.*rt6) + r0414*(WLx/2. + (i*WLy)/2.) - r0513*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0515*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r0514*WLz);
+dr0515_dt = (-(gt*r0515) - (gt + g2)*r0515)/2. - i*(-(conj(Em3a)*conj(r0705))/8. + (conj(Em4a)*r0503)/8. - (conj(Ep4a)*r0505)/(4.*rt6) + (conj(Ep1a)*r1115)/4. + (conj(Ep4a)*r1515)/(4.*rt6) + r0415*(WLx/2. + (i*WLy)/2.) - r0516*((2*WLx)/3. + (2*i*WLy)/3.) - r0514*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0515*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r0515*WLz);
+dr0516_dt = (-(gt*r0516) - (gt + g2)*r0516)/2. - i*(-(conj(Em3a)*conj(r0805))/(4.*rt2) + (conj(Ep4a)*conj(r1615))/(4.*rt6) + (conj(Em4a)*r0504)/(4.*rt6) + (conj(Ep1a)*r1116)/4. - r0515*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*(WLx/2. + (i*WLy)/2.) - r0516*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r0516*WLz);
+dr0601_dt = -(gt*r0601) - i*((conj(Em2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0112))/(4.*rt2) + (conj(Em3a)*conj(r0114))/(8.*rt3) - (Em1a*r0609)/4. + (Em4a*r0613)/(4.*rt6) - r0602*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0601*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0601*WLz);
+dr0602_dt = -(gt*r0602) - i*((conj(Em2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0212))/(4.*rt2) + (conj(Em3a)*conj(r0214))/(8.*rt3) - (Em1a*r0610)/(4.*rt2) - (Ep4a*r0612)/(4.*rt6) + (Em4a*r0614)/8. - r0601*(WLx/2. - (i*WLy)/2.) - r0603*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0602*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - (r0602*WLz)/2.);
+dr0603_dt = -(gt*r0603) - i*((conj(Em2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0312))/(4.*rt2) + (conj(Em3a)*conj(r0314))/(8.*rt3) - (Ep1a*r0609)/(4.*rt6) - (Em1a*r0611)/(4.*rt6) - (Ep4a*r0613)/8. + (Em4a*r0615)/8. - r0602*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0604*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0603*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0604_dt = -(gt*r0604) - i*((conj(Em2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0412))/(4.*rt2) + (conj(Em3a)*conj(r0414))/(8.*rt3) - (Ep1a*r0610)/(4.*rt2) - (Ep4a*r0614)/8. + (Em4a*r0616)/(4.*rt6) - r0605*(WLx/2. + (i*WLy)/2.) - r0603*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0604*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + (r0604*WLz)/2.);
+dr0605_dt = -(gt*r0605) - i*((conj(Em2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0512))/(4.*rt2) + (conj(Em3a)*conj(r0514))/(8.*rt3) - (Ep1a*r0611)/4. - (Ep4a*r0615)/(4.*rt6) - r0604*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0605*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0605*WLz);
+dr0606_dt = gt/8. - gt*r0606 + (g1*r0909)/12. + (g1*r1010)/12. + (g2*r1212)/2. + (g2*r1313)/4. + (g2*r1414)/12. - i*((conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0612))/(4.*rt2) + (conj(Em3a)*conj(r0614))/(8.*rt3) - (Em2a*r0610)/(4.*rt6) - (Ep3a*r0612)/(4.*rt2) - (Em3a*r0614)/(8.*rt3) - conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0609_dt = (-(gt*r0609) - (gt + g1)*r0609)/2. - i*((conj(Ep2a)*conj(r0706))/(4.*rt6) + (conj(Ep3a)*conj(r0912))/(4.*rt2) + (conj(Em3a)*conj(r0914))/(8.*rt3) - (conj(Em1a)*r0601)/4. - (conj(Ep1a)*r0603)/(4.*rt6) + (conj(Em2a)*r1009)/(4.*rt6) - r0610*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0709*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0609*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0609*(-delta1 - v*Kvec1 - WLz/6.));
+dr0610_dt = (-(gt*r0610) - (gt + g1)*r0610)/2. - i*((conj(Ep2a)*conj(r0806))/(4.*rt6) + (conj(Ep3a)*conj(r1012))/(4.*rt2) + (conj(Em3a)*conj(r1014))/(8.*rt3) - (conj(Em1a)*r0602)/(4.*rt2) - (conj(Ep1a)*r0604)/(4.*rt2) - (conj(Em2a)*r0606)/(4.*rt6) + (delta1 + v*Kvec1)*r0610 + (conj(Em2a)*r1010)/(4.*rt6) - r0611*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0609*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0710*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0610*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0611_dt = (-(gt*r0611) - (gt + g1)*r0611)/2. - i*(-(conj(Em2a)*conj(r0706))/(4.*rt6) + (conj(Em2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1112))/(4.*rt2) + (conj(Em3a)*conj(r1114))/(8.*rt3) - (conj(Em1a)*r0603)/(4.*rt6) - (conj(Ep1a)*r0605)/4. - r0610*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0711*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0611*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0611*(-delta1 - v*Kvec1 + WLz/6.));
+dr0612_dt = (-(gt*r0612) - (gt + g2)*r0612)/2. - i*(-(conj(Ep4a)*r0602)/(4.*rt6) - (conj(Ep3a)*r0606)/(4.*rt2) + (conj(Em2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1212)/(4.*rt2) + (conj(Em3a)*r1412)/(8.*rt3) - r0613*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0612*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0613_dt = (-(gt*r0613) - (gt + g2)*r0613)/2. - i*(-(conj(Ep3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1312))/(4.*rt2) + (conj(Em4a)*r0601)/(4.*rt6) - (conj(Ep4a)*r0603)/8. + (conj(Em2a)*r1013)/(4.*rt6) + (conj(Em3a)*r1413)/(8.*rt3) - r0612*((2*WLx)/3. - (2*i*WLy)/3.) - r0614*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0613*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0614_dt = (-(gt*r0614) - (gt + g2)*r0614)/2. - i*(-(conj(Ep3a)*conj(r0806))/(8.*rt3) + (conj(Ep3a)*conj(r1412))/(4.*rt2) + (conj(Em4a)*r0602)/8. - (conj(Ep4a)*r0604)/8. - (conj(Em3a)*r0606)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0614 + (conj(Em2a)*r1014)/(4.*rt6) + (conj(Em3a)*r1414)/(8.*rt3) - r0613*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0615*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0614*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0615_dt = (-(gt*r0615) - (gt + g2)*r0615)/2. - i*(-(conj(Em3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1512))/(4.*rt2) + (conj(Em3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0603)/8. - (conj(Ep4a)*r0605)/(4.*rt6) + (conj(Em2a)*r1015)/(4.*rt6) - r0616*((2*WLx)/3. + (2*i*WLy)/3.) - r0614*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0615*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0616_dt = (-(gt*r0616) - (gt + g2)*r0616)/2. - i*(-(conj(Em3a)*conj(r0806))/(4.*rt2) + (conj(Ep3a)*conj(r1612))/(4.*rt2) + (conj(Em3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0604)/(4.*rt6) + (conj(Em2a)*r1016)/(4.*rt6) - r0615*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0616*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0616*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0701_dt = -(gt*r0701) - i*(-(conj(Ep2a)*conj(r0109))/(4.*rt6) + (conj(Em2a)*conj(r0111))/(4.*rt6) + (conj(Ep3a)*conj(r0113))/8. + (conj(Em3a)*conj(r0115))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0701 - (Em1a*r0709)/4. + (Em4a*r0713)/(4.*rt6) - r0702*(WLx/2. + (i*WLy)/2.) + r0601*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0701*WLz);
+dr0702_dt = -(gt*r0702) - i*(-(conj(Ep2a)*conj(r0209))/(4.*rt6) + (conj(Em2a)*conj(r0211))/(4.*rt6) + (conj(Ep3a)*conj(r0213))/8. + (conj(Em3a)*conj(r0215))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0702 - (Em1a*r0710)/(4.*rt2) - (Ep4a*r0712)/(4.*rt6) + (Em4a*r0714)/8. - r0701*(WLx/2. - (i*WLy)/2.) - r0703*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0602*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - (r0702*WLz)/2.);
+dr0703_dt = -(gt*r0703) - i*(-(conj(Ep2a)*conj(r0309))/(4.*rt6) + (conj(Em2a)*conj(r0311))/(4.*rt6) + (conj(Ep3a)*conj(r0313))/8. + (conj(Em3a)*conj(r0315))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 - (Ep1a*r0709)/(4.*rt6) - (Em1a*r0711)/(4.*rt6) - (Ep4a*r0713)/8. + (Em4a*r0715)/8. - r0702*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0704*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0603*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0704_dt = -(gt*r0704) - i*(-(conj(Ep2a)*conj(r0409))/(4.*rt6) + (conj(Em2a)*conj(r0411))/(4.*rt6) + (conj(Ep3a)*conj(r0413))/8. + (conj(Em3a)*conj(r0415))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0704 - (Ep1a*r0710)/(4.*rt2) - (Ep4a*r0714)/8. + (Em4a*r0716)/(4.*rt6) - r0705*(WLx/2. + (i*WLy)/2.) - r0703*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0604*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + (r0704*WLz)/2.);
+dr0705_dt = -(gt*r0705) - i*(-(conj(Ep2a)*conj(r0509))/(4.*rt6) + (conj(Em2a)*conj(r0511))/(4.*rt6) + (conj(Ep3a)*conj(r0513))/8. + (conj(Em3a)*conj(r0515))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0705 - (Ep1a*r0711)/4. - (Ep4a*r0715)/(4.*rt6) - r0704*(WLx/2. - (i*WLy)/2.) + r0605*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0705*WLz);
+dr0706_dt = -(gt*r0706) + (g1*r1110)/12. + (g2*r1312)/(2.*rt2) + (g2*r1413)/(2.*rt3) + (g2*r1514)/(4.*rt3) - i*(-(conj(Ep2a)*conj(r0609))/(4.*rt6) + (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep3a)*conj(r0613))/8. + (conj(Em3a)*conj(r0615))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0706 - (Em2a*r0710)/(4.*rt6) - (Ep3a*r0712)/(4.*rt2) - (Em3a*r0714)/(8.*rt3) + r0606*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0706*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0707_dt = gt/8. - gt*r0707 + (g1*r0909)/12. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1414)/3. + (g2*r1515)/4. - i*(-(conj(Ep2a)*conj(r0709))/(4.*rt6) + (conj(Em2a)*conj(r0711))/(4.*rt6) + (conj(Ep3a)*conj(r0713))/8. + (conj(Em3a)*conj(r0715))/8. + (Ep2a*r0709)/(4.*rt6) - (Em2a*r0711)/(4.*rt6) - (Ep3a*r0713)/8. - (Em3a*r0715)/8. + conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*((conj(Ep3a)*conj(r0913))/8. + (conj(Em3a)*conj(r0915))/8. - (conj(Em1a)*r0701)/4. - (conj(Ep1a)*r0703)/(4.*rt6) + (conj(Ep2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0709 - (conj(Ep2a)*r0909)/(4.*rt6) + (conj(Em2a)*r1109)/(4.*rt6) + r0609*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0809*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0709*(-delta1 - v*Kvec1 - WLz/6.));
+dr0710_dt = (-(gt*r0710) - (gt + g1)*r0710)/2. - i*((conj(Ep2a)*conj(r0807))/(4.*rt6) - (conj(Ep2a)*conj(r1009))/(4.*rt6) + (conj(Ep3a)*conj(r1013))/8. + (conj(Em3a)*conj(r1015))/8. - (conj(Em1a)*r0702)/(4.*rt2) - (conj(Ep1a)*r0704)/(4.*rt2) - (conj(Em2a)*r0706)/(4.*rt6) + (delta1 + v*Kvec1)*r0710 + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0710 + (conj(Em2a)*r1110)/(4.*rt6) + r0610*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0711*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0709*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0711_dt = (-(gt*r0711) - (gt + g1)*r0711)/2. - i*(-(conj(Ep2a)*conj(r1109))/(4.*rt6) + (conj(Ep3a)*conj(r1113))/8. + (conj(Em3a)*conj(r1115))/8. - (conj(Em1a)*r0703)/(4.*rt6) - (conj(Ep1a)*r0705)/4. - (conj(Em2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0711 + (conj(Em2a)*r1111)/(4.*rt6) + r0611*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0811*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0711*(-delta1 - v*Kvec1 + WLz/6.));
+dr0712_dt = (-(gt*r0712) - (gt + g2)*r0712)/2. - i*(-(conj(Ep4a)*r0702)/(4.*rt6) - (conj(Ep3a)*r0706)/(4.*rt2) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0712 - (conj(Ep2a)*r0912)/(4.*rt6) + (conj(Em2a)*r1112)/(4.*rt6) + (conj(Ep3a)*r1312)/8. + (conj(Em3a)*r1512)/8. - r0713*((2*WLx)/3. + (2*i*WLy)/3.) + r0612*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0712*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0713_dt = (-(gt*r0713) - (gt + g2)*r0713)/2. - i*((conj(Em4a)*r0701)/(4.*rt6) - (conj(Ep4a)*r0703)/8. - (conj(Ep3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0713 - (conj(Ep2a)*r0913)/(4.*rt6) + (conj(Em2a)*r1113)/(4.*rt6) + (conj(Ep3a)*r1313)/8. + (conj(Em3a)*r1513)/8. - r0712*((2*WLx)/3. - (2*i*WLy)/3.) - r0714*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0613*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0713*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0714_dt = (-(gt*r0714) - (gt + g2)*r0714)/2. - i*(-(conj(Ep3a)*conj(r0807))/(8.*rt3) + (conj(Ep3a)*conj(r1413))/8. + (conj(Em4a)*r0702)/8. - (conj(Ep4a)*r0704)/8. - (conj(Em3a)*r0706)/(8.*rt3) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0714 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0714 - (conj(Ep2a)*r0914)/(4.*rt6) + (conj(Em2a)*r1114)/(4.*rt6) + (conj(Em3a)*r1514)/8. - r0713*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0715*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0614*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0715_dt = (-(gt*r0715) - (gt + g2)*r0715)/2. - i*((conj(Ep3a)*conj(r1513))/8. + (conj(Em4a)*r0703)/8. - (conj(Ep4a)*r0705)/(4.*rt6) - (conj(Em3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0715 - (conj(Ep2a)*r0915)/(4.*rt6) + (conj(Em2a)*r1115)/(4.*rt6) + (conj(Em3a)*r1515)/8. - r0716*((2*WLx)/3. + (2*i*WLy)/3.) - r0714*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0615*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0815*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0715*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0716_dt = (-(gt*r0716) - (gt + g2)*r0716)/2. - i*(-(conj(Em3a)*conj(r0807))/(4.*rt2) + (conj(Ep3a)*conj(r1613))/8. + (conj(Em3a)*conj(r1615))/8. + (conj(Em4a)*r0704)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0716 - (conj(Ep2a)*r0916)/(4.*rt6) + (conj(Em2a)*r1116)/(4.*rt6) - r0715*((2*WLx)/3. - (2*i*WLy)/3.) + r0616*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0816*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0716*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr0801_dt = -(gt*r0801) - i*(-(conj(Ep2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0114))/(8.*rt3) + (conj(Em3a)*conj(r0116))/(4.*rt2) - (Em1a*r0809)/4. + (Em4a*r0813)/(4.*rt6) - r0802*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0801*WLz);
+dr0802_dt = -(gt*r0802) - i*(-(conj(Ep2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0214))/(8.*rt3) + (conj(Em3a)*conj(r0216))/(4.*rt2) - (Em1a*r0810)/(4.*rt2) - (Ep4a*r0812)/(4.*rt6) + (Em4a*r0814)/8. - r0801*(WLx/2. - (i*WLy)/2.) - r0803*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - (r0802*WLz)/2.);
+dr0803_dt = -(gt*r0803) - i*(-(conj(Ep2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0314))/(8.*rt3) + (conj(Em3a)*conj(r0316))/(4.*rt2) - (Ep1a*r0809)/(4.*rt6) - (Em1a*r0811)/(4.*rt6) - (Ep4a*r0813)/8. + (Em4a*r0815)/8. - r0802*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0804*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0804_dt = -(gt*r0804) - i*(-(conj(Ep2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0414))/(8.*rt3) + (conj(Em3a)*conj(r0416))/(4.*rt2) - (Ep1a*r0810)/(4.*rt2) - (Ep4a*r0814)/8. + (Em4a*r0816)/(4.*rt6) - r0805*(WLx/2. + (i*WLy)/2.) - r0803*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + (r0804*WLz)/2.);
+dr0805_dt = -(gt*r0805) - i*(-(conj(Ep2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0514))/(8.*rt3) + (conj(Em3a)*conj(r0516))/(4.*rt2) - (Ep1a*r0811)/4. - (Ep4a*r0815)/(4.*rt6) - r0804*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + r0805*WLz);
+dr0806_dt = -(gt*r0806) - (g1*r1109)/12. + (g2*r1412)/(2.*rt6) + (g2*r1513)/4. + (g2*r1614)/(2.*rt6) - i*(-(conj(Ep2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0614))/(8.*rt3) + (conj(Em3a)*conj(r0616))/(4.*rt2) - (Em2a*r0810)/(4.*rt6) - (Ep3a*r0812)/(4.*rt2) - (Em3a*r0814)/(8.*rt3) + r0706*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0807_dt = -(gt*r0807) + (g1*r1009)/12. + (g2*r1413)/(4.*rt3) + (g2*r1514)/(2.*rt3) + (g2*r1615)/(2.*rt2) - i*(-(conj(Ep2a)*conj(r0710))/(4.*rt6) + (conj(Ep3a)*conj(r0714))/(8.*rt3) + (conj(Em3a)*conj(r0716))/(4.*rt2) - (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0807 + (Ep2a*r0809)/(4.*rt6) - (Em2a*r0811)/(4.*rt6) - (Ep3a*r0813)/8. - (Em3a*r0815)/8. + r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0808*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0808_dt = gt/8. - gt*r0808 + (g1*r1010)/12. + (g1*r1111)/12. + (g2*r1414)/12. + (g2*r1515)/4. + (g2*r1616)/2. - i*(-(conj(Ep2a)*conj(r0810))/(4.*rt6) + (conj(Ep3a)*conj(r0814))/(8.*rt3) + (conj(Em3a)*conj(r0816))/(4.*rt2) + (Ep2a*r0810)/(4.*rt6) - (Ep3a*r0814)/(8.*rt3) - (Em3a*r0816)/(4.*rt2) + conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0809_dt = (-(gt*r0809) - (gt + g1)*r0809)/2. - i*((conj(Ep3a)*conj(r0914))/(8.*rt3) + (conj(Em3a)*conj(r0916))/(4.*rt2) - (conj(Em1a)*r0801)/4. - (conj(Ep1a)*r0803)/(4.*rt6) + (conj(Ep2a)*r0807)/(4.*rt6) - (conj(Ep2a)*r1009)/(4.*rt6) + r0709*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-delta1 - v*Kvec1 - WLz/6.) + r0809*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0810_dt = (-(gt*r0810) - (gt + g1)*r0810)/2. - i*((conj(Ep3a)*conj(r1014))/(8.*rt3) + (conj(Em3a)*conj(r1016))/(4.*rt2) - (conj(Em1a)*r0802)/(4.*rt2) - (conj(Ep1a)*r0804)/(4.*rt2) - (conj(Em2a)*r0806)/(4.*rt6) + (conj(Ep2a)*r0808)/(4.*rt6) + (delta1 + v*Kvec1)*r0810 - (conj(Ep2a)*r1010)/(4.*rt6) + r0710*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0811*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0811_dt = (-(gt*r0811) - (gt + g1)*r0811)/2. - i*(-(conj(Ep2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1114))/(8.*rt3) + (conj(Em3a)*conj(r1116))/(4.*rt2) - (conj(Em1a)*r0803)/(4.*rt6) - (conj(Ep1a)*r0805)/4. - (conj(Em2a)*r0807)/(4.*rt6) + r0711*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0811*(-delta1 - v*Kvec1 + WLz/6.) + r0811*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0812_dt = (-(gt*r0812) - (gt + g2)*r0812)/2. - i*(-(conj(Ep4a)*r0802)/(4.*rt6) - (conj(Ep3a)*r0806)/(4.*rt2) - (conj(Ep2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1412)/(8.*rt3) + (conj(Em3a)*r1612)/(4.*rt2) - r0813*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0812*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0813_dt = (-(gt*r0813) - (gt + g2)*r0813)/2. - i*((conj(Em4a)*r0801)/(4.*rt6) - (conj(Ep4a)*r0803)/8. - (conj(Ep3a)*r0807)/8. - (conj(Ep2a)*r1013)/(4.*rt6) + (conj(Ep3a)*r1413)/(8.*rt3) + (conj(Em3a)*r1613)/(4.*rt2) - r0812*((2*WLx)/3. - (2*i*WLy)/3.) - r0814*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0813*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0814_dt = (-(gt*r0814) - (gt + g2)*r0814)/2. - i*((conj(Em4a)*r0802)/8. - (conj(Ep4a)*r0804)/8. - (conj(Em3a)*r0806)/(8.*rt3) - (conj(Ep3a)*r0808)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0814 - (conj(Ep2a)*r1014)/(4.*rt6) + (conj(Ep3a)*r1414)/(8.*rt3) + (conj(Em3a)*r1614)/(4.*rt2) - r0813*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0815*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0815_dt = (-(gt*r0815) - (gt + g2)*r0815)/2. - i*((conj(Ep3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0803)/8. - (conj(Ep4a)*r0805)/(4.*rt6) - (conj(Em3a)*r0807)/8. - (conj(Ep2a)*r1015)/(4.*rt6) + (conj(Em3a)*r1615)/(4.*rt2) - r0816*((2*WLx)/3. + (2*i*WLy)/3.) - r0814*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0815*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0815*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0816_dt = (-(gt*r0816) - (gt + g2)*r0816)/2. - i*((conj(Ep3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0804)/(4.*rt6) - (conj(Em3a)*r0808)/(4.*rt2) - (conj(Ep2a)*r1016)/(4.*rt6) + (conj(Em3a)*r1616)/(4.*rt2) - r0815*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0816*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0816*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0909_dt = -((gt + g1)*r0909) - i*(-(conj(Em1a)*conj(r0109))/4. - (conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Ep2a)*conj(r0709))/(4.*rt6) + (Em1a*r0109)/4. + (Ep1a*r0309)/(4.*rt6) - (Ep2a*r0709)/(4.*rt6) - conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr0912_dt = (-((gt + g1)*r0912) - (gt + g2)*r0912)/2. - i*(-(conj(Ep4a)*conj(r0209))/(4.*rt6) - (conj(Ep3a)*conj(r0609))/(4.*rt2) + (Em1a*r0112)/4. + (Ep1a*r0312)/(4.*rt6) - (Ep2a*r0712)/(4.*rt6) - r0913*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0912*(-delta1 - v*Kvec1 - WLz/6.) - r0912*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0913_dt = (-((gt + g1)*r0913) - (gt + g2)*r0913)/2. - i*((conj(Em4a)*conj(r0109))/(4.*rt6) - (conj(Ep4a)*conj(r0309))/8. - (conj(Ep3a)*conj(r0709))/8. + (Em1a*r0113)/4. + (Ep1a*r0313)/(4.*rt6) - (Ep2a*r0713)/(4.*rt6) - r0912*((2*WLx)/3. - (2*i*WLy)/3.) - r0914*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0913*(-delta1 - v*Kvec1 - WLz/6.) - r0913*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0914_dt = (-((gt + g1)*r0914) - (gt + g2)*r0914)/2. - i*((conj(Em4a)*conj(r0209))/8. - (conj(Ep4a)*conj(r0409))/8. - (conj(Em3a)*conj(r0609))/(8.*rt3) - (conj(Ep3a)*conj(r0809))/(8.*rt3) + (Em1a*r0114)/4. + (Ep1a*r0314)/(4.*rt6) - (Ep2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0914 - r0913*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0915*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0914*(-delta1 - v*Kvec1 - WLz/6.));
+dr0915_dt = (-((gt + g1)*r0915) - (gt + g2)*r0915)/2. - i*((conj(Em4a)*conj(r0309))/8. - (conj(Ep4a)*conj(r0509))/(4.*rt6) - (conj(Em3a)*conj(r0709))/8. + (Em1a*r0115)/4. + (Ep1a*r0315)/(4.*rt6) - (Ep2a*r0715)/(4.*rt6) - r0916*((2*WLx)/3. + (2*i*WLy)/3.) - r0914*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0915*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0915*(-delta1 - v*Kvec1 - WLz/6.));
+dr0916_dt = (-((gt + g1)*r0916) - (gt + g2)*r0916)/2. - i*((conj(Em4a)*conj(r0409))/(4.*rt6) - (conj(Em3a)*conj(r0809))/(4.*rt2) + (Em1a*r0116)/4. + (Ep1a*r0316)/(4.*rt6) - (Ep2a*r0716)/(4.*rt6) - r0915*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0916*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0916*(-delta1 - v*Kvec1 - WLz/6.));
+dr1009_dt = -((gt + g1)*r1009) - i*(-(conj(Em1a)*conj(r0110))/4. - (conj(Ep1a)*conj(r0310))/(4.*rt6) + (conj(Ep2a)*conj(r0710))/(4.*rt6) + (Em1a*r0209)/(4.*rt2) + (Ep1a*r0409)/(4.*rt2) + (Em2a*r0609)/(4.*rt6) - (Ep2a*r0809)/(4.*rt6) - (delta1 + v*Kvec1)*r1009 + r0909*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1009*(-delta1 - v*Kvec1 - WLz/6.));
+dr1010_dt = -((gt + g1)*r1010) - i*(-(conj(Em1a)*conj(r0210))/(4.*rt2) - (conj(Ep1a)*conj(r0410))/(4.*rt2) - (conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep2a)*conj(r0810))/(4.*rt6) + (Em1a*r0210)/(4.*rt2) + (Ep1a*r0410)/(4.*rt2) + (Em2a*r0610)/(4.*rt6) - (Ep2a*r0810)/(4.*rt6) + conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1012_dt = (-((gt + g1)*r1012) - (gt + g2)*r1012)/2. - i*(-(conj(Ep4a)*conj(r0210))/(4.*rt6) - (conj(Ep3a)*conj(r0610))/(4.*rt2) + (Em1a*r0212)/(4.*rt2) + (Ep1a*r0412)/(4.*rt2) + (Em2a*r0612)/(4.*rt6) - (Ep2a*r0812)/(4.*rt6) - (delta1 + v*Kvec1)*r1012 - r1013*((2*WLx)/3. + (2*i*WLy)/3.) + r0912*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1012*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1013_dt = (-((gt + g1)*r1013) - (gt + g2)*r1013)/2. - i*((conj(Em4a)*conj(r0110))/(4.*rt6) - (conj(Ep4a)*conj(r0310))/8. - (conj(Ep3a)*conj(r0710))/8. + (Em1a*r0213)/(4.*rt2) + (Ep1a*r0413)/(4.*rt2) + (Em2a*r0613)/(4.*rt6) - (Ep2a*r0813)/(4.*rt6) - (delta1 + v*Kvec1)*r1013 - r1012*((2*WLx)/3. - (2*i*WLy)/3.) - r1014*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0913*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1013*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1014_dt = (-((gt + g1)*r1014) - (gt + g2)*r1014)/2. - i*((conj(Em4a)*conj(r0210))/8. - (conj(Ep4a)*conj(r0410))/8. - (conj(Em3a)*conj(r0610))/(8.*rt3) - (conj(Ep3a)*conj(r0810))/(8.*rt3) + (Em1a*r0214)/(4.*rt2) + (Ep1a*r0414)/(4.*rt2) + (Em2a*r0614)/(4.*rt6) - (Ep2a*r0814)/(4.*rt6) - (delta1 + v*Kvec1)*r1014 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1014 - r1013*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r1015*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0914*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1015_dt = (-((gt + g1)*r1015) - (gt + g2)*r1015)/2. - i*((conj(Em4a)*conj(r0310))/8. - (conj(Ep4a)*conj(r0510))/(4.*rt6) - (conj(Em3a)*conj(r0710))/8. + (Em1a*r0215)/(4.*rt2) + (Ep1a*r0415)/(4.*rt2) + (Em2a*r0615)/(4.*rt6) - (Ep2a*r0815)/(4.*rt6) - (delta1 + v*Kvec1)*r1015 - r1016*((2*WLx)/3. + (2*i*WLy)/3.) - r1014*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0915*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1115*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1015*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1016_dt = (-((gt + g1)*r1016) - (gt + g2)*r1016)/2. - i*((conj(Em4a)*conj(r0410))/(4.*rt6) - (conj(Em3a)*conj(r0810))/(4.*rt2) + (Em1a*r0216)/(4.*rt2) + (Ep1a*r0416)/(4.*rt2) + (Em2a*r0616)/(4.*rt6) - (Ep2a*r0816)/(4.*rt6) - (delta1 + v*Kvec1)*r1016 - r1015*((2*WLx)/3. - (2*i*WLy)/3.) + r0916*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1116*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1016*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr1109_dt = -((gt + g1)*r1109) - i*(-(conj(Em1a)*conj(r0111))/4. - (conj(Ep1a)*conj(r0311))/(4.*rt6) + (conj(Ep2a)*conj(r0711))/(4.*rt6) + (Em1a*r0309)/(4.*rt6) + (Ep1a*r0509)/4. + (Em2a*r0709)/(4.*rt6) + r1009*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-delta1 - v*Kvec1 - WLz/6.) + r1109*(-delta1 - v*Kvec1 + WLz/6.));
+dr1110_dt = -((gt + g1)*r1110) - i*(-(conj(Em1a)*conj(r0211))/(4.*rt2) - (conj(Ep1a)*conj(r0411))/(4.*rt2) - (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep2a)*conj(r0811))/(4.*rt6) + (Em1a*r0310)/(4.*rt6) + (Ep1a*r0510)/4. + (Em2a*r0710)/(4.*rt6) + (delta1 + v*Kvec1)*r1110 + r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-delta1 - v*Kvec1 + WLz/6.));
+dr1111_dt = -((gt + g1)*r1111) - i*(-(conj(Em1a)*conj(r0311))/(4.*rt6) - (conj(Ep1a)*conj(r0511))/4. - (conj(Em2a)*conj(r0711))/(4.*rt6) + (Em1a*r0311)/(4.*rt6) + (Ep1a*r0511)/4. + (Em2a*r0711)/(4.*rt6) + conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1112_dt = (-((gt + g1)*r1112) - (gt + g2)*r1112)/2. - i*(-(conj(Ep4a)*conj(r0211))/(4.*rt6) - (conj(Ep3a)*conj(r0611))/(4.*rt2) + (Em1a*r0312)/(4.*rt6) + (Ep1a*r0512)/4. + (Em2a*r0712)/(4.*rt6) - r1113*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-delta1 - v*Kvec1 + WLz/6.) - r1112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1113_dt = (-((gt + g1)*r1113) - (gt + g2)*r1113)/2. - i*((conj(Em4a)*conj(r0111))/(4.*rt6) - (conj(Ep4a)*conj(r0311))/8. - (conj(Ep3a)*conj(r0711))/8. + (Em1a*r0313)/(4.*rt6) + (Ep1a*r0513)/4. + (Em2a*r0713)/(4.*rt6) - r1112*((2*WLx)/3. - (2*i*WLy)/3.) - r1114*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-delta1 - v*Kvec1 + WLz/6.) - r1113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1114_dt = (-((gt + g1)*r1114) - (gt + g2)*r1114)/2. - i*((conj(Em4a)*conj(r0211))/8. - (conj(Ep4a)*conj(r0411))/8. - (conj(Em3a)*conj(r0611))/(8.*rt3) - (conj(Ep3a)*conj(r0811))/(8.*rt3) + (Em1a*r0314)/(4.*rt6) + (Ep1a*r0514)/4. + (Em2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1114 - r1113*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r1115*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-delta1 - v*Kvec1 + WLz/6.));
+dr1115_dt = (-((gt + g1)*r1115) - (gt + g2)*r1115)/2. - i*((conj(Em4a)*conj(r0311))/8. - (conj(Ep4a)*conj(r0511))/(4.*rt6) - (conj(Em3a)*conj(r0711))/8. + (Em1a*r0315)/(4.*rt6) + (Ep1a*r0515)/4. + (Em2a*r0715)/(4.*rt6) - r1116*((2*WLx)/3. + (2*i*WLy)/3.) - r1114*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r1115*(-delta1 - v*Kvec1 + WLz/6.));
+dr1116_dt = (-((gt + g1)*r1116) - (gt + g2)*r1116)/2. - i*((conj(Em4a)*conj(r0411))/(4.*rt6) - (conj(Em3a)*conj(r0811))/(4.*rt2) + (Em1a*r0316)/(4.*rt6) + (Ep1a*r0516)/4. + (Em2a*r0716)/(4.*rt6) - r1115*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r1116*(-delta1 - v*Kvec1 + WLz/6.));
+dr1212_dt = -((gt + g2)*r1212) - i*(-(conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Ep3a)*conj(r0612))/(4.*rt2) + (Ep4a*r0212)/(4.*rt6) + (Ep3a*r0612)/(4.*rt2) + r1312*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.));
+dr1312_dt = -((gt + g2)*r1312) - i*(-(conj(Ep4a)*conj(r0213))/(4.*rt6) - (conj(Ep3a)*conj(r0613))/(4.*rt2) - (Em4a*r0112)/(4.*rt6) + (Ep4a*r0312)/8. + (Ep3a*r0712)/8. + r1212*((2*WLx)/3. + (2*i*WLy)/3.) - r1313*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1313_dt = -((gt + g2)*r1313) - i*((conj(Em4a)*conj(r0113))/(4.*rt6) - (conj(Ep4a)*conj(r0313))/8. - (conj(Ep3a)*conj(r0713))/8. - (Em4a*r0113)/(4.*rt6) + (Ep4a*r0313)/8. + (Ep3a*r0713)/8. - r1312*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.) + r1413*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - conj(r1413)*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy));
+dr1412_dt = -((gt + g2)*r1412) - i*(-(conj(Ep4a)*conj(r0214))/(4.*rt6) - (conj(Ep3a)*conj(r0614))/(4.*rt2) - (Em4a*r0212)/8. + (Ep4a*r0412)/8. + (Em3a*r0612)/(8.*rt3) + (Ep3a*r0812)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1412 - r1413*((2*WLx)/3. + (2*i*WLy)/3.) + r1512*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1312*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r1412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1413_dt = -((gt + g2)*r1413) - i*((conj(Em4a)*conj(r0114))/(4.*rt6) - (conj(Ep4a)*conj(r0314))/8. - (conj(Ep3a)*conj(r0714))/8. - (Em4a*r0213)/8. + (Ep4a*r0413)/8. + (Em3a*r0613)/(8.*rt3) + (Ep3a*r0813)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1413 - r1412*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1313*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r1414*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r1413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1414_dt = -((gt + g2)*r1414) - i*((conj(Em4a)*conj(r0214))/8. - (conj(Ep4a)*conj(r0414))/8. - (conj(Em3a)*conj(r0614))/(8.*rt3) - (conj(Ep3a)*conj(r0814))/(8.*rt3) - (Em4a*r0214)/8. + (Ep4a*r0414)/8. + (Em3a*r0614)/(8.*rt3) + (Ep3a*r0814)/(8.*rt3) - r1413*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1514*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + conj(r1413)*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - conj(r1514)*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy));
+dr1512_dt = -((gt + g2)*r1512) - i*(-(conj(Ep4a)*conj(r0215))/(4.*rt6) - (conj(Ep3a)*conj(r0615))/(4.*rt2) - (Em4a*r0312)/8. + (Ep4a*r0512)/(4.*rt6) + (Em3a*r0712)/8. + r1612*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1513_dt = -((gt + g2)*r1513) - i*((conj(Em4a)*conj(r0115))/(4.*rt6) - (conj(Ep4a)*conj(r0315))/8. - (conj(Ep3a)*conj(r0715))/8. - (Em4a*r0313)/8. + (Ep4a*r0513)/(4.*rt6) + (Em3a*r0713)/8. - r1512*((2*WLx)/3. - (2*i*WLy)/3.) + r1613*((2*WLx)/3. - (2*i*WLy)/3.) + r1413*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r1514*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1514_dt = -((gt + g2)*r1514) - i*((conj(Em4a)*conj(r0215))/8. - (conj(Ep4a)*conj(r0415))/8. - (conj(Em3a)*conj(r0615))/(8.*rt3) - (conj(Ep3a)*conj(r0815))/(8.*rt3) - (Em4a*r0314)/8. + (Ep4a*r0514)/(4.*rt6) + (Em3a*r0714)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1514 + r1614*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1414*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r1515*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1514*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1515_dt = -((gt + g2)*r1515) - i*((conj(Em4a)*conj(r0315))/8. - (conj(Ep4a)*conj(r0515))/(4.*rt6) - (conj(Em3a)*conj(r0715))/8. - (Em4a*r0315)/8. + (Ep4a*r0515)/(4.*rt6) + (Em3a*r0715)/8. + r1615*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.) - r1514*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + conj(r1514)*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy));
+dr1612_dt = -((gt + g2)*r1612) - i*(-(conj(Ep4a)*conj(r0216))/(4.*rt6) - (conj(Ep3a)*conj(r0616))/(4.*rt2) - (Em4a*r0412)/(4.*rt6) + (Em3a*r0812)/(4.*rt2) + r1512*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*((2*WLx)/3. + (2*i*WLy)/3.) + r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1613_dt = -((gt + g2)*r1613) - i*((conj(Em4a)*conj(r0116))/(4.*rt6) - (conj(Ep4a)*conj(r0316))/8. - (conj(Ep3a)*conj(r0716))/8. - (Em4a*r0413)/(4.*rt6) + (Em3a*r0813)/(4.*rt2) - r1612*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1614_dt = -((gt + g2)*r1614) - i*((conj(Em4a)*conj(r0216))/8. - (conj(Ep4a)*conj(r0416))/8. - (conj(Em3a)*conj(r0616))/(8.*rt3) - (conj(Ep3a)*conj(r0816))/(8.*rt3) - (Em4a*r0414)/(4.*rt6) + (Em3a*r0814)/(4.*rt2) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1614 + r1514*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r1615*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1614*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr1615_dt = -((gt + g2)*r1615) - i*((conj(Em4a)*conj(r0316))/8. - (conj(Ep4a)*conj(r0516))/(4.*rt6) - (conj(Em3a)*conj(r0716))/8. - (Em4a*r0415)/(4.*rt6) + (Em3a*r0815)/(4.*rt2) + r1515*((2*WLx)/3. + (2*i*WLy)/3.) - r1616*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1616_dt = -((gt + g2)*r1616) - i*((conj(Em4a)*conj(r0416))/(4.*rt6) - (conj(Em3a)*conj(r0816))/(4.*rt2) - (Em4a*r0416)/(4.*rt6) + (Em3a*r0816)/(4.*rt2) - r1615*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.));
+//---------------- RbEquations.txt ends  ------------------
+					]]>
+        </operator>
+				<!--
+							 According to xmds2 docs operator kind="ip" should be faster
+							 but our codes runs about 5% to 10% slower with it.
+							 Maybe because we very close to the stiff condition so I use "ex" kind
+							 <operator kind="ip" constant="yes">
+					 -->
+				<operator kind="ex" constant="yes" type="imaginary">
+					<operator_names>Lt</operator_names>
+					<![CDATA[
+					Lt = -i/c*kt;
+					]]>
+				</operator>
+        <integration_vectors>E_field</integration_vectors>
+				<dependencies>density_matrix</dependencies>
+				<![CDATA[
+				//read from Mathematica generated RbPropEquations.txt
+//---------------- RbPropEquations.txt starts ------------------
+dEp1_dz = -((i*Ndens*(rt2*conj(r0309) + rt6*(conj(r0410) + rt2*conj(r0511)))*eta1)/(rt2*rt6)) - Lt[Ep1];
+dEm1_dz = -((i*Ndens*(rt2*rt6*conj(r0109) + rt6*conj(r0210) + rt2*conj(r0311))*eta1)/(rt2*rt6)) - Lt[Em1];
+dEp2_dz = (i*Ndens*(conj(r0709) + conj(r0810))*eta1)/rt6 - Lt[Ep2];
+dEm2_dz = -((i*Ndens*(conj(r0610) + conj(r0711))*eta1)/rt6) - Lt[Em2];
+dEp3_dz = -((i*Ndens*(rt2*rt3*conj(r0612) + rt3*conj(r0713) + conj(r0814))*eta2)/rt3) - Lt[Ep3];
+dEm3_dz = -((i*Ndens*(conj(r0614) + rt3*(conj(r0715) + rt2*conj(r0816)))*eta2)/rt3) - Lt[Em3];
+dEp4_dz = -((i*Ndens*(rt*conj(r0212) + rt3*conj(r0313) + rt3*conj(r0414) + rt*conj(r0515))*eta2)/rt3) - Lt[Ep4];
+dEm4_dz = (i*Ndens*(rt*conj(r0113) + rt3*conj(r0214) + rt3*conj(r0315) + rt*conj(r0416))*eta2)/rt3 - Lt[Em4];
+//---------------- RbPropEquations.txt ends  ------------------
+				]]>
+			</operators>
+		</integrate>
+	</sequence>
+
+
+
+	<!-- The output to generate -->
+	<output format="binary" filename="realistic_Rb_and_fields.xsil">
+		<group>
+      <sampling basis="t(1000) " initial_sample="yes">
+				<dependencies>E_field_avgd</dependencies>
+				<moments>Ip1_out Im1_out Ip2_out Im2_out Ip3_out Im3_out Ip4_out Im4_out</moments>
+				<![CDATA[
+				Ip1_out = mod2(Ep1a);
+				Im1_out = mod2(Em1a);
+				Ip2_out = mod2(Ep2a);
+				Im2_out = mod2(Em2a);
+				Ip3_out = mod2(Ep3a);
+				Im3_out = mod2(Em3a);
+				Ip4_out = mod2(Ep4a);
+				Im4_out = mod2(Em4a);
+				]]>
+			</sampling>
+		</group>
+	</output>
+
+</simulation>
+	
+<!-- 
+vim: ts=2 sw=2 foldmethod=indent: 
+-->
-- 
cgit v1.2.3


From 92ceaf3edca9d74015b4768224eda4c60da9918d Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Thu, 15 Nov 2012 20:25:17 -0500
Subject: added proper rho elements into the density matrix element

---
 xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
index bfed139..11a98ad 100644
--- a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
+++ b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
@@ -246,7 +246,7 @@ const double rt2 = 1.4142135623730951;
 		<components>
 			<!-- read from Mathematica generated RbChosenRho.txt -->
 <!-- ############### RbChosenRho.txt starts ################ -->
-r0101 r0113 r0202 r0214 r0303 r0309 r0315 r0404 r0410 r0416 r0505 r0511 r0602 r0606 r0614 r0703 r0707 r0709 r0715 r0804 r0808 r0810 r0816 r0909 r0915 r1010 r1016 r1111 r1313 r1414 r1515 r1616 
+r0101 r0109 r0110 r0111 r0112 r0113 r0114 r0115 r0116 r0201 r0202 r0209 r0210 r0211 r0212 r0213 r0214 r0215 r0216 r0301 r0302 r0303 r0309 r0310 r0311 r0312 r0313 r0314 r0315 r0316 r0401 r0402 r0403 r0404 r0409 r0410 r0411 r0412 r0413 r0414 r0415 r0416 r0501 r0502 r0503 r0504 r0505 r0509 r0510 r0511 r0512 r0513 r0514 r0515 r0516 r0601 r0602 r0603 r0604 r0605 r0606 r0609 r0610 r0611 r0612 r0613 r0614 r0615 r0616 r0701 r0702 r0703 r0704 r0705 r0706 r0707 r0709 r0710 r0711 r0712 r0713 r0714 r0715 r0716 r0801 r0802 r0803 r0804 r0805 r0806 r0807 r0808 r0809 r0810 r0811 r0812 r0813 r0814 r0815 r0816 r0909 r0912 r0913 r0914 r0915 r0916 r1009 r1010 r1012 r1013 r1014 r1015 r1016 r1109 r1110 r1111 r1112 r1113 r1114 r1115 r1116 r1212 r1312 r1313 r1412 r1413 r1414 r1512 r1513 r1514 r1515 r1612 r1613 r1614 r1615 r1616 
 <!-- ############### RbChosenRho.txt ends  ################# -->
 		</components>
 		<initialisation>
-- 
cgit v1.2.3


From 97699d1057ae43cb6fdcdae34bb5a4e824134088 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Fri, 16 Nov 2012 09:44:32 -0500
Subject: Added arguments to give magnetic field projection in Larmor frequency
 units

---
 xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
index 11a98ad..e85bb9f 100644
--- a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
+++ b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
@@ -93,10 +93,6 @@ const double rt2 = 1.4142135623730951;
 				// repopulation rate (atoms flying in/out the laser beam)  in [1/s]
 				const double gt=0.01 *(2*M_PI*1e6);
 
-				// Larmor frequency 
-				double WL=0;
-
-
 				// inner use variables 
 				double probability_v; // will be used as p(v) in Maxwell distribution
 
@@ -129,6 +125,10 @@ const double rt2 = 1.4142135623730951;
 			<argument name="Lcell"  type="real" default_value="1.5e-2" />
 			<!--Density of atoms [1/m^3] -->
 			<argument name="Ndens"  type="real" default_value="1e15" />
+			<!-- Projections of magnetic field in Larmor frequency units [1/s] -->
+			<argument name="WLx"  type="real" default_value="0" />
+			<argument name="WLy"  type="real" default_value="0" />
+			<argument name="WLz"  type="real" default_value="0" />
 			<!--Atoms temperature [K] -->
 			<!--TODO: looks like Temperature > 10 K knocks solver, 
 					 I am guessing detunings are too large and thus it became a stiff equation-->
-- 
cgit v1.2.3


From 9aa57a91f8144ee292d0d1cce1336eb1704ba19d Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Fri, 16 Nov 2012 09:55:05 -0500
Subject: xmds: insert proper equations from mathematica where rt --> rt2

---
 xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
index e85bb9f..0f4d50d 100644
--- a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
+++ b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
@@ -604,8 +604,8 @@ dEp2_dz = (i*Ndens*(conj(r0709) + conj(r0810))*eta1)/rt6 - Lt[Ep2];
 dEm2_dz = -((i*Ndens*(conj(r0610) + conj(r0711))*eta1)/rt6) - Lt[Em2];
 dEp3_dz = -((i*Ndens*(rt2*rt3*conj(r0612) + rt3*conj(r0713) + conj(r0814))*eta2)/rt3) - Lt[Ep3];
 dEm3_dz = -((i*Ndens*(conj(r0614) + rt3*(conj(r0715) + rt2*conj(r0816)))*eta2)/rt3) - Lt[Em3];
-dEp4_dz = -((i*Ndens*(rt*conj(r0212) + rt3*conj(r0313) + rt3*conj(r0414) + rt*conj(r0515))*eta2)/rt3) - Lt[Ep4];
-dEm4_dz = (i*Ndens*(rt*conj(r0113) + rt3*conj(r0214) + rt3*conj(r0315) + rt*conj(r0416))*eta2)/rt3 - Lt[Em4];
+dEp4_dz = -((i*Ndens*(rt2*conj(r0212) + rt3*conj(r0313) + rt3*conj(r0414) + rt2*conj(r0515))*eta2)/rt3) - Lt[Ep4];
+dEm4_dz = (i*Ndens*(rt2*conj(r0113) + rt3*conj(r0214) + rt3*conj(r0315) + rt2*conj(r0416))*eta2)/rt3 - Lt[Em4];
 //---------------- RbPropEquations.txt ends  ------------------
 				]]>
 			</operators>
-- 
cgit v1.2.3


From 4c3d740caf4f997d202f51b83cfbf8e90f494339 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Fri, 16 Nov 2012 11:02:58 -0500
Subject: xmds: compilation problem fix Sqrt --> sqrt as generated by
 mathematica

---
 .../realistic_Rb_and_fields.xmds                   | 162 ++++++++++-----------
 1 file changed, 81 insertions(+), 81 deletions(-)

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
index 0f4d50d..d4e663e 100644
--- a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
+++ b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
@@ -447,74 +447,74 @@ dr0109_dt = (-(gt*r0109) - (gt + g1)*r0109)/2. - i*(-(conj(Ep1a)*conj(r0301))/(4
 dr0110_dt = (-(gt*r0110) - (gt + g1)*r0110)/2. - i*(-(conj(Em1a)*conj(r0201))/(4.*rt2) - (conj(Ep1a)*conj(r0401))/(4.*rt2) - (conj(Em2a)*conj(r0601))/(4.*rt6) + (conj(Ep2a)*conj(r0801))/(4.*rt6) + (conj(Em1a)*conj(r1009))/4. - (conj(Em4a)*conj(r1013))/(4.*rt6) + (delta1 + v*Kvec1)*r0110 + r0210*(WLx/2. - (i*WLy)/2.) - r0111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0110*WLz);
 dr0111_dt = (-(gt*r0111) - (gt + g1)*r0111)/2. - i*(-(conj(Em1a)*conj(r0301))/(4.*rt6) - (conj(Ep1a)*conj(r0501))/4. - (conj(Em2a)*conj(r0701))/(4.*rt6) + (conj(Em1a)*conj(r1109))/4. - (conj(Em4a)*conj(r1113))/(4.*rt6) + r0211*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0111*(-delta1 - v*Kvec1 + WLz/6.) + r0111*WLz);
 dr0112_dt = (-(gt*r0112) - (gt + g2)*r0112)/2. - i*(-(conj(Ep4a)*conj(r0201))/(4.*rt6) - (conj(Ep3a)*conj(r0601))/(4.*rt2) + (conj(Em1a)*r0912)/4. - (conj(Em4a)*r1312)/(4.*rt6) + r0212*(WLx/2. - (i*WLy)/2.) - r0113*((2*WLx)/3. + (2*i*WLy)/3.) + r0112*WLz - r0112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0113_dt = (-(gt*r0113) - (gt + g2)*r0113)/2. - i*(-(conj(Ep4a)*conj(r0301))/8. - (conj(Ep3a)*conj(r0701))/8. + (conj(Em4a)*r0101)/(4.*rt6) + (conj(Em1a)*r0913)/4. - (conj(Em4a)*r1313)/(4.*rt6) - r0112*((2*WLx)/3. - (2*i*WLy)/3.) + r0213*(WLx/2. - (i*WLy)/2.) - r0114*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r0113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + r0113*WLz);
-dr0114_dt = (-(gt*r0114) - (gt + g2)*r0114)/2. - i*((conj(Em4a)*conj(r0201))/8. - (conj(Ep4a)*conj(r0401))/8. - (conj(Em3a)*conj(r0601))/(8.*rt3) - (conj(Ep3a)*conj(r0801))/(8.*rt3) - (conj(Em4a)*conj(r1413))/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0114 + (conj(Em1a)*r0914)/4. + r0214*(WLx/2. - (i*WLy)/2.) - r0113*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0115*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0114*WLz);
-dr0115_dt = (-(gt*r0115) - (gt + g2)*r0115)/2. - i*((conj(Em4a)*conj(r0301))/8. - (conj(Ep4a)*conj(r0501))/(4.*rt6) - (conj(Em3a)*conj(r0701))/8. - (conj(Em4a)*conj(r1513))/(4.*rt6) + (conj(Em1a)*r0915)/4. + r0215*(WLx/2. - (i*WLy)/2.) - r0116*((2*WLx)/3. + (2*i*WLy)/3.) - r0114*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0115*WLz);
+dr0113_dt = (-(gt*r0113) - (gt + g2)*r0113)/2. - i*(-(conj(Ep4a)*conj(r0301))/8. - (conj(Ep3a)*conj(r0701))/8. + (conj(Em4a)*r0101)/(4.*rt6) + (conj(Em1a)*r0913)/4. - (conj(Em4a)*r1313)/(4.*rt6) - r0112*((2*WLx)/3. - (2*i*WLy)/3.) + r0213*(WLx/2. - (i*WLy)/2.) - r0114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + r0113*WLz);
+dr0114_dt = (-(gt*r0114) - (gt + g2)*r0114)/2. - i*((conj(Em4a)*conj(r0201))/8. - (conj(Ep4a)*conj(r0401))/8. - (conj(Em3a)*conj(r0601))/(8.*rt3) - (conj(Ep3a)*conj(r0801))/(8.*rt3) - (conj(Em4a)*conj(r1413))/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0114 + (conj(Em1a)*r0914)/4. + r0214*(WLx/2. - (i*WLy)/2.) - r0113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0114*WLz);
+dr0115_dt = (-(gt*r0115) - (gt + g2)*r0115)/2. - i*((conj(Em4a)*conj(r0301))/8. - (conj(Ep4a)*conj(r0501))/(4.*rt6) - (conj(Em3a)*conj(r0701))/8. - (conj(Em4a)*conj(r1513))/(4.*rt6) + (conj(Em1a)*r0915)/4. + r0215*(WLx/2. - (i*WLy)/2.) - r0116*((2*WLx)/3. + (2*i*WLy)/3.) - r0114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0115*WLz);
 dr0116_dt = (-(gt*r0116) - (gt + g2)*r0116)/2. - i*((conj(Em4a)*conj(r0401))/(4.*rt6) - (conj(Em3a)*conj(r0801))/(4.*rt2) - (conj(Em4a)*conj(r1613))/(4.*rt6) + (conj(Em1a)*r0916)/4. - r0115*((2*WLx)/3. - (2*i*WLy)/3.) + r0216*(WLx/2. - (i*WLy)/2.) - r0116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0116*WLz);
-dr0201_dt = -(gt*r0201) + (g1*r1009)/(2.*rt2) + (g2*r1312)/6. + (g2*r1413)/(2.*rt6) - i*((conj(Em1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0112))/(4.*rt6) - (conj(Em4a)*conj(r0114))/8. - (Em1a*r0209)/4. + (Em4a*r0213)/(4.*rt6) + r0101*(WLx/2. + (i*WLy)/2.) - r0202*(WLx/2. + (i*WLy)/2.) + r0301*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - (r0201*WLz)/2.);
-dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1212)/6. + (g2*r1313)/12. + (g2*r1414)/4. - i*((conj(Em1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Em4a)*conj(r0214))/8. - (Em1a*r0210)/(4.*rt2) - (Ep4a*r0212)/(4.*rt6) + (Em4a*r0214)/8. - r0201*(WLx/2. - (i*WLy)/2.) + conj(r0201)*(WLx/2. + (i*WLy)/2.) + r0302*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - conj(r0302)*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.));
-dr0209_dt = (-(gt*r0209) - (gt + g1)*r0209)/2. - i*(-(conj(Ep1a)*conj(r0302))/(4.*rt6) + (conj(Ep2a)*conj(r0702))/(4.*rt6) + (conj(Ep4a)*conj(r0912))/(4.*rt6) - (conj(Em4a)*conj(r0914))/8. - (conj(Em1a)*r0201)/4. + (conj(Em1a)*r1009)/(4.*rt2) + r0109*(WLx/2. + (i*WLy)/2.) + r0309*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-delta1 - v*Kvec1 - WLz/6.) + (r0209*WLz)/2.);
-dr0210_dt = (-(gt*r0210) - (gt + g1)*r0210)/2. - i*(-(conj(Ep1a)*conj(r0402))/(4.*rt2) - (conj(Em2a)*conj(r0602))/(4.*rt6) + (conj(Ep2a)*conj(r0802))/(4.*rt6) + (conj(Ep4a)*conj(r1012))/(4.*rt6) - (conj(Em4a)*conj(r1014))/8. - (conj(Em1a)*r0202)/(4.*rt2) + (delta1 + v*Kvec1)*r0210 + (conj(Em1a)*r1010)/(4.*rt2) + r0110*(WLx/2. + (i*WLy)/2.) + r0310*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0211*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + (r0210*WLz)/2.);
-dr0211_dt = (-(gt*r0211) - (gt + g1)*r0211)/2. - i*(-(conj(Em1a)*conj(r0302))/(4.*rt6) - (conj(Ep1a)*conj(r0502))/4. - (conj(Em2a)*conj(r0702))/(4.*rt6) + (conj(Em1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1112))/(4.*rt6) - (conj(Em4a)*conj(r1114))/8. + r0111*(WLx/2. + (i*WLy)/2.) + r0311*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0211*(-delta1 - v*Kvec1 + WLz/6.) + (r0211*WLz)/2.);
-dr0212_dt = (-(gt*r0212) - (gt + g2)*r0212)/2. - i*(-(conj(Ep3a)*conj(r0602))/(4.*rt2) - (conj(Ep4a)*r0202)/(4.*rt6) + (conj(Em1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1212)/(4.*rt6) - (conj(Em4a)*r1412)/8. + r0112*(WLx/2. + (i*WLy)/2.) - r0213*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + (r0212*WLz)/2. - r0212*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0213_dt = (-(gt*r0213) - (gt + g2)*r0213)/2. - i*(-(conj(Ep4a)*conj(r0302))/8. - (conj(Ep3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1312))/(4.*rt6) + (conj(Em4a)*r0201)/(4.*rt6) + (conj(Em1a)*r1013)/(4.*rt2) - (conj(Em4a)*r1413)/8. - r0212*((2*WLx)/3. - (2*i*WLy)/3.) + r0113*(WLx/2. + (i*WLy)/2.) - r0214*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0313*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0213*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + (r0213*WLz)/2.);
-dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*(-(conj(Ep4a)*conj(r0402))/8. - (conj(Em3a)*conj(r0602))/(8.*rt3) - (conj(Ep3a)*conj(r0802))/(8.*rt3) + (conj(Ep4a)*conj(r1412))/(4.*rt6) + (conj(Em4a)*r0202)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 + (conj(Em1a)*r1014)/(4.*rt2) - (conj(Em4a)*r1414)/8. + r0114*(WLx/2. + (i*WLy)/2.) - r0213*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0215*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0314*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + (r0214*WLz)/2.);
-dr0215_dt = (-(gt*r0215) - (gt + g2)*r0215)/2. - i*((conj(Em4a)*conj(r0302))/8. - (conj(Ep4a)*conj(r0502))/(4.*rt6) - (conj(Em3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1512))/(4.*rt6) - (conj(Em4a)*conj(r1514))/8. + (conj(Em1a)*r1015)/(4.*rt2) + r0115*(WLx/2. + (i*WLy)/2.) - r0216*((2*WLx)/3. + (2*i*WLy)/3.) - r0214*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0315*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0215*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + (r0215*WLz)/2.);
-dr0216_dt = (-(gt*r0216) - (gt + g2)*r0216)/2. - i*((conj(Em4a)*conj(r0402))/(4.*rt6) - (conj(Em3a)*conj(r0802))/(4.*rt2) + (conj(Ep4a)*conj(r1612))/(4.*rt6) - (conj(Em4a)*conj(r1614))/8. + (conj(Em1a)*r1016)/(4.*rt2) - r0215*((2*WLx)/3. - (2*i*WLy)/3.) + r0116*(WLx/2. + (i*WLy)/2.) + r0316*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0216*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + (r0216*WLz)/2.);
-dr0301_dt = -(gt*r0301) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0109))/(4.*rt6) + (conj(Em1a)*conj(r0111))/(4.*rt6) + (conj(Ep4a)*conj(r0113))/8. - (conj(Em4a)*conj(r0115))/8. - (Em1a*r0309)/4. + (Em4a*r0313)/(4.*rt6) - r0302*(WLx/2. + (i*WLy)/2.) + r0401*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0201*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0301*WLz);
-dr0302_dt = -(gt*r0302) + (g1*r1009)/(2.*rt3) + (g1*r1110)/(4.*rt3) + (g2*r1312)/(2.*rt6) + (g2*r1514)/4. - i*((conj(Ep1a)*conj(r0209))/(4.*rt6) + (conj(Em1a)*conj(r0211))/(4.*rt6) + (conj(Ep4a)*conj(r0213))/8. - (conj(Em4a)*conj(r0215))/8. - (Em1a*r0310)/(4.*rt2) - (Ep4a*r0312)/(4.*rt6) + (Em4a*r0314)/8. - r0301*(WLx/2. - (i*WLy)/2.) + r0402*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0202*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0303*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (r0302*WLz)/2.);
-dr0303_dt = gt/8. - gt*r0303 + (g1*r0909)/12. + (g1*r1010)/3. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1515)/4. - i*((conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Em1a)*conj(r0311))/(4.*rt6) + (conj(Ep4a)*conj(r0313))/8. - (conj(Em4a)*conj(r0315))/8. - (Ep1a*r0309)/(4.*rt6) - (Em1a*r0311)/(4.*rt6) - (Ep4a*r0313)/8. + (Em4a*r0315)/8. - r0302*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0403*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + conj(r0302)*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - conj(r0403)*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.));
-dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*((conj(Ep2a)*conj(r0703))/(4.*rt6) + (conj(Ep4a)*conj(r0913))/8. - (conj(Em4a)*conj(r0915))/8. - (conj(Em1a)*r0301)/4. - (conj(Ep1a)*r0303)/(4.*rt6) + (conj(Ep1a)*r0909)/(4.*rt6) + (conj(Em1a)*r1109)/(4.*rt6) + r0409*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0209*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-delta1 - v*Kvec1 - WLz/6.));
-dr0310_dt = (-(gt*r0310) - (gt + g1)*r0310)/2. - i*(-(conj(Ep1a)*conj(r0403))/(4.*rt2) - (conj(Em2a)*conj(r0603))/(4.*rt6) + (conj(Ep2a)*conj(r0803))/(4.*rt6) + (conj(Ep1a)*conj(r1009))/(4.*rt6) + (conj(Ep4a)*conj(r1013))/8. - (conj(Em4a)*conj(r1015))/8. - (conj(Em1a)*r0302)/(4.*rt2) + (delta1 + v*Kvec1)*r0310 + (conj(Em1a)*r1110)/(4.*rt6) + r0410*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0210*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0311*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
-dr0311_dt = (-(gt*r0311) - (gt + g1)*r0311)/2. - i*(-(conj(Ep1a)*conj(r0503))/4. - (conj(Em2a)*conj(r0703))/(4.*rt6) + (conj(Ep1a)*conj(r1109))/(4.*rt6) + (conj(Ep4a)*conj(r1113))/8. - (conj(Em4a)*conj(r1115))/8. - (conj(Em1a)*r0303)/(4.*rt6) + (conj(Em1a)*r1111)/(4.*rt6) + r0411*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0211*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0311*(-delta1 - v*Kvec1 + WLz/6.));
-dr0312_dt = (-(gt*r0312) - (gt + g2)*r0312)/2. - i*(-(conj(Ep3a)*conj(r0603))/(4.*rt2) - (conj(Ep4a)*r0302)/(4.*rt6) + (conj(Ep1a)*r0912)/(4.*rt6) + (conj(Em1a)*r1112)/(4.*rt6) + (conj(Ep4a)*r1312)/8. - (conj(Em4a)*r1512)/8. - r0313*((2*WLx)/3. + (2*i*WLy)/3.) + r0412*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0212*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0313_dt = (-(gt*r0313) - (gt + g2)*r0313)/2. - i*(-(conj(Ep3a)*conj(r0703))/8. + (conj(Em4a)*r0301)/(4.*rt6) - (conj(Ep4a)*r0303)/8. + (conj(Ep1a)*r0913)/(4.*rt6) + (conj(Em1a)*r1113)/(4.*rt6) + (conj(Ep4a)*r1313)/8. - (conj(Em4a)*r1513)/8. - r0312*((2*WLx)/3. - (2*i*WLy)/3.) - r0314*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0413*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0213*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0313*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr0314_dt = (-(gt*r0314) - (gt + g2)*r0314)/2. - i*(-(conj(Ep4a)*conj(r0403))/8. - (conj(Em3a)*conj(r0603))/(8.*rt3) - (conj(Ep3a)*conj(r0803))/(8.*rt3) + (conj(Ep4a)*conj(r1413))/8. + (conj(Em4a)*r0302)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0314 + (conj(Ep1a)*r0914)/(4.*rt6) + (conj(Em1a)*r1114)/(4.*rt6) - (conj(Em4a)*r1514)/8. - r0313*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0315*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0414*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0214*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.));
-dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(conj(Ep4a)*conj(r0503))/(4.*rt6) - (conj(Em3a)*conj(r0703))/8. + (conj(Ep4a)*conj(r1513))/8. + (conj(Em4a)*r0303)/8. + (conj(Ep1a)*r0915)/(4.*rt6) + (conj(Em1a)*r1115)/(4.*rt6) - (conj(Em4a)*r1515)/8. - r0316*((2*WLx)/3. + (2*i*WLy)/3.) - r0314*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0415*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0215*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0315*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
-dr0316_dt = (-(gt*r0316) - (gt + g2)*r0316)/2. - i*((conj(Em4a)*conj(r0403))/(4.*rt6) - (conj(Em3a)*conj(r0803))/(4.*rt2) + (conj(Ep4a)*conj(r1613))/8. - (conj(Em4a)*conj(r1615))/8. + (conj(Ep1a)*r0916)/(4.*rt6) + (conj(Em1a)*r1116)/(4.*rt6) - r0315*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0216*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0316*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
-dr0401_dt = -(gt*r0401) - (g2*r1512)/6. + (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0114))/8. - (conj(Em4a)*conj(r0116))/(4.*rt6) - (Em1a*r0409)/4. + (Em4a*r0413)/(4.*rt6) + r0501*(WLx/2. - (i*WLy)/2.) - r0402*(WLx/2. + (i*WLy)/2.) + r0301*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (3*r0401*WLz)/2.);
-dr0402_dt = -(gt*r0402) + (g1*r1109)/4. + (g2*r1412)/(2.*rt6) - (g2*r1513)/12. + (g2*r1614)/(2.*rt6) - i*((conj(Ep1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0214))/8. - (conj(Em4a)*conj(r0216))/(4.*rt6) - (Em1a*r0410)/(4.*rt2) - (Ep4a*r0412)/(4.*rt6) + (Em4a*r0414)/8. - r0401*(WLx/2. - (i*WLy)/2.) + r0502*(WLx/2. - (i*WLy)/2.) + r0302*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0403*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0402*WLz);
-dr0403_dt = -(gt*r0403) + (g1*r1009)/(4.*rt3) + (g1*r1110)/(2.*rt3) + (g2*r1413)/4. + (g2*r1615)/(2.*rt6) - i*((conj(Ep1a)*conj(r0310))/(4.*rt2) + (conj(Ep4a)*conj(r0314))/8. - (conj(Em4a)*conj(r0316))/(4.*rt6) - (Ep1a*r0409)/(4.*rt6) - (Em1a*r0411)/(4.*rt6) - (Ep4a*r0413)/8. + (Em4a*r0415)/8. + r0503*(WLx/2. - (i*WLy)/2.) - r0402*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0303*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0404*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (r0403*WLz)/2.);
-dr0404_dt = gt/8. - gt*r0404 + (g1*r1010)/4. + (g1*r1111)/4. + (g2*r1414)/4. + (g2*r1515)/12. + (g2*r1616)/6. - i*((conj(Ep1a)*conj(r0410))/(4.*rt2) + (conj(Ep4a)*conj(r0414))/8. - (conj(Em4a)*conj(r0416))/(4.*rt6) - (Ep1a*r0410)/(4.*rt2) - (Ep4a*r0414)/8. + (Em4a*r0416)/(4.*rt6) + r0504*(WLx/2. - (i*WLy)/2.) - conj(r0504)*(WLx/2. + (i*WLy)/2.) - r0403*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + conj(r0403)*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.));
-dr0409_dt = (-(gt*r0409) - (gt + g1)*r0409)/2. - i*((conj(Ep2a)*conj(r0704))/(4.*rt6) + (conj(Ep4a)*conj(r0914))/8. - (conj(Em4a)*conj(r0916))/(4.*rt6) - (conj(Em1a)*r0401)/4. - (conj(Ep1a)*r0403)/(4.*rt6) + (conj(Ep1a)*r1009)/(4.*rt2) + r0509*(WLx/2. - (i*WLy)/2.) + r0309*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-delta1 - v*Kvec1 - WLz/6.) - (r0409*WLz)/2.);
-dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(conj(Em2a)*conj(r0604))/(4.*rt6) + (conj(Ep2a)*conj(r0804))/(4.*rt6) + (conj(Ep4a)*conj(r1014))/8. - (conj(Em4a)*conj(r1016))/(4.*rt6) - (conj(Em1a)*r0402)/(4.*rt2) - (conj(Ep1a)*r0404)/(4.*rt2) + (delta1 + v*Kvec1)*r0410 + (conj(Ep1a)*r1010)/(4.*rt2) + r0510*(WLx/2. - (i*WLy)/2.) + r0310*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0411*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - (r0410*WLz)/2.);
-dr0411_dt = (-(gt*r0411) - (gt + g1)*r0411)/2. - i*(-(conj(Ep1a)*conj(r0504))/4. - (conj(Em2a)*conj(r0704))/(4.*rt6) + (conj(Ep1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1114))/8. - (conj(Em4a)*conj(r1116))/(4.*rt6) - (conj(Em1a)*r0403)/(4.*rt6) + r0511*(WLx/2. - (i*WLy)/2.) + r0311*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0411*(-delta1 - v*Kvec1 + WLz/6.) - (r0411*WLz)/2.);
-dr0412_dt = (-(gt*r0412) - (gt + g2)*r0412)/2. - i*(-(conj(Ep3a)*conj(r0604))/(4.*rt2) - (conj(Ep4a)*r0402)/(4.*rt6) + (conj(Ep1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1412)/8. - (conj(Em4a)*r1612)/(4.*rt6) + r0512*(WLx/2. - (i*WLy)/2.) - r0413*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (r0412*WLz)/2. - r0412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0413_dt = (-(gt*r0413) - (gt + g2)*r0413)/2. - i*(-(conj(Ep3a)*conj(r0704))/8. + (conj(Em4a)*r0401)/(4.*rt6) - (conj(Ep4a)*r0403)/8. + (conj(Ep1a)*r1013)/(4.*rt2) + (conj(Ep4a)*r1413)/8. - (conj(Em4a)*r1613)/(4.*rt6) - r0412*((2*WLx)/3. - (2*i*WLy)/3.) + r0513*(WLx/2. - (i*WLy)/2.) - r0414*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0313*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - (r0413*WLz)/2.);
-dr0414_dt = (-(gt*r0414) - (gt + g2)*r0414)/2. - i*(-(conj(Em3a)*conj(r0604))/(8.*rt3) - (conj(Ep3a)*conj(r0804))/(8.*rt3) + (conj(Em4a)*r0402)/8. - (conj(Ep4a)*r0404)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0414 + (conj(Ep1a)*r1014)/(4.*rt2) + (conj(Ep4a)*r1414)/8. - (conj(Em4a)*r1614)/(4.*rt6) + r0514*(WLx/2. - (i*WLy)/2.) - r0413*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0415*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0314*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (r0414*WLz)/2.);
-dr0415_dt = (-(gt*r0415) - (gt + g2)*r0415)/2. - i*(-(conj(Ep4a)*conj(r0504))/(4.*rt6) - (conj(Em3a)*conj(r0704))/8. + (conj(Ep4a)*conj(r1514))/8. + (conj(Em4a)*r0403)/8. + (conj(Ep1a)*r1015)/(4.*rt2) - (conj(Em4a)*r1615)/(4.*rt6) + r0515*(WLx/2. - (i*WLy)/2.) - r0416*((2*WLx)/3. + (2*i*WLy)/3.) - r0414*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0315*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0415*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - (r0415*WLz)/2.);
-dr0416_dt = (-(gt*r0416) - (gt + g2)*r0416)/2. - i*(-(conj(Em3a)*conj(r0804))/(4.*rt2) + (conj(Ep4a)*conj(r1614))/8. + (conj(Em4a)*r0404)/(4.*rt6) + (conj(Ep1a)*r1016)/(4.*rt2) - (conj(Em4a)*r1616)/(4.*rt6) - r0415*((2*WLx)/3. - (2*i*WLy)/3.) + r0516*(WLx/2. - (i*WLy)/2.) + r0316*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0416*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - (r0416*WLz)/2.);
+dr0201_dt = -(gt*r0201) + (g1*r1009)/(2.*rt2) + (g2*r1312)/6. + (g2*r1413)/(2.*rt6) - i*((conj(Em1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0112))/(4.*rt6) - (conj(Em4a)*conj(r0114))/8. - (Em1a*r0209)/4. + (Em4a*r0213)/(4.*rt6) + r0101*(WLx/2. + (i*WLy)/2.) - r0202*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0201*WLz)/2.);
+dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1212)/6. + (g2*r1313)/12. + (g2*r1414)/4. - i*((conj(Em1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Em4a)*conj(r0214))/8. - (Em1a*r0210)/(4.*rt2) - (Ep4a*r0212)/(4.*rt6) + (Em4a*r0214)/8. - r0201*(WLx/2. - (i*WLy)/2.) + conj(r0201)*(WLx/2. + (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0209_dt = (-(gt*r0209) - (gt + g1)*r0209)/2. - i*(-(conj(Ep1a)*conj(r0302))/(4.*rt6) + (conj(Ep2a)*conj(r0702))/(4.*rt6) + (conj(Ep4a)*conj(r0912))/(4.*rt6) - (conj(Em4a)*conj(r0914))/8. - (conj(Em1a)*r0201)/4. + (conj(Em1a)*r1009)/(4.*rt2) + r0109*(WLx/2. + (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-delta1 - v*Kvec1 - WLz/6.) + (r0209*WLz)/2.);
+dr0210_dt = (-(gt*r0210) - (gt + g1)*r0210)/2. - i*(-(conj(Ep1a)*conj(r0402))/(4.*rt2) - (conj(Em2a)*conj(r0602))/(4.*rt6) + (conj(Ep2a)*conj(r0802))/(4.*rt6) + (conj(Ep4a)*conj(r1012))/(4.*rt6) - (conj(Em4a)*conj(r1014))/8. - (conj(Em1a)*r0202)/(4.*rt2) + (delta1 + v*Kvec1)*r0210 + (conj(Em1a)*r1010)/(4.*rt2) + r0110*(WLx/2. + (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0211*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + (r0210*WLz)/2.);
+dr0211_dt = (-(gt*r0211) - (gt + g1)*r0211)/2. - i*(-(conj(Em1a)*conj(r0302))/(4.*rt6) - (conj(Ep1a)*conj(r0502))/4. - (conj(Em2a)*conj(r0702))/(4.*rt6) + (conj(Em1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1112))/(4.*rt6) - (conj(Em4a)*conj(r1114))/8. + r0111*(WLx/2. + (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0211*(-delta1 - v*Kvec1 + WLz/6.) + (r0211*WLz)/2.);
+dr0212_dt = (-(gt*r0212) - (gt + g2)*r0212)/2. - i*(-(conj(Ep3a)*conj(r0602))/(4.*rt2) - (conj(Ep4a)*r0202)/(4.*rt6) + (conj(Em1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1212)/(4.*rt6) - (conj(Em4a)*r1412)/8. + r0112*(WLx/2. + (i*WLy)/2.) - r0213*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0212*WLz)/2. - r0212*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0213_dt = (-(gt*r0213) - (gt + g2)*r0213)/2. - i*(-(conj(Ep4a)*conj(r0302))/8. - (conj(Ep3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1312))/(4.*rt6) + (conj(Em4a)*r0201)/(4.*rt6) + (conj(Em1a)*r1013)/(4.*rt2) - (conj(Em4a)*r1413)/8. - r0212*((2*WLx)/3. - (2*i*WLy)/3.) + r0113*(WLx/2. + (i*WLy)/2.) - r0214*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0213*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + (r0213*WLz)/2.);
+dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*(-(conj(Ep4a)*conj(r0402))/8. - (conj(Em3a)*conj(r0602))/(8.*rt3) - (conj(Ep3a)*conj(r0802))/(8.*rt3) + (conj(Ep4a)*conj(r1412))/(4.*rt6) + (conj(Em4a)*r0202)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 + (conj(Em1a)*r1014)/(4.*rt2) - (conj(Em4a)*r1414)/8. + r0114*(WLx/2. + (i*WLy)/2.) - r0213*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0215*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0214*WLz)/2.);
+dr0215_dt = (-(gt*r0215) - (gt + g2)*r0215)/2. - i*((conj(Em4a)*conj(r0302))/8. - (conj(Ep4a)*conj(r0502))/(4.*rt6) - (conj(Em3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1512))/(4.*rt6) - (conj(Em4a)*conj(r1514))/8. + (conj(Em1a)*r1015)/(4.*rt2) + r0115*(WLx/2. + (i*WLy)/2.) - r0216*((2*WLx)/3. + (2*i*WLy)/3.) - r0214*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0215*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + (r0215*WLz)/2.);
+dr0216_dt = (-(gt*r0216) - (gt + g2)*r0216)/2. - i*((conj(Em4a)*conj(r0402))/(4.*rt6) - (conj(Em3a)*conj(r0802))/(4.*rt2) + (conj(Ep4a)*conj(r1612))/(4.*rt6) - (conj(Em4a)*conj(r1614))/8. + (conj(Em1a)*r1016)/(4.*rt2) - r0215*((2*WLx)/3. - (2*i*WLy)/3.) + r0116*(WLx/2. + (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0216*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + (r0216*WLz)/2.);
+dr0301_dt = -(gt*r0301) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0109))/(4.*rt6) + (conj(Em1a)*conj(r0111))/(4.*rt6) + (conj(Ep4a)*conj(r0113))/8. - (conj(Em4a)*conj(r0115))/8. - (Em1a*r0309)/4. + (Em4a*r0313)/(4.*rt6) - r0302*(WLx/2. + (i*WLy)/2.) + r0401*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0201*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0301*WLz);
+dr0302_dt = -(gt*r0302) + (g1*r1009)/(2.*rt3) + (g1*r1110)/(4.*rt3) + (g2*r1312)/(2.*rt6) + (g2*r1514)/4. - i*((conj(Ep1a)*conj(r0209))/(4.*rt6) + (conj(Em1a)*conj(r0211))/(4.*rt6) + (conj(Ep4a)*conj(r0213))/8. - (conj(Em4a)*conj(r0215))/8. - (Em1a*r0310)/(4.*rt2) - (Ep4a*r0312)/(4.*rt6) + (Em4a*r0314)/8. - r0301*(WLx/2. - (i*WLy)/2.) + r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0202*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0302*WLz)/2.);
+dr0303_dt = gt/8. - gt*r0303 + (g1*r0909)/12. + (g1*r1010)/3. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1515)/4. - i*((conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Em1a)*conj(r0311))/(4.*rt6) + (conj(Ep4a)*conj(r0313))/8. - (conj(Em4a)*conj(r0315))/8. - (Ep1a*r0309)/(4.*rt6) - (Em1a*r0311)/(4.*rt6) - (Ep4a*r0313)/8. + (Em4a*r0315)/8. - r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*((conj(Ep2a)*conj(r0703))/(4.*rt6) + (conj(Ep4a)*conj(r0913))/8. - (conj(Em4a)*conj(r0915))/8. - (conj(Em1a)*r0301)/4. - (conj(Ep1a)*r0303)/(4.*rt6) + (conj(Ep1a)*r0909)/(4.*rt6) + (conj(Em1a)*r1109)/(4.*rt6) + r0409*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0209*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-delta1 - v*Kvec1 - WLz/6.));
+dr0310_dt = (-(gt*r0310) - (gt + g1)*r0310)/2. - i*(-(conj(Ep1a)*conj(r0403))/(4.*rt2) - (conj(Em2a)*conj(r0603))/(4.*rt6) + (conj(Ep2a)*conj(r0803))/(4.*rt6) + (conj(Ep1a)*conj(r1009))/(4.*rt6) + (conj(Ep4a)*conj(r1013))/8. - (conj(Em4a)*conj(r1015))/8. - (conj(Em1a)*r0302)/(4.*rt2) + (delta1 + v*Kvec1)*r0310 + (conj(Em1a)*r1110)/(4.*rt6) + r0410*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0210*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0311*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr0311_dt = (-(gt*r0311) - (gt + g1)*r0311)/2. - i*(-(conj(Ep1a)*conj(r0503))/4. - (conj(Em2a)*conj(r0703))/(4.*rt6) + (conj(Ep1a)*conj(r1109))/(4.*rt6) + (conj(Ep4a)*conj(r1113))/8. - (conj(Em4a)*conj(r1115))/8. - (conj(Em1a)*r0303)/(4.*rt6) + (conj(Em1a)*r1111)/(4.*rt6) + r0411*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0211*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0311*(-delta1 - v*Kvec1 + WLz/6.));
+dr0312_dt = (-(gt*r0312) - (gt + g2)*r0312)/2. - i*(-(conj(Ep3a)*conj(r0603))/(4.*rt2) - (conj(Ep4a)*r0302)/(4.*rt6) + (conj(Ep1a)*r0912)/(4.*rt6) + (conj(Em1a)*r1112)/(4.*rt6) + (conj(Ep4a)*r1312)/8. - (conj(Em4a)*r1512)/8. - r0313*((2*WLx)/3. + (2*i*WLy)/3.) + r0412*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0212*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0313_dt = (-(gt*r0313) - (gt + g2)*r0313)/2. - i*(-(conj(Ep3a)*conj(r0703))/8. + (conj(Em4a)*r0301)/(4.*rt6) - (conj(Ep4a)*r0303)/8. + (conj(Ep1a)*r0913)/(4.*rt6) + (conj(Em1a)*r1113)/(4.*rt6) + (conj(Ep4a)*r1313)/8. - (conj(Em4a)*r1513)/8. - r0312*((2*WLx)/3. - (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0413*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0213*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0313*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0314_dt = (-(gt*r0314) - (gt + g2)*r0314)/2. - i*(-(conj(Ep4a)*conj(r0403))/8. - (conj(Em3a)*conj(r0603))/(8.*rt3) - (conj(Ep3a)*conj(r0803))/(8.*rt3) + (conj(Ep4a)*conj(r1413))/8. + (conj(Em4a)*r0302)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0314 + (conj(Ep1a)*r0914)/(4.*rt6) + (conj(Em1a)*r1114)/(4.*rt6) - (conj(Em4a)*r1514)/8. - r0313*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0315*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0414*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0214*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(conj(Ep4a)*conj(r0503))/(4.*rt6) - (conj(Em3a)*conj(r0703))/8. + (conj(Ep4a)*conj(r1513))/8. + (conj(Em4a)*r0303)/8. + (conj(Ep1a)*r0915)/(4.*rt6) + (conj(Em1a)*r1115)/(4.*rt6) - (conj(Em4a)*r1515)/8. - r0316*((2*WLx)/3. + (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0415*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0215*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0315*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0316_dt = (-(gt*r0316) - (gt + g2)*r0316)/2. - i*((conj(Em4a)*conj(r0403))/(4.*rt6) - (conj(Em3a)*conj(r0803))/(4.*rt2) + (conj(Ep4a)*conj(r1613))/8. - (conj(Em4a)*conj(r1615))/8. + (conj(Ep1a)*r0916)/(4.*rt6) + (conj(Em1a)*r1116)/(4.*rt6) - r0315*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0216*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0316*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr0401_dt = -(gt*r0401) - (g2*r1512)/6. + (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0114))/8. - (conj(Em4a)*conj(r0116))/(4.*rt6) - (Em1a*r0409)/4. + (Em4a*r0413)/(4.*rt6) + r0501*(WLx/2. - (i*WLy)/2.) - r0402*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0401*WLz)/2.);
+dr0402_dt = -(gt*r0402) + (g1*r1109)/4. + (g2*r1412)/(2.*rt6) - (g2*r1513)/12. + (g2*r1614)/(2.*rt6) - i*((conj(Ep1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0214))/8. - (conj(Em4a)*conj(r0216))/(4.*rt6) - (Em1a*r0410)/(4.*rt2) - (Ep4a*r0412)/(4.*rt6) + (Em4a*r0414)/8. - r0401*(WLx/2. - (i*WLy)/2.) + r0502*(WLx/2. - (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0402*WLz);
+dr0403_dt = -(gt*r0403) + (g1*r1009)/(4.*rt3) + (g1*r1110)/(2.*rt3) + (g2*r1413)/4. + (g2*r1615)/(2.*rt6) - i*((conj(Ep1a)*conj(r0310))/(4.*rt2) + (conj(Ep4a)*conj(r0314))/8. - (conj(Em4a)*conj(r0316))/(4.*rt6) - (Ep1a*r0409)/(4.*rt6) - (Em1a*r0411)/(4.*rt6) - (Ep4a*r0413)/8. + (Em4a*r0415)/8. + r0503*(WLx/2. - (i*WLy)/2.) - r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0404*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0403*WLz)/2.);
+dr0404_dt = gt/8. - gt*r0404 + (g1*r1010)/4. + (g1*r1111)/4. + (g2*r1414)/4. + (g2*r1515)/12. + (g2*r1616)/6. - i*((conj(Ep1a)*conj(r0410))/(4.*rt2) + (conj(Ep4a)*conj(r0414))/8. - (conj(Em4a)*conj(r0416))/(4.*rt6) - (Ep1a*r0410)/(4.*rt2) - (Ep4a*r0414)/8. + (Em4a*r0416)/(4.*rt6) + r0504*(WLx/2. - (i*WLy)/2.) - conj(r0504)*(WLx/2. + (i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0409_dt = (-(gt*r0409) - (gt + g1)*r0409)/2. - i*((conj(Ep2a)*conj(r0704))/(4.*rt6) + (conj(Ep4a)*conj(r0914))/8. - (conj(Em4a)*conj(r0916))/(4.*rt6) - (conj(Em1a)*r0401)/4. - (conj(Ep1a)*r0403)/(4.*rt6) + (conj(Ep1a)*r1009)/(4.*rt2) + r0509*(WLx/2. - (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-delta1 - v*Kvec1 - WLz/6.) - (r0409*WLz)/2.);
+dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(conj(Em2a)*conj(r0604))/(4.*rt6) + (conj(Ep2a)*conj(r0804))/(4.*rt6) + (conj(Ep4a)*conj(r1014))/8. - (conj(Em4a)*conj(r1016))/(4.*rt6) - (conj(Em1a)*r0402)/(4.*rt2) - (conj(Ep1a)*r0404)/(4.*rt2) + (delta1 + v*Kvec1)*r0410 + (conj(Ep1a)*r1010)/(4.*rt2) + r0510*(WLx/2. - (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0411*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - (r0410*WLz)/2.);
+dr0411_dt = (-(gt*r0411) - (gt + g1)*r0411)/2. - i*(-(conj(Ep1a)*conj(r0504))/4. - (conj(Em2a)*conj(r0704))/(4.*rt6) + (conj(Ep1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1114))/8. - (conj(Em4a)*conj(r1116))/(4.*rt6) - (conj(Em1a)*r0403)/(4.*rt6) + r0511*(WLx/2. - (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0411*(-delta1 - v*Kvec1 + WLz/6.) - (r0411*WLz)/2.);
+dr0412_dt = (-(gt*r0412) - (gt + g2)*r0412)/2. - i*(-(conj(Ep3a)*conj(r0604))/(4.*rt2) - (conj(Ep4a)*r0402)/(4.*rt6) + (conj(Ep1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1412)/8. - (conj(Em4a)*r1612)/(4.*rt6) + r0512*(WLx/2. - (i*WLy)/2.) - r0413*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0412*WLz)/2. - r0412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0413_dt = (-(gt*r0413) - (gt + g2)*r0413)/2. - i*(-(conj(Ep3a)*conj(r0704))/8. + (conj(Em4a)*r0401)/(4.*rt6) - (conj(Ep4a)*r0403)/8. + (conj(Ep1a)*r1013)/(4.*rt2) + (conj(Ep4a)*r1413)/8. - (conj(Em4a)*r1613)/(4.*rt6) - r0412*((2*WLx)/3. - (2*i*WLy)/3.) + r0513*(WLx/2. - (i*WLy)/2.) - r0414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - (r0413*WLz)/2.);
+dr0414_dt = (-(gt*r0414) - (gt + g2)*r0414)/2. - i*(-(conj(Em3a)*conj(r0604))/(8.*rt3) - (conj(Ep3a)*conj(r0804))/(8.*rt3) + (conj(Em4a)*r0402)/8. - (conj(Ep4a)*r0404)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0414 + (conj(Ep1a)*r1014)/(4.*rt2) + (conj(Ep4a)*r1414)/8. - (conj(Em4a)*r1614)/(4.*rt6) + r0514*(WLx/2. - (i*WLy)/2.) - r0413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0415*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0414*WLz)/2.);
+dr0415_dt = (-(gt*r0415) - (gt + g2)*r0415)/2. - i*(-(conj(Ep4a)*conj(r0504))/(4.*rt6) - (conj(Em3a)*conj(r0704))/8. + (conj(Ep4a)*conj(r1514))/8. + (conj(Em4a)*r0403)/8. + (conj(Ep1a)*r1015)/(4.*rt2) - (conj(Em4a)*r1615)/(4.*rt6) + r0515*(WLx/2. - (i*WLy)/2.) - r0416*((2*WLx)/3. + (2*i*WLy)/3.) - r0414*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0415*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - (r0415*WLz)/2.);
+dr0416_dt = (-(gt*r0416) - (gt + g2)*r0416)/2. - i*(-(conj(Em3a)*conj(r0804))/(4.*rt2) + (conj(Ep4a)*conj(r1614))/8. + (conj(Em4a)*r0404)/(4.*rt6) + (conj(Ep1a)*r1016)/(4.*rt2) - (conj(Em4a)*r1616)/(4.*rt6) - r0415*((2*WLx)/3. - (2*i*WLy)/3.) + r0516*(WLx/2. - (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0416*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - (r0416*WLz)/2.);
 dr0501_dt = -(gt*r0501) - (g2*r1612)/3. - i*((conj(Ep1a)*conj(r0111))/4. + (conj(Ep4a)*conj(r0115))/(4.*rt6) - (Em1a*r0509)/4. + (Em4a*r0513)/(4.*rt6) + r0401*(WLx/2. + (i*WLy)/2.) - r0502*(WLx/2. + (i*WLy)/2.) - 2*r0501*WLz);
-dr0502_dt = -(gt*r0502) + (g2*r1512)/6. - (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0211))/4. + (conj(Ep4a)*conj(r0215))/(4.*rt6) - (Em1a*r0510)/(4.*rt2) - (Ep4a*r0512)/(4.*rt6) + (Em4a*r0514)/8. - r0501*(WLx/2. - (i*WLy)/2.) + r0402*(WLx/2. + (i*WLy)/2.) - r0503*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - (3*r0502*WLz)/2.);
-dr0503_dt = -(gt*r0503) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0311))/4. + (conj(Ep4a)*conj(r0315))/(4.*rt6) - (Ep1a*r0509)/(4.*rt6) - (Em1a*r0511)/(4.*rt6) - (Ep4a*r0513)/8. + (Em4a*r0515)/8. + r0403*(WLx/2. + (i*WLy)/2.) - r0502*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0504*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) - r0503*WLz);
-dr0504_dt = -(gt*r0504) + (g1*r1110)/(2.*rt2) + (g2*r1514)/(2.*rt6) + (g2*r1615)/6. - i*((conj(Ep1a)*conj(r0411))/4. + (conj(Ep4a)*conj(r0415))/(4.*rt6) - (Ep1a*r0510)/(4.*rt2) - (Ep4a*r0514)/8. + (Em4a*r0516)/(4.*rt6) + r0404*(WLx/2. + (i*WLy)/2.) - r0505*(WLx/2. + (i*WLy)/2.) - r0503*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - (r0504*WLz)/2.);
+dr0502_dt = -(gt*r0502) + (g2*r1512)/6. - (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0211))/4. + (conj(Ep4a)*conj(r0215))/(4.*rt6) - (Em1a*r0510)/(4.*rt2) - (Ep4a*r0512)/(4.*rt6) + (Em4a*r0514)/8. - r0501*(WLx/2. - (i*WLy)/2.) + r0402*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0502*WLz)/2.);
+dr0503_dt = -(gt*r0503) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0311))/4. + (conj(Ep4a)*conj(r0315))/(4.*rt6) - (Ep1a*r0509)/(4.*rt6) - (Em1a*r0511)/(4.*rt6) - (Ep4a*r0513)/8. + (Em4a*r0515)/8. + r0403*(WLx/2. + (i*WLy)/2.) - r0502*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0504*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0503*WLz);
+dr0504_dt = -(gt*r0504) + (g1*r1110)/(2.*rt2) + (g2*r1514)/(2.*rt6) + (g2*r1615)/6. - i*((conj(Ep1a)*conj(r0411))/4. + (conj(Ep4a)*conj(r0415))/(4.*rt6) - (Ep1a*r0510)/(4.*rt2) - (Ep4a*r0514)/8. + (Em4a*r0516)/(4.*rt6) + r0404*(WLx/2. + (i*WLy)/2.) - r0505*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0504*WLz)/2.);
 dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((conj(Ep1a)*conj(r0511))/4. + (conj(Ep4a)*conj(r0515))/(4.*rt6) - (Ep1a*r0511)/4. - (Ep4a*r0515)/(4.*rt6) - r0504*(WLx/2. - (i*WLy)/2.) + conj(r0504)*(WLx/2. + (i*WLy)/2.));
 dr0509_dt = (-(gt*r0509) - (gt + g1)*r0509)/2. - i*((conj(Ep2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r0915))/(4.*rt6) - (conj(Em1a)*r0501)/4. - (conj(Ep1a)*r0503)/(4.*rt6) + (conj(Ep1a)*r1109)/4. + r0409*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-delta1 - v*Kvec1 - WLz/6.) - r0509*WLz);
 dr0510_dt = (-(gt*r0510) - (gt + g1)*r0510)/2. - i*(-(conj(Em2a)*conj(r0605))/(4.*rt6) + (conj(Ep2a)*conj(r0805))/(4.*rt6) + (conj(Ep4a)*conj(r1015))/(4.*rt6) - (conj(Em1a)*r0502)/(4.*rt2) - (conj(Ep1a)*r0504)/(4.*rt2) + (delta1 + v*Kvec1)*r0510 + (conj(Ep1a)*r1110)/4. + r0410*(WLx/2. + (i*WLy)/2.) - r0511*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0510*WLz);
 dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(conj(Em2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r1115))/(4.*rt6) - (conj(Em1a)*r0503)/(4.*rt6) - (conj(Ep1a)*r0505)/4. + (conj(Ep1a)*r1111)/4. + r0411*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0511*(-delta1 - v*Kvec1 + WLz/6.) - r0511*WLz);
 dr0512_dt = (-(gt*r0512) - (gt + g2)*r0512)/2. - i*(-(conj(Ep3a)*conj(r0605))/(4.*rt2) - (conj(Ep4a)*r0502)/(4.*rt6) + (conj(Ep1a)*r1112)/4. + (conj(Ep4a)*r1512)/(4.*rt6) + r0412*(WLx/2. + (i*WLy)/2.) - r0513*((2*WLx)/3. + (2*i*WLy)/3.) - r0512*WLz - r0512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0513_dt = (-(gt*r0513) - (gt + g2)*r0513)/2. - i*(-(conj(Ep3a)*conj(r0705))/8. + (conj(Em4a)*r0501)/(4.*rt6) - (conj(Ep4a)*r0503)/8. + (conj(Ep1a)*r1113)/4. + (conj(Ep4a)*r1513)/(4.*rt6) - r0512*((2*WLx)/3. - (2*i*WLy)/3.) + r0413*(WLx/2. + (i*WLy)/2.) - r0514*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r0513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r0513*WLz);
-dr0514_dt = (-(gt*r0514) - (gt + g2)*r0514)/2. - i*(-(conj(Em3a)*conj(r0605))/(8.*rt3) - (conj(Ep3a)*conj(r0805))/(8.*rt3) + (conj(Em4a)*r0502)/8. - (conj(Ep4a)*r0504)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0514 + (conj(Ep1a)*r1114)/4. + (conj(Ep4a)*r1514)/(4.*rt6) + r0414*(WLx/2. + (i*WLy)/2.) - r0513*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0515*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r0514*WLz);
-dr0515_dt = (-(gt*r0515) - (gt + g2)*r0515)/2. - i*(-(conj(Em3a)*conj(r0705))/8. + (conj(Em4a)*r0503)/8. - (conj(Ep4a)*r0505)/(4.*rt6) + (conj(Ep1a)*r1115)/4. + (conj(Ep4a)*r1515)/(4.*rt6) + r0415*(WLx/2. + (i*WLy)/2.) - r0516*((2*WLx)/3. + (2*i*WLy)/3.) - r0514*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0515*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r0515*WLz);
+dr0513_dt = (-(gt*r0513) - (gt + g2)*r0513)/2. - i*(-(conj(Ep3a)*conj(r0705))/8. + (conj(Em4a)*r0501)/(4.*rt6) - (conj(Ep4a)*r0503)/8. + (conj(Ep1a)*r1113)/4. + (conj(Ep4a)*r1513)/(4.*rt6) - r0512*((2*WLx)/3. - (2*i*WLy)/3.) + r0413*(WLx/2. + (i*WLy)/2.) - r0514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r0513*WLz);
+dr0514_dt = (-(gt*r0514) - (gt + g2)*r0514)/2. - i*(-(conj(Em3a)*conj(r0605))/(8.*rt3) - (conj(Ep3a)*conj(r0805))/(8.*rt3) + (conj(Em4a)*r0502)/8. - (conj(Ep4a)*r0504)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0514 + (conj(Ep1a)*r1114)/4. + (conj(Ep4a)*r1514)/(4.*rt6) + r0414*(WLx/2. + (i*WLy)/2.) - r0513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0514*WLz);
+dr0515_dt = (-(gt*r0515) - (gt + g2)*r0515)/2. - i*(-(conj(Em3a)*conj(r0705))/8. + (conj(Em4a)*r0503)/8. - (conj(Ep4a)*r0505)/(4.*rt6) + (conj(Ep1a)*r1115)/4. + (conj(Ep4a)*r1515)/(4.*rt6) + r0415*(WLx/2. + (i*WLy)/2.) - r0516*((2*WLx)/3. + (2*i*WLy)/3.) - r0514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r0515*WLz);
 dr0516_dt = (-(gt*r0516) - (gt + g2)*r0516)/2. - i*(-(conj(Em3a)*conj(r0805))/(4.*rt2) + (conj(Ep4a)*conj(r1615))/(4.*rt6) + (conj(Em4a)*r0504)/(4.*rt6) + (conj(Ep1a)*r1116)/4. - r0515*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*(WLx/2. + (i*WLy)/2.) - r0516*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r0516*WLz);
 dr0601_dt = -(gt*r0601) - i*((conj(Em2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0112))/(4.*rt2) + (conj(Em3a)*conj(r0114))/(8.*rt3) - (Em1a*r0609)/4. + (Em4a*r0613)/(4.*rt6) - r0602*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0601*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0601*WLz);
-dr0602_dt = -(gt*r0602) - i*((conj(Em2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0212))/(4.*rt2) + (conj(Em3a)*conj(r0214))/(8.*rt3) - (Em1a*r0610)/(4.*rt2) - (Ep4a*r0612)/(4.*rt6) + (Em4a*r0614)/8. - r0601*(WLx/2. - (i*WLy)/2.) - r0603*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0602*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - (r0602*WLz)/2.);
-dr0603_dt = -(gt*r0603) - i*((conj(Em2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0312))/(4.*rt2) + (conj(Em3a)*conj(r0314))/(8.*rt3) - (Ep1a*r0609)/(4.*rt6) - (Em1a*r0611)/(4.*rt6) - (Ep4a*r0613)/8. + (Em4a*r0615)/8. - r0602*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0604*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0603*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
-dr0604_dt = -(gt*r0604) - i*((conj(Em2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0412))/(4.*rt2) + (conj(Em3a)*conj(r0414))/(8.*rt3) - (Ep1a*r0610)/(4.*rt2) - (Ep4a*r0614)/8. + (Em4a*r0616)/(4.*rt6) - r0605*(WLx/2. + (i*WLy)/2.) - r0603*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0604*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + (r0604*WLz)/2.);
+dr0602_dt = -(gt*r0602) - i*((conj(Em2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0212))/(4.*rt2) + (conj(Em3a)*conj(r0214))/(8.*rt3) - (Em1a*r0610)/(4.*rt2) - (Ep4a*r0612)/(4.*rt6) + (Em4a*r0614)/8. - r0601*(WLx/2. - (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0602*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - (r0602*WLz)/2.);
+dr0603_dt = -(gt*r0603) - i*((conj(Em2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0312))/(4.*rt2) + (conj(Em3a)*conj(r0314))/(8.*rt3) - (Ep1a*r0609)/(4.*rt6) - (Em1a*r0611)/(4.*rt6) - (Ep4a*r0613)/8. + (Em4a*r0615)/8. - r0602*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0604*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0603*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0604_dt = -(gt*r0604) - i*((conj(Em2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0412))/(4.*rt2) + (conj(Em3a)*conj(r0414))/(8.*rt3) - (Ep1a*r0610)/(4.*rt2) - (Ep4a*r0614)/8. + (Em4a*r0616)/(4.*rt6) - r0605*(WLx/2. + (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0604*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + (r0604*WLz)/2.);
 dr0605_dt = -(gt*r0605) - i*((conj(Em2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0512))/(4.*rt2) + (conj(Em3a)*conj(r0514))/(8.*rt3) - (Ep1a*r0611)/4. - (Ep4a*r0615)/(4.*rt6) - r0604*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0605*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0605*WLz);
 dr0606_dt = gt/8. - gt*r0606 + (g1*r0909)/12. + (g1*r1010)/12. + (g2*r1212)/2. + (g2*r1313)/4. + (g2*r1414)/12. - i*((conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0612))/(4.*rt2) + (conj(Em3a)*conj(r0614))/(8.*rt3) - (Em2a*r0610)/(4.*rt6) - (Ep3a*r0612)/(4.*rt2) - (Em3a*r0614)/(8.*rt3) - conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
 dr0609_dt = (-(gt*r0609) - (gt + g1)*r0609)/2. - i*((conj(Ep2a)*conj(r0706))/(4.*rt6) + (conj(Ep3a)*conj(r0912))/(4.*rt2) + (conj(Em3a)*conj(r0914))/(8.*rt3) - (conj(Em1a)*r0601)/4. - (conj(Ep1a)*r0603)/(4.*rt6) + (conj(Em2a)*r1009)/(4.*rt6) - r0610*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0709*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0609*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0609*(-delta1 - v*Kvec1 - WLz/6.));
 dr0610_dt = (-(gt*r0610) - (gt + g1)*r0610)/2. - i*((conj(Ep2a)*conj(r0806))/(4.*rt6) + (conj(Ep3a)*conj(r1012))/(4.*rt2) + (conj(Em3a)*conj(r1014))/(8.*rt3) - (conj(Em1a)*r0602)/(4.*rt2) - (conj(Ep1a)*r0604)/(4.*rt2) - (conj(Em2a)*r0606)/(4.*rt6) + (delta1 + v*Kvec1)*r0610 + (conj(Em2a)*r1010)/(4.*rt6) - r0611*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0609*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0710*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0610*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
 dr0611_dt = (-(gt*r0611) - (gt + g1)*r0611)/2. - i*(-(conj(Em2a)*conj(r0706))/(4.*rt6) + (conj(Em2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1112))/(4.*rt2) + (conj(Em3a)*conj(r1114))/(8.*rt3) - (conj(Em1a)*r0603)/(4.*rt6) - (conj(Ep1a)*r0605)/4. - r0610*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0711*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0611*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0611*(-delta1 - v*Kvec1 + WLz/6.));
 dr0612_dt = (-(gt*r0612) - (gt + g2)*r0612)/2. - i*(-(conj(Ep4a)*r0602)/(4.*rt6) - (conj(Ep3a)*r0606)/(4.*rt2) + (conj(Em2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1212)/(4.*rt2) + (conj(Em3a)*r1412)/(8.*rt3) - r0613*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0612*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0613_dt = (-(gt*r0613) - (gt + g2)*r0613)/2. - i*(-(conj(Ep3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1312))/(4.*rt2) + (conj(Em4a)*r0601)/(4.*rt6) - (conj(Ep4a)*r0603)/8. + (conj(Em2a)*r1013)/(4.*rt6) + (conj(Em3a)*r1413)/(8.*rt3) - r0612*((2*WLx)/3. - (2*i*WLy)/3.) - r0614*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0613*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr0614_dt = (-(gt*r0614) - (gt + g2)*r0614)/2. - i*(-(conj(Ep3a)*conj(r0806))/(8.*rt3) + (conj(Ep3a)*conj(r1412))/(4.*rt2) + (conj(Em4a)*r0602)/8. - (conj(Ep4a)*r0604)/8. - (conj(Em3a)*r0606)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0614 + (conj(Em2a)*r1014)/(4.*rt6) + (conj(Em3a)*r1414)/(8.*rt3) - r0613*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0615*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0614*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
-dr0615_dt = (-(gt*r0615) - (gt + g2)*r0615)/2. - i*(-(conj(Em3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1512))/(4.*rt2) + (conj(Em3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0603)/8. - (conj(Ep4a)*r0605)/(4.*rt6) + (conj(Em2a)*r1015)/(4.*rt6) - r0616*((2*WLx)/3. + (2*i*WLy)/3.) - r0614*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0615*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0613_dt = (-(gt*r0613) - (gt + g2)*r0613)/2. - i*(-(conj(Ep3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1312))/(4.*rt2) + (conj(Em4a)*r0601)/(4.*rt6) - (conj(Ep4a)*r0603)/8. + (conj(Em2a)*r1013)/(4.*rt6) + (conj(Em3a)*r1413)/(8.*rt3) - r0612*((2*WLx)/3. - (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0613*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0614_dt = (-(gt*r0614) - (gt + g2)*r0614)/2. - i*(-(conj(Ep3a)*conj(r0806))/(8.*rt3) + (conj(Ep3a)*conj(r1412))/(4.*rt2) + (conj(Em4a)*r0602)/8. - (conj(Ep4a)*r0604)/8. - (conj(Em3a)*r0606)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0614 + (conj(Em2a)*r1014)/(4.*rt6) + (conj(Em3a)*r1414)/(8.*rt3) - r0613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0614*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0615_dt = (-(gt*r0615) - (gt + g2)*r0615)/2. - i*(-(conj(Em3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1512))/(4.*rt2) + (conj(Em3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0603)/8. - (conj(Ep4a)*r0605)/(4.*rt6) + (conj(Em2a)*r1015)/(4.*rt6) - r0616*((2*WLx)/3. + (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0615*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
 dr0616_dt = (-(gt*r0616) - (gt + g2)*r0616)/2. - i*(-(conj(Em3a)*conj(r0806))/(4.*rt2) + (conj(Ep3a)*conj(r1612))/(4.*rt2) + (conj(Em3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0604)/(4.*rt6) + (conj(Em2a)*r1016)/(4.*rt6) - r0615*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0616*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0616*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
 dr0701_dt = -(gt*r0701) - i*(-(conj(Ep2a)*conj(r0109))/(4.*rt6) + (conj(Em2a)*conj(r0111))/(4.*rt6) + (conj(Ep3a)*conj(r0113))/8. + (conj(Em3a)*conj(r0115))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0701 - (Em1a*r0709)/4. + (Em4a*r0713)/(4.*rt6) - r0702*(WLx/2. + (i*WLy)/2.) + r0601*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0701*WLz);
-dr0702_dt = -(gt*r0702) - i*(-(conj(Ep2a)*conj(r0209))/(4.*rt6) + (conj(Em2a)*conj(r0211))/(4.*rt6) + (conj(Ep3a)*conj(r0213))/8. + (conj(Em3a)*conj(r0215))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0702 - (Em1a*r0710)/(4.*rt2) - (Ep4a*r0712)/(4.*rt6) + (Em4a*r0714)/8. - r0701*(WLx/2. - (i*WLy)/2.) - r0703*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0602*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - (r0702*WLz)/2.);
-dr0703_dt = -(gt*r0703) - i*(-(conj(Ep2a)*conj(r0309))/(4.*rt6) + (conj(Em2a)*conj(r0311))/(4.*rt6) + (conj(Ep3a)*conj(r0313))/8. + (conj(Em3a)*conj(r0315))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 - (Ep1a*r0709)/(4.*rt6) - (Em1a*r0711)/(4.*rt6) - (Ep4a*r0713)/8. + (Em4a*r0715)/8. - r0702*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0704*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0603*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
-dr0704_dt = -(gt*r0704) - i*(-(conj(Ep2a)*conj(r0409))/(4.*rt6) + (conj(Em2a)*conj(r0411))/(4.*rt6) + (conj(Ep3a)*conj(r0413))/8. + (conj(Em3a)*conj(r0415))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0704 - (Ep1a*r0710)/(4.*rt2) - (Ep4a*r0714)/8. + (Em4a*r0716)/(4.*rt6) - r0705*(WLx/2. + (i*WLy)/2.) - r0703*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0604*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + (r0704*WLz)/2.);
+dr0702_dt = -(gt*r0702) - i*(-(conj(Ep2a)*conj(r0209))/(4.*rt6) + (conj(Em2a)*conj(r0211))/(4.*rt6) + (conj(Ep3a)*conj(r0213))/8. + (conj(Em3a)*conj(r0215))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0702 - (Em1a*r0710)/(4.*rt2) - (Ep4a*r0712)/(4.*rt6) + (Em4a*r0714)/8. - r0701*(WLx/2. - (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0602*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - (r0702*WLz)/2.);
+dr0703_dt = -(gt*r0703) - i*(-(conj(Ep2a)*conj(r0309))/(4.*rt6) + (conj(Em2a)*conj(r0311))/(4.*rt6) + (conj(Ep3a)*conj(r0313))/8. + (conj(Em3a)*conj(r0315))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 - (Ep1a*r0709)/(4.*rt6) - (Em1a*r0711)/(4.*rt6) - (Ep4a*r0713)/8. + (Em4a*r0715)/8. - r0702*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0704*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0603*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0704_dt = -(gt*r0704) - i*(-(conj(Ep2a)*conj(r0409))/(4.*rt6) + (conj(Em2a)*conj(r0411))/(4.*rt6) + (conj(Ep3a)*conj(r0413))/8. + (conj(Em3a)*conj(r0415))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0704 - (Ep1a*r0710)/(4.*rt2) - (Ep4a*r0714)/8. + (Em4a*r0716)/(4.*rt6) - r0705*(WLx/2. + (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0604*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + (r0704*WLz)/2.);
 dr0705_dt = -(gt*r0705) - i*(-(conj(Ep2a)*conj(r0509))/(4.*rt6) + (conj(Em2a)*conj(r0511))/(4.*rt6) + (conj(Ep3a)*conj(r0513))/8. + (conj(Em3a)*conj(r0515))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0705 - (Ep1a*r0711)/4. - (Ep4a*r0715)/(4.*rt6) - r0704*(WLx/2. - (i*WLy)/2.) + r0605*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0705*WLz);
 dr0706_dt = -(gt*r0706) + (g1*r1110)/12. + (g2*r1312)/(2.*rt2) + (g2*r1413)/(2.*rt3) + (g2*r1514)/(4.*rt3) - i*(-(conj(Ep2a)*conj(r0609))/(4.*rt6) + (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep3a)*conj(r0613))/8. + (conj(Em3a)*conj(r0615))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0706 - (Em2a*r0710)/(4.*rt6) - (Ep3a*r0712)/(4.*rt2) - (Em3a*r0714)/(8.*rt3) + r0606*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0706*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
 dr0707_dt = gt/8. - gt*r0707 + (g1*r0909)/12. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1414)/3. + (g2*r1515)/4. - i*(-(conj(Ep2a)*conj(r0709))/(4.*rt6) + (conj(Em2a)*conj(r0711))/(4.*rt6) + (conj(Ep3a)*conj(r0713))/8. + (conj(Em3a)*conj(r0715))/8. + (Ep2a*r0709)/(4.*rt6) - (Em2a*r0711)/(4.*rt6) - (Ep3a*r0713)/8. - (Em3a*r0715)/8. + conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
@@ -522,14 +522,14 @@ dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*((conj(Ep3a)*conj(r0913))/8.
 dr0710_dt = (-(gt*r0710) - (gt + g1)*r0710)/2. - i*((conj(Ep2a)*conj(r0807))/(4.*rt6) - (conj(Ep2a)*conj(r1009))/(4.*rt6) + (conj(Ep3a)*conj(r1013))/8. + (conj(Em3a)*conj(r1015))/8. - (conj(Em1a)*r0702)/(4.*rt2) - (conj(Ep1a)*r0704)/(4.*rt2) - (conj(Em2a)*r0706)/(4.*rt6) + (delta1 + v*Kvec1)*r0710 + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0710 + (conj(Em2a)*r1110)/(4.*rt6) + r0610*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0711*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0709*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
 dr0711_dt = (-(gt*r0711) - (gt + g1)*r0711)/2. - i*(-(conj(Ep2a)*conj(r1109))/(4.*rt6) + (conj(Ep3a)*conj(r1113))/8. + (conj(Em3a)*conj(r1115))/8. - (conj(Em1a)*r0703)/(4.*rt6) - (conj(Ep1a)*r0705)/4. - (conj(Em2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0711 + (conj(Em2a)*r1111)/(4.*rt6) + r0611*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0811*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0711*(-delta1 - v*Kvec1 + WLz/6.));
 dr0712_dt = (-(gt*r0712) - (gt + g2)*r0712)/2. - i*(-(conj(Ep4a)*r0702)/(4.*rt6) - (conj(Ep3a)*r0706)/(4.*rt2) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0712 - (conj(Ep2a)*r0912)/(4.*rt6) + (conj(Em2a)*r1112)/(4.*rt6) + (conj(Ep3a)*r1312)/8. + (conj(Em3a)*r1512)/8. - r0713*((2*WLx)/3. + (2*i*WLy)/3.) + r0612*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0712*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0713_dt = (-(gt*r0713) - (gt + g2)*r0713)/2. - i*((conj(Em4a)*r0701)/(4.*rt6) - (conj(Ep4a)*r0703)/8. - (conj(Ep3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0713 - (conj(Ep2a)*r0913)/(4.*rt6) + (conj(Em2a)*r1113)/(4.*rt6) + (conj(Ep3a)*r1313)/8. + (conj(Em3a)*r1513)/8. - r0712*((2*WLx)/3. - (2*i*WLy)/3.) - r0714*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0613*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0713*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr0714_dt = (-(gt*r0714) - (gt + g2)*r0714)/2. - i*(-(conj(Ep3a)*conj(r0807))/(8.*rt3) + (conj(Ep3a)*conj(r1413))/8. + (conj(Em4a)*r0702)/8. - (conj(Ep4a)*r0704)/8. - (conj(Em3a)*r0706)/(8.*rt3) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0714 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0714 - (conj(Ep2a)*r0914)/(4.*rt6) + (conj(Em2a)*r1114)/(4.*rt6) + (conj(Em3a)*r1514)/8. - r0713*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0715*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0614*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
-dr0715_dt = (-(gt*r0715) - (gt + g2)*r0715)/2. - i*((conj(Ep3a)*conj(r1513))/8. + (conj(Em4a)*r0703)/8. - (conj(Ep4a)*r0705)/(4.*rt6) - (conj(Em3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0715 - (conj(Ep2a)*r0915)/(4.*rt6) + (conj(Em2a)*r1115)/(4.*rt6) + (conj(Em3a)*r1515)/8. - r0716*((2*WLx)/3. + (2*i*WLy)/3.) - r0714*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0615*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0815*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0715*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0713_dt = (-(gt*r0713) - (gt + g2)*r0713)/2. - i*((conj(Em4a)*r0701)/(4.*rt6) - (conj(Ep4a)*r0703)/8. - (conj(Ep3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0713 - (conj(Ep2a)*r0913)/(4.*rt6) + (conj(Em2a)*r1113)/(4.*rt6) + (conj(Ep3a)*r1313)/8. + (conj(Em3a)*r1513)/8. - r0712*((2*WLx)/3. - (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0613*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0713*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0714_dt = (-(gt*r0714) - (gt + g2)*r0714)/2. - i*(-(conj(Ep3a)*conj(r0807))/(8.*rt3) + (conj(Ep3a)*conj(r1413))/8. + (conj(Em4a)*r0702)/8. - (conj(Ep4a)*r0704)/8. - (conj(Em3a)*r0706)/(8.*rt3) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0714 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0714 - (conj(Ep2a)*r0914)/(4.*rt6) + (conj(Em2a)*r1114)/(4.*rt6) + (conj(Em3a)*r1514)/8. - r0713*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0715*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0614*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0715_dt = (-(gt*r0715) - (gt + g2)*r0715)/2. - i*((conj(Ep3a)*conj(r1513))/8. + (conj(Em4a)*r0703)/8. - (conj(Ep4a)*r0705)/(4.*rt6) - (conj(Em3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0715 - (conj(Ep2a)*r0915)/(4.*rt6) + (conj(Em2a)*r1115)/(4.*rt6) + (conj(Em3a)*r1515)/8. - r0716*((2*WLx)/3. + (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0615*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0815*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0715*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
 dr0716_dt = (-(gt*r0716) - (gt + g2)*r0716)/2. - i*(-(conj(Em3a)*conj(r0807))/(4.*rt2) + (conj(Ep3a)*conj(r1613))/8. + (conj(Em3a)*conj(r1615))/8. + (conj(Em4a)*r0704)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0716 - (conj(Ep2a)*r0916)/(4.*rt6) + (conj(Em2a)*r1116)/(4.*rt6) - r0715*((2*WLx)/3. - (2*i*WLy)/3.) + r0616*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0816*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0716*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
 dr0801_dt = -(gt*r0801) - i*(-(conj(Ep2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0114))/(8.*rt3) + (conj(Em3a)*conj(r0116))/(4.*rt2) - (Em1a*r0809)/4. + (Em4a*r0813)/(4.*rt6) - r0802*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0801*WLz);
-dr0802_dt = -(gt*r0802) - i*(-(conj(Ep2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0214))/(8.*rt3) + (conj(Em3a)*conj(r0216))/(4.*rt2) - (Em1a*r0810)/(4.*rt2) - (Ep4a*r0812)/(4.*rt6) + (Em4a*r0814)/8. - r0801*(WLx/2. - (i*WLy)/2.) - r0803*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - (r0802*WLz)/2.);
-dr0803_dt = -(gt*r0803) - i*(-(conj(Ep2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0314))/(8.*rt3) + (conj(Em3a)*conj(r0316))/(4.*rt2) - (Ep1a*r0809)/(4.*rt6) - (Em1a*r0811)/(4.*rt6) - (Ep4a*r0813)/8. + (Em4a*r0815)/8. - r0802*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) - r0804*((Sqrt(1.5)*WLx)/2. + (Sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
-dr0804_dt = -(gt*r0804) - i*(-(conj(Ep2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0414))/(8.*rt3) + (conj(Em3a)*conj(r0416))/(4.*rt2) - (Ep1a*r0810)/(4.*rt2) - (Ep4a*r0814)/8. + (Em4a*r0816)/(4.*rt6) - r0805*(WLx/2. + (i*WLy)/2.) - r0803*((Sqrt(1.5)*WLx)/2. - (Sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + (r0804*WLz)/2.);
+dr0802_dt = -(gt*r0802) - i*(-(conj(Ep2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0214))/(8.*rt3) + (conj(Em3a)*conj(r0216))/(4.*rt2) - (Em1a*r0810)/(4.*rt2) - (Ep4a*r0812)/(4.*rt6) + (Em4a*r0814)/8. - r0801*(WLx/2. - (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - (r0802*WLz)/2.);
+dr0803_dt = -(gt*r0803) - i*(-(conj(Ep2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0314))/(8.*rt3) + (conj(Em3a)*conj(r0316))/(4.*rt2) - (Ep1a*r0809)/(4.*rt6) - (Em1a*r0811)/(4.*rt6) - (Ep4a*r0813)/8. + (Em4a*r0815)/8. - r0802*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0804*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0804_dt = -(gt*r0804) - i*(-(conj(Ep2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0414))/(8.*rt3) + (conj(Em3a)*conj(r0416))/(4.*rt2) - (Ep1a*r0810)/(4.*rt2) - (Ep4a*r0814)/8. + (Em4a*r0816)/(4.*rt6) - r0805*(WLx/2. + (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + (r0804*WLz)/2.);
 dr0805_dt = -(gt*r0805) - i*(-(conj(Ep2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0514))/(8.*rt3) + (conj(Em3a)*conj(r0516))/(4.*rt2) - (Ep1a*r0811)/4. - (Ep4a*r0815)/(4.*rt6) - r0804*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + r0805*WLz);
 dr0806_dt = -(gt*r0806) - (g1*r1109)/12. + (g2*r1412)/(2.*rt6) + (g2*r1513)/4. + (g2*r1614)/(2.*rt6) - i*(-(conj(Ep2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0614))/(8.*rt3) + (conj(Em3a)*conj(r0616))/(4.*rt2) - (Em2a*r0810)/(4.*rt6) - (Ep3a*r0812)/(4.*rt2) - (Em3a*r0814)/(8.*rt3) + r0706*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
 dr0807_dt = -(gt*r0807) + (g1*r1009)/12. + (g2*r1413)/(4.*rt3) + (g2*r1514)/(2.*rt3) + (g2*r1615)/(2.*rt2) - i*(-(conj(Ep2a)*conj(r0710))/(4.*rt6) + (conj(Ep3a)*conj(r0714))/(8.*rt3) + (conj(Em3a)*conj(r0716))/(4.*rt2) - (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0807 + (Ep2a*r0809)/(4.*rt6) - (Em2a*r0811)/(4.*rt6) - (Ep3a*r0813)/8. - (Em3a*r0815)/8. + r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0808*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
@@ -538,45 +538,45 @@ dr0809_dt = (-(gt*r0809) - (gt + g1)*r0809)/2. - i*((conj(Ep3a)*conj(r0914))/(8.
 dr0810_dt = (-(gt*r0810) - (gt + g1)*r0810)/2. - i*((conj(Ep3a)*conj(r1014))/(8.*rt3) + (conj(Em3a)*conj(r1016))/(4.*rt2) - (conj(Em1a)*r0802)/(4.*rt2) - (conj(Ep1a)*r0804)/(4.*rt2) - (conj(Em2a)*r0806)/(4.*rt6) + (conj(Ep2a)*r0808)/(4.*rt6) + (delta1 + v*Kvec1)*r0810 - (conj(Ep2a)*r1010)/(4.*rt6) + r0710*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0811*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
 dr0811_dt = (-(gt*r0811) - (gt + g1)*r0811)/2. - i*(-(conj(Ep2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1114))/(8.*rt3) + (conj(Em3a)*conj(r1116))/(4.*rt2) - (conj(Em1a)*r0803)/(4.*rt6) - (conj(Ep1a)*r0805)/4. - (conj(Em2a)*r0807)/(4.*rt6) + r0711*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0811*(-delta1 - v*Kvec1 + WLz/6.) + r0811*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
 dr0812_dt = (-(gt*r0812) - (gt + g2)*r0812)/2. - i*(-(conj(Ep4a)*r0802)/(4.*rt6) - (conj(Ep3a)*r0806)/(4.*rt2) - (conj(Ep2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1412)/(8.*rt3) + (conj(Em3a)*r1612)/(4.*rt2) - r0813*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0812*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0813_dt = (-(gt*r0813) - (gt + g2)*r0813)/2. - i*((conj(Em4a)*r0801)/(4.*rt6) - (conj(Ep4a)*r0803)/8. - (conj(Ep3a)*r0807)/8. - (conj(Ep2a)*r1013)/(4.*rt6) + (conj(Ep3a)*r1413)/(8.*rt3) + (conj(Em3a)*r1613)/(4.*rt2) - r0812*((2*WLx)/3. - (2*i*WLy)/3.) - r0814*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0813*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr0814_dt = (-(gt*r0814) - (gt + g2)*r0814)/2. - i*((conj(Em4a)*r0802)/8. - (conj(Ep4a)*r0804)/8. - (conj(Em3a)*r0806)/(8.*rt3) - (conj(Ep3a)*r0808)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0814 - (conj(Ep2a)*r1014)/(4.*rt6) + (conj(Ep3a)*r1414)/(8.*rt3) + (conj(Em3a)*r1614)/(4.*rt2) - r0813*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0815*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
-dr0815_dt = (-(gt*r0815) - (gt + g2)*r0815)/2. - i*((conj(Ep3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0803)/8. - (conj(Ep4a)*r0805)/(4.*rt6) - (conj(Em3a)*r0807)/8. - (conj(Ep2a)*r1015)/(4.*rt6) + (conj(Em3a)*r1615)/(4.*rt2) - r0816*((2*WLx)/3. + (2*i*WLy)/3.) - r0814*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0815*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0815*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0813_dt = (-(gt*r0813) - (gt + g2)*r0813)/2. - i*((conj(Em4a)*r0801)/(4.*rt6) - (conj(Ep4a)*r0803)/8. - (conj(Ep3a)*r0807)/8. - (conj(Ep2a)*r1013)/(4.*rt6) + (conj(Ep3a)*r1413)/(8.*rt3) + (conj(Em3a)*r1613)/(4.*rt2) - r0812*((2*WLx)/3. - (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0813*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0814_dt = (-(gt*r0814) - (gt + g2)*r0814)/2. - i*((conj(Em4a)*r0802)/8. - (conj(Ep4a)*r0804)/8. - (conj(Em3a)*r0806)/(8.*rt3) - (conj(Ep3a)*r0808)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0814 - (conj(Ep2a)*r1014)/(4.*rt6) + (conj(Ep3a)*r1414)/(8.*rt3) + (conj(Em3a)*r1614)/(4.*rt2) - r0813*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0815*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0815_dt = (-(gt*r0815) - (gt + g2)*r0815)/2. - i*((conj(Ep3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0803)/8. - (conj(Ep4a)*r0805)/(4.*rt6) - (conj(Em3a)*r0807)/8. - (conj(Ep2a)*r1015)/(4.*rt6) + (conj(Em3a)*r1615)/(4.*rt2) - r0816*((2*WLx)/3. + (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0815*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0815*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
 dr0816_dt = (-(gt*r0816) - (gt + g2)*r0816)/2. - i*((conj(Ep3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0804)/(4.*rt6) - (conj(Em3a)*r0808)/(4.*rt2) - (conj(Ep2a)*r1016)/(4.*rt6) + (conj(Em3a)*r1616)/(4.*rt2) - r0815*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0816*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0816*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
 dr0909_dt = -((gt + g1)*r0909) - i*(-(conj(Em1a)*conj(r0109))/4. - (conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Ep2a)*conj(r0709))/(4.*rt6) + (Em1a*r0109)/4. + (Ep1a*r0309)/(4.*rt6) - (Ep2a*r0709)/(4.*rt6) - conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
 dr0912_dt = (-((gt + g1)*r0912) - (gt + g2)*r0912)/2. - i*(-(conj(Ep4a)*conj(r0209))/(4.*rt6) - (conj(Ep3a)*conj(r0609))/(4.*rt2) + (Em1a*r0112)/4. + (Ep1a*r0312)/(4.*rt6) - (Ep2a*r0712)/(4.*rt6) - r0913*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0912*(-delta1 - v*Kvec1 - WLz/6.) - r0912*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0913_dt = (-((gt + g1)*r0913) - (gt + g2)*r0913)/2. - i*((conj(Em4a)*conj(r0109))/(4.*rt6) - (conj(Ep4a)*conj(r0309))/8. - (conj(Ep3a)*conj(r0709))/8. + (Em1a*r0113)/4. + (Ep1a*r0313)/(4.*rt6) - (Ep2a*r0713)/(4.*rt6) - r0912*((2*WLx)/3. - (2*i*WLy)/3.) - r0914*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0913*(-delta1 - v*Kvec1 - WLz/6.) - r0913*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr0914_dt = (-((gt + g1)*r0914) - (gt + g2)*r0914)/2. - i*((conj(Em4a)*conj(r0209))/8. - (conj(Ep4a)*conj(r0409))/8. - (conj(Em3a)*conj(r0609))/(8.*rt3) - (conj(Ep3a)*conj(r0809))/(8.*rt3) + (Em1a*r0114)/4. + (Ep1a*r0314)/(4.*rt6) - (Ep2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0914 - r0913*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r0915*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0914*(-delta1 - v*Kvec1 - WLz/6.));
-dr0915_dt = (-((gt + g1)*r0915) - (gt + g2)*r0915)/2. - i*((conj(Em4a)*conj(r0309))/8. - (conj(Ep4a)*conj(r0509))/(4.*rt6) - (conj(Em3a)*conj(r0709))/8. + (Em1a*r0115)/4. + (Ep1a*r0315)/(4.*rt6) - (Ep2a*r0715)/(4.*rt6) - r0916*((2*WLx)/3. + (2*i*WLy)/3.) - r0914*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0915*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0915*(-delta1 - v*Kvec1 - WLz/6.));
+dr0913_dt = (-((gt + g1)*r0913) - (gt + g2)*r0913)/2. - i*((conj(Em4a)*conj(r0109))/(4.*rt6) - (conj(Ep4a)*conj(r0309))/8. - (conj(Ep3a)*conj(r0709))/8. + (Em1a*r0113)/4. + (Ep1a*r0313)/(4.*rt6) - (Ep2a*r0713)/(4.*rt6) - r0912*((2*WLx)/3. - (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0913*(-delta1 - v*Kvec1 - WLz/6.) - r0913*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0914_dt = (-((gt + g1)*r0914) - (gt + g2)*r0914)/2. - i*((conj(Em4a)*conj(r0209))/8. - (conj(Ep4a)*conj(r0409))/8. - (conj(Em3a)*conj(r0609))/(8.*rt3) - (conj(Ep3a)*conj(r0809))/(8.*rt3) + (Em1a*r0114)/4. + (Ep1a*r0314)/(4.*rt6) - (Ep2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0914 - r0913*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0915*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0914*(-delta1 - v*Kvec1 - WLz/6.));
+dr0915_dt = (-((gt + g1)*r0915) - (gt + g2)*r0915)/2. - i*((conj(Em4a)*conj(r0309))/8. - (conj(Ep4a)*conj(r0509))/(4.*rt6) - (conj(Em3a)*conj(r0709))/8. + (Em1a*r0115)/4. + (Ep1a*r0315)/(4.*rt6) - (Ep2a*r0715)/(4.*rt6) - r0916*((2*WLx)/3. + (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0915*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0915*(-delta1 - v*Kvec1 - WLz/6.));
 dr0916_dt = (-((gt + g1)*r0916) - (gt + g2)*r0916)/2. - i*((conj(Em4a)*conj(r0409))/(4.*rt6) - (conj(Em3a)*conj(r0809))/(4.*rt2) + (Em1a*r0116)/4. + (Ep1a*r0316)/(4.*rt6) - (Ep2a*r0716)/(4.*rt6) - r0915*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0916*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0916*(-delta1 - v*Kvec1 - WLz/6.));
 dr1009_dt = -((gt + g1)*r1009) - i*(-(conj(Em1a)*conj(r0110))/4. - (conj(Ep1a)*conj(r0310))/(4.*rt6) + (conj(Ep2a)*conj(r0710))/(4.*rt6) + (Em1a*r0209)/(4.*rt2) + (Ep1a*r0409)/(4.*rt2) + (Em2a*r0609)/(4.*rt6) - (Ep2a*r0809)/(4.*rt6) - (delta1 + v*Kvec1)*r1009 + r0909*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1009*(-delta1 - v*Kvec1 - WLz/6.));
 dr1010_dt = -((gt + g1)*r1010) - i*(-(conj(Em1a)*conj(r0210))/(4.*rt2) - (conj(Ep1a)*conj(r0410))/(4.*rt2) - (conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep2a)*conj(r0810))/(4.*rt6) + (Em1a*r0210)/(4.*rt2) + (Ep1a*r0410)/(4.*rt2) + (Em2a*r0610)/(4.*rt6) - (Ep2a*r0810)/(4.*rt6) + conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
 dr1012_dt = (-((gt + g1)*r1012) - (gt + g2)*r1012)/2. - i*(-(conj(Ep4a)*conj(r0210))/(4.*rt6) - (conj(Ep3a)*conj(r0610))/(4.*rt2) + (Em1a*r0212)/(4.*rt2) + (Ep1a*r0412)/(4.*rt2) + (Em2a*r0612)/(4.*rt6) - (Ep2a*r0812)/(4.*rt6) - (delta1 + v*Kvec1)*r1012 - r1013*((2*WLx)/3. + (2*i*WLy)/3.) + r0912*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1012*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1013_dt = (-((gt + g1)*r1013) - (gt + g2)*r1013)/2. - i*((conj(Em4a)*conj(r0110))/(4.*rt6) - (conj(Ep4a)*conj(r0310))/8. - (conj(Ep3a)*conj(r0710))/8. + (Em1a*r0213)/(4.*rt2) + (Ep1a*r0413)/(4.*rt2) + (Em2a*r0613)/(4.*rt6) - (Ep2a*r0813)/(4.*rt6) - (delta1 + v*Kvec1)*r1013 - r1012*((2*WLx)/3. - (2*i*WLy)/3.) - r1014*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0913*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1013*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr1014_dt = (-((gt + g1)*r1014) - (gt + g2)*r1014)/2. - i*((conj(Em4a)*conj(r0210))/8. - (conj(Ep4a)*conj(r0410))/8. - (conj(Em3a)*conj(r0610))/(8.*rt3) - (conj(Ep3a)*conj(r0810))/(8.*rt3) + (Em1a*r0214)/(4.*rt2) + (Ep1a*r0414)/(4.*rt2) + (Em2a*r0614)/(4.*rt6) - (Ep2a*r0814)/(4.*rt6) - (delta1 + v*Kvec1)*r1014 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1014 - r1013*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r1015*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r0914*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
-dr1015_dt = (-((gt + g1)*r1015) - (gt + g2)*r1015)/2. - i*((conj(Em4a)*conj(r0310))/8. - (conj(Ep4a)*conj(r0510))/(4.*rt6) - (conj(Em3a)*conj(r0710))/8. + (Em1a*r0215)/(4.*rt2) + (Ep1a*r0415)/(4.*rt2) + (Em2a*r0615)/(4.*rt6) - (Ep2a*r0815)/(4.*rt6) - (delta1 + v*Kvec1)*r1015 - r1016*((2*WLx)/3. + (2*i*WLy)/3.) - r1014*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r0915*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1115*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1015*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1013_dt = (-((gt + g1)*r1013) - (gt + g2)*r1013)/2. - i*((conj(Em4a)*conj(r0110))/(4.*rt6) - (conj(Ep4a)*conj(r0310))/8. - (conj(Ep3a)*conj(r0710))/8. + (Em1a*r0213)/(4.*rt2) + (Ep1a*r0413)/(4.*rt2) + (Em2a*r0613)/(4.*rt6) - (Ep2a*r0813)/(4.*rt6) - (delta1 + v*Kvec1)*r1013 - r1012*((2*WLx)/3. - (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0913*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1013*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1014_dt = (-((gt + g1)*r1014) - (gt + g2)*r1014)/2. - i*((conj(Em4a)*conj(r0210))/8. - (conj(Ep4a)*conj(r0410))/8. - (conj(Em3a)*conj(r0610))/(8.*rt3) - (conj(Ep3a)*conj(r0810))/(8.*rt3) + (Em1a*r0214)/(4.*rt2) + (Ep1a*r0414)/(4.*rt2) + (Em2a*r0614)/(4.*rt6) - (Ep2a*r0814)/(4.*rt6) - (delta1 + v*Kvec1)*r1014 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1014 - r1013*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1015*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0914*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1015_dt = (-((gt + g1)*r1015) - (gt + g2)*r1015)/2. - i*((conj(Em4a)*conj(r0310))/8. - (conj(Ep4a)*conj(r0510))/(4.*rt6) - (conj(Em3a)*conj(r0710))/8. + (Em1a*r0215)/(4.*rt2) + (Ep1a*r0415)/(4.*rt2) + (Em2a*r0615)/(4.*rt6) - (Ep2a*r0815)/(4.*rt6) - (delta1 + v*Kvec1)*r1015 - r1016*((2*WLx)/3. + (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0915*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1115*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1015*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
 dr1016_dt = (-((gt + g1)*r1016) - (gt + g2)*r1016)/2. - i*((conj(Em4a)*conj(r0410))/(4.*rt6) - (conj(Em3a)*conj(r0810))/(4.*rt2) + (Em1a*r0216)/(4.*rt2) + (Ep1a*r0416)/(4.*rt2) + (Em2a*r0616)/(4.*rt6) - (Ep2a*r0816)/(4.*rt6) - (delta1 + v*Kvec1)*r1016 - r1015*((2*WLx)/3. - (2*i*WLy)/3.) + r0916*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1116*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1016*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
 dr1109_dt = -((gt + g1)*r1109) - i*(-(conj(Em1a)*conj(r0111))/4. - (conj(Ep1a)*conj(r0311))/(4.*rt6) + (conj(Ep2a)*conj(r0711))/(4.*rt6) + (Em1a*r0309)/(4.*rt6) + (Ep1a*r0509)/4. + (Em2a*r0709)/(4.*rt6) + r1009*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-delta1 - v*Kvec1 - WLz/6.) + r1109*(-delta1 - v*Kvec1 + WLz/6.));
 dr1110_dt = -((gt + g1)*r1110) - i*(-(conj(Em1a)*conj(r0211))/(4.*rt2) - (conj(Ep1a)*conj(r0411))/(4.*rt2) - (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep2a)*conj(r0811))/(4.*rt6) + (Em1a*r0310)/(4.*rt6) + (Ep1a*r0510)/4. + (Em2a*r0710)/(4.*rt6) + (delta1 + v*Kvec1)*r1110 + r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-delta1 - v*Kvec1 + WLz/6.));
 dr1111_dt = -((gt + g1)*r1111) - i*(-(conj(Em1a)*conj(r0311))/(4.*rt6) - (conj(Ep1a)*conj(r0511))/4. - (conj(Em2a)*conj(r0711))/(4.*rt6) + (Em1a*r0311)/(4.*rt6) + (Ep1a*r0511)/4. + (Em2a*r0711)/(4.*rt6) + conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
 dr1112_dt = (-((gt + g1)*r1112) - (gt + g2)*r1112)/2. - i*(-(conj(Ep4a)*conj(r0211))/(4.*rt6) - (conj(Ep3a)*conj(r0611))/(4.*rt2) + (Em1a*r0312)/(4.*rt6) + (Ep1a*r0512)/4. + (Em2a*r0712)/(4.*rt6) - r1113*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-delta1 - v*Kvec1 + WLz/6.) - r1112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1113_dt = (-((gt + g1)*r1113) - (gt + g2)*r1113)/2. - i*((conj(Em4a)*conj(r0111))/(4.*rt6) - (conj(Ep4a)*conj(r0311))/8. - (conj(Ep3a)*conj(r0711))/8. + (Em1a*r0313)/(4.*rt6) + (Ep1a*r0513)/4. + (Em2a*r0713)/(4.*rt6) - r1112*((2*WLx)/3. - (2*i*WLy)/3.) - r1114*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-delta1 - v*Kvec1 + WLz/6.) - r1113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr1114_dt = (-((gt + g1)*r1114) - (gt + g2)*r1114)/2. - i*((conj(Em4a)*conj(r0211))/8. - (conj(Ep4a)*conj(r0411))/8. - (conj(Em3a)*conj(r0611))/(8.*rt3) - (conj(Ep3a)*conj(r0811))/(8.*rt3) + (Em1a*r0314)/(4.*rt6) + (Ep1a*r0514)/4. + (Em2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1114 - r1113*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r1115*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-delta1 - v*Kvec1 + WLz/6.));
-dr1115_dt = (-((gt + g1)*r1115) - (gt + g2)*r1115)/2. - i*((conj(Em4a)*conj(r0311))/8. - (conj(Ep4a)*conj(r0511))/(4.*rt6) - (conj(Em3a)*conj(r0711))/8. + (Em1a*r0315)/(4.*rt6) + (Ep1a*r0515)/4. + (Em2a*r0715)/(4.*rt6) - r1116*((2*WLx)/3. + (2*i*WLy)/3.) - r1114*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r1115*(-delta1 - v*Kvec1 + WLz/6.));
+dr1113_dt = (-((gt + g1)*r1113) - (gt + g2)*r1113)/2. - i*((conj(Em4a)*conj(r0111))/(4.*rt6) - (conj(Ep4a)*conj(r0311))/8. - (conj(Ep3a)*conj(r0711))/8. + (Em1a*r0313)/(4.*rt6) + (Ep1a*r0513)/4. + (Em2a*r0713)/(4.*rt6) - r1112*((2*WLx)/3. - (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-delta1 - v*Kvec1 + WLz/6.) - r1113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1114_dt = (-((gt + g1)*r1114) - (gt + g2)*r1114)/2. - i*((conj(Em4a)*conj(r0211))/8. - (conj(Ep4a)*conj(r0411))/8. - (conj(Em3a)*conj(r0611))/(8.*rt3) - (conj(Ep3a)*conj(r0811))/(8.*rt3) + (Em1a*r0314)/(4.*rt6) + (Ep1a*r0514)/4. + (Em2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1114 - r1113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-delta1 - v*Kvec1 + WLz/6.));
+dr1115_dt = (-((gt + g1)*r1115) - (gt + g2)*r1115)/2. - i*((conj(Em4a)*conj(r0311))/8. - (conj(Ep4a)*conj(r0511))/(4.*rt6) - (conj(Em3a)*conj(r0711))/8. + (Em1a*r0315)/(4.*rt6) + (Ep1a*r0515)/4. + (Em2a*r0715)/(4.*rt6) - r1116*((2*WLx)/3. + (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r1115*(-delta1 - v*Kvec1 + WLz/6.));
 dr1116_dt = (-((gt + g1)*r1116) - (gt + g2)*r1116)/2. - i*((conj(Em4a)*conj(r0411))/(4.*rt6) - (conj(Em3a)*conj(r0811))/(4.*rt2) + (Em1a*r0316)/(4.*rt6) + (Ep1a*r0516)/4. + (Em2a*r0716)/(4.*rt6) - r1115*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r1116*(-delta1 - v*Kvec1 + WLz/6.));
 dr1212_dt = -((gt + g2)*r1212) - i*(-(conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Ep3a)*conj(r0612))/(4.*rt2) + (Ep4a*r0212)/(4.*rt6) + (Ep3a*r0612)/(4.*rt2) + r1312*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.));
-dr1312_dt = -((gt + g2)*r1312) - i*(-(conj(Ep4a)*conj(r0213))/(4.*rt6) - (conj(Ep3a)*conj(r0613))/(4.*rt2) - (Em4a*r0112)/(4.*rt6) + (Ep4a*r0312)/8. + (Ep3a*r0712)/8. + r1212*((2*WLx)/3. + (2*i*WLy)/3.) - r1313*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1313_dt = -((gt + g2)*r1313) - i*((conj(Em4a)*conj(r0113))/(4.*rt6) - (conj(Ep4a)*conj(r0313))/8. - (conj(Ep3a)*conj(r0713))/8. - (Em4a*r0113)/(4.*rt6) + (Ep4a*r0313)/8. + (Ep3a*r0713)/8. - r1312*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.) + r1413*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - conj(r1413)*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy));
-dr1412_dt = -((gt + g2)*r1412) - i*(-(conj(Ep4a)*conj(r0214))/(4.*rt6) - (conj(Ep3a)*conj(r0614))/(4.*rt2) - (Em4a*r0212)/8. + (Ep4a*r0412)/8. + (Em3a*r0612)/(8.*rt3) + (Ep3a*r0812)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1412 - r1413*((2*WLx)/3. + (2*i*WLy)/3.) + r1512*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1312*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r1412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1413_dt = -((gt + g2)*r1413) - i*((conj(Em4a)*conj(r0114))/(4.*rt6) - (conj(Ep4a)*conj(r0314))/8. - (conj(Ep3a)*conj(r0714))/8. - (Em4a*r0213)/8. + (Ep4a*r0413)/8. + (Em3a*r0613)/(8.*rt3) + (Ep3a*r0813)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1413 - r1412*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1313*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r1414*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r1413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr1414_dt = -((gt + g2)*r1414) - i*((conj(Em4a)*conj(r0214))/8. - (conj(Ep4a)*conj(r0414))/8. - (conj(Em3a)*conj(r0614))/(8.*rt3) - (conj(Ep3a)*conj(r0814))/(8.*rt3) - (Em4a*r0214)/8. + (Ep4a*r0414)/8. + (Em3a*r0614)/(8.*rt3) + (Ep3a*r0814)/(8.*rt3) - r1413*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1514*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + conj(r1413)*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - conj(r1514)*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy));
-dr1512_dt = -((gt + g2)*r1512) - i*(-(conj(Ep4a)*conj(r0215))/(4.*rt6) - (conj(Ep3a)*conj(r0615))/(4.*rt2) - (Em4a*r0312)/8. + (Ep4a*r0512)/(4.*rt6) + (Em3a*r0712)/8. + r1612*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1513_dt = -((gt + g2)*r1513) - i*((conj(Em4a)*conj(r0115))/(4.*rt6) - (conj(Ep4a)*conj(r0315))/8. - (conj(Ep3a)*conj(r0715))/8. - (Em4a*r0313)/8. + (Ep4a*r0513)/(4.*rt6) + (Em3a*r0713)/8. - r1512*((2*WLx)/3. - (2*i*WLy)/3.) + r1613*((2*WLx)/3. - (2*i*WLy)/3.) + r1413*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r1514*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr1514_dt = -((gt + g2)*r1514) - i*((conj(Em4a)*conj(r0215))/8. - (conj(Ep4a)*conj(r0415))/8. - (conj(Em3a)*conj(r0615))/(8.*rt3) - (conj(Ep3a)*conj(r0815))/(8.*rt3) - (Em4a*r0314)/8. + (Ep4a*r0514)/(4.*rt6) + (Em3a*r0714)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1514 + r1614*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1414*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) - r1515*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1514*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
-dr1515_dt = -((gt + g2)*r1515) - i*((conj(Em4a)*conj(r0315))/8. - (conj(Ep4a)*conj(r0515))/(4.*rt6) - (conj(Em3a)*conj(r0715))/8. - (Em4a*r0315)/8. + (Ep4a*r0515)/(4.*rt6) + (Em3a*r0715)/8. + r1615*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.) - r1514*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + conj(r1514)*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy));
+dr1312_dt = -((gt + g2)*r1312) - i*(-(conj(Ep4a)*conj(r0213))/(4.*rt6) - (conj(Ep3a)*conj(r0613))/(4.*rt2) - (Em4a*r0112)/(4.*rt6) + (Ep4a*r0312)/8. + (Ep3a*r0712)/8. + r1212*((2*WLx)/3. + (2*i*WLy)/3.) - r1313*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1313_dt = -((gt + g2)*r1313) - i*((conj(Em4a)*conj(r0113))/(4.*rt6) - (conj(Ep4a)*conj(r0313))/8. - (conj(Ep3a)*conj(r0713))/8. - (Em4a*r0113)/(4.*rt6) + (Ep4a*r0313)/8. + (Ep3a*r0713)/8. - r1312*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1412_dt = -((gt + g2)*r1412) - i*(-(conj(Ep4a)*conj(r0214))/(4.*rt6) - (conj(Ep3a)*conj(r0614))/(4.*rt2) - (Em4a*r0212)/8. + (Ep4a*r0412)/8. + (Em3a*r0612)/(8.*rt3) + (Ep3a*r0812)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1412 - r1413*((2*WLx)/3. + (2*i*WLy)/3.) + r1512*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1413_dt = -((gt + g2)*r1413) - i*((conj(Em4a)*conj(r0114))/(4.*rt6) - (conj(Ep4a)*conj(r0314))/8. - (conj(Ep3a)*conj(r0714))/8. - (Em4a*r0213)/8. + (Ep4a*r0413)/8. + (Em3a*r0613)/(8.*rt3) + (Ep3a*r0813)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1413 - r1412*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1313*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1414_dt = -((gt + g2)*r1414) - i*((conj(Em4a)*conj(r0214))/8. - (conj(Ep4a)*conj(r0414))/8. - (conj(Em3a)*conj(r0614))/(8.*rt3) - (conj(Ep3a)*conj(r0814))/(8.*rt3) - (Em4a*r0214)/8. + (Ep4a*r0414)/8. + (Em3a*r0614)/(8.*rt3) + (Ep3a*r0814)/(8.*rt3) - r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1512_dt = -((gt + g2)*r1512) - i*(-(conj(Ep4a)*conj(r0215))/(4.*rt6) - (conj(Ep3a)*conj(r0615))/(4.*rt2) - (Em4a*r0312)/8. + (Ep4a*r0512)/(4.*rt6) + (Em3a*r0712)/8. + r1612*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1513_dt = -((gt + g2)*r1513) - i*((conj(Em4a)*conj(r0115))/(4.*rt6) - (conj(Ep4a)*conj(r0315))/8. - (conj(Ep3a)*conj(r0715))/8. - (Em4a*r0313)/8. + (Ep4a*r0513)/(4.*rt6) + (Em3a*r0713)/8. - r1512*((2*WLx)/3. - (2*i*WLy)/3.) + r1613*((2*WLx)/3. - (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1514_dt = -((gt + g2)*r1514) - i*((conj(Em4a)*conj(r0215))/8. - (conj(Ep4a)*conj(r0415))/8. - (conj(Em3a)*conj(r0615))/(8.*rt3) - (conj(Ep3a)*conj(r0815))/(8.*rt3) - (Em4a*r0314)/8. + (Ep4a*r0514)/(4.*rt6) + (Em3a*r0714)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1514 + r1614*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1514*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1515_dt = -((gt + g2)*r1515) - i*((conj(Em4a)*conj(r0315))/8. - (conj(Ep4a)*conj(r0515))/(4.*rt6) - (conj(Em3a)*conj(r0715))/8. - (Em4a*r0315)/8. + (Ep4a*r0515)/(4.*rt6) + (Em3a*r0715)/8. + r1615*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.) - r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
 dr1612_dt = -((gt + g2)*r1612) - i*(-(conj(Ep4a)*conj(r0216))/(4.*rt6) - (conj(Ep3a)*conj(r0616))/(4.*rt2) - (Em4a*r0412)/(4.*rt6) + (Em3a*r0812)/(4.*rt2) + r1512*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*((2*WLx)/3. + (2*i*WLy)/3.) + r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1613_dt = -((gt + g2)*r1613) - i*((conj(Em4a)*conj(r0116))/(4.*rt6) - (conj(Ep4a)*conj(r0316))/8. - (conj(Ep3a)*conj(r0716))/8. - (Em4a*r0413)/(4.*rt6) + (Em3a*r0813)/(4.*rt2) - r1612*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr1614_dt = -((gt + g2)*r1614) - i*((conj(Em4a)*conj(r0216))/8. - (conj(Ep4a)*conj(r0416))/8. - (conj(Em3a)*conj(r0616))/(8.*rt3) - (conj(Ep3a)*conj(r0816))/(8.*rt3) - (Em4a*r0414)/(4.*rt6) + (Em3a*r0814)/(4.*rt2) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1614 + r1514*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) - r1615*(Sqrt(0.6666666666666666)*WLx + Sqrt(0.6666666666666666)*i*WLy) + r1614*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
-dr1615_dt = -((gt + g2)*r1615) - i*((conj(Em4a)*conj(r0316))/8. - (conj(Ep4a)*conj(r0516))/(4.*rt6) - (conj(Em3a)*conj(r0716))/8. - (Em4a*r0415)/(4.*rt6) + (Em3a*r0815)/(4.*rt2) + r1515*((2*WLx)/3. + (2*i*WLy)/3.) - r1616*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(Sqrt(0.6666666666666666)*WLx - Sqrt(0.6666666666666666)*i*WLy) + r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1613_dt = -((gt + g2)*r1613) - i*((conj(Em4a)*conj(r0116))/(4.*rt6) - (conj(Ep4a)*conj(r0316))/8. - (conj(Ep3a)*conj(r0716))/8. - (Em4a*r0413)/(4.*rt6) + (Em3a*r0813)/(4.*rt2) - r1612*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1614_dt = -((gt + g2)*r1614) - i*((conj(Em4a)*conj(r0216))/8. - (conj(Ep4a)*conj(r0416))/8. - (conj(Em3a)*conj(r0616))/(8.*rt3) - (conj(Ep3a)*conj(r0816))/(8.*rt3) - (Em4a*r0414)/(4.*rt6) + (Em3a*r0814)/(4.*rt2) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1614 + r1514*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1614*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr1615_dt = -((gt + g2)*r1615) - i*((conj(Em4a)*conj(r0316))/8. - (conj(Ep4a)*conj(r0516))/(4.*rt6) - (conj(Em3a)*conj(r0716))/8. - (Em4a*r0415)/(4.*rt6) + (Em3a*r0815)/(4.*rt2) + r1515*((2*WLx)/3. + (2*i*WLy)/3.) - r1616*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
 dr1616_dt = -((gt + g2)*r1616) - i*((conj(Em4a)*conj(r0416))/(4.*rt6) - (conj(Em3a)*conj(r0816))/(4.*rt2) - (Em4a*r0416)/(4.*rt6) + (Em3a*r0816)/(4.*rt2) - r1615*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.));
 //---------------- RbEquations.txt ends  ------------------
 					]]>
-- 
cgit v1.2.3


From f5f65bcf043f58a071ff6f39de9b897107fccf30 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Tue, 27 Nov 2012 18:11:39 -0500
Subject: Added proper output xsil file name

---
 xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
index d4e663e..ea6252a 100644
--- a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
+++ b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
@@ -2,7 +2,7 @@
 <simulation xmds-version="2">
 	<testing>
 		<arguments> --Ndens=1e15 --Lcell=10.0e-2  --Temperature=1e-3  --Pwidth=0.4e-6  --delta1=0 --delta2=0 --delta3=0  --E1o=0 --E2o=1e2 --E3o=0 --E4o=0</arguments>
-		<xsil_file name="realistic_Rb.xsil" expected="realistic_Rb_expected.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5">
+		<xsil_file name="realistic_Rb_and_fields.xsil" expected="realistic_Rb_and_fields_expected.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5">
 			<moment_group number="0" absolute_tolerance="1e-7" relative_tolerance="1e-6" />
 		</xsil_file>
 	</testing>
-- 
cgit v1.2.3


From b8ff606ca81bd2bffbf1fccce8d8460cfce64e88 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Tue, 27 Nov 2012 21:45:57 -0500
Subject: git ci tests are added

---
 .../realistic_Rb_and_fields_expected.xsil          | 676 +++++++++++++++++++++
 .../realistic_Rb_and_fields_expected_mg0.dat       | Bin 0 -> 6472848 bytes
 2 files changed, 676 insertions(+)
 create mode 100644 xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected.xsil
 create mode 100644 xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected_mg0.dat

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected.xsil b/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected.xsil
new file mode 100644
index 0000000..c09460c
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected.xsil
@@ -0,0 +1,676 @@
+<?xml version="1.0"?>
+<simulation xmds-version="2">
+        <testing>
+                <arguments> --Ndens=1e15 --Lcell=10.0e-2  --Temperature=1e-3  --Pwidth=0.4e-6  --delta1=0 --delta2=0 --delta3=0  --Ep1o=1e4 --Ep2o=1e2 --Ep3o=1e1 --Ep4o=1e1 --Em1o=1e4 --Em2o=1e2 --Em3o=1e1 --Em4o=1e1 --WLx=0 --WLy=0 --WLz=0</arguments>
+                <xsil_file name="realistic_Rb_and_fields.xsil" expected="realistic_Rb_and_fields_expected.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5">
+                        <moment_group number="0" absolute_tolerance="1e-7" relative_tolerance="1e-6" />
+                </xsil_file>
+        </testing>
+
+        <name>realistic_Rb_and_fields</name>
+
+        <author>Eugeniy Mikhailov</author>
+        <description>
+                License GPL.
+
+                Solving simplified Rb atom model
+                with fields propagation along spatial axis Z
+                with Doppler broadening.
+
+
+                We assume four-wave mixing condition when w3-w4=w2-w1 i.e. fields E3 and E4 drive the same
+                resonance as fields E2 and E1.
+
+
+                *              --------------- | F=1, 2P_3/2 >
+                *                \        \    
+                *                 \ E3_r   \    -------- | F=2, 2P_+1/2 >
+                *                  \   E4_r \   /    \
+                *                   \        \ / E2_l \ 
+                *                    \        /        \ E1_l
+                *   | F=2, 2S_1/2 > --------------      \
+                *                               \        \
+                *                                \        \
+                *                               ------------- | F=1, 2S_1/2 >
+                *            
+
+
+                We are solving 
+                        dE/dz+(1/c)*dE/dt=i*eta*rho_ij,  where j level is higher than i.
+                        Note that E is actually a Rabi frequency of electromagnetic field not the EM field
+                in xmds terms it looks like
+                        dE_dz = i*eta*rhoij - 1/c*L[E], here we moved t dependence to Fourier space
+
+                VERY IMPORTANT: all Rabi frequency should be given in [1/s], if you want to
+                normalize it to something else look drho/dt equation.
+                No need to renormalizes eta as long as its express through
+                the upper level decay rate in the same units as Rabi frequency.
+        </description>
+
+        <features>
+                <globals>
+                        <![CDATA[
+                                // Some numerical constants
+                                const double pi = M_PI; 
+
+                                // atom related constants
+                                //read from Mathematica generated Constants.txt
+//---------------- Constants.txt starts ------------------
+const double ha0 = 2.1471788680034824e10;
+const double ha1 = 2.558764384495815e9;
+const double g1 = 3.612847284945266e7;
+const double ha2 = 5.323020344462938e8;
+const double hb2 = 7.85178251911697e7;
+const double g2 = 3.8117309832741246e7;
+const double lambda1 = 7.949788511562656e-7;
+const double lambda2 = 7.802412096860509e-7;
+const double eta1 = 5.450949336831401e-6;
+const double eta2 = 5.5397657647874e-6;
+const double rt6 = 2.449489742783178;
+const double rt3 = 1.7320508075688772;
+const double rt2 = 1.4142135623730951;
+//---------------- Constants.txt ends   ------------------
+
+                                const double c=3.e8;
+                                const double k_boltzmann= 1.3806505e-23; // Boltzmann knostant in [J/K]
+                                const double lambda=794.7e-9; //wavelength in m
+                                // Fields k-vector
+                                const double Kvec = 2*M_PI/lambda;  
+                                // Simplified k-vectors
+                                const double Kvec1 = Kvec, Kvec2=Kvec, Kvec3=Kvec;
+
+                                //  ---------  Atom and cell properties -------------------------
+                                // range of Maxwell distribution atomic velocities
+                                const double mass = (86.909180527 * 1.660538921e-27); // atom mass in [kg] 
+                                // above mass expression is written as (expression is isotopic_mass * atomic_mass_unit)
+
+                                // Average sqrt(v^2) in Maxwell distribution for one dimension
+                                // Maxwell related parameters will be calculated in <arguments> section
+                                double v_thermal_averaged=0;
+                                // Maxwell distribution velocities range to take in account in [m/s]
+                                double V_maxwell_min = 0, V_maxwell_max = 0;
+
+                                // repopulation rate (atoms flying in/out the laser beam)  in [1/s]
+                                const double gt=0.01 *(2*M_PI*1e6);
+
+                                // inner use variables 
+                                double probability_v; // will be used as p(v) in Maxwell distribution
+
+                        ]]>
+                </globals>
+                <validation kind="run-time"/> <!--allows to put ranges as variables-->
+                <benchmark />
+    <arguments>
+                        <!-- Rabi frequency divided by 2 in [1/s] -->
+      <argument name="Ep1o" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+      <argument name="Em1o" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+      <argument name="Ep2o" type="real" default_value="0.05*(2*M_PI*1e6)" />
+      <argument name="Em2o" type="real" default_value="0.05*(2*M_PI*1e6)" />
+      <argument name="Ep3o" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+      <argument name="Em3o" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+      <argument name="Ep4o" type="real" default_value=".01*(2*M_PI*1e6)" />
+      <argument name="Em4o" type="real" default_value=".01*(2*M_PI*1e6)" />
+                        <!-- Fields detuning in [1/s] -->
+      <argument name="delta1"  type="real" default_value="0.0" />
+      <argument name="delta2"  type="real" default_value="0.0" />
+      <argument name="delta3"  type="real" default_value="0.0" />
+                        <!--Pulse duration/width [s] -->
+                        <argument name="Pwidth"  type="real" default_value="0.1e-6" />
+                        <!--  Atom and cell properties -->
+                        <!--Cell length [m] -->
+                        <argument name="Lcell"  type="real" default_value="1.5e-2" />
+                        <!--Density of atoms [1/m^3] -->
+                        <argument name="Ndens"  type="real" default_value="1e15" />
+                        <!-- Projections of magnetic field in Larmor frequency units [1/s] -->
+                        <argument name="WLx"  type="real" default_value="0" />
+                        <argument name="WLy"  type="real" default_value="0" />
+                        <argument name="WLz"  type="real" default_value="0" />
+                        <!--Atoms temperature [K] -->
+                        <!--TODO: looks like Temperature > 10 K knocks solver, 
+                                         I am guessing detunings are too large and thus it became a stiff equation-->
+                        <!--! make sure it is not equal to zero!-->
+                        <argument name="Temperature"  type="real" default_value="5" />
+                        <!-- This will be executed after arguments/parameters are parsed -->
+                        <!-- Read the code Luke: took me a while of reading the xmds2 sources to find it -->
+                        <![CDATA[
+                                // Average sqrt(v^2) in Maxwell distribution for one dimension
+                                if (Temperature == 0)
+                                        _LOG(_ERROR_LOG_LEVEL, "ERROR: Temperature should be >0 to provide range for Maxwell velocity distribution\n");
+                                v_thermal_averaged=sqrt(k_boltzmann*Temperature/mass); 
+                                // Maxwell distribution velocities range to take in account in [m/s]
+                                // there is almost zero probability for higher velocity p(4*v_av) = 3.3e-04 * p(0)
+                                V_maxwell_min = -4*v_thermal_averaged; V_maxwell_max = -V_maxwell_min; 
+                        ]]>
+    </arguments>
+                <bing />
+                <diagnostics /> 
+                <fftw plan="estimate" threads="1" />
+                <!--<fftw plan="patient" threads="1" />-->
+                <!-- I don't see any speed up on 6 core CPU even if use threads="6" -->
+                <!--<openmp />-->
+                <auto_vectorise />
+                <halt_non_finite />
+        </features>
+
+        <!-- 'z', 't', and 'v'  to have dimensions [m], [s], and [m/s]   -->
+        <geometry>
+                <propagation_dimension> z </propagation_dimension>
+                <transverse_dimensions>
+                        <!-- IMPORTANT: looks like having a lot of points in time helps with convergence.
+                                         I suspect that time spacing should be small enough to catch
+                                         all pulse harmonics and more importantly 1/dt should be larger than
+                                         the largest detuning (including Doppler shifts).
+                                         Unfortunately calculation time is proportional to lattice size
+                                         so we cannot just blindly increase it.
+                                         Some rules of thumb:  
+                                                * lattice="1000"   domain="(-1e-6, 1e-6)" 
+                                                        was good enough detunings up to 155 MHz (980 rad/s) notice that 1/dt=500 MHz
+                                                * lattice="10000"   domain="(-1e-6, 1e-6)" 
+                                                        works for Doppler averaging in up to 400K for Rb when lasers are zero detuned
+                         -->
+                        <dimension name="t"   lattice="10000"   domain="(-1e-6, 1e-6)" />
+                        <dimension name="v"   lattice="2"   domain="(V_maxwell_min, V_maxwell_max)" />
+                </transverse_dimensions>
+        </geometry>
+
+        <!-- Rabi frequency --> 
+        <vector name="E_field" type="complex" initial_space="t">
+                 <!--plus/minus circular polarization components-->
+                <components>Ep1 Em1 Ep2 Em2 Ep3 Em3 Ep4 Em4</components>
+                <initialisation>
+                        <![CDATA[
+                        // Initial (at starting 'z' position) electromagnetic field does not depend on detuning
+                        // as well as time
+                        Ep1=Ep1o;
+                        Em1=Em1o;
+                        Ep2=Ep2o*exp(-pow( ((t-0.0)/Pwidth),2) );
+                        Em2=Em2o*exp(-pow( ((t-0.0)/Pwidth),2) );
+                        Ep3=Ep3o;
+                        Em3=Em3o;
+                        Ep4=Ep4o;
+                        Em4=Em4o;
+                        ]]>
+                </initialisation>
+        </vector>
+
+        <!--Maxwell distribution probability p(v)-->
+        <computed_vector name="Maxwell_distribution_probabilities" dimensions="v" type="real">
+                <components>probability_v</components>
+                <evaluation>
+                        <![CDATA[
+                        // TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during  the script lifetime since 'v' is fixed.
+                        probability_v=1.0/(v_thermal_averaged*sqrt(2*M_PI)) * exp( - mod2(v/v_thermal_averaged)/2.0 ); 
+                        ]]>
+                </evaluation>
+        </computed_vector>
+
+        <!--Maxwell distribution norm sum(p(v))
+                         Needed since we sum over the grid instead of true integral,
+                         we also have finite cut off velocities-->
+        <computed_vector name="Maxwell_distribution_probabilities_norm" dimensions="" type="real">
+                <components>probability_v_norm</components>
+                <evaluation>
+                        <dependencies basis="v">Maxwell_distribution_probabilities</dependencies>
+                        <![CDATA[
+                        // TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during  the script lifetime since 'v' is fixed.
+                        probability_v_norm=probability_v;
+                        ]]>
+                </evaluation>
+        </computed_vector>
+
+
+        <!-- Averaged across Maxwell distribution fields amplitudes -->
+        <computed_vector name="E_field_avgd" dimensions="t" type="complex">
+                <components>Ep1a Em1a Ep2a Em2a Ep3a Em3a Ep4a Em4a</components>
+                <evaluation>
+                        <dependencies basis="v">E_field Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm</dependencies>
+                        <![CDATA[
+                        double prob_v_normalized=probability_v/probability_v_norm;
+                        Ep1a=Ep1*prob_v_normalized;
+                        Em1a=Em1*prob_v_normalized;
+                        Ep2a=Ep2*prob_v_normalized;
+                        Em2a=Em2*prob_v_normalized;
+                        Ep3a=Ep3*prob_v_normalized;
+                        Em3a=Em3*prob_v_normalized;
+                        Ep4a=Ep4*prob_v_normalized;
+                        Em4a=Em4*prob_v_normalized;
+                        ]]>
+                </evaluation>
+        </computed_vector>
+
+        <vector name="density_matrix" type="complex" initial_space="t">
+                <components>
+                        <!-- read from Mathematica generated RbChosenRho.txt -->
+<!-- ############### RbChosenRho.txt starts ################ -->
+r0101 r0109 r0110 r0111 r0112 r0113 r0114 r0115 r0116 r0201 r0202 r0209 r0210 r0211 r0212 r0213 r0214 r0215 r0216 r0301 r0302 r0303 r0309 r0310 r0311 r0312 r0313 r0314 r0315 r0316 r0401 r0402 r0403 r0404 r0409 r0410 r0411 r0412 r0413 r0414 r0415 r0416 r0501 r0502 r0503 r0504 r0505 r0509 r0510 r0511 r0512 r0513 r0514 r0515 r0516 r0601 r0602 r0603 r0604 r0605 r0606 r0609 r0610 r0611 r0612 r0613 r0614 r0615 r0616 r0701 r0702 r0703 r0704 r0705 r0706 r0707 r0709 r0710 r0711 r0712 r0713 r0714 r0715 r0716 r0801 r0802 r0803 r0804 r0805 r0806 r0807 r0808 r0809 r0810 r0811 r0812 r0813 r0814 r0815 r0816 r0909 r0912 r0913 r0914 r0915 r0916 r1009 r1010 r1012 r1013 r1014 r1015 r1016 r1109 r1110 r1111 r1112 r1113 r1114 r1115 r1116 r1212 r1312 r1313 r1412 r1413 r1414 r1512 r1513 r1514 r1515 r1612 r1613 r1614 r1615 r1616 
+<!-- ############### RbChosenRho.txt ends  ################# -->
+                </components>
+                <initialisation>
+                        <!--This sets boundary condition at all times and left border of z (i.e. z=0)-->
+                        <![CDATA[
+                        // Note: 
+                        // convergence is really slow if all populations concentrated at the bottom level |1>
+                        // this is because if r11=1, everything else is 0 and then every small increment 
+                        // seems to be huge and adaptive solver makes smaller and smaller steps.
+                        // As quick and dirty fix I reshuffle initial population  
+                        // so some of the population sits at the  second ground level |2>
+                        // TODO: Fix above. Make the equation of motion for r11 
+                        //       and express other level, let's say r44
+                        //       through population normalization
+
+                        //read from Mathematica generated RbInits.txt
+//---------------- RbInits.txt starts ------------------
+r0101 = 0.125;
+r0109 = 0;
+r0110 = 0;
+r0111 = 0;
+r0112 = 0;
+r0113 = 0;
+r0114 = 0;
+r0115 = 0;
+r0116 = 0;
+r0201 = 0;
+r0202 = 0.125;
+r0209 = 0;
+r0210 = 0;
+r0211 = 0;
+r0212 = 0;
+r0213 = 0;
+r0214 = 0;
+r0215 = 0;
+r0216 = 0;
+r0301 = 0;
+r0302 = 0;
+r0303 = 0.125;
+r0309 = 0;
+r0310 = 0;
+r0311 = 0;
+r0312 = 0;
+r0313 = 0;
+r0314 = 0;
+r0315 = 0;
+r0316 = 0;
+r0401 = 0;
+r0402 = 0;
+r0403 = 0;
+r0404 = 0.125;
+r0409 = 0;
+r0410 = 0;
+r0411 = 0;
+r0412 = 0;
+r0413 = 0;
+r0414 = 0;
+r0415 = 0;
+r0416 = 0;
+r0501 = 0;
+r0502 = 0;
+r0503 = 0;
+r0504 = 0;
+r0505 = 0.125;
+r0509 = 0;
+r0510 = 0;
+r0511 = 0;
+r0512 = 0;
+r0513 = 0;
+r0514 = 0;
+r0515 = 0;
+r0516 = 0;
+r0601 = 0;
+r0602 = 0;
+r0603 = 0;
+r0604 = 0;
+r0605 = 0;
+r0606 = 0.125;
+r0609 = 0;
+r0610 = 0;
+r0611 = 0;
+r0612 = 0;
+r0613 = 0;
+r0614 = 0;
+r0615 = 0;
+r0616 = 0;
+r0701 = 0;
+r0702 = 0;
+r0703 = 0;
+r0704 = 0;
+r0705 = 0;
+r0706 = 0;
+r0707 = 0.125;
+r0709 = 0;
+r0710 = 0;
+r0711 = 0;
+r0712 = 0;
+r0713 = 0;
+r0714 = 0;
+r0715 = 0;
+r0716 = 0;
+r0801 = 0;
+r0802 = 0;
+r0803 = 0;
+r0804 = 0;
+r0805 = 0;
+r0806 = 0;
+r0807 = 0;
+r0808 = 0.125;
+r0809 = 0;
+r0810 = 0;
+r0811 = 0;
+r0812 = 0;
+r0813 = 0;
+r0814 = 0;
+r0815 = 0;
+r0816 = 0;
+r0909 = 0;
+r0912 = 0;
+r0913 = 0;
+r0914 = 0;
+r0915 = 0;
+r0916 = 0;
+r1009 = 0;
+r1010 = 0;
+r1012 = 0;
+r1013 = 0;
+r1014 = 0;
+r1015 = 0;
+r1016 = 0;
+r1109 = 0;
+r1110 = 0;
+r1111 = 0;
+r1112 = 0;
+r1113 = 0;
+r1114 = 0;
+r1115 = 0;
+r1116 = 0;
+r1212 = 0;
+r1312 = 0;
+r1313 = 0;
+r1412 = 0;
+r1413 = 0;
+r1414 = 0;
+r1512 = 0;
+r1513 = 0;
+r1514 = 0;
+r1515 = 0;
+r1612 = 0;
+r1613 = 0;
+r1614 = 0;
+r1615 = 0;
+r1616 = 0;
+//---------------- RbInits.txt ends  ------------------
+                        ]]>
+                </initialisation>
+        </vector>
+
+        <sequence>
+                <!--For this set of conditions ARK45 is faster than ARK89-->
+                <!--ARK45 is good for small detuning when all frequency like term are close to zero-->
+                <integrate algorithm="ARK45" tolerance="1e-5" interval="Lcell"> 
+                <!--<integrate algorithm="SI" steps="200" interval="Lcell"> -->
+                <!--RK4 is good for large detunings when frequency like term are big, it does not try to be too smart about adaptive step which ARK seems to make too small-->
+                <!--When ARK45 works it about 3 times faster than RK4 with 1000 steps-->
+                <!--<integrate algorithm="RK4" steps="100" interval="1.5e-2">-->
+                <!--SIC algorithm seems to be much slower and needs fine 'z'  step tuning and much finer time grid-->
+                <!--For example I had to quadruple the time grid from 1000 to 4000 when increased z distance from 0.02 to 0.04-->
+
+                <!--<integrate algorithm="SIC" interval="4e-2" steps="200">-->
+
+                        <samples>100</samples>
+                        <!--<samples>100 100</samples>-->
+                        <!--Use the next line for debuging to see velocity dependence. Uncomment/switch on output groups 3,4-->
+                        <!--<samples>100 100 100 100</samples>--> 
+                        <operators>
+        <operator kind="cross_propagation" algorithm="SI" propagation_dimension="t">
+                                        <integration_vectors>density_matrix</integration_vectors>
+          <dependencies>E_field_avgd</dependencies>
+          <boundary_condition kind="left">
+                                                <!--This set boundary condition at all 'z'  and left border of 't' (i.e. min(t))-->
+                                                <!--
+            <![CDATA[
+                                                        r11 = 0; r22 = 1; r33 = 0; r44 = 0;
+                                                        r12 = 0; r13 = 0; r14 = 0;
+                                                        r23 = 0; r24 = 0;
+                                                        r34 = 0;
+                                                        printf("z= %g, t= %g\n", z, t);
+            ]]>
+                                                -->
+          </boundary_condition>
+                                        <![CDATA[
+                                                // Equations of motions according to Simon's mathematica code
+                                                //read from Mathematica generated RbEquations.txt
+//---------------- RbEquations.txt starts ------------------
+dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1212)/3. + (g2*r1313)/6. - i*((conj(Em1a)*conj(r0109))/4. - (conj(Em4a)*conj(r0113))/(4.*rt6) - (Em1a*r0109)/4. + (Em4a*r0113)/(4.*rt6) + r0201*(WLx/2. - (i*WLy)/2.) - conj(r0201)*(WLx/2. + (i*WLy)/2.));
+dr0109_dt = (-(gt*r0109) - (gt + g1)*r0109)/2. - i*(-(conj(Ep1a)*conj(r0301))/(4.*rt6) + (conj(Ep2a)*conj(r0701))/(4.*rt6) - (conj(Em4a)*conj(r0913))/(4.*rt6) - (conj(Em1a)*r0101)/4. + (conj(Em1a)*r0909)/4. + r0209*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-delta1 - v*Kvec1 - WLz/6.) + r0109*WLz);
+dr0110_dt = (-(gt*r0110) - (gt + g1)*r0110)/2. - i*(-(conj(Em1a)*conj(r0201))/(4.*rt2) - (conj(Ep1a)*conj(r0401))/(4.*rt2) - (conj(Em2a)*conj(r0601))/(4.*rt6) + (conj(Ep2a)*conj(r0801))/(4.*rt6) + (conj(Em1a)*conj(r1009))/4. - (conj(Em4a)*conj(r1013))/(4.*rt6) + (delta1 + v*Kvec1)*r0110 + r0210*(WLx/2. - (i*WLy)/2.) - r0111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0110*WLz);
+dr0111_dt = (-(gt*r0111) - (gt + g1)*r0111)/2. - i*(-(conj(Em1a)*conj(r0301))/(4.*rt6) - (conj(Ep1a)*conj(r0501))/4. - (conj(Em2a)*conj(r0701))/(4.*rt6) + (conj(Em1a)*conj(r1109))/4. - (conj(Em4a)*conj(r1113))/(4.*rt6) + r0211*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0111*(-delta1 - v*Kvec1 + WLz/6.) + r0111*WLz);
+dr0112_dt = (-(gt*r0112) - (gt + g2)*r0112)/2. - i*(-(conj(Ep4a)*conj(r0201))/(4.*rt6) - (conj(Ep3a)*conj(r0601))/(4.*rt2) + (conj(Em1a)*r0912)/4. - (conj(Em4a)*r1312)/(4.*rt6) + r0212*(WLx/2. - (i*WLy)/2.) - r0113*((2*WLx)/3. + (2*i*WLy)/3.) + r0112*WLz - r0112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0113_dt = (-(gt*r0113) - (gt + g2)*r0113)/2. - i*(-(conj(Ep4a)*conj(r0301))/8. - (conj(Ep3a)*conj(r0701))/8. + (conj(Em4a)*r0101)/(4.*rt6) + (conj(Em1a)*r0913)/4. - (conj(Em4a)*r1313)/(4.*rt6) - r0112*((2*WLx)/3. - (2*i*WLy)/3.) + r0213*(WLx/2. - (i*WLy)/2.) - r0114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + r0113*WLz);
+dr0114_dt = (-(gt*r0114) - (gt + g2)*r0114)/2. - i*((conj(Em4a)*conj(r0201))/8. - (conj(Ep4a)*conj(r0401))/8. - (conj(Em3a)*conj(r0601))/(8.*rt3) - (conj(Ep3a)*conj(r0801))/(8.*rt3) - (conj(Em4a)*conj(r1413))/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0114 + (conj(Em1a)*r0914)/4. + r0214*(WLx/2. - (i*WLy)/2.) - r0113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0114*WLz);
+dr0115_dt = (-(gt*r0115) - (gt + g2)*r0115)/2. - i*((conj(Em4a)*conj(r0301))/8. - (conj(Ep4a)*conj(r0501))/(4.*rt6) - (conj(Em3a)*conj(r0701))/8. - (conj(Em4a)*conj(r1513))/(4.*rt6) + (conj(Em1a)*r0915)/4. + r0215*(WLx/2. - (i*WLy)/2.) - r0116*((2*WLx)/3. + (2*i*WLy)/3.) - r0114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0115*WLz);
+dr0116_dt = (-(gt*r0116) - (gt + g2)*r0116)/2. - i*((conj(Em4a)*conj(r0401))/(4.*rt6) - (conj(Em3a)*conj(r0801))/(4.*rt2) - (conj(Em4a)*conj(r1613))/(4.*rt6) + (conj(Em1a)*r0916)/4. - r0115*((2*WLx)/3. - (2*i*WLy)/3.) + r0216*(WLx/2. - (i*WLy)/2.) - r0116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0116*WLz);
+dr0201_dt = -(gt*r0201) + (g1*r1009)/(2.*rt2) + (g2*r1312)/6. + (g2*r1413)/(2.*rt6) - i*((conj(Em1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0112))/(4.*rt6) - (conj(Em4a)*conj(r0114))/8. - (Em1a*r0209)/4. + (Em4a*r0213)/(4.*rt6) + r0101*(WLx/2. + (i*WLy)/2.) - r0202*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0201*WLz)/2.);
+dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1212)/6. + (g2*r1313)/12. + (g2*r1414)/4. - i*((conj(Em1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Em4a)*conj(r0214))/8. - (Em1a*r0210)/(4.*rt2) - (Ep4a*r0212)/(4.*rt6) + (Em4a*r0214)/8. - r0201*(WLx/2. - (i*WLy)/2.) + conj(r0201)*(WLx/2. + (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0209_dt = (-(gt*r0209) - (gt + g1)*r0209)/2. - i*(-(conj(Ep1a)*conj(r0302))/(4.*rt6) + (conj(Ep2a)*conj(r0702))/(4.*rt6) + (conj(Ep4a)*conj(r0912))/(4.*rt6) - (conj(Em4a)*conj(r0914))/8. - (conj(Em1a)*r0201)/4. + (conj(Em1a)*r1009)/(4.*rt2) + r0109*(WLx/2. + (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-delta1 - v*Kvec1 - WLz/6.) + (r0209*WLz)/2.);
+dr0210_dt = (-(gt*r0210) - (gt + g1)*r0210)/2. - i*(-(conj(Ep1a)*conj(r0402))/(4.*rt2) - (conj(Em2a)*conj(r0602))/(4.*rt6) + (conj(Ep2a)*conj(r0802))/(4.*rt6) + (conj(Ep4a)*conj(r1012))/(4.*rt6) - (conj(Em4a)*conj(r1014))/8. - (conj(Em1a)*r0202)/(4.*rt2) + (delta1 + v*Kvec1)*r0210 + (conj(Em1a)*r1010)/(4.*rt2) + r0110*(WLx/2. + (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0211*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + (r0210*WLz)/2.);
+dr0211_dt = (-(gt*r0211) - (gt + g1)*r0211)/2. - i*(-(conj(Em1a)*conj(r0302))/(4.*rt6) - (conj(Ep1a)*conj(r0502))/4. - (conj(Em2a)*conj(r0702))/(4.*rt6) + (conj(Em1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1112))/(4.*rt6) - (conj(Em4a)*conj(r1114))/8. + r0111*(WLx/2. + (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0211*(-delta1 - v*Kvec1 + WLz/6.) + (r0211*WLz)/2.);
+dr0212_dt = (-(gt*r0212) - (gt + g2)*r0212)/2. - i*(-(conj(Ep3a)*conj(r0602))/(4.*rt2) - (conj(Ep4a)*r0202)/(4.*rt6) + (conj(Em1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1212)/(4.*rt6) - (conj(Em4a)*r1412)/8. + r0112*(WLx/2. + (i*WLy)/2.) - r0213*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0212*WLz)/2. - r0212*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0213_dt = (-(gt*r0213) - (gt + g2)*r0213)/2. - i*(-(conj(Ep4a)*conj(r0302))/8. - (conj(Ep3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1312))/(4.*rt6) + (conj(Em4a)*r0201)/(4.*rt6) + (conj(Em1a)*r1013)/(4.*rt2) - (conj(Em4a)*r1413)/8. - r0212*((2*WLx)/3. - (2*i*WLy)/3.) + r0113*(WLx/2. + (i*WLy)/2.) - r0214*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0213*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + (r0213*WLz)/2.);
+dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*(-(conj(Ep4a)*conj(r0402))/8. - (conj(Em3a)*conj(r0602))/(8.*rt3) - (conj(Ep3a)*conj(r0802))/(8.*rt3) + (conj(Ep4a)*conj(r1412))/(4.*rt6) + (conj(Em4a)*r0202)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 + (conj(Em1a)*r1014)/(4.*rt2) - (conj(Em4a)*r1414)/8. + r0114*(WLx/2. + (i*WLy)/2.) - r0213*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0215*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0214*WLz)/2.);
+dr0215_dt = (-(gt*r0215) - (gt + g2)*r0215)/2. - i*((conj(Em4a)*conj(r0302))/8. - (conj(Ep4a)*conj(r0502))/(4.*rt6) - (conj(Em3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1512))/(4.*rt6) - (conj(Em4a)*conj(r1514))/8. + (conj(Em1a)*r1015)/(4.*rt2) + r0115*(WLx/2. + (i*WLy)/2.) - r0216*((2*WLx)/3. + (2*i*WLy)/3.) - r0214*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0215*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + (r0215*WLz)/2.);
+dr0216_dt = (-(gt*r0216) - (gt + g2)*r0216)/2. - i*((conj(Em4a)*conj(r0402))/(4.*rt6) - (conj(Em3a)*conj(r0802))/(4.*rt2) + (conj(Ep4a)*conj(r1612))/(4.*rt6) - (conj(Em4a)*conj(r1614))/8. + (conj(Em1a)*r1016)/(4.*rt2) - r0215*((2*WLx)/3. - (2*i*WLy)/3.) + r0116*(WLx/2. + (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0216*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + (r0216*WLz)/2.);
+dr0301_dt = -(gt*r0301) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0109))/(4.*rt6) + (conj(Em1a)*conj(r0111))/(4.*rt6) + (conj(Ep4a)*conj(r0113))/8. - (conj(Em4a)*conj(r0115))/8. - (Em1a*r0309)/4. + (Em4a*r0313)/(4.*rt6) - r0302*(WLx/2. + (i*WLy)/2.) + r0401*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0201*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0301*WLz);
+dr0302_dt = -(gt*r0302) + (g1*r1009)/(2.*rt3) + (g1*r1110)/(4.*rt3) + (g2*r1312)/(2.*rt6) + (g2*r1514)/4. - i*((conj(Ep1a)*conj(r0209))/(4.*rt6) + (conj(Em1a)*conj(r0211))/(4.*rt6) + (conj(Ep4a)*conj(r0213))/8. - (conj(Em4a)*conj(r0215))/8. - (Em1a*r0310)/(4.*rt2) - (Ep4a*r0312)/(4.*rt6) + (Em4a*r0314)/8. - r0301*(WLx/2. - (i*WLy)/2.) + r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0202*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0302*WLz)/2.);
+dr0303_dt = gt/8. - gt*r0303 + (g1*r0909)/12. + (g1*r1010)/3. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1515)/4. - i*((conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Em1a)*conj(r0311))/(4.*rt6) + (conj(Ep4a)*conj(r0313))/8. - (conj(Em4a)*conj(r0315))/8. - (Ep1a*r0309)/(4.*rt6) - (Em1a*r0311)/(4.*rt6) - (Ep4a*r0313)/8. + (Em4a*r0315)/8. - r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*((conj(Ep2a)*conj(r0703))/(4.*rt6) + (conj(Ep4a)*conj(r0913))/8. - (conj(Em4a)*conj(r0915))/8. - (conj(Em1a)*r0301)/4. - (conj(Ep1a)*r0303)/(4.*rt6) + (conj(Ep1a)*r0909)/(4.*rt6) + (conj(Em1a)*r1109)/(4.*rt6) + r0409*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0209*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-delta1 - v*Kvec1 - WLz/6.));
+dr0310_dt = (-(gt*r0310) - (gt + g1)*r0310)/2. - i*(-(conj(Ep1a)*conj(r0403))/(4.*rt2) - (conj(Em2a)*conj(r0603))/(4.*rt6) + (conj(Ep2a)*conj(r0803))/(4.*rt6) + (conj(Ep1a)*conj(r1009))/(4.*rt6) + (conj(Ep4a)*conj(r1013))/8. - (conj(Em4a)*conj(r1015))/8. - (conj(Em1a)*r0302)/(4.*rt2) + (delta1 + v*Kvec1)*r0310 + (conj(Em1a)*r1110)/(4.*rt6) + r0410*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0210*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0311*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr0311_dt = (-(gt*r0311) - (gt + g1)*r0311)/2. - i*(-(conj(Ep1a)*conj(r0503))/4. - (conj(Em2a)*conj(r0703))/(4.*rt6) + (conj(Ep1a)*conj(r1109))/(4.*rt6) + (conj(Ep4a)*conj(r1113))/8. - (conj(Em4a)*conj(r1115))/8. - (conj(Em1a)*r0303)/(4.*rt6) + (conj(Em1a)*r1111)/(4.*rt6) + r0411*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0211*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0311*(-delta1 - v*Kvec1 + WLz/6.));
+dr0312_dt = (-(gt*r0312) - (gt + g2)*r0312)/2. - i*(-(conj(Ep3a)*conj(r0603))/(4.*rt2) - (conj(Ep4a)*r0302)/(4.*rt6) + (conj(Ep1a)*r0912)/(4.*rt6) + (conj(Em1a)*r1112)/(4.*rt6) + (conj(Ep4a)*r1312)/8. - (conj(Em4a)*r1512)/8. - r0313*((2*WLx)/3. + (2*i*WLy)/3.) + r0412*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0212*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0313_dt = (-(gt*r0313) - (gt + g2)*r0313)/2. - i*(-(conj(Ep3a)*conj(r0703))/8. + (conj(Em4a)*r0301)/(4.*rt6) - (conj(Ep4a)*r0303)/8. + (conj(Ep1a)*r0913)/(4.*rt6) + (conj(Em1a)*r1113)/(4.*rt6) + (conj(Ep4a)*r1313)/8. - (conj(Em4a)*r1513)/8. - r0312*((2*WLx)/3. - (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0413*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0213*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0313*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0314_dt = (-(gt*r0314) - (gt + g2)*r0314)/2. - i*(-(conj(Ep4a)*conj(r0403))/8. - (conj(Em3a)*conj(r0603))/(8.*rt3) - (conj(Ep3a)*conj(r0803))/(8.*rt3) + (conj(Ep4a)*conj(r1413))/8. + (conj(Em4a)*r0302)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0314 + (conj(Ep1a)*r0914)/(4.*rt6) + (conj(Em1a)*r1114)/(4.*rt6) - (conj(Em4a)*r1514)/8. - r0313*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0315*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0414*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0214*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(conj(Ep4a)*conj(r0503))/(4.*rt6) - (conj(Em3a)*conj(r0703))/8. + (conj(Ep4a)*conj(r1513))/8. + (conj(Em4a)*r0303)/8. + (conj(Ep1a)*r0915)/(4.*rt6) + (conj(Em1a)*r1115)/(4.*rt6) - (conj(Em4a)*r1515)/8. - r0316*((2*WLx)/3. + (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0415*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0215*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0315*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0316_dt = (-(gt*r0316) - (gt + g2)*r0316)/2. - i*((conj(Em4a)*conj(r0403))/(4.*rt6) - (conj(Em3a)*conj(r0803))/(4.*rt2) + (conj(Ep4a)*conj(r1613))/8. - (conj(Em4a)*conj(r1615))/8. + (conj(Ep1a)*r0916)/(4.*rt6) + (conj(Em1a)*r1116)/(4.*rt6) - r0315*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0216*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0316*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr0401_dt = -(gt*r0401) - (g2*r1512)/6. + (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0114))/8. - (conj(Em4a)*conj(r0116))/(4.*rt6) - (Em1a*r0409)/4. + (Em4a*r0413)/(4.*rt6) + r0501*(WLx/2. - (i*WLy)/2.) - r0402*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0401*WLz)/2.);
+dr0402_dt = -(gt*r0402) + (g1*r1109)/4. + (g2*r1412)/(2.*rt6) - (g2*r1513)/12. + (g2*r1614)/(2.*rt6) - i*((conj(Ep1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0214))/8. - (conj(Em4a)*conj(r0216))/(4.*rt6) - (Em1a*r0410)/(4.*rt2) - (Ep4a*r0412)/(4.*rt6) + (Em4a*r0414)/8. - r0401*(WLx/2. - (i*WLy)/2.) + r0502*(WLx/2. - (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0402*WLz);
+dr0403_dt = -(gt*r0403) + (g1*r1009)/(4.*rt3) + (g1*r1110)/(2.*rt3) + (g2*r1413)/4. + (g2*r1615)/(2.*rt6) - i*((conj(Ep1a)*conj(r0310))/(4.*rt2) + (conj(Ep4a)*conj(r0314))/8. - (conj(Em4a)*conj(r0316))/(4.*rt6) - (Ep1a*r0409)/(4.*rt6) - (Em1a*r0411)/(4.*rt6) - (Ep4a*r0413)/8. + (Em4a*r0415)/8. + r0503*(WLx/2. - (i*WLy)/2.) - r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0404*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0403*WLz)/2.);
+dr0404_dt = gt/8. - gt*r0404 + (g1*r1010)/4. + (g1*r1111)/4. + (g2*r1414)/4. + (g2*r1515)/12. + (g2*r1616)/6. - i*((conj(Ep1a)*conj(r0410))/(4.*rt2) + (conj(Ep4a)*conj(r0414))/8. - (conj(Em4a)*conj(r0416))/(4.*rt6) - (Ep1a*r0410)/(4.*rt2) - (Ep4a*r0414)/8. + (Em4a*r0416)/(4.*rt6) + r0504*(WLx/2. - (i*WLy)/2.) - conj(r0504)*(WLx/2. + (i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0409_dt = (-(gt*r0409) - (gt + g1)*r0409)/2. - i*((conj(Ep2a)*conj(r0704))/(4.*rt6) + (conj(Ep4a)*conj(r0914))/8. - (conj(Em4a)*conj(r0916))/(4.*rt6) - (conj(Em1a)*r0401)/4. - (conj(Ep1a)*r0403)/(4.*rt6) + (conj(Ep1a)*r1009)/(4.*rt2) + r0509*(WLx/2. - (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-delta1 - v*Kvec1 - WLz/6.) - (r0409*WLz)/2.);
+dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(conj(Em2a)*conj(r0604))/(4.*rt6) + (conj(Ep2a)*conj(r0804))/(4.*rt6) + (conj(Ep4a)*conj(r1014))/8. - (conj(Em4a)*conj(r1016))/(4.*rt6) - (conj(Em1a)*r0402)/(4.*rt2) - (conj(Ep1a)*r0404)/(4.*rt2) + (delta1 + v*Kvec1)*r0410 + (conj(Ep1a)*r1010)/(4.*rt2) + r0510*(WLx/2. - (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0411*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - (r0410*WLz)/2.);
+dr0411_dt = (-(gt*r0411) - (gt + g1)*r0411)/2. - i*(-(conj(Ep1a)*conj(r0504))/4. - (conj(Em2a)*conj(r0704))/(4.*rt6) + (conj(Ep1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1114))/8. - (conj(Em4a)*conj(r1116))/(4.*rt6) - (conj(Em1a)*r0403)/(4.*rt6) + r0511*(WLx/2. - (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0411*(-delta1 - v*Kvec1 + WLz/6.) - (r0411*WLz)/2.);
+dr0412_dt = (-(gt*r0412) - (gt + g2)*r0412)/2. - i*(-(conj(Ep3a)*conj(r0604))/(4.*rt2) - (conj(Ep4a)*r0402)/(4.*rt6) + (conj(Ep1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1412)/8. - (conj(Em4a)*r1612)/(4.*rt6) + r0512*(WLx/2. - (i*WLy)/2.) - r0413*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0412*WLz)/2. - r0412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0413_dt = (-(gt*r0413) - (gt + g2)*r0413)/2. - i*(-(conj(Ep3a)*conj(r0704))/8. + (conj(Em4a)*r0401)/(4.*rt6) - (conj(Ep4a)*r0403)/8. + (conj(Ep1a)*r1013)/(4.*rt2) + (conj(Ep4a)*r1413)/8. - (conj(Em4a)*r1613)/(4.*rt6) - r0412*((2*WLx)/3. - (2*i*WLy)/3.) + r0513*(WLx/2. - (i*WLy)/2.) - r0414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - (r0413*WLz)/2.);
+dr0414_dt = (-(gt*r0414) - (gt + g2)*r0414)/2. - i*(-(conj(Em3a)*conj(r0604))/(8.*rt3) - (conj(Ep3a)*conj(r0804))/(8.*rt3) + (conj(Em4a)*r0402)/8. - (conj(Ep4a)*r0404)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0414 + (conj(Ep1a)*r1014)/(4.*rt2) + (conj(Ep4a)*r1414)/8. - (conj(Em4a)*r1614)/(4.*rt6) + r0514*(WLx/2. - (i*WLy)/2.) - r0413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0415*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0414*WLz)/2.);
+dr0415_dt = (-(gt*r0415) - (gt + g2)*r0415)/2. - i*(-(conj(Ep4a)*conj(r0504))/(4.*rt6) - (conj(Em3a)*conj(r0704))/8. + (conj(Ep4a)*conj(r1514))/8. + (conj(Em4a)*r0403)/8. + (conj(Ep1a)*r1015)/(4.*rt2) - (conj(Em4a)*r1615)/(4.*rt6) + r0515*(WLx/2. - (i*WLy)/2.) - r0416*((2*WLx)/3. + (2*i*WLy)/3.) - r0414*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0415*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - (r0415*WLz)/2.);
+dr0416_dt = (-(gt*r0416) - (gt + g2)*r0416)/2. - i*(-(conj(Em3a)*conj(r0804))/(4.*rt2) + (conj(Ep4a)*conj(r1614))/8. + (conj(Em4a)*r0404)/(4.*rt6) + (conj(Ep1a)*r1016)/(4.*rt2) - (conj(Em4a)*r1616)/(4.*rt6) - r0415*((2*WLx)/3. - (2*i*WLy)/3.) + r0516*(WLx/2. - (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0416*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - (r0416*WLz)/2.);
+dr0501_dt = -(gt*r0501) - (g2*r1612)/3. - i*((conj(Ep1a)*conj(r0111))/4. + (conj(Ep4a)*conj(r0115))/(4.*rt6) - (Em1a*r0509)/4. + (Em4a*r0513)/(4.*rt6) + r0401*(WLx/2. + (i*WLy)/2.) - r0502*(WLx/2. + (i*WLy)/2.) - 2*r0501*WLz);
+dr0502_dt = -(gt*r0502) + (g2*r1512)/6. - (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0211))/4. + (conj(Ep4a)*conj(r0215))/(4.*rt6) - (Em1a*r0510)/(4.*rt2) - (Ep4a*r0512)/(4.*rt6) + (Em4a*r0514)/8. - r0501*(WLx/2. - (i*WLy)/2.) + r0402*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0502*WLz)/2.);
+dr0503_dt = -(gt*r0503) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0311))/4. + (conj(Ep4a)*conj(r0315))/(4.*rt6) - (Ep1a*r0509)/(4.*rt6) - (Em1a*r0511)/(4.*rt6) - (Ep4a*r0513)/8. + (Em4a*r0515)/8. + r0403*(WLx/2. + (i*WLy)/2.) - r0502*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0504*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0503*WLz);
+dr0504_dt = -(gt*r0504) + (g1*r1110)/(2.*rt2) + (g2*r1514)/(2.*rt6) + (g2*r1615)/6. - i*((conj(Ep1a)*conj(r0411))/4. + (conj(Ep4a)*conj(r0415))/(4.*rt6) - (Ep1a*r0510)/(4.*rt2) - (Ep4a*r0514)/8. + (Em4a*r0516)/(4.*rt6) + r0404*(WLx/2. + (i*WLy)/2.) - r0505*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0504*WLz)/2.);
+dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((conj(Ep1a)*conj(r0511))/4. + (conj(Ep4a)*conj(r0515))/(4.*rt6) - (Ep1a*r0511)/4. - (Ep4a*r0515)/(4.*rt6) - r0504*(WLx/2. - (i*WLy)/2.) + conj(r0504)*(WLx/2. + (i*WLy)/2.));
+dr0509_dt = (-(gt*r0509) - (gt + g1)*r0509)/2. - i*((conj(Ep2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r0915))/(4.*rt6) - (conj(Em1a)*r0501)/4. - (conj(Ep1a)*r0503)/(4.*rt6) + (conj(Ep1a)*r1109)/4. + r0409*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-delta1 - v*Kvec1 - WLz/6.) - r0509*WLz);
+dr0510_dt = (-(gt*r0510) - (gt + g1)*r0510)/2. - i*(-(conj(Em2a)*conj(r0605))/(4.*rt6) + (conj(Ep2a)*conj(r0805))/(4.*rt6) + (conj(Ep4a)*conj(r1015))/(4.*rt6) - (conj(Em1a)*r0502)/(4.*rt2) - (conj(Ep1a)*r0504)/(4.*rt2) + (delta1 + v*Kvec1)*r0510 + (conj(Ep1a)*r1110)/4. + r0410*(WLx/2. + (i*WLy)/2.) - r0511*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0510*WLz);
+dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(conj(Em2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r1115))/(4.*rt6) - (conj(Em1a)*r0503)/(4.*rt6) - (conj(Ep1a)*r0505)/4. + (conj(Ep1a)*r1111)/4. + r0411*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0511*(-delta1 - v*Kvec1 + WLz/6.) - r0511*WLz);
+dr0512_dt = (-(gt*r0512) - (gt + g2)*r0512)/2. - i*(-(conj(Ep3a)*conj(r0605))/(4.*rt2) - (conj(Ep4a)*r0502)/(4.*rt6) + (conj(Ep1a)*r1112)/4. + (conj(Ep4a)*r1512)/(4.*rt6) + r0412*(WLx/2. + (i*WLy)/2.) - r0513*((2*WLx)/3. + (2*i*WLy)/3.) - r0512*WLz - r0512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0513_dt = (-(gt*r0513) - (gt + g2)*r0513)/2. - i*(-(conj(Ep3a)*conj(r0705))/8. + (conj(Em4a)*r0501)/(4.*rt6) - (conj(Ep4a)*r0503)/8. + (conj(Ep1a)*r1113)/4. + (conj(Ep4a)*r1513)/(4.*rt6) - r0512*((2*WLx)/3. - (2*i*WLy)/3.) + r0413*(WLx/2. + (i*WLy)/2.) - r0514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r0513*WLz);
+dr0514_dt = (-(gt*r0514) - (gt + g2)*r0514)/2. - i*(-(conj(Em3a)*conj(r0605))/(8.*rt3) - (conj(Ep3a)*conj(r0805))/(8.*rt3) + (conj(Em4a)*r0502)/8. - (conj(Ep4a)*r0504)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0514 + (conj(Ep1a)*r1114)/4. + (conj(Ep4a)*r1514)/(4.*rt6) + r0414*(WLx/2. + (i*WLy)/2.) - r0513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0514*WLz);
+dr0515_dt = (-(gt*r0515) - (gt + g2)*r0515)/2. - i*(-(conj(Em3a)*conj(r0705))/8. + (conj(Em4a)*r0503)/8. - (conj(Ep4a)*r0505)/(4.*rt6) + (conj(Ep1a)*r1115)/4. + (conj(Ep4a)*r1515)/(4.*rt6) + r0415*(WLx/2. + (i*WLy)/2.) - r0516*((2*WLx)/3. + (2*i*WLy)/3.) - r0514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r0515*WLz);
+dr0516_dt = (-(gt*r0516) - (gt + g2)*r0516)/2. - i*(-(conj(Em3a)*conj(r0805))/(4.*rt2) + (conj(Ep4a)*conj(r1615))/(4.*rt6) + (conj(Em4a)*r0504)/(4.*rt6) + (conj(Ep1a)*r1116)/4. - r0515*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*(WLx/2. + (i*WLy)/2.) - r0516*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r0516*WLz);
+dr0601_dt = -(gt*r0601) - i*((conj(Em2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0112))/(4.*rt2) + (conj(Em3a)*conj(r0114))/(8.*rt3) - (Em1a*r0609)/4. + (Em4a*r0613)/(4.*rt6) - r0602*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0601*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0601*WLz);
+dr0602_dt = -(gt*r0602) - i*((conj(Em2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0212))/(4.*rt2) + (conj(Em3a)*conj(r0214))/(8.*rt3) - (Em1a*r0610)/(4.*rt2) - (Ep4a*r0612)/(4.*rt6) + (Em4a*r0614)/8. - r0601*(WLx/2. - (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0602*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - (r0602*WLz)/2.);
+dr0603_dt = -(gt*r0603) - i*((conj(Em2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0312))/(4.*rt2) + (conj(Em3a)*conj(r0314))/(8.*rt3) - (Ep1a*r0609)/(4.*rt6) - (Em1a*r0611)/(4.*rt6) - (Ep4a*r0613)/8. + (Em4a*r0615)/8. - r0602*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0604*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0603*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0604_dt = -(gt*r0604) - i*((conj(Em2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0412))/(4.*rt2) + (conj(Em3a)*conj(r0414))/(8.*rt3) - (Ep1a*r0610)/(4.*rt2) - (Ep4a*r0614)/8. + (Em4a*r0616)/(4.*rt6) - r0605*(WLx/2. + (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0604*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + (r0604*WLz)/2.);
+dr0605_dt = -(gt*r0605) - i*((conj(Em2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0512))/(4.*rt2) + (conj(Em3a)*conj(r0514))/(8.*rt3) - (Ep1a*r0611)/4. - (Ep4a*r0615)/(4.*rt6) - r0604*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0605*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0605*WLz);
+dr0606_dt = gt/8. - gt*r0606 + (g1*r0909)/12. + (g1*r1010)/12. + (g2*r1212)/2. + (g2*r1313)/4. + (g2*r1414)/12. - i*((conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0612))/(4.*rt2) + (conj(Em3a)*conj(r0614))/(8.*rt3) - (Em2a*r0610)/(4.*rt6) - (Ep3a*r0612)/(4.*rt2) - (Em3a*r0614)/(8.*rt3) - conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0609_dt = (-(gt*r0609) - (gt + g1)*r0609)/2. - i*((conj(Ep2a)*conj(r0706))/(4.*rt6) + (conj(Ep3a)*conj(r0912))/(4.*rt2) + (conj(Em3a)*conj(r0914))/(8.*rt3) - (conj(Em1a)*r0601)/4. - (conj(Ep1a)*r0603)/(4.*rt6) + (conj(Em2a)*r1009)/(4.*rt6) - r0610*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0709*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0609*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0609*(-delta1 - v*Kvec1 - WLz/6.));
+dr0610_dt = (-(gt*r0610) - (gt + g1)*r0610)/2. - i*((conj(Ep2a)*conj(r0806))/(4.*rt6) + (conj(Ep3a)*conj(r1012))/(4.*rt2) + (conj(Em3a)*conj(r1014))/(8.*rt3) - (conj(Em1a)*r0602)/(4.*rt2) - (conj(Ep1a)*r0604)/(4.*rt2) - (conj(Em2a)*r0606)/(4.*rt6) + (delta1 + v*Kvec1)*r0610 + (conj(Em2a)*r1010)/(4.*rt6) - r0611*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0609*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0710*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0610*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0611_dt = (-(gt*r0611) - (gt + g1)*r0611)/2. - i*(-(conj(Em2a)*conj(r0706))/(4.*rt6) + (conj(Em2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1112))/(4.*rt2) + (conj(Em3a)*conj(r1114))/(8.*rt3) - (conj(Em1a)*r0603)/(4.*rt6) - (conj(Ep1a)*r0605)/4. - r0610*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0711*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0611*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0611*(-delta1 - v*Kvec1 + WLz/6.));
+dr0612_dt = (-(gt*r0612) - (gt + g2)*r0612)/2. - i*(-(conj(Ep4a)*r0602)/(4.*rt6) - (conj(Ep3a)*r0606)/(4.*rt2) + (conj(Em2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1212)/(4.*rt2) + (conj(Em3a)*r1412)/(8.*rt3) - r0613*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0612*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0613_dt = (-(gt*r0613) - (gt + g2)*r0613)/2. - i*(-(conj(Ep3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1312))/(4.*rt2) + (conj(Em4a)*r0601)/(4.*rt6) - (conj(Ep4a)*r0603)/8. + (conj(Em2a)*r1013)/(4.*rt6) + (conj(Em3a)*r1413)/(8.*rt3) - r0612*((2*WLx)/3. - (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0613*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0614_dt = (-(gt*r0614) - (gt + g2)*r0614)/2. - i*(-(conj(Ep3a)*conj(r0806))/(8.*rt3) + (conj(Ep3a)*conj(r1412))/(4.*rt2) + (conj(Em4a)*r0602)/8. - (conj(Ep4a)*r0604)/8. - (conj(Em3a)*r0606)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0614 + (conj(Em2a)*r1014)/(4.*rt6) + (conj(Em3a)*r1414)/(8.*rt3) - r0613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0614*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0615_dt = (-(gt*r0615) - (gt + g2)*r0615)/2. - i*(-(conj(Em3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1512))/(4.*rt2) + (conj(Em3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0603)/8. - (conj(Ep4a)*r0605)/(4.*rt6) + (conj(Em2a)*r1015)/(4.*rt6) - r0616*((2*WLx)/3. + (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0615*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0616_dt = (-(gt*r0616) - (gt + g2)*r0616)/2. - i*(-(conj(Em3a)*conj(r0806))/(4.*rt2) + (conj(Ep3a)*conj(r1612))/(4.*rt2) + (conj(Em3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0604)/(4.*rt6) + (conj(Em2a)*r1016)/(4.*rt6) - r0615*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0616*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0616*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0701_dt = -(gt*r0701) - i*(-(conj(Ep2a)*conj(r0109))/(4.*rt6) + (conj(Em2a)*conj(r0111))/(4.*rt6) + (conj(Ep3a)*conj(r0113))/8. + (conj(Em3a)*conj(r0115))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0701 - (Em1a*r0709)/4. + (Em4a*r0713)/(4.*rt6) - r0702*(WLx/2. + (i*WLy)/2.) + r0601*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0701*WLz);
+dr0702_dt = -(gt*r0702) - i*(-(conj(Ep2a)*conj(r0209))/(4.*rt6) + (conj(Em2a)*conj(r0211))/(4.*rt6) + (conj(Ep3a)*conj(r0213))/8. + (conj(Em3a)*conj(r0215))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0702 - (Em1a*r0710)/(4.*rt2) - (Ep4a*r0712)/(4.*rt6) + (Em4a*r0714)/8. - r0701*(WLx/2. - (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0602*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - (r0702*WLz)/2.);
+dr0703_dt = -(gt*r0703) - i*(-(conj(Ep2a)*conj(r0309))/(4.*rt6) + (conj(Em2a)*conj(r0311))/(4.*rt6) + (conj(Ep3a)*conj(r0313))/8. + (conj(Em3a)*conj(r0315))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 - (Ep1a*r0709)/(4.*rt6) - (Em1a*r0711)/(4.*rt6) - (Ep4a*r0713)/8. + (Em4a*r0715)/8. - r0702*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0704*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0603*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0704_dt = -(gt*r0704) - i*(-(conj(Ep2a)*conj(r0409))/(4.*rt6) + (conj(Em2a)*conj(r0411))/(4.*rt6) + (conj(Ep3a)*conj(r0413))/8. + (conj(Em3a)*conj(r0415))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0704 - (Ep1a*r0710)/(4.*rt2) - (Ep4a*r0714)/8. + (Em4a*r0716)/(4.*rt6) - r0705*(WLx/2. + (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0604*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + (r0704*WLz)/2.);
+dr0705_dt = -(gt*r0705) - i*(-(conj(Ep2a)*conj(r0509))/(4.*rt6) + (conj(Em2a)*conj(r0511))/(4.*rt6) + (conj(Ep3a)*conj(r0513))/8. + (conj(Em3a)*conj(r0515))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0705 - (Ep1a*r0711)/4. - (Ep4a*r0715)/(4.*rt6) - r0704*(WLx/2. - (i*WLy)/2.) + r0605*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0705*WLz);
+dr0706_dt = -(gt*r0706) + (g1*r1110)/12. + (g2*r1312)/(2.*rt2) + (g2*r1413)/(2.*rt3) + (g2*r1514)/(4.*rt3) - i*(-(conj(Ep2a)*conj(r0609))/(4.*rt6) + (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep3a)*conj(r0613))/8. + (conj(Em3a)*conj(r0615))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0706 - (Em2a*r0710)/(4.*rt6) - (Ep3a*r0712)/(4.*rt2) - (Em3a*r0714)/(8.*rt3) + r0606*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0706*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0707_dt = gt/8. - gt*r0707 + (g1*r0909)/12. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1414)/3. + (g2*r1515)/4. - i*(-(conj(Ep2a)*conj(r0709))/(4.*rt6) + (conj(Em2a)*conj(r0711))/(4.*rt6) + (conj(Ep3a)*conj(r0713))/8. + (conj(Em3a)*conj(r0715))/8. + (Ep2a*r0709)/(4.*rt6) - (Em2a*r0711)/(4.*rt6) - (Ep3a*r0713)/8. - (Em3a*r0715)/8. + conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*((conj(Ep3a)*conj(r0913))/8. + (conj(Em3a)*conj(r0915))/8. - (conj(Em1a)*r0701)/4. - (conj(Ep1a)*r0703)/(4.*rt6) + (conj(Ep2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0709 - (conj(Ep2a)*r0909)/(4.*rt6) + (conj(Em2a)*r1109)/(4.*rt6) + r0609*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0809*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0709*(-delta1 - v*Kvec1 - WLz/6.));
+dr0710_dt = (-(gt*r0710) - (gt + g1)*r0710)/2. - i*((conj(Ep2a)*conj(r0807))/(4.*rt6) - (conj(Ep2a)*conj(r1009))/(4.*rt6) + (conj(Ep3a)*conj(r1013))/8. + (conj(Em3a)*conj(r1015))/8. - (conj(Em1a)*r0702)/(4.*rt2) - (conj(Ep1a)*r0704)/(4.*rt2) - (conj(Em2a)*r0706)/(4.*rt6) + (delta1 + v*Kvec1)*r0710 + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0710 + (conj(Em2a)*r1110)/(4.*rt6) + r0610*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0711*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0709*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0711_dt = (-(gt*r0711) - (gt + g1)*r0711)/2. - i*(-(conj(Ep2a)*conj(r1109))/(4.*rt6) + (conj(Ep3a)*conj(r1113))/8. + (conj(Em3a)*conj(r1115))/8. - (conj(Em1a)*r0703)/(4.*rt6) - (conj(Ep1a)*r0705)/4. - (conj(Em2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0711 + (conj(Em2a)*r1111)/(4.*rt6) + r0611*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0811*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0711*(-delta1 - v*Kvec1 + WLz/6.));
+dr0712_dt = (-(gt*r0712) - (gt + g2)*r0712)/2. - i*(-(conj(Ep4a)*r0702)/(4.*rt6) - (conj(Ep3a)*r0706)/(4.*rt2) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0712 - (conj(Ep2a)*r0912)/(4.*rt6) + (conj(Em2a)*r1112)/(4.*rt6) + (conj(Ep3a)*r1312)/8. + (conj(Em3a)*r1512)/8. - r0713*((2*WLx)/3. + (2*i*WLy)/3.) + r0612*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0712*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0713_dt = (-(gt*r0713) - (gt + g2)*r0713)/2. - i*((conj(Em4a)*r0701)/(4.*rt6) - (conj(Ep4a)*r0703)/8. - (conj(Ep3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0713 - (conj(Ep2a)*r0913)/(4.*rt6) + (conj(Em2a)*r1113)/(4.*rt6) + (conj(Ep3a)*r1313)/8. + (conj(Em3a)*r1513)/8. - r0712*((2*WLx)/3. - (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0613*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0713*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0714_dt = (-(gt*r0714) - (gt + g2)*r0714)/2. - i*(-(conj(Ep3a)*conj(r0807))/(8.*rt3) + (conj(Ep3a)*conj(r1413))/8. + (conj(Em4a)*r0702)/8. - (conj(Ep4a)*r0704)/8. - (conj(Em3a)*r0706)/(8.*rt3) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0714 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0714 - (conj(Ep2a)*r0914)/(4.*rt6) + (conj(Em2a)*r1114)/(4.*rt6) + (conj(Em3a)*r1514)/8. - r0713*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0715*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0614*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0715_dt = (-(gt*r0715) - (gt + g2)*r0715)/2. - i*((conj(Ep3a)*conj(r1513))/8. + (conj(Em4a)*r0703)/8. - (conj(Ep4a)*r0705)/(4.*rt6) - (conj(Em3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0715 - (conj(Ep2a)*r0915)/(4.*rt6) + (conj(Em2a)*r1115)/(4.*rt6) + (conj(Em3a)*r1515)/8. - r0716*((2*WLx)/3. + (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0615*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0815*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0715*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0716_dt = (-(gt*r0716) - (gt + g2)*r0716)/2. - i*(-(conj(Em3a)*conj(r0807))/(4.*rt2) + (conj(Ep3a)*conj(r1613))/8. + (conj(Em3a)*conj(r1615))/8. + (conj(Em4a)*r0704)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0716 - (conj(Ep2a)*r0916)/(4.*rt6) + (conj(Em2a)*r1116)/(4.*rt6) - r0715*((2*WLx)/3. - (2*i*WLy)/3.) + r0616*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0816*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0716*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr0801_dt = -(gt*r0801) - i*(-(conj(Ep2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0114))/(8.*rt3) + (conj(Em3a)*conj(r0116))/(4.*rt2) - (Em1a*r0809)/4. + (Em4a*r0813)/(4.*rt6) - r0802*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0801*WLz);
+dr0802_dt = -(gt*r0802) - i*(-(conj(Ep2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0214))/(8.*rt3) + (conj(Em3a)*conj(r0216))/(4.*rt2) - (Em1a*r0810)/(4.*rt2) - (Ep4a*r0812)/(4.*rt6) + (Em4a*r0814)/8. - r0801*(WLx/2. - (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - (r0802*WLz)/2.);
+dr0803_dt = -(gt*r0803) - i*(-(conj(Ep2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0314))/(8.*rt3) + (conj(Em3a)*conj(r0316))/(4.*rt2) - (Ep1a*r0809)/(4.*rt6) - (Em1a*r0811)/(4.*rt6) - (Ep4a*r0813)/8. + (Em4a*r0815)/8. - r0802*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0804*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0804_dt = -(gt*r0804) - i*(-(conj(Ep2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0414))/(8.*rt3) + (conj(Em3a)*conj(r0416))/(4.*rt2) - (Ep1a*r0810)/(4.*rt2) - (Ep4a*r0814)/8. + (Em4a*r0816)/(4.*rt6) - r0805*(WLx/2. + (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + (r0804*WLz)/2.);
+dr0805_dt = -(gt*r0805) - i*(-(conj(Ep2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0514))/(8.*rt3) + (conj(Em3a)*conj(r0516))/(4.*rt2) - (Ep1a*r0811)/4. - (Ep4a*r0815)/(4.*rt6) - r0804*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + r0805*WLz);
+dr0806_dt = -(gt*r0806) - (g1*r1109)/12. + (g2*r1412)/(2.*rt6) + (g2*r1513)/4. + (g2*r1614)/(2.*rt6) - i*(-(conj(Ep2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0614))/(8.*rt3) + (conj(Em3a)*conj(r0616))/(4.*rt2) - (Em2a*r0810)/(4.*rt6) - (Ep3a*r0812)/(4.*rt2) - (Em3a*r0814)/(8.*rt3) + r0706*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0807_dt = -(gt*r0807) + (g1*r1009)/12. + (g2*r1413)/(4.*rt3) + (g2*r1514)/(2.*rt3) + (g2*r1615)/(2.*rt2) - i*(-(conj(Ep2a)*conj(r0710))/(4.*rt6) + (conj(Ep3a)*conj(r0714))/(8.*rt3) + (conj(Em3a)*conj(r0716))/(4.*rt2) - (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0807 + (Ep2a*r0809)/(4.*rt6) - (Em2a*r0811)/(4.*rt6) - (Ep3a*r0813)/8. - (Em3a*r0815)/8. + r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0808*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0808_dt = gt/8. - gt*r0808 + (g1*r1010)/12. + (g1*r1111)/12. + (g2*r1414)/12. + (g2*r1515)/4. + (g2*r1616)/2. - i*(-(conj(Ep2a)*conj(r0810))/(4.*rt6) + (conj(Ep3a)*conj(r0814))/(8.*rt3) + (conj(Em3a)*conj(r0816))/(4.*rt2) + (Ep2a*r0810)/(4.*rt6) - (Ep3a*r0814)/(8.*rt3) - (Em3a*r0816)/(4.*rt2) + conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0809_dt = (-(gt*r0809) - (gt + g1)*r0809)/2. - i*((conj(Ep3a)*conj(r0914))/(8.*rt3) + (conj(Em3a)*conj(r0916))/(4.*rt2) - (conj(Em1a)*r0801)/4. - (conj(Ep1a)*r0803)/(4.*rt6) + (conj(Ep2a)*r0807)/(4.*rt6) - (conj(Ep2a)*r1009)/(4.*rt6) + r0709*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-delta1 - v*Kvec1 - WLz/6.) + r0809*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0810_dt = (-(gt*r0810) - (gt + g1)*r0810)/2. - i*((conj(Ep3a)*conj(r1014))/(8.*rt3) + (conj(Em3a)*conj(r1016))/(4.*rt2) - (conj(Em1a)*r0802)/(4.*rt2) - (conj(Ep1a)*r0804)/(4.*rt2) - (conj(Em2a)*r0806)/(4.*rt6) + (conj(Ep2a)*r0808)/(4.*rt6) + (delta1 + v*Kvec1)*r0810 - (conj(Ep2a)*r1010)/(4.*rt6) + r0710*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0811*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0811_dt = (-(gt*r0811) - (gt + g1)*r0811)/2. - i*(-(conj(Ep2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1114))/(8.*rt3) + (conj(Em3a)*conj(r1116))/(4.*rt2) - (conj(Em1a)*r0803)/(4.*rt6) - (conj(Ep1a)*r0805)/4. - (conj(Em2a)*r0807)/(4.*rt6) + r0711*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0811*(-delta1 - v*Kvec1 + WLz/6.) + r0811*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0812_dt = (-(gt*r0812) - (gt + g2)*r0812)/2. - i*(-(conj(Ep4a)*r0802)/(4.*rt6) - (conj(Ep3a)*r0806)/(4.*rt2) - (conj(Ep2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1412)/(8.*rt3) + (conj(Em3a)*r1612)/(4.*rt2) - r0813*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0812*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0813_dt = (-(gt*r0813) - (gt + g2)*r0813)/2. - i*((conj(Em4a)*r0801)/(4.*rt6) - (conj(Ep4a)*r0803)/8. - (conj(Ep3a)*r0807)/8. - (conj(Ep2a)*r1013)/(4.*rt6) + (conj(Ep3a)*r1413)/(8.*rt3) + (conj(Em3a)*r1613)/(4.*rt2) - r0812*((2*WLx)/3. - (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0813*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0814_dt = (-(gt*r0814) - (gt + g2)*r0814)/2. - i*((conj(Em4a)*r0802)/8. - (conj(Ep4a)*r0804)/8. - (conj(Em3a)*r0806)/(8.*rt3) - (conj(Ep3a)*r0808)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0814 - (conj(Ep2a)*r1014)/(4.*rt6) + (conj(Ep3a)*r1414)/(8.*rt3) + (conj(Em3a)*r1614)/(4.*rt2) - r0813*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0815*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0815_dt = (-(gt*r0815) - (gt + g2)*r0815)/2. - i*((conj(Ep3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0803)/8. - (conj(Ep4a)*r0805)/(4.*rt6) - (conj(Em3a)*r0807)/8. - (conj(Ep2a)*r1015)/(4.*rt6) + (conj(Em3a)*r1615)/(4.*rt2) - r0816*((2*WLx)/3. + (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0815*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0815*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0816_dt = (-(gt*r0816) - (gt + g2)*r0816)/2. - i*((conj(Ep3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0804)/(4.*rt6) - (conj(Em3a)*r0808)/(4.*rt2) - (conj(Ep2a)*r1016)/(4.*rt6) + (conj(Em3a)*r1616)/(4.*rt2) - r0815*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0816*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0816*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0909_dt = -((gt + g1)*r0909) - i*(-(conj(Em1a)*conj(r0109))/4. - (conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Ep2a)*conj(r0709))/(4.*rt6) + (Em1a*r0109)/4. + (Ep1a*r0309)/(4.*rt6) - (Ep2a*r0709)/(4.*rt6) - conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr0912_dt = (-((gt + g1)*r0912) - (gt + g2)*r0912)/2. - i*(-(conj(Ep4a)*conj(r0209))/(4.*rt6) - (conj(Ep3a)*conj(r0609))/(4.*rt2) + (Em1a*r0112)/4. + (Ep1a*r0312)/(4.*rt6) - (Ep2a*r0712)/(4.*rt6) - r0913*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0912*(-delta1 - v*Kvec1 - WLz/6.) - r0912*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0913_dt = (-((gt + g1)*r0913) - (gt + g2)*r0913)/2. - i*((conj(Em4a)*conj(r0109))/(4.*rt6) - (conj(Ep4a)*conj(r0309))/8. - (conj(Ep3a)*conj(r0709))/8. + (Em1a*r0113)/4. + (Ep1a*r0313)/(4.*rt6) - (Ep2a*r0713)/(4.*rt6) - r0912*((2*WLx)/3. - (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0913*(-delta1 - v*Kvec1 - WLz/6.) - r0913*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0914_dt = (-((gt + g1)*r0914) - (gt + g2)*r0914)/2. - i*((conj(Em4a)*conj(r0209))/8. - (conj(Ep4a)*conj(r0409))/8. - (conj(Em3a)*conj(r0609))/(8.*rt3) - (conj(Ep3a)*conj(r0809))/(8.*rt3) + (Em1a*r0114)/4. + (Ep1a*r0314)/(4.*rt6) - (Ep2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0914 - r0913*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0915*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0914*(-delta1 - v*Kvec1 - WLz/6.));
+dr0915_dt = (-((gt + g1)*r0915) - (gt + g2)*r0915)/2. - i*((conj(Em4a)*conj(r0309))/8. - (conj(Ep4a)*conj(r0509))/(4.*rt6) - (conj(Em3a)*conj(r0709))/8. + (Em1a*r0115)/4. + (Ep1a*r0315)/(4.*rt6) - (Ep2a*r0715)/(4.*rt6) - r0916*((2*WLx)/3. + (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0915*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0915*(-delta1 - v*Kvec1 - WLz/6.));
+dr0916_dt = (-((gt + g1)*r0916) - (gt + g2)*r0916)/2. - i*((conj(Em4a)*conj(r0409))/(4.*rt6) - (conj(Em3a)*conj(r0809))/(4.*rt2) + (Em1a*r0116)/4. + (Ep1a*r0316)/(4.*rt6) - (Ep2a*r0716)/(4.*rt6) - r0915*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0916*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0916*(-delta1 - v*Kvec1 - WLz/6.));
+dr1009_dt = -((gt + g1)*r1009) - i*(-(conj(Em1a)*conj(r0110))/4. - (conj(Ep1a)*conj(r0310))/(4.*rt6) + (conj(Ep2a)*conj(r0710))/(4.*rt6) + (Em1a*r0209)/(4.*rt2) + (Ep1a*r0409)/(4.*rt2) + (Em2a*r0609)/(4.*rt6) - (Ep2a*r0809)/(4.*rt6) - (delta1 + v*Kvec1)*r1009 + r0909*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1009*(-delta1 - v*Kvec1 - WLz/6.));
+dr1010_dt = -((gt + g1)*r1010) - i*(-(conj(Em1a)*conj(r0210))/(4.*rt2) - (conj(Ep1a)*conj(r0410))/(4.*rt2) - (conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep2a)*conj(r0810))/(4.*rt6) + (Em1a*r0210)/(4.*rt2) + (Ep1a*r0410)/(4.*rt2) + (Em2a*r0610)/(4.*rt6) - (Ep2a*r0810)/(4.*rt6) + conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1012_dt = (-((gt + g1)*r1012) - (gt + g2)*r1012)/2. - i*(-(conj(Ep4a)*conj(r0210))/(4.*rt6) - (conj(Ep3a)*conj(r0610))/(4.*rt2) + (Em1a*r0212)/(4.*rt2) + (Ep1a*r0412)/(4.*rt2) + (Em2a*r0612)/(4.*rt6) - (Ep2a*r0812)/(4.*rt6) - (delta1 + v*Kvec1)*r1012 - r1013*((2*WLx)/3. + (2*i*WLy)/3.) + r0912*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1012*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1013_dt = (-((gt + g1)*r1013) - (gt + g2)*r1013)/2. - i*((conj(Em4a)*conj(r0110))/(4.*rt6) - (conj(Ep4a)*conj(r0310))/8. - (conj(Ep3a)*conj(r0710))/8. + (Em1a*r0213)/(4.*rt2) + (Ep1a*r0413)/(4.*rt2) + (Em2a*r0613)/(4.*rt6) - (Ep2a*r0813)/(4.*rt6) - (delta1 + v*Kvec1)*r1013 - r1012*((2*WLx)/3. - (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0913*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1013*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1014_dt = (-((gt + g1)*r1014) - (gt + g2)*r1014)/2. - i*((conj(Em4a)*conj(r0210))/8. - (conj(Ep4a)*conj(r0410))/8. - (conj(Em3a)*conj(r0610))/(8.*rt3) - (conj(Ep3a)*conj(r0810))/(8.*rt3) + (Em1a*r0214)/(4.*rt2) + (Ep1a*r0414)/(4.*rt2) + (Em2a*r0614)/(4.*rt6) - (Ep2a*r0814)/(4.*rt6) - (delta1 + v*Kvec1)*r1014 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1014 - r1013*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1015*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0914*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1015_dt = (-((gt + g1)*r1015) - (gt + g2)*r1015)/2. - i*((conj(Em4a)*conj(r0310))/8. - (conj(Ep4a)*conj(r0510))/(4.*rt6) - (conj(Em3a)*conj(r0710))/8. + (Em1a*r0215)/(4.*rt2) + (Ep1a*r0415)/(4.*rt2) + (Em2a*r0615)/(4.*rt6) - (Ep2a*r0815)/(4.*rt6) - (delta1 + v*Kvec1)*r1015 - r1016*((2*WLx)/3. + (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0915*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1115*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1015*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1016_dt = (-((gt + g1)*r1016) - (gt + g2)*r1016)/2. - i*((conj(Em4a)*conj(r0410))/(4.*rt6) - (conj(Em3a)*conj(r0810))/(4.*rt2) + (Em1a*r0216)/(4.*rt2) + (Ep1a*r0416)/(4.*rt2) + (Em2a*r0616)/(4.*rt6) - (Ep2a*r0816)/(4.*rt6) - (delta1 + v*Kvec1)*r1016 - r1015*((2*WLx)/3. - (2*i*WLy)/3.) + r0916*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1116*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1016*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr1109_dt = -((gt + g1)*r1109) - i*(-(conj(Em1a)*conj(r0111))/4. - (conj(Ep1a)*conj(r0311))/(4.*rt6) + (conj(Ep2a)*conj(r0711))/(4.*rt6) + (Em1a*r0309)/(4.*rt6) + (Ep1a*r0509)/4. + (Em2a*r0709)/(4.*rt6) + r1009*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-delta1 - v*Kvec1 - WLz/6.) + r1109*(-delta1 - v*Kvec1 + WLz/6.));
+dr1110_dt = -((gt + g1)*r1110) - i*(-(conj(Em1a)*conj(r0211))/(4.*rt2) - (conj(Ep1a)*conj(r0411))/(4.*rt2) - (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep2a)*conj(r0811))/(4.*rt6) + (Em1a*r0310)/(4.*rt6) + (Ep1a*r0510)/4. + (Em2a*r0710)/(4.*rt6) + (delta1 + v*Kvec1)*r1110 + r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-delta1 - v*Kvec1 + WLz/6.));
+dr1111_dt = -((gt + g1)*r1111) - i*(-(conj(Em1a)*conj(r0311))/(4.*rt6) - (conj(Ep1a)*conj(r0511))/4. - (conj(Em2a)*conj(r0711))/(4.*rt6) + (Em1a*r0311)/(4.*rt6) + (Ep1a*r0511)/4. + (Em2a*r0711)/(4.*rt6) + conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1112_dt = (-((gt + g1)*r1112) - (gt + g2)*r1112)/2. - i*(-(conj(Ep4a)*conj(r0211))/(4.*rt6) - (conj(Ep3a)*conj(r0611))/(4.*rt2) + (Em1a*r0312)/(4.*rt6) + (Ep1a*r0512)/4. + (Em2a*r0712)/(4.*rt6) - r1113*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-delta1 - v*Kvec1 + WLz/6.) - r1112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1113_dt = (-((gt + g1)*r1113) - (gt + g2)*r1113)/2. - i*((conj(Em4a)*conj(r0111))/(4.*rt6) - (conj(Ep4a)*conj(r0311))/8. - (conj(Ep3a)*conj(r0711))/8. + (Em1a*r0313)/(4.*rt6) + (Ep1a*r0513)/4. + (Em2a*r0713)/(4.*rt6) - r1112*((2*WLx)/3. - (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-delta1 - v*Kvec1 + WLz/6.) - r1113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1114_dt = (-((gt + g1)*r1114) - (gt + g2)*r1114)/2. - i*((conj(Em4a)*conj(r0211))/8. - (conj(Ep4a)*conj(r0411))/8. - (conj(Em3a)*conj(r0611))/(8.*rt3) - (conj(Ep3a)*conj(r0811))/(8.*rt3) + (Em1a*r0314)/(4.*rt6) + (Ep1a*r0514)/4. + (Em2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1114 - r1113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-delta1 - v*Kvec1 + WLz/6.));
+dr1115_dt = (-((gt + g1)*r1115) - (gt + g2)*r1115)/2. - i*((conj(Em4a)*conj(r0311))/8. - (conj(Ep4a)*conj(r0511))/(4.*rt6) - (conj(Em3a)*conj(r0711))/8. + (Em1a*r0315)/(4.*rt6) + (Ep1a*r0515)/4. + (Em2a*r0715)/(4.*rt6) - r1116*((2*WLx)/3. + (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r1115*(-delta1 - v*Kvec1 + WLz/6.));
+dr1116_dt = (-((gt + g1)*r1116) - (gt + g2)*r1116)/2. - i*((conj(Em4a)*conj(r0411))/(4.*rt6) - (conj(Em3a)*conj(r0811))/(4.*rt2) + (Em1a*r0316)/(4.*rt6) + (Ep1a*r0516)/4. + (Em2a*r0716)/(4.*rt6) - r1115*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r1116*(-delta1 - v*Kvec1 + WLz/6.));
+dr1212_dt = -((gt + g2)*r1212) - i*(-(conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Ep3a)*conj(r0612))/(4.*rt2) + (Ep4a*r0212)/(4.*rt6) + (Ep3a*r0612)/(4.*rt2) + r1312*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.));
+dr1312_dt = -((gt + g2)*r1312) - i*(-(conj(Ep4a)*conj(r0213))/(4.*rt6) - (conj(Ep3a)*conj(r0613))/(4.*rt2) - (Em4a*r0112)/(4.*rt6) + (Ep4a*r0312)/8. + (Ep3a*r0712)/8. + r1212*((2*WLx)/3. + (2*i*WLy)/3.) - r1313*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1313_dt = -((gt + g2)*r1313) - i*((conj(Em4a)*conj(r0113))/(4.*rt6) - (conj(Ep4a)*conj(r0313))/8. - (conj(Ep3a)*conj(r0713))/8. - (Em4a*r0113)/(4.*rt6) + (Ep4a*r0313)/8. + (Ep3a*r0713)/8. - r1312*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1412_dt = -((gt + g2)*r1412) - i*(-(conj(Ep4a)*conj(r0214))/(4.*rt6) - (conj(Ep3a)*conj(r0614))/(4.*rt2) - (Em4a*r0212)/8. + (Ep4a*r0412)/8. + (Em3a*r0612)/(8.*rt3) + (Ep3a*r0812)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1412 - r1413*((2*WLx)/3. + (2*i*WLy)/3.) + r1512*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1413_dt = -((gt + g2)*r1413) - i*((conj(Em4a)*conj(r0114))/(4.*rt6) - (conj(Ep4a)*conj(r0314))/8. - (conj(Ep3a)*conj(r0714))/8. - (Em4a*r0213)/8. + (Ep4a*r0413)/8. + (Em3a*r0613)/(8.*rt3) + (Ep3a*r0813)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1413 - r1412*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1313*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1414_dt = -((gt + g2)*r1414) - i*((conj(Em4a)*conj(r0214))/8. - (conj(Ep4a)*conj(r0414))/8. - (conj(Em3a)*conj(r0614))/(8.*rt3) - (conj(Ep3a)*conj(r0814))/(8.*rt3) - (Em4a*r0214)/8. + (Ep4a*r0414)/8. + (Em3a*r0614)/(8.*rt3) + (Ep3a*r0814)/(8.*rt3) - r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1512_dt = -((gt + g2)*r1512) - i*(-(conj(Ep4a)*conj(r0215))/(4.*rt6) - (conj(Ep3a)*conj(r0615))/(4.*rt2) - (Em4a*r0312)/8. + (Ep4a*r0512)/(4.*rt6) + (Em3a*r0712)/8. + r1612*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1513_dt = -((gt + g2)*r1513) - i*((conj(Em4a)*conj(r0115))/(4.*rt6) - (conj(Ep4a)*conj(r0315))/8. - (conj(Ep3a)*conj(r0715))/8. - (Em4a*r0313)/8. + (Ep4a*r0513)/(4.*rt6) + (Em3a*r0713)/8. - r1512*((2*WLx)/3. - (2*i*WLy)/3.) + r1613*((2*WLx)/3. - (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1514_dt = -((gt + g2)*r1514) - i*((conj(Em4a)*conj(r0215))/8. - (conj(Ep4a)*conj(r0415))/8. - (conj(Em3a)*conj(r0615))/(8.*rt3) - (conj(Ep3a)*conj(r0815))/(8.*rt3) - (Em4a*r0314)/8. + (Ep4a*r0514)/(4.*rt6) + (Em3a*r0714)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1514 + r1614*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1514*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1515_dt = -((gt + g2)*r1515) - i*((conj(Em4a)*conj(r0315))/8. - (conj(Ep4a)*conj(r0515))/(4.*rt6) - (conj(Em3a)*conj(r0715))/8. - (Em4a*r0315)/8. + (Ep4a*r0515)/(4.*rt6) + (Em3a*r0715)/8. + r1615*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.) - r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1612_dt = -((gt + g2)*r1612) - i*(-(conj(Ep4a)*conj(r0216))/(4.*rt6) - (conj(Ep3a)*conj(r0616))/(4.*rt2) - (Em4a*r0412)/(4.*rt6) + (Em3a*r0812)/(4.*rt2) + r1512*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*((2*WLx)/3. + (2*i*WLy)/3.) + r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1613_dt = -((gt + g2)*r1613) - i*((conj(Em4a)*conj(r0116))/(4.*rt6) - (conj(Ep4a)*conj(r0316))/8. - (conj(Ep3a)*conj(r0716))/8. - (Em4a*r0413)/(4.*rt6) + (Em3a*r0813)/(4.*rt2) - r1612*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1614_dt = -((gt + g2)*r1614) - i*((conj(Em4a)*conj(r0216))/8. - (conj(Ep4a)*conj(r0416))/8. - (conj(Em3a)*conj(r0616))/(8.*rt3) - (conj(Ep3a)*conj(r0816))/(8.*rt3) - (Em4a*r0414)/(4.*rt6) + (Em3a*r0814)/(4.*rt2) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1614 + r1514*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1614*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr1615_dt = -((gt + g2)*r1615) - i*((conj(Em4a)*conj(r0316))/8. - (conj(Ep4a)*conj(r0516))/(4.*rt6) - (conj(Em3a)*conj(r0716))/8. - (Em4a*r0415)/(4.*rt6) + (Em3a*r0815)/(4.*rt2) + r1515*((2*WLx)/3. + (2*i*WLy)/3.) - r1616*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1616_dt = -((gt + g2)*r1616) - i*((conj(Em4a)*conj(r0416))/(4.*rt6) - (conj(Em3a)*conj(r0816))/(4.*rt2) - (Em4a*r0416)/(4.*rt6) + (Em3a*r0816)/(4.*rt2) - r1615*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.));
+//---------------- RbEquations.txt ends  ------------------
+                                        ]]>
+        </operator>
+                                <!--
+                                                         According to xmds2 docs operator kind="ip" should be faster
+                                                         but our codes runs about 5% to 10% slower with it.
+                                                         Maybe because we very close to the stiff condition so I use "ex" kind
+                                                         <operator kind="ip" constant="yes">
+                                         -->
+                                <operator kind="ex" constant="yes" type="imaginary">
+                                        <operator_names>Lt</operator_names>
+                                        <![CDATA[
+                                        Lt = -i/c*kt;
+                                        ]]>
+                                </operator>
+        <integration_vectors>E_field</integration_vectors>
+                                <dependencies>density_matrix</dependencies>
+                                <![CDATA[
+                                //read from Mathematica generated RbPropEquations.txt
+//---------------- RbPropEquations.txt starts ------------------
+dEp1_dz = -((i*Ndens*(rt2*conj(r0309) + rt6*(conj(r0410) + rt2*conj(r0511)))*eta1)/(rt2*rt6)) - Lt[Ep1];
+dEm1_dz = -((i*Ndens*(rt2*rt6*conj(r0109) + rt6*conj(r0210) + rt2*conj(r0311))*eta1)/(rt2*rt6)) - Lt[Em1];
+dEp2_dz = (i*Ndens*(conj(r0709) + conj(r0810))*eta1)/rt6 - Lt[Ep2];
+dEm2_dz = -((i*Ndens*(conj(r0610) + conj(r0711))*eta1)/rt6) - Lt[Em2];
+dEp3_dz = -((i*Ndens*(rt2*rt3*conj(r0612) + rt3*conj(r0713) + conj(r0814))*eta2)/rt3) - Lt[Ep3];
+dEm3_dz = -((i*Ndens*(conj(r0614) + rt3*(conj(r0715) + rt2*conj(r0816)))*eta2)/rt3) - Lt[Em3];
+dEp4_dz = -((i*Ndens*(rt2*conj(r0212) + rt3*conj(r0313) + rt3*conj(r0414) + rt2*conj(r0515))*eta2)/rt3) - Lt[Ep4];
+dEm4_dz = (i*Ndens*(rt2*conj(r0113) + rt3*conj(r0214) + rt3*conj(r0315) + rt2*conj(r0416))*eta2)/rt3 - Lt[Em4];
+//---------------- RbPropEquations.txt ends  ------------------
+                                ]]>
+                        </operators>
+                </integrate>
+        </sequence>
+
+
+
+        <!-- The output to generate -->
+        <output format="binary" filename="realistic_Rb_and_fields.xsil">
+                <group>
+      <sampling basis="t(1000) " initial_sample="yes">
+                                <dependencies>E_field_avgd</dependencies>
+                                <moments>Ip1_out Im1_out Ip2_out Im2_out Ip3_out Im3_out Ip4_out Im4_out</moments>
+                                <![CDATA[
+                                Ip1_out = mod2(Ep1a);
+                                Im1_out = mod2(Em1a);
+                                Ip2_out = mod2(Ep2a);
+                                Im2_out = mod2(Em2a);
+                                Ip3_out = mod2(Ep3a);
+                                Im3_out = mod2(Em3a);
+                                Ip4_out = mod2(Ep4a);
+                                Im4_out = mod2(Em4a);
+                                ]]>
+                        </sampling>
+                </group>
+        </output>
+
+
+<info>
+Script compiled with XMDS2 version VERSION_PLACEHOLDER (SUBVERSION_REVISION_PLACEHOLDER)
+See http://www.xmds.org for more information.
+
+Variables that can be specified on the command line:
+  Command line argument Ep1o = 1.000000e+04
+  Command line argument Em1o = 1.000000e+04
+  Command line argument Ep2o = 1.000000e+02
+  Command line argument Em2o = 1.000000e+02
+  Command line argument Ep3o = 1.000000e+01
+  Command line argument Em3o = 1.000000e+01
+  Command line argument Ep4o = 1.000000e+01
+  Command line argument Em4o = 1.000000e+01
+  Command line argument delta1 = 0.000000e+00
+  Command line argument delta2 = 0.000000e+00
+  Command line argument delta3 = 0.000000e+00
+  Command line argument Pwidth = 4.000000e-07
+  Command line argument Lcell = 1.000000e-01
+  Command line argument Ndens = 1.000000e+15
+  Command line argument WLx = 0.000000e+00
+  Command line argument WLy = 0.000000e+00
+  Command line argument WLz = 0.000000e+00
+  Command line argument Temperature = 1.000000e-03
+</info>
+
+<XSIL Name="moment_group_1">
+  <Param Name="n_independent">2</Param>
+  <Array Name="variables" Type="Text">
+    <Dim>10</Dim>
+    <Stream><Metalink Format="Text" Delimiter=" \n"/>
+z t Ip1_out Im1_out Ip2_out Im2_out Ip3_out Im3_out Ip4_out Im4_out 
+    </Stream>
+  </Array>
+  <Array Name="data" Type="double">
+    <Dim>101</Dim>
+    <Dim>1000</Dim>
+    <Dim>10</Dim>
+    <Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="LittleEndian"/>
+realistic_Rb_and_fields_expected_mg0.dat
+    </Stream>
+  </Array>
+</XSIL>
+</simulation>
diff --git a/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected_mg0.dat b/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected_mg0.dat
new file mode 100644
index 0000000..c301bc7
Binary files /dev/null and b/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected_mg0.dat differ
-- 
cgit v1.2.3


From c9c327cc7ed2ce8f7438d64961696ca631979987 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Tue, 27 Nov 2012 22:26:36 -0500
Subject: changed argument and variables name to a shorter version

thanks to my bugreport and patch xmds can now handle multiple similar
sounding arguments
---
 .../realistic_Rb_and_fields.xmds                   | 38 ++++++++++------------
 1 file changed, 17 insertions(+), 21 deletions(-)

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
index ea6252a..7e310ae 100644
--- a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
+++ b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
@@ -1,7 +1,7 @@
 <?xml version="1.0"?>
 <simulation xmds-version="2">
 	<testing>
-		<arguments> --Ndens=1e15 --Lcell=10.0e-2  --Temperature=1e-3  --Pwidth=0.4e-6  --delta1=0 --delta2=0 --delta3=0  --E1o=0 --E2o=1e2 --E3o=0 --E4o=0</arguments>
+		<arguments> --Ndens=1e15 --Lcell=10.0e-2  --Temperature=1e-3  --Pwidth=0.4e-6  --delta1=0 --delta2=0 --delta3=0  --Ep1o=1e4 --Ep2o=1e2 --Ep3o=1e1 --Ep4o=1e1 --Em1o=1e4 --Em2o=1e2 --Em3o=1e1 --Em4o=1e1 --WLx=0 --WLy=0 --WLz=0</arguments>
 		<xsil_file name="realistic_Rb_and_fields.xsil" expected="realistic_Rb_and_fields_expected.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5">
 			<moment_group number="0" absolute_tolerance="1e-7" relative_tolerance="1e-6" />
 		</xsil_file>
@@ -102,18 +102,14 @@ const double rt2 = 1.4142135623730951;
 		<benchmark />
     <arguments>
 			<!-- Rabi frequency divided by 2 in [1/s] -->
-			<!--
-				Had to be very verbal with fields names, since otherwise short options name
-				algorithm runs out of choices
-			-->
-      <argument name="Ep1o_field" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
-      <argument name="Em1o_field" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
-      <argument name="Ep2o_field" type="real" default_value="0.05*(2*M_PI*1e6)" />
-      <argument name="Em2o_field" type="real" default_value="0.05*(2*M_PI*1e6)" />
-      <argument name="Ep3o_field" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
-      <argument name="Em3o_field" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
-      <argument name="Ep4o_field" type="real" default_value=".01*(2*M_PI*1e6)" />
-      <argument name="Em4o_field" type="real" default_value=".01*(2*M_PI*1e6)" />
+      <argument name="Ep1o" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+      <argument name="Em1o" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+      <argument name="Ep2o" type="real" default_value="0.05*(2*M_PI*1e6)" />
+      <argument name="Em2o" type="real" default_value="0.05*(2*M_PI*1e6)" />
+      <argument name="Ep3o" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+      <argument name="Em3o" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+      <argument name="Ep4o" type="real" default_value=".01*(2*M_PI*1e6)" />
+      <argument name="Em4o" type="real" default_value=".01*(2*M_PI*1e6)" />
 			<!-- Fields detuning in [1/s] -->
       <argument name="delta1"  type="real" default_value="0.0" />
       <argument name="delta2"  type="real" default_value="0.0" />
@@ -185,14 +181,14 @@ const double rt2 = 1.4142135623730951;
 			<![CDATA[
 			// Initial (at starting 'z' position) electromagnetic field does not depend on detuning
 			// as well as time
-			Ep1=Ep1o_field;
-			Em1=Em1o_field;
-			Ep2=Ep2o_field*exp(-pow( ((t-0.0)/Pwidth),2) );
-			Em2=Em2o_field*exp(-pow( ((t-0.0)/Pwidth),2) );
-			Ep3=Ep3o_field;
-			Em3=Em3o_field;
-			Ep4=Ep4o_field;
-			Em4=Em4o_field;
+			Ep1=Ep1o;
+			Em1=Em1o;
+			Ep2=Ep2o*exp(-pow( ((t-0.0)/Pwidth),2) );
+			Em2=Em2o*exp(-pow( ((t-0.0)/Pwidth),2) );
+			Ep3=Ep3o;
+			Em3=Em3o;
+			Ep4=Ep4o;
+			Em4=Em4o;
 			]]>
 		</initialisation>
 	</vector>
-- 
cgit v1.2.3


From df1ce8081df7a44e108bb290d06bbdf0dd574e38 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Tue, 27 Nov 2012 23:21:05 -0500
Subject: change Maxwell probability related vectors to static one

---
 .../realistic_Rb_and_fields/realistic_Rb_and_fields.xmds | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
index 7e310ae..5b00664 100644
--- a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
+++ b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
@@ -194,29 +194,29 @@ const double rt2 = 1.4142135623730951;
 	</vector>
 
 	<!--Maxwell distribution probability p(v)-->
-	<computed_vector name="Maxwell_distribution_probabilities" dimensions="v" type="real">
+	<vector name="Maxwell_distribution_probabilities" dimensions="v" type="real">
 		<components>probability_v</components>
-		<evaluation>
+		<initialisation>
 			<![CDATA[
 			// TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during  the script lifetime since 'v' is fixed.
 			probability_v=1.0/(v_thermal_averaged*sqrt(2*M_PI)) * exp( - mod2(v/v_thermal_averaged)/2.0 ); 
 			]]>
-		</evaluation>
-	</computed_vector>
+		</initialisation>
+	</vector>
 
 	<!--Maxwell distribution norm sum(p(v))
 			 Needed since we sum over the grid instead of true integral,
 			 we also have finite cut off velocities-->
-	<computed_vector name="Maxwell_distribution_probabilities_norm" dimensions="" type="real">
+	<vector name="Maxwell_distribution_probabilities_norm" dimensions="" type="real">
 		<components>probability_v_norm</components>
-		<evaluation>
+		<initialisation>
 			<dependencies basis="v">Maxwell_distribution_probabilities</dependencies>
 			<![CDATA[
 			// TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during  the script lifetime since 'v' is fixed.
 			probability_v_norm=probability_v;
 			]]>
-		</evaluation>
-	</computed_vector>
+		</initialisation>
+	</vector>
 
 
 	<!-- Averaged across Maxwell distribution fields amplitudes -->
-- 
cgit v1.2.3


From 94f7490fc5155e4f319c0872690f91748acdc28f Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Wed, 28 Nov 2012 00:30:41 -0500
Subject: some mathematica generated files are now inserted via c++ #include

---
 xmds2/realistic_Rb_and_fields/RbAtomConstants.h    |  15 ++
 xmds2/realistic_Rb_and_fields/RbInits.h            | 138 +++++++++++++++++
 .../realistic_Rb_and_fields.xmds                   | 165 ++-------------------
 3 files changed, 163 insertions(+), 155 deletions(-)
 create mode 100644 xmds2/realistic_Rb_and_fields/RbAtomConstants.h
 create mode 100644 xmds2/realistic_Rb_and_fields/RbInits.h

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/RbAtomConstants.h b/xmds2/realistic_Rb_and_fields/RbAtomConstants.h
new file mode 100644
index 0000000..5be3a6e
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/RbAtomConstants.h
@@ -0,0 +1,15 @@
+//---------------- Constants.txt starts ------------------
+const double ha0 = 2.1471788680034824e10;
+const double ha1 = 2.558764384495815e9;
+const double g1 = 3.612847284945266e7;
+const double ha2 = 5.323020344462938e8;
+const double hb2 = 7.85178251911697e7;
+const double g2 = 3.8117309832741246e7;
+const double lambda1 = 7.949788511562656e-7;
+const double lambda2 = 7.802412096860509e-7;
+const double eta1 = 5.450949336831401e-6;
+const double eta2 = 5.5397657647874e-6;
+const double rt6 = 2.449489742783178;
+const double rt3 = 1.7320508075688772;
+const double rt2 = 1.4142135623730951;
+//---------------- Constants.txt ends   ------------------
diff --git a/xmds2/realistic_Rb_and_fields/RbInits.h b/xmds2/realistic_Rb_and_fields/RbInits.h
new file mode 100644
index 0000000..e4926b2
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/RbInits.h
@@ -0,0 +1,138 @@
+//---------------- RbInits.txt starts ------------------
+r0101 = 0.125;
+r0109 = 0;
+r0110 = 0;
+r0111 = 0;
+r0112 = 0;
+r0113 = 0;
+r0114 = 0;
+r0115 = 0;
+r0116 = 0;
+r0201 = 0;
+r0202 = 0.125;
+r0209 = 0;
+r0210 = 0;
+r0211 = 0;
+r0212 = 0;
+r0213 = 0;
+r0214 = 0;
+r0215 = 0;
+r0216 = 0;
+r0301 = 0;
+r0302 = 0;
+r0303 = 0.125;
+r0309 = 0;
+r0310 = 0;
+r0311 = 0;
+r0312 = 0;
+r0313 = 0;
+r0314 = 0;
+r0315 = 0;
+r0316 = 0;
+r0401 = 0;
+r0402 = 0;
+r0403 = 0;
+r0404 = 0.125;
+r0409 = 0;
+r0410 = 0;
+r0411 = 0;
+r0412 = 0;
+r0413 = 0;
+r0414 = 0;
+r0415 = 0;
+r0416 = 0;
+r0501 = 0;
+r0502 = 0;
+r0503 = 0;
+r0504 = 0;
+r0505 = 0.125;
+r0509 = 0;
+r0510 = 0;
+r0511 = 0;
+r0512 = 0;
+r0513 = 0;
+r0514 = 0;
+r0515 = 0;
+r0516 = 0;
+r0601 = 0;
+r0602 = 0;
+r0603 = 0;
+r0604 = 0;
+r0605 = 0;
+r0606 = 0.125;
+r0609 = 0;
+r0610 = 0;
+r0611 = 0;
+r0612 = 0;
+r0613 = 0;
+r0614 = 0;
+r0615 = 0;
+r0616 = 0;
+r0701 = 0;
+r0702 = 0;
+r0703 = 0;
+r0704 = 0;
+r0705 = 0;
+r0706 = 0;
+r0707 = 0.125;
+r0709 = 0;
+r0710 = 0;
+r0711 = 0;
+r0712 = 0;
+r0713 = 0;
+r0714 = 0;
+r0715 = 0;
+r0716 = 0;
+r0801 = 0;
+r0802 = 0;
+r0803 = 0;
+r0804 = 0;
+r0805 = 0;
+r0806 = 0;
+r0807 = 0;
+r0808 = 0.125;
+r0809 = 0;
+r0810 = 0;
+r0811 = 0;
+r0812 = 0;
+r0813 = 0;
+r0814 = 0;
+r0815 = 0;
+r0816 = 0;
+r0909 = 0;
+r0912 = 0;
+r0913 = 0;
+r0914 = 0;
+r0915 = 0;
+r0916 = 0;
+r1009 = 0;
+r1010 = 0;
+r1012 = 0;
+r1013 = 0;
+r1014 = 0;
+r1015 = 0;
+r1016 = 0;
+r1109 = 0;
+r1110 = 0;
+r1111 = 0;
+r1112 = 0;
+r1113 = 0;
+r1114 = 0;
+r1115 = 0;
+r1116 = 0;
+r1212 = 0;
+r1312 = 0;
+r1313 = 0;
+r1412 = 0;
+r1413 = 0;
+r1414 = 0;
+r1512 = 0;
+r1513 = 0;
+r1514 = 0;
+r1515 = 0;
+r1612 = 0;
+r1613 = 0;
+r1614 = 0;
+r1615 = 0;
+r1616 = 0;
+//---------------- RbInits.txt ends  ------------------
diff --git a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
index 5b00664..d10dbad 100644
--- a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
+++ b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
@@ -1,4 +1,9 @@
 <?xml version="1.0"?>
+<!--Below text defines necessary included files and references to them-->
+<!DOCTYPE simulation [
+<!ENTITY RbChosenRhoFile SYSTEM "RbChosenRho.txt" >
+<!ENTITY RbEquationsFile SYSTEM "RbEquations.txt" >
+]>
 <simulation xmds-version="2">
 	<testing>
 		<arguments> --Ndens=1e15 --Lcell=10.0e-2  --Temperature=1e-3  --Pwidth=0.4e-6  --delta1=0 --delta2=0 --delta3=0  --Ep1o=1e4 --Ep2o=1e2 --Ep3o=1e1 --Ep4o=1e1 --Em1o=1e4 --Em2o=1e2 --Em3o=1e1 --Em4o=1e1 --WLx=0 --WLy=0 --WLz=0</arguments>
@@ -54,22 +59,8 @@
 				const double pi = M_PI; 
 
 				// atom related constants
-				//read from Mathematica generated Constants.txt
-//---------------- Constants.txt starts ------------------
-const double ha0 = 2.1471788680034824e10;
-const double ha1 = 2.558764384495815e9;
-const double g1 = 3.612847284945266e7;
-const double ha2 = 5.323020344462938e8;
-const double hb2 = 7.85178251911697e7;
-const double g2 = 3.8117309832741246e7;
-const double lambda1 = 7.949788511562656e-7;
-const double lambda2 = 7.802412096860509e-7;
-const double eta1 = 5.450949336831401e-6;
-const double eta2 = 5.5397657647874e-6;
-const double rt6 = 2.449489742783178;
-const double rt3 = 1.7320508075688772;
-const double rt2 = 1.4142135623730951;
-//---------------- Constants.txt ends   ------------------
+				//read from Mathematica generated RbAtomConstants.h
+				#include "RbAtomConstants.h"
 
 				const double c=3.e8;
 				const double k_boltzmann= 1.3806505e-23; // Boltzmann knostant in [J/K]
@@ -258,145 +249,8 @@ r0101 r0109 r0110 r0111 r0112 r0113 r0114 r0115 r0116 r0201 r0202 r0209 r0210 r0
 			//       and express other level, let's say r44
 			//       through population normalization
 
-			//read from Mathematica generated RbInits.txt
-//---------------- RbInits.txt starts ------------------
-r0101 = 0.125;
-r0109 = 0;
-r0110 = 0;
-r0111 = 0;
-r0112 = 0;
-r0113 = 0;
-r0114 = 0;
-r0115 = 0;
-r0116 = 0;
-r0201 = 0;
-r0202 = 0.125;
-r0209 = 0;
-r0210 = 0;
-r0211 = 0;
-r0212 = 0;
-r0213 = 0;
-r0214 = 0;
-r0215 = 0;
-r0216 = 0;
-r0301 = 0;
-r0302 = 0;
-r0303 = 0.125;
-r0309 = 0;
-r0310 = 0;
-r0311 = 0;
-r0312 = 0;
-r0313 = 0;
-r0314 = 0;
-r0315 = 0;
-r0316 = 0;
-r0401 = 0;
-r0402 = 0;
-r0403 = 0;
-r0404 = 0.125;
-r0409 = 0;
-r0410 = 0;
-r0411 = 0;
-r0412 = 0;
-r0413 = 0;
-r0414 = 0;
-r0415 = 0;
-r0416 = 0;
-r0501 = 0;
-r0502 = 0;
-r0503 = 0;
-r0504 = 0;
-r0505 = 0.125;
-r0509 = 0;
-r0510 = 0;
-r0511 = 0;
-r0512 = 0;
-r0513 = 0;
-r0514 = 0;
-r0515 = 0;
-r0516 = 0;
-r0601 = 0;
-r0602 = 0;
-r0603 = 0;
-r0604 = 0;
-r0605 = 0;
-r0606 = 0.125;
-r0609 = 0;
-r0610 = 0;
-r0611 = 0;
-r0612 = 0;
-r0613 = 0;
-r0614 = 0;
-r0615 = 0;
-r0616 = 0;
-r0701 = 0;
-r0702 = 0;
-r0703 = 0;
-r0704 = 0;
-r0705 = 0;
-r0706 = 0;
-r0707 = 0.125;
-r0709 = 0;
-r0710 = 0;
-r0711 = 0;
-r0712 = 0;
-r0713 = 0;
-r0714 = 0;
-r0715 = 0;
-r0716 = 0;
-r0801 = 0;
-r0802 = 0;
-r0803 = 0;
-r0804 = 0;
-r0805 = 0;
-r0806 = 0;
-r0807 = 0;
-r0808 = 0.125;
-r0809 = 0;
-r0810 = 0;
-r0811 = 0;
-r0812 = 0;
-r0813 = 0;
-r0814 = 0;
-r0815 = 0;
-r0816 = 0;
-r0909 = 0;
-r0912 = 0;
-r0913 = 0;
-r0914 = 0;
-r0915 = 0;
-r0916 = 0;
-r1009 = 0;
-r1010 = 0;
-r1012 = 0;
-r1013 = 0;
-r1014 = 0;
-r1015 = 0;
-r1016 = 0;
-r1109 = 0;
-r1110 = 0;
-r1111 = 0;
-r1112 = 0;
-r1113 = 0;
-r1114 = 0;
-r1115 = 0;
-r1116 = 0;
-r1212 = 0;
-r1312 = 0;
-r1313 = 0;
-r1412 = 0;
-r1413 = 0;
-r1414 = 0;
-r1512 = 0;
-r1513 = 0;
-r1514 = 0;
-r1515 = 0;
-r1612 = 0;
-r1613 = 0;
-r1614 = 0;
-r1615 = 0;
-r1616 = 0;
-//---------------- RbInits.txt ends  ------------------
+			//read from Mathematica generated RbInits.h
+			#include "RbInits.h"
 			]]>
 		</initialisation>
 	</vector>
@@ -576,6 +430,7 @@ dr1615_dt = -((gt + g2)*r1615) - i*((conj(Em4a)*conj(r0316))/8. - (conj(Ep4a)*co
 dr1616_dt = -((gt + g2)*r1616) - i*((conj(Em4a)*conj(r0416))/(4.*rt6) - (conj(Em3a)*conj(r0816))/(4.*rt2) - (Em4a*r0416)/(4.*rt6) + (Em3a*r0816)/(4.*rt2) - r1615*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.));
 //---------------- RbEquations.txt ends  ------------------
 					]]>
+
         </operator>
 				<!--
 							 According to xmds2 docs operator kind="ip" should be faster
-- 
cgit v1.2.3


From 205e2ca65058d77825ba787cbf64b2ee8a3925f9 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Wed, 28 Nov 2012 17:49:50 -0500
Subject: renamed content of the file to reflect file name

---
 xmds2/realistic_Rb_and_fields/RbAtomConstants.h | 4 ++--
 xmds2/realistic_Rb_and_fields/RbInits.h         | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/RbAtomConstants.h b/xmds2/realistic_Rb_and_fields/RbAtomConstants.h
index 5be3a6e..11b7f2b 100644
--- a/xmds2/realistic_Rb_and_fields/RbAtomConstants.h
+++ b/xmds2/realistic_Rb_and_fields/RbAtomConstants.h
@@ -1,4 +1,4 @@
-//---------------- Constants.txt starts ------------------
+//---------------- RbAtomConstants.h starts ------------------
 const double ha0 = 2.1471788680034824e10;
 const double ha1 = 2.558764384495815e9;
 const double g1 = 3.612847284945266e7;
@@ -12,4 +12,4 @@ const double eta2 = 5.5397657647874e-6;
 const double rt6 = 2.449489742783178;
 const double rt3 = 1.7320508075688772;
 const double rt2 = 1.4142135623730951;
-//---------------- Constants.txt ends   ------------------
+//---------------- RbAtomConstants.h ends   ------------------
diff --git a/xmds2/realistic_Rb_and_fields/RbInits.h b/xmds2/realistic_Rb_and_fields/RbInits.h
index e4926b2..a52ec17 100644
--- a/xmds2/realistic_Rb_and_fields/RbInits.h
+++ b/xmds2/realistic_Rb_and_fields/RbInits.h
@@ -1,4 +1,4 @@
-//---------------- RbInits.txt starts ------------------
+//---------------- RbInits.h starts ------------------
 r0101 = 0.125;
 r0109 = 0;
 r0110 = 0;
@@ -135,4 +135,4 @@ r1613 = 0;
 r1614 = 0;
 r1615 = 0;
 r1616 = 0;
-//---------------- RbInits.txt ends  ------------------
+//---------------- RbInits.h ends  ------------------
-- 
cgit v1.2.3


From d74f75c1a634ac93a4666ef96d120858a39fbee6 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Wed, 28 Nov 2012 18:45:28 -0500
Subject: use headers files for test

---
 xmds2/realistic_Rb_and_fields/Makefile | 67 ++++++++++++++++++++++++++++++++++
 1 file changed, 67 insertions(+)
 create mode 100644 xmds2/realistic_Rb_and_fields/Makefile

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/Makefile b/xmds2/realistic_Rb_and_fields/Makefile
new file mode 100644
index 0000000..d485891
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/Makefile
@@ -0,0 +1,67 @@
+###  -*- make -*-
+### This file is part of the Debian xmds package
+### Copyright (C) 2006 Rafael Laboissiere
+### This file is relased under the GNU General Public License
+### NO WARRANTIES!
+
+### This makefile can be used to build and run the XMDS examples
+
+XMDS_FILES = $(shell ls *.xmds)
+RUN_FILES = $(patsubst %.xmds,%.run,$(XMDS_FILES))
+CC_FILES = $(patsubst %.xmds,%.cc,$(XMDS_FILES))
+XSIL_FILES = $(patsubst %.xmds,%.xsil,$(XMDS_FILES))
+M_FILES = $(patsubst %.xmds,%.m,$(XMDS_FILES))
+
+XMDS_INCLUDES = RbAtomConstants.h RbInits.h
+
+XMDS = xmds2
+XSIL2GRAPHICS = xsil2graphics
+
+all: $(RUN_FILES) 
+
+%.run: %.xmds $(XMDS_INCLUDES)
+	$(XMDS) $<
+	mv $(patsubst %.xmds,%,$<) $@
+
+%.xsil: %.run
+	./$<  --E1o=0 --E3o=0
+
+%.m: %.xsil
+	$(XSIL2GRAPHICS) $<
+
+plot: $(M_FILES)
+	octave pp.m
+
+clean:
+	rm -f $(CC_FILES) $(RUN_FILES) $(M_FILES) $(XSIL_FILES) *.wisdom.fftw3 *.dat octave-core *.wisdom *.pdf 
+	rm -f $(png_targets)
+	rm -f $(eps_targets)
+
+eps_targets  = $(wildcard *.eps)
+pdf_targets  = $(eps_targets:%.eps=%.pdf)	
+png_targets  = $(pdf_targets:%.pdf=%.png)
+
+png: pdf $(png_targets) 
+
+$(png_targets): %.png : %.pdf
+	convert -density 300 $< $@
+
+pdf: $(pdf_targets) 
+
+test:
+	cp $(XMDS_FILES) tests/testsuite/
+	mkdir -p tests/testsuite_results
+	cp $(XMDS_INCLUDES) tests/testsuite_results/
+	cd tests; ./run_tests.py
+
+test_from_scratch:
+	rm -r tests/testsuite_results
+
+
+$(pdf_targets): %.pdf : %.eps
+	cat $< | ps2eps -B > __tt.eps
+	epspdf __tt.eps $@
+	rm -f __tt.eps
+	#ps2eps -B $< | epspdf $< $@
+.PRECIOUS: %.run %.xsil %.m
+.PHONY: all clean
-- 
cgit v1.2.3


From 3a4ba8676f1c265e4631c065efa5c67476886326 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Wed, 28 Nov 2012 22:58:07 -0500
Subject: now we use proper xml includes in xmds file for generated code

---
 xmds2/realistic_Rb/RbAtomConstans.cdata |  18 ++++++
 xmds2/realistic_Rb/RbEquations.cdata    |  37 +++++++++++
 xmds2/realistic_Rb/RbInits.cdata        |  37 +++++++++++
 xmds2/realistic_Rb/realistic_Rb.xmds    | 109 +++++---------------------------
 4 files changed, 107 insertions(+), 94 deletions(-)
 create mode 100644 xmds2/realistic_Rb/RbAtomConstans.cdata
 create mode 100644 xmds2/realistic_Rb/RbEquations.cdata
 create mode 100644 xmds2/realistic_Rb/RbInits.cdata

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb/RbAtomConstans.cdata b/xmds2/realistic_Rb/RbAtomConstans.cdata
new file mode 100644
index 0000000..040d3c9
--- /dev/null
+++ b/xmds2/realistic_Rb/RbAtomConstans.cdata
@@ -0,0 +1,18 @@
+<![CDATA[
+//---------------- RbAtomConstans.cdata starts ------------------
+const double ha0 = 2.1471788680034824e10;
+const double ha1 = 2.558764384495815e9;
+const double g1 = 3.612847284945266e7;
+const double ha2 = 5.323020344462938e8;
+const double hb2 = 7.85178251911697e7;
+const double g2 = 3.8117309832741246e7;
+const double lambda1 = 7.949788511562656e-7;
+const double lambda2 = 7.802412096860509e-7;
+const double eta1 = 5.450949336831401e-6;
+const double eta2 = 5.5397657647874e-6;
+const double rt6 = 2.449489742783178;
+const double rt3 = 1.7320508075688772;
+const double rt2 = 1.4142135623730951;
+//---------------- RbAtomConstans.cdata ends   ------------------
+]]>
+
diff --git a/xmds2/realistic_Rb/RbEquations.cdata b/xmds2/realistic_Rb/RbEquations.cdata
new file mode 100644
index 0000000..1c9f18a
--- /dev/null
+++ b/xmds2/realistic_Rb/RbEquations.cdata
@@ -0,0 +1,37 @@
+<![CDATA[
+//---------------- RbEquations.cdata starts ------------------
+dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1313)/6. - i*((r0113*E4a)/(4.*rt6) - (conj(r0113)*conj(E4a))/(4.*rt6));
+dr0113_dt = (-(gt*r0113) - (gt + g2)*r0113)/2. - i*(WL*r0113 - ((2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0113 + (r0101*conj(E4a))/(4.*rt6) - (r1313*conj(E4a))/(4.*rt6));
+dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1313)/12. + (g2*r1414)/4. - i*((r0214*E4a)/8. - (conj(r0214)*conj(E4a))/8.);
+dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*((WL*r0214)/2. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 - (conj(r0602)*conj(E3a))/(8.*rt3) + (r0202*conj(E4a))/8. - (r1414*conj(E4a))/8.);
+dr0303_dt = gt/8. - gt*r0303 + (g1*r0909)/12. + (g1*r1010)/3. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1515)/4. - i*((r0309*E1a)/(4.*rt6) + (r0315*E4a)/8. - (conj(r0309)*conj(E1a))/(4.*rt6) - (conj(r0315)*conj(E4a))/8.);
+dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*(-((-WL/6. - delta1 - v*Kvec1)*r0309) + (r0303*conj(E1a))/(4.*rt6) - (r0909*conj(E1a))/(4.*rt6) - (conj(r0703)*conj(E2a))/(4.*rt6) - (conj(r0915)*conj(E4a))/8.);
+dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(((-2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0315) - (r0915*conj(E1a))/(4.*rt6) - (conj(r0703)*conj(E3a))/8. + (r0303*conj(E4a))/8. - (r1515*conj(E4a))/8.);
+dr0404_dt = gt/8. - gt*r0404 + (g1*r1010)/4. + (g1*r1111)/4. + (g2*r1414)/4. + (g2*r1515)/12. + (g2*r1616)/6. - i*((r0410*E1a)/(4.*rt2) + (r0416*E4a)/(4.*rt6) - (conj(r0410)*conj(E1a))/(4.*rt2) - (conj(r0416)*conj(E4a))/(4.*rt6));
+dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(WL*r0410)/2. + (delta1 + v*Kvec1)*r0410 + (r0404*conj(E1a))/(4.*rt2) - (r1010*conj(E1a))/(4.*rt2) - (conj(r0804)*conj(E2a))/(4.*rt6) - (conj(r1016)*conj(E4a))/(4.*rt6));
+dr0416_dt = (-(gt*r0416) - (gt + g2)*r0416)/2. - i*(-(WL*r0416)/2. - ((-4*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0416 - (r1016*conj(E1a))/(4.*rt2) - (conj(r0804)*conj(E3a))/(4.*rt2) + (r0404*conj(E4a))/(4.*rt6) - (r1616*conj(E4a))/(4.*rt6));
+dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((r0511*E1a)/4. - (conj(r0511)*conj(E1a))/4.);
+dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(WL*r0511) - (WL/6. - delta1 - v*Kvec1)*r0511 + (r0505*conj(E1a))/4. - (r1111*conj(E1a))/4.);
+dr0602_dt = -(gt*r0602) - i*(-(WL*r0602)/2. + (-WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0602 + (r0614*E4a)/8. + (conj(r0214)*conj(E3a))/(8.*rt3));
+dr0606_dt = gt/8. - gt*r0606 + (g1*r0909)/12. + (g1*r1010)/12. + (g2*r1313)/4. + (g2*r1414)/12. - i*(-(r0614*E3a)/(8.*rt3) + (conj(r0614)*conj(E3a))/(8.*rt3));
+dr0614_dt = (-(gt*r0614) - (gt + g2)*r0614)/2. - i*((-WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0614 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0614 - (r0606*conj(E3a))/(8.*rt3) + (r1414*conj(E3a))/(8.*rt3) + (r0602*conj(E4a))/8.);
+dr0703_dt = -(gt*r0703) - i*((-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 + (r0709*E1a)/(4.*rt6) + (r0715*E4a)/8. + (conj(r0309)*conj(E2a))/(4.*rt6) + (conj(r0315)*conj(E3a))/8.);
+dr0707_dt = gt/8. - gt*r0707 + (g1*r0909)/12. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1414)/3. + (g2*r1515)/4. - i*(-(r0709*E2a)/(4.*rt6) - (r0715*E3a)/8. + (conj(r0709)*conj(E2a))/(4.*rt6) + (conj(r0715)*conj(E3a))/8.);
+dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*(-((-WL/6. - delta1 - v*Kvec1)*r0709) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0709 + (r0703*conj(E1a))/(4.*rt6) - (r0707*conj(E2a))/(4.*rt6) + (r0909*conj(E2a))/(4.*rt6) + (conj(r0915)*conj(E3a))/8.);
+dr0715_dt = (-(gt*r0715) - (gt + g2)*r0715)/2. - i*((-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0715 - ((-2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0715 + (r0915*conj(E2a))/(4.*rt6) - (r0707*conj(E3a))/8. + (r1515*conj(E3a))/8. + (r0703*conj(E4a))/8.);
+dr0804_dt = -(gt*r0804) - i*((WL*r0804)/2. + (WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0804 + (r0810*E1a)/(4.*rt2) + (r0816*E4a)/(4.*rt6) + (conj(r0410)*conj(E2a))/(4.*rt6) + (conj(r0416)*conj(E3a))/(4.*rt2));
+dr0808_dt = gt/8. - gt*r0808 + (g1*r1010)/12. + (g1*r1111)/12. + (g2*r1414)/12. + (g2*r1515)/4. + (g2*r1616)/2. - i*(-(r0810*E2a)/(4.*rt6) - (r0816*E3a)/(4.*rt2) + (conj(r0810)*conj(E2a))/(4.*rt6) + (conj(r0816)*conj(E3a))/(4.*rt2));
+dr0810_dt = (-(gt*r0810) - (gt + g1)*r0810)/2. - i*((delta1 + v*Kvec1)*r0810 + (WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0810 + (r0804*conj(E1a))/(4.*rt2) - (r0808*conj(E2a))/(4.*rt6) + (r1010*conj(E2a))/(4.*rt6) + (conj(r1016)*conj(E3a))/(4.*rt2));
+dr0816_dt = (-(gt*r0816) - (gt + g2)*r0816)/2. - i*((WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0816 - ((-4*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0816 + (r1016*conj(E2a))/(4.*rt6) - (r0808*conj(E3a))/(4.*rt2) + (r1616*conj(E3a))/(4.*rt2) + (r0804*conj(E4a))/(4.*rt6));
+dr0909_dt = -((gt + g1)*r0909) - i*(-(r0309*E1a)/(4.*rt6) + (r0709*E2a)/(4.*rt6) + (conj(r0309)*conj(E1a))/(4.*rt6) - (conj(r0709)*conj(E2a))/(4.*rt6));
+dr0915_dt = (-((gt + g1)*r0915) - (gt + g2)*r0915)/2. - i*((-WL/6. - delta1 - v*Kvec1)*r0915 - ((-2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0915 - (r0315*E1a)/(4.*rt6) + (r0715*E2a)/(4.*rt6) - (conj(r0709)*conj(E3a))/8. + (conj(r0309)*conj(E4a))/8.);
+dr1010_dt = -((gt + g1)*r1010) - i*(-(r0410*E1a)/(4.*rt2) + (r0810*E2a)/(4.*rt6) + (conj(r0410)*conj(E1a))/(4.*rt2) - (conj(r0810)*conj(E2a))/(4.*rt6));
+dr1016_dt = (-((gt + g1)*r1016) - (gt + g2)*r1016)/2. - i*(-((delta1 + v*Kvec1)*r1016) - ((-4*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1016 - (r0416*E1a)/(4.*rt2) + (r0816*E2a)/(4.*rt6) - (conj(r0810)*conj(E3a))/(4.*rt2) + (conj(r0410)*conj(E4a))/(4.*rt6));
+dr1111_dt = -((gt + g1)*r1111) - i*(-(r0511*E1a)/4. + (conj(r0511)*conj(E1a))/4.);
+dr1313_dt = -((gt + g2)*r1313) - i*(-(r0113*E4a)/(4.*rt6) + (conj(r0113)*conj(E4a))/(4.*rt6));
+dr1414_dt = -((gt + g2)*r1414) - i*((r0614*E3a)/(8.*rt3) - (r0214*E4a)/8. - (conj(r0614)*conj(E3a))/(8.*rt3) + (conj(r0214)*conj(E4a))/8.);
+dr1515_dt = -((gt + g2)*r1515) - i*((r0715*E3a)/8. - (r0315*E4a)/8. - (conj(r0715)*conj(E3a))/8. + (conj(r0315)*conj(E4a))/8.);
+dr1616_dt = -((gt + g2)*r1616) - i*((r0816*E3a)/(4.*rt2) - (r0416*E4a)/(4.*rt6) - (conj(r0816)*conj(E3a))/(4.*rt2) + (conj(r0416)*conj(E4a))/(4.*rt6));
+//---------------- RbEquations.cdata ends  ------------------
+]]>
+
diff --git a/xmds2/realistic_Rb/RbInits.cdata b/xmds2/realistic_Rb/RbInits.cdata
new file mode 100644
index 0000000..77a5cf7
--- /dev/null
+++ b/xmds2/realistic_Rb/RbInits.cdata
@@ -0,0 +1,37 @@
+<![CDATA[
+//---------------- RbInits.cdata starts ------------------
+r0101 = 0.125;
+r0113 = 0;
+r0202 = 0.125;
+r0214 = 0;
+r0303 = 0.125;
+r0309 = 0;
+r0315 = 0;
+r0404 = 0.125;
+r0410 = 0;
+r0416 = 0;
+r0505 = 0.125;
+r0511 = 0;
+r0602 = 0;
+r0606 = 0.125;
+r0614 = 0;
+r0703 = 0;
+r0707 = 0.125;
+r0709 = 0;
+r0715 = 0;
+r0804 = 0;
+r0808 = 0.125;
+r0810 = 0;
+r0816 = 0;
+r0909 = 0;
+r0915 = 0;
+r1010 = 0;
+r1016 = 0;
+r1111 = 0;
+r1313 = 0;
+r1414 = 0;
+r1515 = 0;
+r1616 = 0;
+//---------------- RbInits.cdata ends  ------------------
+]]>
+
diff --git a/xmds2/realistic_Rb/realistic_Rb.xmds b/xmds2/realistic_Rb/realistic_Rb.xmds
index 94b398c..7744dd8 100644
--- a/xmds2/realistic_Rb/realistic_Rb.xmds
+++ b/xmds2/realistic_Rb/realistic_Rb.xmds
@@ -1,4 +1,11 @@
 <?xml version="1.0"?>
+<!--Below text defines necessary included files and references to them-->
+<!DOCTYPE simulation [
+<!ENTITY RbAtomConstansFile SYSTEM "RbAtomConstans.cdata" >
+<!ENTITY RbChosenRhoFile SYSTEM "RbChosenRho.txt" >
+<!ENTITY RbInitsFile SYSTEM "RbInits.cdata" >
+<!ENTITY RbEquationsFile SYSTEM "RbEquations.cdata" >
+]>
 <simulation xmds-version="2">
 	<testing>
 		<arguments> --Ndens=1e15 --Lcell=10.0e-2  --Temperature=1e-3  --Pwidth=0.4e-6  --delta1=0 --delta2=0 --delta3=0  --E1o=0 --E2o=1e2 --E3o=0 --E4o=0</arguments>
@@ -49,28 +56,12 @@
 
 	<features>
 		<globals>
+			<!-- read from Mathematica generated RbAtomConstans.cdata-->
+			&RbAtomConstansFile;
 			<![CDATA[
 				// Some numerical constants
 				const double pi = M_PI; 
 
-				// atom related constants
-				//read from Mathematica generated Constants.txt
-//---------------- Constants.txt starts ------------------
-const double ha0 = 2.1471788680034824e10;
-const double ha1 = 2.558764384495815e9;
-const double g1 = 3.612847284945266e7;
-const double ha2 = 5.323020344462938e8;
-const double hb2 = 7.85178251911697e7;
-const double g2 = 3.8117309832741246e7;
-const double lambda1 = 7.949788511562656e-7;
-const double lambda2 = 7.802412096860509e-7;
-const double eta1 = 5.450949336831401e-6;
-const double eta2 = 5.5397657647874e-6;
-const double rt6 = 2.449489742783178;
-const double rt3 = 1.7320508075688772;
-const double rt2 = 1.4142135623730951;
-//---------------- Constants.txt ends   ------------------
-
 				const double c=3.e8;
 				const double k_boltzmann= 1.3806505e-23; // Boltzmann knostant in [J/K]
 				const double lambda=794.7e-9; //wavelength in m
@@ -228,9 +219,7 @@ const double rt2 = 1.4142135623730951;
 	<vector name="density_matrix" type="complex" initial_space="t">
 		<components>
 			<!-- read from Mathematica generated RbChosenRho.txt -->
-<!-- ############### RbChosenRho.txt starts ################ -->
-r0101 r0113 r0202 r0214 r0303 r0309 r0315 r0404 r0410 r0416 r0505 r0511 r0602 r0606 r0614 r0703 r0707 r0709 r0715 r0804 r0808 r0810 r0816 r0909 r0915 r1010 r1016 r1111 r1313 r1414 r1515 r1616 
-<!-- ############### RbChosenRho.txt ends  ################# -->
+			&RbChosenRhoFile;
 		</components>
 		<initialisation>
 			<!--This sets boundary condition at all times and left border of z (i.e. z=0)-->
@@ -245,42 +234,9 @@ r0101 r0113 r0202 r0214 r0303 r0309 r0315 r0404 r0410 r0416 r0505 r0511 r0602 r0
 			//       and express other level, let's say r44
 			//       through population normalization
 
-			//read from Mathematica generated RbInits.txt
-//---------------- RbInits.txt starts ------------------
-r0101 = 0.125;
-r0113 = 0;
-r0202 = 0.125;
-r0214 = 0;
-r0303 = 0.125;
-r0309 = 0;
-r0315 = 0;
-r0404 = 0.125;
-r0410 = 0;
-r0416 = 0;
-r0505 = 0.125;
-r0511 = 0;
-r0602 = 0;
-r0606 = 0.125;
-r0614 = 0;
-r0703 = 0;
-r0707 = 0.125;
-r0709 = 0;
-r0715 = 0;
-r0804 = 0;
-r0808 = 0.125;
-r0810 = 0;
-r0816 = 0;
-r0909 = 0;
-r0915 = 0;
-r1010 = 0;
-r1016 = 0;
-r1111 = 0;
-r1313 = 0;
-r1414 = 0;
-r1515 = 0;
-r1616 = 0;
-//---------------- RbInits.txt ends  ------------------
 			]]>
+			<!--read from Mathematica generated RbInits.cdata-->
+			&RbInitsFile;
 		</initialisation>
 	</vector>
 
@@ -317,44 +273,9 @@ r1616 = 0;
             ]]>
 						-->
           </boundary_condition>
-					<![CDATA[
-						// Equations of motions according to Simon's mathematica code
-						//read from Mathematica generated RbEquations.txt
-//---------------- RbEquations.txt starts ------------------
-dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1313)/6. - i*((r0113*E4a)/(4.*rt6) - (conj(r0113)*conj(E4a))/(4.*rt6));
-dr0113_dt = (-(gt*r0113) - (gt + g2)*r0113)/2. - i*(WL*r0113 - ((2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0113 + (r0101*conj(E4a))/(4.*rt6) - (r1313*conj(E4a))/(4.*rt6));
-dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1313)/12. + (g2*r1414)/4. - i*((r0214*E4a)/8. - (conj(r0214)*conj(E4a))/8.);
-dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*((WL*r0214)/2. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 - (conj(r0602)*conj(E3a))/(8.*rt3) + (r0202*conj(E4a))/8. - (r1414*conj(E4a))/8.);
-dr0303_dt = gt/8. - gt*r0303 + (g1*r0909)/12. + (g1*r1010)/3. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1515)/4. - i*((r0309*E1a)/(4.*rt6) + (r0315*E4a)/8. - (conj(r0309)*conj(E1a))/(4.*rt6) - (conj(r0315)*conj(E4a))/8.);
-dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*(-((-WL/6. - delta1 - v*Kvec1)*r0309) + (r0303*conj(E1a))/(4.*rt6) - (r0909*conj(E1a))/(4.*rt6) - (conj(r0703)*conj(E2a))/(4.*rt6) - (conj(r0915)*conj(E4a))/8.);
-dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(((-2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0315) - (r0915*conj(E1a))/(4.*rt6) - (conj(r0703)*conj(E3a))/8. + (r0303*conj(E4a))/8. - (r1515*conj(E4a))/8.);
-dr0404_dt = gt/8. - gt*r0404 + (g1*r1010)/4. + (g1*r1111)/4. + (g2*r1414)/4. + (g2*r1515)/12. + (g2*r1616)/6. - i*((r0410*E1a)/(4.*rt2) + (r0416*E4a)/(4.*rt6) - (conj(r0410)*conj(E1a))/(4.*rt2) - (conj(r0416)*conj(E4a))/(4.*rt6));
-dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(WL*r0410)/2. + (delta1 + v*Kvec1)*r0410 + (r0404*conj(E1a))/(4.*rt2) - (r1010*conj(E1a))/(4.*rt2) - (conj(r0804)*conj(E2a))/(4.*rt6) - (conj(r1016)*conj(E4a))/(4.*rt6));
-dr0416_dt = (-(gt*r0416) - (gt + g2)*r0416)/2. - i*(-(WL*r0416)/2. - ((-4*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0416 - (r1016*conj(E1a))/(4.*rt2) - (conj(r0804)*conj(E3a))/(4.*rt2) + (r0404*conj(E4a))/(4.*rt6) - (r1616*conj(E4a))/(4.*rt6));
-dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((r0511*E1a)/4. - (conj(r0511)*conj(E1a))/4.);
-dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(WL*r0511) - (WL/6. - delta1 - v*Kvec1)*r0511 + (r0505*conj(E1a))/4. - (r1111*conj(E1a))/4.);
-dr0602_dt = -(gt*r0602) - i*(-(WL*r0602)/2. + (-WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0602 + (r0614*E4a)/8. + (conj(r0214)*conj(E3a))/(8.*rt3));
-dr0606_dt = gt/8. - gt*r0606 + (g1*r0909)/12. + (g1*r1010)/12. + (g2*r1313)/4. + (g2*r1414)/12. - i*(-(r0614*E3a)/(8.*rt3) + (conj(r0614)*conj(E3a))/(8.*rt3));
-dr0614_dt = (-(gt*r0614) - (gt + g2)*r0614)/2. - i*((-WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0614 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0614 - (r0606*conj(E3a))/(8.*rt3) + (r1414*conj(E3a))/(8.*rt3) + (r0602*conj(E4a))/8.);
-dr0703_dt = -(gt*r0703) - i*((-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 + (r0709*E1a)/(4.*rt6) + (r0715*E4a)/8. + (conj(r0309)*conj(E2a))/(4.*rt6) + (conj(r0315)*conj(E3a))/8.);
-dr0707_dt = gt/8. - gt*r0707 + (g1*r0909)/12. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1414)/3. + (g2*r1515)/4. - i*(-(r0709*E2a)/(4.*rt6) - (r0715*E3a)/8. + (conj(r0709)*conj(E2a))/(4.*rt6) + (conj(r0715)*conj(E3a))/8.);
-dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*(-((-WL/6. - delta1 - v*Kvec1)*r0709) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0709 + (r0703*conj(E1a))/(4.*rt6) - (r0707*conj(E2a))/(4.*rt6) + (r0909*conj(E2a))/(4.*rt6) + (conj(r0915)*conj(E3a))/8.);
-dr0715_dt = (-(gt*r0715) - (gt + g2)*r0715)/2. - i*((-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0715 - ((-2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0715 + (r0915*conj(E2a))/(4.*rt6) - (r0707*conj(E3a))/8. + (r1515*conj(E3a))/8. + (r0703*conj(E4a))/8.);
-dr0804_dt = -(gt*r0804) - i*((WL*r0804)/2. + (WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0804 + (r0810*E1a)/(4.*rt2) + (r0816*E4a)/(4.*rt6) + (conj(r0410)*conj(E2a))/(4.*rt6) + (conj(r0416)*conj(E3a))/(4.*rt2));
-dr0808_dt = gt/8. - gt*r0808 + (g1*r1010)/12. + (g1*r1111)/12. + (g2*r1414)/12. + (g2*r1515)/4. + (g2*r1616)/2. - i*(-(r0810*E2a)/(4.*rt6) - (r0816*E3a)/(4.*rt2) + (conj(r0810)*conj(E2a))/(4.*rt6) + (conj(r0816)*conj(E3a))/(4.*rt2));
-dr0810_dt = (-(gt*r0810) - (gt + g1)*r0810)/2. - i*((delta1 + v*Kvec1)*r0810 + (WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0810 + (r0804*conj(E1a))/(4.*rt2) - (r0808*conj(E2a))/(4.*rt6) + (r1010*conj(E2a))/(4.*rt6) + (conj(r1016)*conj(E3a))/(4.*rt2));
-dr0816_dt = (-(gt*r0816) - (gt + g2)*r0816)/2. - i*((WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0816 - ((-4*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0816 + (r1016*conj(E2a))/(4.*rt6) - (r0808*conj(E3a))/(4.*rt2) + (r1616*conj(E3a))/(4.*rt2) + (r0804*conj(E4a))/(4.*rt6));
-dr0909_dt = -((gt + g1)*r0909) - i*(-(r0309*E1a)/(4.*rt6) + (r0709*E2a)/(4.*rt6) + (conj(r0309)*conj(E1a))/(4.*rt6) - (conj(r0709)*conj(E2a))/(4.*rt6));
-dr0915_dt = (-((gt + g1)*r0915) - (gt + g2)*r0915)/2. - i*((-WL/6. - delta1 - v*Kvec1)*r0915 - ((-2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0915 - (r0315*E1a)/(4.*rt6) + (r0715*E2a)/(4.*rt6) - (conj(r0709)*conj(E3a))/8. + (conj(r0309)*conj(E4a))/8.);
-dr1010_dt = -((gt + g1)*r1010) - i*(-(r0410*E1a)/(4.*rt2) + (r0810*E2a)/(4.*rt6) + (conj(r0410)*conj(E1a))/(4.*rt2) - (conj(r0810)*conj(E2a))/(4.*rt6));
-dr1016_dt = (-((gt + g1)*r1016) - (gt + g2)*r1016)/2. - i*(-((delta1 + v*Kvec1)*r1016) - ((-4*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1016 - (r0416*E1a)/(4.*rt2) + (r0816*E2a)/(4.*rt6) - (conj(r0810)*conj(E3a))/(4.*rt2) + (conj(r0410)*conj(E4a))/(4.*rt6));
-dr1111_dt = -((gt + g1)*r1111) - i*(-(r0511*E1a)/4. + (conj(r0511)*conj(E1a))/4.);
-dr1313_dt = -((gt + g2)*r1313) - i*(-(r0113*E4a)/(4.*rt6) + (conj(r0113)*conj(E4a))/(4.*rt6));
-dr1414_dt = -((gt + g2)*r1414) - i*((r0614*E3a)/(8.*rt3) - (r0214*E4a)/8. - (conj(r0614)*conj(E3a))/(8.*rt3) + (conj(r0214)*conj(E4a))/8.);
-dr1515_dt = -((gt + g2)*r1515) - i*((r0715*E3a)/8. - (r0315*E4a)/8. - (conj(r0715)*conj(E3a))/8. + (conj(r0315)*conj(E4a))/8.);
-dr1616_dt = -((gt + g2)*r1616) - i*((r0816*E3a)/(4.*rt2) - (r0416*E4a)/(4.*rt6) - (conj(r0816)*conj(E3a))/(4.*rt2) + (conj(r0416)*conj(E4a))/(4.*rt6));
-//---------------- RbEquations.txt ends  ------------------
-					]]>
+						<!-- Equations of motions according to Simon's mathematica code-->
+						<!-- read from Mathematica generated RbEquations.cdata-->
+						&RbEquationsFile;
         </operator>
 				<!--
 							 According to xmds2 docs operator kind="ip" should be faster
-- 
cgit v1.2.3


From 3d3c605845be51eaf7a8d1085567797d71dc8d7e Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Wed, 28 Nov 2012 22:58:50 -0500
Subject: Makefile test properly works with included to xmds files

---
 xmds2/realistic_Rb/Makefile | 20 +++++++++++++++++---
 1 file changed, 17 insertions(+), 3 deletions(-)

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb/Makefile b/xmds2/realistic_Rb/Makefile
index ae7d4a9..583bc6a 100644
--- a/xmds2/realistic_Rb/Makefile
+++ b/xmds2/realistic_Rb/Makefile
@@ -1,9 +1,11 @@
 ###  -*- make -*-
 ### This file is part of the Debian xmds package
 ### Copyright (C) 2006 Rafael Laboissiere
-### This file is relased under the GNU General Public License
+### This file is released under the GNU General Public License
 ### NO WARRANTIES!
 
+INSTALL = install --mode=664 -D 
+
 ### This makefile can be used to build and run the XMDS examples
 
 XMDS_FILES = $(shell ls *.xmds)
@@ -12,6 +14,12 @@ CC_FILES = $(patsubst %.xmds,%.cc,$(XMDS_FILES))
 XSIL_FILES = $(patsubst %.xmds,%.xsil,$(XMDS_FILES))
 M_FILES = $(patsubst %.xmds,%.m,$(XMDS_FILES))
 
+test_dir = tests
+test_result_dir = $(test_dir)/testsuite_results
+XMDS_INCLUDES_misc  = RbChosenRho.txt RbInits.cdata RbEquations.cdata RbAtomConstans.cdata
+XMDS_INCLUDES_xmds_in_target_dir = $(XMDS_INCLUDES_misc:%=$(test_dir)/%)
+XMDS_INCLUDES_cdata_in_target_dir = $(XMDS_INCLUDES_misc:%=$(test_result_dir)/%)
+
 XMDS = xmds2
 XSIL2GRAPHICS = xsil2graphics
 
@@ -46,8 +54,14 @@ $(png_targets): %.png : %.pdf
 
 pdf: $(pdf_targets) 
 
-test:
-	cp $(XMDS_FILES) tests/testsuite/
+$(XMDS_INCLUDES_cdata_in_target_dir): $(test_result_dir)/% : %
+	$(INSTALL) $< $@
+
+$(XMDS_INCLUDES_xmds_in_target_dir): $(test_dir)/% : %
+	$(INSTALL) $< $@
+
+test: $(XMDS_INCLUDES_cdata_in_target_dir) $(XMDS_INCLUDES_xmds_in_target_dir)
+	$(INSTALL) $(XMDS_FILES) tests/testsuite/
 	cd tests; ./run_tests.py
 
 test_from_scratch:
-- 
cgit v1.2.3


From f58688cf1b100bca69475f0b66c81012078f8a1a Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Wed, 28 Nov 2012 23:26:46 -0500
Subject: mathematica generated files are used as includes now

---
 .../realistic_Rb_and_fields/RbAtomConstants.cdata  |  17 ++
 xmds2/realistic_Rb_and_fields/RbAtomConstants.h    |  15 --
 xmds2/realistic_Rb_and_fields/RbEquations.cdata    | 140 +++++++++++++++
 xmds2/realistic_Rb_and_fields/RbInits.cdata        | 140 +++++++++++++++
 xmds2/realistic_Rb_and_fields/RbInits.h            | 138 ---------------
 .../realistic_Rb_and_fields/RbPropEquations.cdata  |  12 ++
 .../realistic_Rb_and_fields.xmds                   | 187 ++-------------------
 7 files changed, 327 insertions(+), 322 deletions(-)
 create mode 100644 xmds2/realistic_Rb_and_fields/RbAtomConstants.cdata
 delete mode 100644 xmds2/realistic_Rb_and_fields/RbAtomConstants.h
 create mode 100644 xmds2/realistic_Rb_and_fields/RbEquations.cdata
 create mode 100644 xmds2/realistic_Rb_and_fields/RbInits.cdata
 delete mode 100644 xmds2/realistic_Rb_and_fields/RbInits.h
 create mode 100644 xmds2/realistic_Rb_and_fields/RbPropEquations.cdata

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/RbAtomConstants.cdata b/xmds2/realistic_Rb_and_fields/RbAtomConstants.cdata
new file mode 100644
index 0000000..49b96a1
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/RbAtomConstants.cdata
@@ -0,0 +1,17 @@
+<![CDATA[
+//---------------- RbAtomConstants.cdata starts ------------------
+const double ha0 = 2.1471788680034824e10;
+const double ha1 = 2.558764384495815e9;
+const double g1 = 3.612847284945266e7;
+const double ha2 = 5.323020344462938e8;
+const double hb2 = 7.85178251911697e7;
+const double g2 = 3.8117309832741246e7;
+const double lambda1 = 7.949788511562656e-7;
+const double lambda2 = 7.802412096860509e-7;
+const double eta1 = 5.450949336831401e-6;
+const double eta2 = 5.5397657647874e-6;
+const double rt6 = 2.449489742783178;
+const double rt3 = 1.7320508075688772;
+const double rt2 = 1.4142135623730951;
+//---------------- RbAtomConstants.cdata ends   ------------------
+]]>
diff --git a/xmds2/realistic_Rb_and_fields/RbAtomConstants.h b/xmds2/realistic_Rb_and_fields/RbAtomConstants.h
deleted file mode 100644
index 11b7f2b..0000000
--- a/xmds2/realistic_Rb_and_fields/RbAtomConstants.h
+++ /dev/null
@@ -1,15 +0,0 @@
-//---------------- RbAtomConstants.h starts ------------------
-const double ha0 = 2.1471788680034824e10;
-const double ha1 = 2.558764384495815e9;
-const double g1 = 3.612847284945266e7;
-const double ha2 = 5.323020344462938e8;
-const double hb2 = 7.85178251911697e7;
-const double g2 = 3.8117309832741246e7;
-const double lambda1 = 7.949788511562656e-7;
-const double lambda2 = 7.802412096860509e-7;
-const double eta1 = 5.450949336831401e-6;
-const double eta2 = 5.5397657647874e-6;
-const double rt6 = 2.449489742783178;
-const double rt3 = 1.7320508075688772;
-const double rt2 = 1.4142135623730951;
-//---------------- RbAtomConstants.h ends   ------------------
diff --git a/xmds2/realistic_Rb_and_fields/RbEquations.cdata b/xmds2/realistic_Rb_and_fields/RbEquations.cdata
new file mode 100644
index 0000000..39bd357
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/RbEquations.cdata
@@ -0,0 +1,140 @@
+<![CDATA[
+//---------------- RbEquations.cdata starts ------------------
+dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1212)/3. + (g2*r1313)/6. - i*((conj(Em1a)*conj(r0109))/4. - (conj(Em4a)*conj(r0113))/(4.*rt6) - (Em1a*r0109)/4. + (Em4a*r0113)/(4.*rt6) + r0201*(WLx/2. - (i*WLy)/2.) - conj(r0201)*(WLx/2. + (i*WLy)/2.));
+dr0109_dt = (-(gt*r0109) - (gt + g1)*r0109)/2. - i*(-(conj(Ep1a)*conj(r0301))/(4.*rt6) + (conj(Ep2a)*conj(r0701))/(4.*rt6) - (conj(Em4a)*conj(r0913))/(4.*rt6) - (conj(Em1a)*r0101)/4. + (conj(Em1a)*r0909)/4. + r0209*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-delta1 - v*Kvec1 - WLz/6.) + r0109*WLz);
+dr0110_dt = (-(gt*r0110) - (gt + g1)*r0110)/2. - i*(-(conj(Em1a)*conj(r0201))/(4.*rt2) - (conj(Ep1a)*conj(r0401))/(4.*rt2) - (conj(Em2a)*conj(r0601))/(4.*rt6) + (conj(Ep2a)*conj(r0801))/(4.*rt6) + (conj(Em1a)*conj(r1009))/4. - (conj(Em4a)*conj(r1013))/(4.*rt6) + (delta1 + v*Kvec1)*r0110 + r0210*(WLx/2. - (i*WLy)/2.) - r0111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0110*WLz);
+dr0111_dt = (-(gt*r0111) - (gt + g1)*r0111)/2. - i*(-(conj(Em1a)*conj(r0301))/(4.*rt6) - (conj(Ep1a)*conj(r0501))/4. - (conj(Em2a)*conj(r0701))/(4.*rt6) + (conj(Em1a)*conj(r1109))/4. - (conj(Em4a)*conj(r1113))/(4.*rt6) + r0211*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0111*(-delta1 - v*Kvec1 + WLz/6.) + r0111*WLz);
+dr0112_dt = (-(gt*r0112) - (gt + g2)*r0112)/2. - i*(-(conj(Ep4a)*conj(r0201))/(4.*rt6) - (conj(Ep3a)*conj(r0601))/(4.*rt2) + (conj(Em1a)*r0912)/4. - (conj(Em4a)*r1312)/(4.*rt6) + r0212*(WLx/2. - (i*WLy)/2.) - r0113*((2*WLx)/3. + (2*i*WLy)/3.) + r0112*WLz - r0112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0113_dt = (-(gt*r0113) - (gt + g2)*r0113)/2. - i*(-(conj(Ep4a)*conj(r0301))/8. - (conj(Ep3a)*conj(r0701))/8. + (conj(Em4a)*r0101)/(4.*rt6) + (conj(Em1a)*r0913)/4. - (conj(Em4a)*r1313)/(4.*rt6) - r0112*((2*WLx)/3. - (2*i*WLy)/3.) + r0213*(WLx/2. - (i*WLy)/2.) - r0114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + r0113*WLz);
+dr0114_dt = (-(gt*r0114) - (gt + g2)*r0114)/2. - i*((conj(Em4a)*conj(r0201))/8. - (conj(Ep4a)*conj(r0401))/8. - (conj(Em3a)*conj(r0601))/(8.*rt3) - (conj(Ep3a)*conj(r0801))/(8.*rt3) - (conj(Em4a)*conj(r1413))/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0114 + (conj(Em1a)*r0914)/4. + r0214*(WLx/2. - (i*WLy)/2.) - r0113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0114*WLz);
+dr0115_dt = (-(gt*r0115) - (gt + g2)*r0115)/2. - i*((conj(Em4a)*conj(r0301))/8. - (conj(Ep4a)*conj(r0501))/(4.*rt6) - (conj(Em3a)*conj(r0701))/8. - (conj(Em4a)*conj(r1513))/(4.*rt6) + (conj(Em1a)*r0915)/4. + r0215*(WLx/2. - (i*WLy)/2.) - r0116*((2*WLx)/3. + (2*i*WLy)/3.) - r0114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0115*WLz);
+dr0116_dt = (-(gt*r0116) - (gt + g2)*r0116)/2. - i*((conj(Em4a)*conj(r0401))/(4.*rt6) - (conj(Em3a)*conj(r0801))/(4.*rt2) - (conj(Em4a)*conj(r1613))/(4.*rt6) + (conj(Em1a)*r0916)/4. - r0115*((2*WLx)/3. - (2*i*WLy)/3.) + r0216*(WLx/2. - (i*WLy)/2.) - r0116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0116*WLz);
+dr0201_dt = -(gt*r0201) + (g1*r1009)/(2.*rt2) + (g2*r1312)/6. + (g2*r1413)/(2.*rt6) - i*((conj(Em1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0112))/(4.*rt6) - (conj(Em4a)*conj(r0114))/8. - (Em1a*r0209)/4. + (Em4a*r0213)/(4.*rt6) + r0101*(WLx/2. + (i*WLy)/2.) - r0202*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0201*WLz)/2.);
+dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1212)/6. + (g2*r1313)/12. + (g2*r1414)/4. - i*((conj(Em1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Em4a)*conj(r0214))/8. - (Em1a*r0210)/(4.*rt2) - (Ep4a*r0212)/(4.*rt6) + (Em4a*r0214)/8. - r0201*(WLx/2. - (i*WLy)/2.) + conj(r0201)*(WLx/2. + (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0209_dt = (-(gt*r0209) - (gt + g1)*r0209)/2. - i*(-(conj(Ep1a)*conj(r0302))/(4.*rt6) + (conj(Ep2a)*conj(r0702))/(4.*rt6) + (conj(Ep4a)*conj(r0912))/(4.*rt6) - (conj(Em4a)*conj(r0914))/8. - (conj(Em1a)*r0201)/4. + (conj(Em1a)*r1009)/(4.*rt2) + r0109*(WLx/2. + (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-delta1 - v*Kvec1 - WLz/6.) + (r0209*WLz)/2.);
+dr0210_dt = (-(gt*r0210) - (gt + g1)*r0210)/2. - i*(-(conj(Ep1a)*conj(r0402))/(4.*rt2) - (conj(Em2a)*conj(r0602))/(4.*rt6) + (conj(Ep2a)*conj(r0802))/(4.*rt6) + (conj(Ep4a)*conj(r1012))/(4.*rt6) - (conj(Em4a)*conj(r1014))/8. - (conj(Em1a)*r0202)/(4.*rt2) + (delta1 + v*Kvec1)*r0210 + (conj(Em1a)*r1010)/(4.*rt2) + r0110*(WLx/2. + (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0211*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + (r0210*WLz)/2.);
+dr0211_dt = (-(gt*r0211) - (gt + g1)*r0211)/2. - i*(-(conj(Em1a)*conj(r0302))/(4.*rt6) - (conj(Ep1a)*conj(r0502))/4. - (conj(Em2a)*conj(r0702))/(4.*rt6) + (conj(Em1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1112))/(4.*rt6) - (conj(Em4a)*conj(r1114))/8. + r0111*(WLx/2. + (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0211*(-delta1 - v*Kvec1 + WLz/6.) + (r0211*WLz)/2.);
+dr0212_dt = (-(gt*r0212) - (gt + g2)*r0212)/2. - i*(-(conj(Ep3a)*conj(r0602))/(4.*rt2) - (conj(Ep4a)*r0202)/(4.*rt6) + (conj(Em1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1212)/(4.*rt6) - (conj(Em4a)*r1412)/8. + r0112*(WLx/2. + (i*WLy)/2.) - r0213*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0212*WLz)/2. - r0212*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0213_dt = (-(gt*r0213) - (gt + g2)*r0213)/2. - i*(-(conj(Ep4a)*conj(r0302))/8. - (conj(Ep3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1312))/(4.*rt6) + (conj(Em4a)*r0201)/(4.*rt6) + (conj(Em1a)*r1013)/(4.*rt2) - (conj(Em4a)*r1413)/8. - r0212*((2*WLx)/3. - (2*i*WLy)/3.) + r0113*(WLx/2. + (i*WLy)/2.) - r0214*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0213*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + (r0213*WLz)/2.);
+dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*(-(conj(Ep4a)*conj(r0402))/8. - (conj(Em3a)*conj(r0602))/(8.*rt3) - (conj(Ep3a)*conj(r0802))/(8.*rt3) + (conj(Ep4a)*conj(r1412))/(4.*rt6) + (conj(Em4a)*r0202)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 + (conj(Em1a)*r1014)/(4.*rt2) - (conj(Em4a)*r1414)/8. + r0114*(WLx/2. + (i*WLy)/2.) - r0213*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0215*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0214*WLz)/2.);
+dr0215_dt = (-(gt*r0215) - (gt + g2)*r0215)/2. - i*((conj(Em4a)*conj(r0302))/8. - (conj(Ep4a)*conj(r0502))/(4.*rt6) - (conj(Em3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1512))/(4.*rt6) - (conj(Em4a)*conj(r1514))/8. + (conj(Em1a)*r1015)/(4.*rt2) + r0115*(WLx/2. + (i*WLy)/2.) - r0216*((2*WLx)/3. + (2*i*WLy)/3.) - r0214*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0215*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + (r0215*WLz)/2.);
+dr0216_dt = (-(gt*r0216) - (gt + g2)*r0216)/2. - i*((conj(Em4a)*conj(r0402))/(4.*rt6) - (conj(Em3a)*conj(r0802))/(4.*rt2) + (conj(Ep4a)*conj(r1612))/(4.*rt6) - (conj(Em4a)*conj(r1614))/8. + (conj(Em1a)*r1016)/(4.*rt2) - r0215*((2*WLx)/3. - (2*i*WLy)/3.) + r0116*(WLx/2. + (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0216*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + (r0216*WLz)/2.);
+dr0301_dt = -(gt*r0301) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0109))/(4.*rt6) + (conj(Em1a)*conj(r0111))/(4.*rt6) + (conj(Ep4a)*conj(r0113))/8. - (conj(Em4a)*conj(r0115))/8. - (Em1a*r0309)/4. + (Em4a*r0313)/(4.*rt6) - r0302*(WLx/2. + (i*WLy)/2.) + r0401*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0201*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0301*WLz);
+dr0302_dt = -(gt*r0302) + (g1*r1009)/(2.*rt3) + (g1*r1110)/(4.*rt3) + (g2*r1312)/(2.*rt6) + (g2*r1514)/4. - i*((conj(Ep1a)*conj(r0209))/(4.*rt6) + (conj(Em1a)*conj(r0211))/(4.*rt6) + (conj(Ep4a)*conj(r0213))/8. - (conj(Em4a)*conj(r0215))/8. - (Em1a*r0310)/(4.*rt2) - (Ep4a*r0312)/(4.*rt6) + (Em4a*r0314)/8. - r0301*(WLx/2. - (i*WLy)/2.) + r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0202*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0302*WLz)/2.);
+dr0303_dt = gt/8. - gt*r0303 + (g1*r0909)/12. + (g1*r1010)/3. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1515)/4. - i*((conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Em1a)*conj(r0311))/(4.*rt6) + (conj(Ep4a)*conj(r0313))/8. - (conj(Em4a)*conj(r0315))/8. - (Ep1a*r0309)/(4.*rt6) - (Em1a*r0311)/(4.*rt6) - (Ep4a*r0313)/8. + (Em4a*r0315)/8. - r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*((conj(Ep2a)*conj(r0703))/(4.*rt6) + (conj(Ep4a)*conj(r0913))/8. - (conj(Em4a)*conj(r0915))/8. - (conj(Em1a)*r0301)/4. - (conj(Ep1a)*r0303)/(4.*rt6) + (conj(Ep1a)*r0909)/(4.*rt6) + (conj(Em1a)*r1109)/(4.*rt6) + r0409*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0209*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-delta1 - v*Kvec1 - WLz/6.));
+dr0310_dt = (-(gt*r0310) - (gt + g1)*r0310)/2. - i*(-(conj(Ep1a)*conj(r0403))/(4.*rt2) - (conj(Em2a)*conj(r0603))/(4.*rt6) + (conj(Ep2a)*conj(r0803))/(4.*rt6) + (conj(Ep1a)*conj(r1009))/(4.*rt6) + (conj(Ep4a)*conj(r1013))/8. - (conj(Em4a)*conj(r1015))/8. - (conj(Em1a)*r0302)/(4.*rt2) + (delta1 + v*Kvec1)*r0310 + (conj(Em1a)*r1110)/(4.*rt6) + r0410*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0210*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0311*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr0311_dt = (-(gt*r0311) - (gt + g1)*r0311)/2. - i*(-(conj(Ep1a)*conj(r0503))/4. - (conj(Em2a)*conj(r0703))/(4.*rt6) + (conj(Ep1a)*conj(r1109))/(4.*rt6) + (conj(Ep4a)*conj(r1113))/8. - (conj(Em4a)*conj(r1115))/8. - (conj(Em1a)*r0303)/(4.*rt6) + (conj(Em1a)*r1111)/(4.*rt6) + r0411*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0211*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0311*(-delta1 - v*Kvec1 + WLz/6.));
+dr0312_dt = (-(gt*r0312) - (gt + g2)*r0312)/2. - i*(-(conj(Ep3a)*conj(r0603))/(4.*rt2) - (conj(Ep4a)*r0302)/(4.*rt6) + (conj(Ep1a)*r0912)/(4.*rt6) + (conj(Em1a)*r1112)/(4.*rt6) + (conj(Ep4a)*r1312)/8. - (conj(Em4a)*r1512)/8. - r0313*((2*WLx)/3. + (2*i*WLy)/3.) + r0412*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0212*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0313_dt = (-(gt*r0313) - (gt + g2)*r0313)/2. - i*(-(conj(Ep3a)*conj(r0703))/8. + (conj(Em4a)*r0301)/(4.*rt6) - (conj(Ep4a)*r0303)/8. + (conj(Ep1a)*r0913)/(4.*rt6) + (conj(Em1a)*r1113)/(4.*rt6) + (conj(Ep4a)*r1313)/8. - (conj(Em4a)*r1513)/8. - r0312*((2*WLx)/3. - (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0413*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0213*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0313*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0314_dt = (-(gt*r0314) - (gt + g2)*r0314)/2. - i*(-(conj(Ep4a)*conj(r0403))/8. - (conj(Em3a)*conj(r0603))/(8.*rt3) - (conj(Ep3a)*conj(r0803))/(8.*rt3) + (conj(Ep4a)*conj(r1413))/8. + (conj(Em4a)*r0302)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0314 + (conj(Ep1a)*r0914)/(4.*rt6) + (conj(Em1a)*r1114)/(4.*rt6) - (conj(Em4a)*r1514)/8. - r0313*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0315*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0414*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0214*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(conj(Ep4a)*conj(r0503))/(4.*rt6) - (conj(Em3a)*conj(r0703))/8. + (conj(Ep4a)*conj(r1513))/8. + (conj(Em4a)*r0303)/8. + (conj(Ep1a)*r0915)/(4.*rt6) + (conj(Em1a)*r1115)/(4.*rt6) - (conj(Em4a)*r1515)/8. - r0316*((2*WLx)/3. + (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0415*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0215*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0315*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0316_dt = (-(gt*r0316) - (gt + g2)*r0316)/2. - i*((conj(Em4a)*conj(r0403))/(4.*rt6) - (conj(Em3a)*conj(r0803))/(4.*rt2) + (conj(Ep4a)*conj(r1613))/8. - (conj(Em4a)*conj(r1615))/8. + (conj(Ep1a)*r0916)/(4.*rt6) + (conj(Em1a)*r1116)/(4.*rt6) - r0315*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0216*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0316*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr0401_dt = -(gt*r0401) - (g2*r1512)/6. + (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0114))/8. - (conj(Em4a)*conj(r0116))/(4.*rt6) - (Em1a*r0409)/4. + (Em4a*r0413)/(4.*rt6) + r0501*(WLx/2. - (i*WLy)/2.) - r0402*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0401*WLz)/2.);
+dr0402_dt = -(gt*r0402) + (g1*r1109)/4. + (g2*r1412)/(2.*rt6) - (g2*r1513)/12. + (g2*r1614)/(2.*rt6) - i*((conj(Ep1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0214))/8. - (conj(Em4a)*conj(r0216))/(4.*rt6) - (Em1a*r0410)/(4.*rt2) - (Ep4a*r0412)/(4.*rt6) + (Em4a*r0414)/8. - r0401*(WLx/2. - (i*WLy)/2.) + r0502*(WLx/2. - (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0402*WLz);
+dr0403_dt = -(gt*r0403) + (g1*r1009)/(4.*rt3) + (g1*r1110)/(2.*rt3) + (g2*r1413)/4. + (g2*r1615)/(2.*rt6) - i*((conj(Ep1a)*conj(r0310))/(4.*rt2) + (conj(Ep4a)*conj(r0314))/8. - (conj(Em4a)*conj(r0316))/(4.*rt6) - (Ep1a*r0409)/(4.*rt6) - (Em1a*r0411)/(4.*rt6) - (Ep4a*r0413)/8. + (Em4a*r0415)/8. + r0503*(WLx/2. - (i*WLy)/2.) - r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0404*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0403*WLz)/2.);
+dr0404_dt = gt/8. - gt*r0404 + (g1*r1010)/4. + (g1*r1111)/4. + (g2*r1414)/4. + (g2*r1515)/12. + (g2*r1616)/6. - i*((conj(Ep1a)*conj(r0410))/(4.*rt2) + (conj(Ep4a)*conj(r0414))/8. - (conj(Em4a)*conj(r0416))/(4.*rt6) - (Ep1a*r0410)/(4.*rt2) - (Ep4a*r0414)/8. + (Em4a*r0416)/(4.*rt6) + r0504*(WLx/2. - (i*WLy)/2.) - conj(r0504)*(WLx/2. + (i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0409_dt = (-(gt*r0409) - (gt + g1)*r0409)/2. - i*((conj(Ep2a)*conj(r0704))/(4.*rt6) + (conj(Ep4a)*conj(r0914))/8. - (conj(Em4a)*conj(r0916))/(4.*rt6) - (conj(Em1a)*r0401)/4. - (conj(Ep1a)*r0403)/(4.*rt6) + (conj(Ep1a)*r1009)/(4.*rt2) + r0509*(WLx/2. - (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-delta1 - v*Kvec1 - WLz/6.) - (r0409*WLz)/2.);
+dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(conj(Em2a)*conj(r0604))/(4.*rt6) + (conj(Ep2a)*conj(r0804))/(4.*rt6) + (conj(Ep4a)*conj(r1014))/8. - (conj(Em4a)*conj(r1016))/(4.*rt6) - (conj(Em1a)*r0402)/(4.*rt2) - (conj(Ep1a)*r0404)/(4.*rt2) + (delta1 + v*Kvec1)*r0410 + (conj(Ep1a)*r1010)/(4.*rt2) + r0510*(WLx/2. - (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0411*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - (r0410*WLz)/2.);
+dr0411_dt = (-(gt*r0411) - (gt + g1)*r0411)/2. - i*(-(conj(Ep1a)*conj(r0504))/4. - (conj(Em2a)*conj(r0704))/(4.*rt6) + (conj(Ep1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1114))/8. - (conj(Em4a)*conj(r1116))/(4.*rt6) - (conj(Em1a)*r0403)/(4.*rt6) + r0511*(WLx/2. - (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0411*(-delta1 - v*Kvec1 + WLz/6.) - (r0411*WLz)/2.);
+dr0412_dt = (-(gt*r0412) - (gt + g2)*r0412)/2. - i*(-(conj(Ep3a)*conj(r0604))/(4.*rt2) - (conj(Ep4a)*r0402)/(4.*rt6) + (conj(Ep1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1412)/8. - (conj(Em4a)*r1612)/(4.*rt6) + r0512*(WLx/2. - (i*WLy)/2.) - r0413*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0412*WLz)/2. - r0412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0413_dt = (-(gt*r0413) - (gt + g2)*r0413)/2. - i*(-(conj(Ep3a)*conj(r0704))/8. + (conj(Em4a)*r0401)/(4.*rt6) - (conj(Ep4a)*r0403)/8. + (conj(Ep1a)*r1013)/(4.*rt2) + (conj(Ep4a)*r1413)/8. - (conj(Em4a)*r1613)/(4.*rt6) - r0412*((2*WLx)/3. - (2*i*WLy)/3.) + r0513*(WLx/2. - (i*WLy)/2.) - r0414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - (r0413*WLz)/2.);
+dr0414_dt = (-(gt*r0414) - (gt + g2)*r0414)/2. - i*(-(conj(Em3a)*conj(r0604))/(8.*rt3) - (conj(Ep3a)*conj(r0804))/(8.*rt3) + (conj(Em4a)*r0402)/8. - (conj(Ep4a)*r0404)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0414 + (conj(Ep1a)*r1014)/(4.*rt2) + (conj(Ep4a)*r1414)/8. - (conj(Em4a)*r1614)/(4.*rt6) + r0514*(WLx/2. - (i*WLy)/2.) - r0413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0415*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0414*WLz)/2.);
+dr0415_dt = (-(gt*r0415) - (gt + g2)*r0415)/2. - i*(-(conj(Ep4a)*conj(r0504))/(4.*rt6) - (conj(Em3a)*conj(r0704))/8. + (conj(Ep4a)*conj(r1514))/8. + (conj(Em4a)*r0403)/8. + (conj(Ep1a)*r1015)/(4.*rt2) - (conj(Em4a)*r1615)/(4.*rt6) + r0515*(WLx/2. - (i*WLy)/2.) - r0416*((2*WLx)/3. + (2*i*WLy)/3.) - r0414*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0415*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - (r0415*WLz)/2.);
+dr0416_dt = (-(gt*r0416) - (gt + g2)*r0416)/2. - i*(-(conj(Em3a)*conj(r0804))/(4.*rt2) + (conj(Ep4a)*conj(r1614))/8. + (conj(Em4a)*r0404)/(4.*rt6) + (conj(Ep1a)*r1016)/(4.*rt2) - (conj(Em4a)*r1616)/(4.*rt6) - r0415*((2*WLx)/3. - (2*i*WLy)/3.) + r0516*(WLx/2. - (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0416*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - (r0416*WLz)/2.);
+dr0501_dt = -(gt*r0501) - (g2*r1612)/3. - i*((conj(Ep1a)*conj(r0111))/4. + (conj(Ep4a)*conj(r0115))/(4.*rt6) - (Em1a*r0509)/4. + (Em4a*r0513)/(4.*rt6) + r0401*(WLx/2. + (i*WLy)/2.) - r0502*(WLx/2. + (i*WLy)/2.) - 2*r0501*WLz);
+dr0502_dt = -(gt*r0502) + (g2*r1512)/6. - (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0211))/4. + (conj(Ep4a)*conj(r0215))/(4.*rt6) - (Em1a*r0510)/(4.*rt2) - (Ep4a*r0512)/(4.*rt6) + (Em4a*r0514)/8. - r0501*(WLx/2. - (i*WLy)/2.) + r0402*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0502*WLz)/2.);
+dr0503_dt = -(gt*r0503) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0311))/4. + (conj(Ep4a)*conj(r0315))/(4.*rt6) - (Ep1a*r0509)/(4.*rt6) - (Em1a*r0511)/(4.*rt6) - (Ep4a*r0513)/8. + (Em4a*r0515)/8. + r0403*(WLx/2. + (i*WLy)/2.) - r0502*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0504*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0503*WLz);
+dr0504_dt = -(gt*r0504) + (g1*r1110)/(2.*rt2) + (g2*r1514)/(2.*rt6) + (g2*r1615)/6. - i*((conj(Ep1a)*conj(r0411))/4. + (conj(Ep4a)*conj(r0415))/(4.*rt6) - (Ep1a*r0510)/(4.*rt2) - (Ep4a*r0514)/8. + (Em4a*r0516)/(4.*rt6) + r0404*(WLx/2. + (i*WLy)/2.) - r0505*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0504*WLz)/2.);
+dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((conj(Ep1a)*conj(r0511))/4. + (conj(Ep4a)*conj(r0515))/(4.*rt6) - (Ep1a*r0511)/4. - (Ep4a*r0515)/(4.*rt6) - r0504*(WLx/2. - (i*WLy)/2.) + conj(r0504)*(WLx/2. + (i*WLy)/2.));
+dr0509_dt = (-(gt*r0509) - (gt + g1)*r0509)/2. - i*((conj(Ep2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r0915))/(4.*rt6) - (conj(Em1a)*r0501)/4. - (conj(Ep1a)*r0503)/(4.*rt6) + (conj(Ep1a)*r1109)/4. + r0409*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-delta1 - v*Kvec1 - WLz/6.) - r0509*WLz);
+dr0510_dt = (-(gt*r0510) - (gt + g1)*r0510)/2. - i*(-(conj(Em2a)*conj(r0605))/(4.*rt6) + (conj(Ep2a)*conj(r0805))/(4.*rt6) + (conj(Ep4a)*conj(r1015))/(4.*rt6) - (conj(Em1a)*r0502)/(4.*rt2) - (conj(Ep1a)*r0504)/(4.*rt2) + (delta1 + v*Kvec1)*r0510 + (conj(Ep1a)*r1110)/4. + r0410*(WLx/2. + (i*WLy)/2.) - r0511*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0510*WLz);
+dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(conj(Em2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r1115))/(4.*rt6) - (conj(Em1a)*r0503)/(4.*rt6) - (conj(Ep1a)*r0505)/4. + (conj(Ep1a)*r1111)/4. + r0411*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0511*(-delta1 - v*Kvec1 + WLz/6.) - r0511*WLz);
+dr0512_dt = (-(gt*r0512) - (gt + g2)*r0512)/2. - i*(-(conj(Ep3a)*conj(r0605))/(4.*rt2) - (conj(Ep4a)*r0502)/(4.*rt6) + (conj(Ep1a)*r1112)/4. + (conj(Ep4a)*r1512)/(4.*rt6) + r0412*(WLx/2. + (i*WLy)/2.) - r0513*((2*WLx)/3. + (2*i*WLy)/3.) - r0512*WLz - r0512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0513_dt = (-(gt*r0513) - (gt + g2)*r0513)/2. - i*(-(conj(Ep3a)*conj(r0705))/8. + (conj(Em4a)*r0501)/(4.*rt6) - (conj(Ep4a)*r0503)/8. + (conj(Ep1a)*r1113)/4. + (conj(Ep4a)*r1513)/(4.*rt6) - r0512*((2*WLx)/3. - (2*i*WLy)/3.) + r0413*(WLx/2. + (i*WLy)/2.) - r0514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r0513*WLz);
+dr0514_dt = (-(gt*r0514) - (gt + g2)*r0514)/2. - i*(-(conj(Em3a)*conj(r0605))/(8.*rt3) - (conj(Ep3a)*conj(r0805))/(8.*rt3) + (conj(Em4a)*r0502)/8. - (conj(Ep4a)*r0504)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0514 + (conj(Ep1a)*r1114)/4. + (conj(Ep4a)*r1514)/(4.*rt6) + r0414*(WLx/2. + (i*WLy)/2.) - r0513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0514*WLz);
+dr0515_dt = (-(gt*r0515) - (gt + g2)*r0515)/2. - i*(-(conj(Em3a)*conj(r0705))/8. + (conj(Em4a)*r0503)/8. - (conj(Ep4a)*r0505)/(4.*rt6) + (conj(Ep1a)*r1115)/4. + (conj(Ep4a)*r1515)/(4.*rt6) + r0415*(WLx/2. + (i*WLy)/2.) - r0516*((2*WLx)/3. + (2*i*WLy)/3.) - r0514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r0515*WLz);
+dr0516_dt = (-(gt*r0516) - (gt + g2)*r0516)/2. - i*(-(conj(Em3a)*conj(r0805))/(4.*rt2) + (conj(Ep4a)*conj(r1615))/(4.*rt6) + (conj(Em4a)*r0504)/(4.*rt6) + (conj(Ep1a)*r1116)/4. - r0515*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*(WLx/2. + (i*WLy)/2.) - r0516*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r0516*WLz);
+dr0601_dt = -(gt*r0601) - i*((conj(Em2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0112))/(4.*rt2) + (conj(Em3a)*conj(r0114))/(8.*rt3) - (Em1a*r0609)/4. + (Em4a*r0613)/(4.*rt6) - r0602*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0601*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0601*WLz);
+dr0602_dt = -(gt*r0602) - i*((conj(Em2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0212))/(4.*rt2) + (conj(Em3a)*conj(r0214))/(8.*rt3) - (Em1a*r0610)/(4.*rt2) - (Ep4a*r0612)/(4.*rt6) + (Em4a*r0614)/8. - r0601*(WLx/2. - (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0602*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - (r0602*WLz)/2.);
+dr0603_dt = -(gt*r0603) - i*((conj(Em2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0312))/(4.*rt2) + (conj(Em3a)*conj(r0314))/(8.*rt3) - (Ep1a*r0609)/(4.*rt6) - (Em1a*r0611)/(4.*rt6) - (Ep4a*r0613)/8. + (Em4a*r0615)/8. - r0602*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0604*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0603*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0604_dt = -(gt*r0604) - i*((conj(Em2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0412))/(4.*rt2) + (conj(Em3a)*conj(r0414))/(8.*rt3) - (Ep1a*r0610)/(4.*rt2) - (Ep4a*r0614)/8. + (Em4a*r0616)/(4.*rt6) - r0605*(WLx/2. + (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0604*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + (r0604*WLz)/2.);
+dr0605_dt = -(gt*r0605) - i*((conj(Em2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0512))/(4.*rt2) + (conj(Em3a)*conj(r0514))/(8.*rt3) - (Ep1a*r0611)/4. - (Ep4a*r0615)/(4.*rt6) - r0604*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0605*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0605*WLz);
+dr0606_dt = gt/8. - gt*r0606 + (g1*r0909)/12. + (g1*r1010)/12. + (g2*r1212)/2. + (g2*r1313)/4. + (g2*r1414)/12. - i*((conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0612))/(4.*rt2) + (conj(Em3a)*conj(r0614))/(8.*rt3) - (Em2a*r0610)/(4.*rt6) - (Ep3a*r0612)/(4.*rt2) - (Em3a*r0614)/(8.*rt3) - conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0609_dt = (-(gt*r0609) - (gt + g1)*r0609)/2. - i*((conj(Ep2a)*conj(r0706))/(4.*rt6) + (conj(Ep3a)*conj(r0912))/(4.*rt2) + (conj(Em3a)*conj(r0914))/(8.*rt3) - (conj(Em1a)*r0601)/4. - (conj(Ep1a)*r0603)/(4.*rt6) + (conj(Em2a)*r1009)/(4.*rt6) - r0610*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0709*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0609*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0609*(-delta1 - v*Kvec1 - WLz/6.));
+dr0610_dt = (-(gt*r0610) - (gt + g1)*r0610)/2. - i*((conj(Ep2a)*conj(r0806))/(4.*rt6) + (conj(Ep3a)*conj(r1012))/(4.*rt2) + (conj(Em3a)*conj(r1014))/(8.*rt3) - (conj(Em1a)*r0602)/(4.*rt2) - (conj(Ep1a)*r0604)/(4.*rt2) - (conj(Em2a)*r0606)/(4.*rt6) + (delta1 + v*Kvec1)*r0610 + (conj(Em2a)*r1010)/(4.*rt6) - r0611*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0609*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0710*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0610*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0611_dt = (-(gt*r0611) - (gt + g1)*r0611)/2. - i*(-(conj(Em2a)*conj(r0706))/(4.*rt6) + (conj(Em2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1112))/(4.*rt2) + (conj(Em3a)*conj(r1114))/(8.*rt3) - (conj(Em1a)*r0603)/(4.*rt6) - (conj(Ep1a)*r0605)/4. - r0610*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0711*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0611*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0611*(-delta1 - v*Kvec1 + WLz/6.));
+dr0612_dt = (-(gt*r0612) - (gt + g2)*r0612)/2. - i*(-(conj(Ep4a)*r0602)/(4.*rt6) - (conj(Ep3a)*r0606)/(4.*rt2) + (conj(Em2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1212)/(4.*rt2) + (conj(Em3a)*r1412)/(8.*rt3) - r0613*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0612*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0613_dt = (-(gt*r0613) - (gt + g2)*r0613)/2. - i*(-(conj(Ep3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1312))/(4.*rt2) + (conj(Em4a)*r0601)/(4.*rt6) - (conj(Ep4a)*r0603)/8. + (conj(Em2a)*r1013)/(4.*rt6) + (conj(Em3a)*r1413)/(8.*rt3) - r0612*((2*WLx)/3. - (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0613*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0614_dt = (-(gt*r0614) - (gt + g2)*r0614)/2. - i*(-(conj(Ep3a)*conj(r0806))/(8.*rt3) + (conj(Ep3a)*conj(r1412))/(4.*rt2) + (conj(Em4a)*r0602)/8. - (conj(Ep4a)*r0604)/8. - (conj(Em3a)*r0606)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0614 + (conj(Em2a)*r1014)/(4.*rt6) + (conj(Em3a)*r1414)/(8.*rt3) - r0613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0614*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0615_dt = (-(gt*r0615) - (gt + g2)*r0615)/2. - i*(-(conj(Em3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1512))/(4.*rt2) + (conj(Em3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0603)/8. - (conj(Ep4a)*r0605)/(4.*rt6) + (conj(Em2a)*r1015)/(4.*rt6) - r0616*((2*WLx)/3. + (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0615*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0616_dt = (-(gt*r0616) - (gt + g2)*r0616)/2. - i*(-(conj(Em3a)*conj(r0806))/(4.*rt2) + (conj(Ep3a)*conj(r1612))/(4.*rt2) + (conj(Em3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0604)/(4.*rt6) + (conj(Em2a)*r1016)/(4.*rt6) - r0615*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0616*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0616*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0701_dt = -(gt*r0701) - i*(-(conj(Ep2a)*conj(r0109))/(4.*rt6) + (conj(Em2a)*conj(r0111))/(4.*rt6) + (conj(Ep3a)*conj(r0113))/8. + (conj(Em3a)*conj(r0115))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0701 - (Em1a*r0709)/4. + (Em4a*r0713)/(4.*rt6) - r0702*(WLx/2. + (i*WLy)/2.) + r0601*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0701*WLz);
+dr0702_dt = -(gt*r0702) - i*(-(conj(Ep2a)*conj(r0209))/(4.*rt6) + (conj(Em2a)*conj(r0211))/(4.*rt6) + (conj(Ep3a)*conj(r0213))/8. + (conj(Em3a)*conj(r0215))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0702 - (Em1a*r0710)/(4.*rt2) - (Ep4a*r0712)/(4.*rt6) + (Em4a*r0714)/8. - r0701*(WLx/2. - (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0602*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - (r0702*WLz)/2.);
+dr0703_dt = -(gt*r0703) - i*(-(conj(Ep2a)*conj(r0309))/(4.*rt6) + (conj(Em2a)*conj(r0311))/(4.*rt6) + (conj(Ep3a)*conj(r0313))/8. + (conj(Em3a)*conj(r0315))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 - (Ep1a*r0709)/(4.*rt6) - (Em1a*r0711)/(4.*rt6) - (Ep4a*r0713)/8. + (Em4a*r0715)/8. - r0702*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0704*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0603*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0704_dt = -(gt*r0704) - i*(-(conj(Ep2a)*conj(r0409))/(4.*rt6) + (conj(Em2a)*conj(r0411))/(4.*rt6) + (conj(Ep3a)*conj(r0413))/8. + (conj(Em3a)*conj(r0415))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0704 - (Ep1a*r0710)/(4.*rt2) - (Ep4a*r0714)/8. + (Em4a*r0716)/(4.*rt6) - r0705*(WLx/2. + (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0604*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + (r0704*WLz)/2.);
+dr0705_dt = -(gt*r0705) - i*(-(conj(Ep2a)*conj(r0509))/(4.*rt6) + (conj(Em2a)*conj(r0511))/(4.*rt6) + (conj(Ep3a)*conj(r0513))/8. + (conj(Em3a)*conj(r0515))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0705 - (Ep1a*r0711)/4. - (Ep4a*r0715)/(4.*rt6) - r0704*(WLx/2. - (i*WLy)/2.) + r0605*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0705*WLz);
+dr0706_dt = -(gt*r0706) + (g1*r1110)/12. + (g2*r1312)/(2.*rt2) + (g2*r1413)/(2.*rt3) + (g2*r1514)/(4.*rt3) - i*(-(conj(Ep2a)*conj(r0609))/(4.*rt6) + (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep3a)*conj(r0613))/8. + (conj(Em3a)*conj(r0615))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0706 - (Em2a*r0710)/(4.*rt6) - (Ep3a*r0712)/(4.*rt2) - (Em3a*r0714)/(8.*rt3) + r0606*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0706*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0707_dt = gt/8. - gt*r0707 + (g1*r0909)/12. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1414)/3. + (g2*r1515)/4. - i*(-(conj(Ep2a)*conj(r0709))/(4.*rt6) + (conj(Em2a)*conj(r0711))/(4.*rt6) + (conj(Ep3a)*conj(r0713))/8. + (conj(Em3a)*conj(r0715))/8. + (Ep2a*r0709)/(4.*rt6) - (Em2a*r0711)/(4.*rt6) - (Ep3a*r0713)/8. - (Em3a*r0715)/8. + conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*((conj(Ep3a)*conj(r0913))/8. + (conj(Em3a)*conj(r0915))/8. - (conj(Em1a)*r0701)/4. - (conj(Ep1a)*r0703)/(4.*rt6) + (conj(Ep2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0709 - (conj(Ep2a)*r0909)/(4.*rt6) + (conj(Em2a)*r1109)/(4.*rt6) + r0609*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0809*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0709*(-delta1 - v*Kvec1 - WLz/6.));
+dr0710_dt = (-(gt*r0710) - (gt + g1)*r0710)/2. - i*((conj(Ep2a)*conj(r0807))/(4.*rt6) - (conj(Ep2a)*conj(r1009))/(4.*rt6) + (conj(Ep3a)*conj(r1013))/8. + (conj(Em3a)*conj(r1015))/8. - (conj(Em1a)*r0702)/(4.*rt2) - (conj(Ep1a)*r0704)/(4.*rt2) - (conj(Em2a)*r0706)/(4.*rt6) + (delta1 + v*Kvec1)*r0710 + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0710 + (conj(Em2a)*r1110)/(4.*rt6) + r0610*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0711*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0709*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0711_dt = (-(gt*r0711) - (gt + g1)*r0711)/2. - i*(-(conj(Ep2a)*conj(r1109))/(4.*rt6) + (conj(Ep3a)*conj(r1113))/8. + (conj(Em3a)*conj(r1115))/8. - (conj(Em1a)*r0703)/(4.*rt6) - (conj(Ep1a)*r0705)/4. - (conj(Em2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0711 + (conj(Em2a)*r1111)/(4.*rt6) + r0611*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0811*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0711*(-delta1 - v*Kvec1 + WLz/6.));
+dr0712_dt = (-(gt*r0712) - (gt + g2)*r0712)/2. - i*(-(conj(Ep4a)*r0702)/(4.*rt6) - (conj(Ep3a)*r0706)/(4.*rt2) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0712 - (conj(Ep2a)*r0912)/(4.*rt6) + (conj(Em2a)*r1112)/(4.*rt6) + (conj(Ep3a)*r1312)/8. + (conj(Em3a)*r1512)/8. - r0713*((2*WLx)/3. + (2*i*WLy)/3.) + r0612*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0712*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0713_dt = (-(gt*r0713) - (gt + g2)*r0713)/2. - i*((conj(Em4a)*r0701)/(4.*rt6) - (conj(Ep4a)*r0703)/8. - (conj(Ep3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0713 - (conj(Ep2a)*r0913)/(4.*rt6) + (conj(Em2a)*r1113)/(4.*rt6) + (conj(Ep3a)*r1313)/8. + (conj(Em3a)*r1513)/8. - r0712*((2*WLx)/3. - (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0613*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0713*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0714_dt = (-(gt*r0714) - (gt + g2)*r0714)/2. - i*(-(conj(Ep3a)*conj(r0807))/(8.*rt3) + (conj(Ep3a)*conj(r1413))/8. + (conj(Em4a)*r0702)/8. - (conj(Ep4a)*r0704)/8. - (conj(Em3a)*r0706)/(8.*rt3) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0714 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0714 - (conj(Ep2a)*r0914)/(4.*rt6) + (conj(Em2a)*r1114)/(4.*rt6) + (conj(Em3a)*r1514)/8. - r0713*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0715*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0614*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0715_dt = (-(gt*r0715) - (gt + g2)*r0715)/2. - i*((conj(Ep3a)*conj(r1513))/8. + (conj(Em4a)*r0703)/8. - (conj(Ep4a)*r0705)/(4.*rt6) - (conj(Em3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0715 - (conj(Ep2a)*r0915)/(4.*rt6) + (conj(Em2a)*r1115)/(4.*rt6) + (conj(Em3a)*r1515)/8. - r0716*((2*WLx)/3. + (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0615*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0815*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0715*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0716_dt = (-(gt*r0716) - (gt + g2)*r0716)/2. - i*(-(conj(Em3a)*conj(r0807))/(4.*rt2) + (conj(Ep3a)*conj(r1613))/8. + (conj(Em3a)*conj(r1615))/8. + (conj(Em4a)*r0704)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0716 - (conj(Ep2a)*r0916)/(4.*rt6) + (conj(Em2a)*r1116)/(4.*rt6) - r0715*((2*WLx)/3. - (2*i*WLy)/3.) + r0616*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0816*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0716*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr0801_dt = -(gt*r0801) - i*(-(conj(Ep2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0114))/(8.*rt3) + (conj(Em3a)*conj(r0116))/(4.*rt2) - (Em1a*r0809)/4. + (Em4a*r0813)/(4.*rt6) - r0802*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0801*WLz);
+dr0802_dt = -(gt*r0802) - i*(-(conj(Ep2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0214))/(8.*rt3) + (conj(Em3a)*conj(r0216))/(4.*rt2) - (Em1a*r0810)/(4.*rt2) - (Ep4a*r0812)/(4.*rt6) + (Em4a*r0814)/8. - r0801*(WLx/2. - (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - (r0802*WLz)/2.);
+dr0803_dt = -(gt*r0803) - i*(-(conj(Ep2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0314))/(8.*rt3) + (conj(Em3a)*conj(r0316))/(4.*rt2) - (Ep1a*r0809)/(4.*rt6) - (Em1a*r0811)/(4.*rt6) - (Ep4a*r0813)/8. + (Em4a*r0815)/8. - r0802*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0804*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0804_dt = -(gt*r0804) - i*(-(conj(Ep2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0414))/(8.*rt3) + (conj(Em3a)*conj(r0416))/(4.*rt2) - (Ep1a*r0810)/(4.*rt2) - (Ep4a*r0814)/8. + (Em4a*r0816)/(4.*rt6) - r0805*(WLx/2. + (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + (r0804*WLz)/2.);
+dr0805_dt = -(gt*r0805) - i*(-(conj(Ep2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0514))/(8.*rt3) + (conj(Em3a)*conj(r0516))/(4.*rt2) - (Ep1a*r0811)/4. - (Ep4a*r0815)/(4.*rt6) - r0804*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + r0805*WLz);
+dr0806_dt = -(gt*r0806) - (g1*r1109)/12. + (g2*r1412)/(2.*rt6) + (g2*r1513)/4. + (g2*r1614)/(2.*rt6) - i*(-(conj(Ep2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0614))/(8.*rt3) + (conj(Em3a)*conj(r0616))/(4.*rt2) - (Em2a*r0810)/(4.*rt6) - (Ep3a*r0812)/(4.*rt2) - (Em3a*r0814)/(8.*rt3) + r0706*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0807_dt = -(gt*r0807) + (g1*r1009)/12. + (g2*r1413)/(4.*rt3) + (g2*r1514)/(2.*rt3) + (g2*r1615)/(2.*rt2) - i*(-(conj(Ep2a)*conj(r0710))/(4.*rt6) + (conj(Ep3a)*conj(r0714))/(8.*rt3) + (conj(Em3a)*conj(r0716))/(4.*rt2) - (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0807 + (Ep2a*r0809)/(4.*rt6) - (Em2a*r0811)/(4.*rt6) - (Ep3a*r0813)/8. - (Em3a*r0815)/8. + r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0808*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0808_dt = gt/8. - gt*r0808 + (g1*r1010)/12. + (g1*r1111)/12. + (g2*r1414)/12. + (g2*r1515)/4. + (g2*r1616)/2. - i*(-(conj(Ep2a)*conj(r0810))/(4.*rt6) + (conj(Ep3a)*conj(r0814))/(8.*rt3) + (conj(Em3a)*conj(r0816))/(4.*rt2) + (Ep2a*r0810)/(4.*rt6) - (Ep3a*r0814)/(8.*rt3) - (Em3a*r0816)/(4.*rt2) + conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0809_dt = (-(gt*r0809) - (gt + g1)*r0809)/2. - i*((conj(Ep3a)*conj(r0914))/(8.*rt3) + (conj(Em3a)*conj(r0916))/(4.*rt2) - (conj(Em1a)*r0801)/4. - (conj(Ep1a)*r0803)/(4.*rt6) + (conj(Ep2a)*r0807)/(4.*rt6) - (conj(Ep2a)*r1009)/(4.*rt6) + r0709*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-delta1 - v*Kvec1 - WLz/6.) + r0809*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0810_dt = (-(gt*r0810) - (gt + g1)*r0810)/2. - i*((conj(Ep3a)*conj(r1014))/(8.*rt3) + (conj(Em3a)*conj(r1016))/(4.*rt2) - (conj(Em1a)*r0802)/(4.*rt2) - (conj(Ep1a)*r0804)/(4.*rt2) - (conj(Em2a)*r0806)/(4.*rt6) + (conj(Ep2a)*r0808)/(4.*rt6) + (delta1 + v*Kvec1)*r0810 - (conj(Ep2a)*r1010)/(4.*rt6) + r0710*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0811*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0811_dt = (-(gt*r0811) - (gt + g1)*r0811)/2. - i*(-(conj(Ep2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1114))/(8.*rt3) + (conj(Em3a)*conj(r1116))/(4.*rt2) - (conj(Em1a)*r0803)/(4.*rt6) - (conj(Ep1a)*r0805)/4. - (conj(Em2a)*r0807)/(4.*rt6) + r0711*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0811*(-delta1 - v*Kvec1 + WLz/6.) + r0811*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0812_dt = (-(gt*r0812) - (gt + g2)*r0812)/2. - i*(-(conj(Ep4a)*r0802)/(4.*rt6) - (conj(Ep3a)*r0806)/(4.*rt2) - (conj(Ep2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1412)/(8.*rt3) + (conj(Em3a)*r1612)/(4.*rt2) - r0813*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0812*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0813_dt = (-(gt*r0813) - (gt + g2)*r0813)/2. - i*((conj(Em4a)*r0801)/(4.*rt6) - (conj(Ep4a)*r0803)/8. - (conj(Ep3a)*r0807)/8. - (conj(Ep2a)*r1013)/(4.*rt6) + (conj(Ep3a)*r1413)/(8.*rt3) + (conj(Em3a)*r1613)/(4.*rt2) - r0812*((2*WLx)/3. - (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0813*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0814_dt = (-(gt*r0814) - (gt + g2)*r0814)/2. - i*((conj(Em4a)*r0802)/8. - (conj(Ep4a)*r0804)/8. - (conj(Em3a)*r0806)/(8.*rt3) - (conj(Ep3a)*r0808)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0814 - (conj(Ep2a)*r1014)/(4.*rt6) + (conj(Ep3a)*r1414)/(8.*rt3) + (conj(Em3a)*r1614)/(4.*rt2) - r0813*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0815*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0815_dt = (-(gt*r0815) - (gt + g2)*r0815)/2. - i*((conj(Ep3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0803)/8. - (conj(Ep4a)*r0805)/(4.*rt6) - (conj(Em3a)*r0807)/8. - (conj(Ep2a)*r1015)/(4.*rt6) + (conj(Em3a)*r1615)/(4.*rt2) - r0816*((2*WLx)/3. + (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0815*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0815*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0816_dt = (-(gt*r0816) - (gt + g2)*r0816)/2. - i*((conj(Ep3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0804)/(4.*rt6) - (conj(Em3a)*r0808)/(4.*rt2) - (conj(Ep2a)*r1016)/(4.*rt6) + (conj(Em3a)*r1616)/(4.*rt2) - r0815*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0816*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0816*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0909_dt = -((gt + g1)*r0909) - i*(-(conj(Em1a)*conj(r0109))/4. - (conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Ep2a)*conj(r0709))/(4.*rt6) + (Em1a*r0109)/4. + (Ep1a*r0309)/(4.*rt6) - (Ep2a*r0709)/(4.*rt6) - conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr0912_dt = (-((gt + g1)*r0912) - (gt + g2)*r0912)/2. - i*(-(conj(Ep4a)*conj(r0209))/(4.*rt6) - (conj(Ep3a)*conj(r0609))/(4.*rt2) + (Em1a*r0112)/4. + (Ep1a*r0312)/(4.*rt6) - (Ep2a*r0712)/(4.*rt6) - r0913*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0912*(-delta1 - v*Kvec1 - WLz/6.) - r0912*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0913_dt = (-((gt + g1)*r0913) - (gt + g2)*r0913)/2. - i*((conj(Em4a)*conj(r0109))/(4.*rt6) - (conj(Ep4a)*conj(r0309))/8. - (conj(Ep3a)*conj(r0709))/8. + (Em1a*r0113)/4. + (Ep1a*r0313)/(4.*rt6) - (Ep2a*r0713)/(4.*rt6) - r0912*((2*WLx)/3. - (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0913*(-delta1 - v*Kvec1 - WLz/6.) - r0913*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0914_dt = (-((gt + g1)*r0914) - (gt + g2)*r0914)/2. - i*((conj(Em4a)*conj(r0209))/8. - (conj(Ep4a)*conj(r0409))/8. - (conj(Em3a)*conj(r0609))/(8.*rt3) - (conj(Ep3a)*conj(r0809))/(8.*rt3) + (Em1a*r0114)/4. + (Ep1a*r0314)/(4.*rt6) - (Ep2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0914 - r0913*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0915*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0914*(-delta1 - v*Kvec1 - WLz/6.));
+dr0915_dt = (-((gt + g1)*r0915) - (gt + g2)*r0915)/2. - i*((conj(Em4a)*conj(r0309))/8. - (conj(Ep4a)*conj(r0509))/(4.*rt6) - (conj(Em3a)*conj(r0709))/8. + (Em1a*r0115)/4. + (Ep1a*r0315)/(4.*rt6) - (Ep2a*r0715)/(4.*rt6) - r0916*((2*WLx)/3. + (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0915*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0915*(-delta1 - v*Kvec1 - WLz/6.));
+dr0916_dt = (-((gt + g1)*r0916) - (gt + g2)*r0916)/2. - i*((conj(Em4a)*conj(r0409))/(4.*rt6) - (conj(Em3a)*conj(r0809))/(4.*rt2) + (Em1a*r0116)/4. + (Ep1a*r0316)/(4.*rt6) - (Ep2a*r0716)/(4.*rt6) - r0915*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0916*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0916*(-delta1 - v*Kvec1 - WLz/6.));
+dr1009_dt = -((gt + g1)*r1009) - i*(-(conj(Em1a)*conj(r0110))/4. - (conj(Ep1a)*conj(r0310))/(4.*rt6) + (conj(Ep2a)*conj(r0710))/(4.*rt6) + (Em1a*r0209)/(4.*rt2) + (Ep1a*r0409)/(4.*rt2) + (Em2a*r0609)/(4.*rt6) - (Ep2a*r0809)/(4.*rt6) - (delta1 + v*Kvec1)*r1009 + r0909*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1009*(-delta1 - v*Kvec1 - WLz/6.));
+dr1010_dt = -((gt + g1)*r1010) - i*(-(conj(Em1a)*conj(r0210))/(4.*rt2) - (conj(Ep1a)*conj(r0410))/(4.*rt2) - (conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep2a)*conj(r0810))/(4.*rt6) + (Em1a*r0210)/(4.*rt2) + (Ep1a*r0410)/(4.*rt2) + (Em2a*r0610)/(4.*rt6) - (Ep2a*r0810)/(4.*rt6) + conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1012_dt = (-((gt + g1)*r1012) - (gt + g2)*r1012)/2. - i*(-(conj(Ep4a)*conj(r0210))/(4.*rt6) - (conj(Ep3a)*conj(r0610))/(4.*rt2) + (Em1a*r0212)/(4.*rt2) + (Ep1a*r0412)/(4.*rt2) + (Em2a*r0612)/(4.*rt6) - (Ep2a*r0812)/(4.*rt6) - (delta1 + v*Kvec1)*r1012 - r1013*((2*WLx)/3. + (2*i*WLy)/3.) + r0912*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1012*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1013_dt = (-((gt + g1)*r1013) - (gt + g2)*r1013)/2. - i*((conj(Em4a)*conj(r0110))/(4.*rt6) - (conj(Ep4a)*conj(r0310))/8. - (conj(Ep3a)*conj(r0710))/8. + (Em1a*r0213)/(4.*rt2) + (Ep1a*r0413)/(4.*rt2) + (Em2a*r0613)/(4.*rt6) - (Ep2a*r0813)/(4.*rt6) - (delta1 + v*Kvec1)*r1013 - r1012*((2*WLx)/3. - (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0913*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1013*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1014_dt = (-((gt + g1)*r1014) - (gt + g2)*r1014)/2. - i*((conj(Em4a)*conj(r0210))/8. - (conj(Ep4a)*conj(r0410))/8. - (conj(Em3a)*conj(r0610))/(8.*rt3) - (conj(Ep3a)*conj(r0810))/(8.*rt3) + (Em1a*r0214)/(4.*rt2) + (Ep1a*r0414)/(4.*rt2) + (Em2a*r0614)/(4.*rt6) - (Ep2a*r0814)/(4.*rt6) - (delta1 + v*Kvec1)*r1014 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1014 - r1013*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1015*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0914*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1015_dt = (-((gt + g1)*r1015) - (gt + g2)*r1015)/2. - i*((conj(Em4a)*conj(r0310))/8. - (conj(Ep4a)*conj(r0510))/(4.*rt6) - (conj(Em3a)*conj(r0710))/8. + (Em1a*r0215)/(4.*rt2) + (Ep1a*r0415)/(4.*rt2) + (Em2a*r0615)/(4.*rt6) - (Ep2a*r0815)/(4.*rt6) - (delta1 + v*Kvec1)*r1015 - r1016*((2*WLx)/3. + (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0915*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1115*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1015*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1016_dt = (-((gt + g1)*r1016) - (gt + g2)*r1016)/2. - i*((conj(Em4a)*conj(r0410))/(4.*rt6) - (conj(Em3a)*conj(r0810))/(4.*rt2) + (Em1a*r0216)/(4.*rt2) + (Ep1a*r0416)/(4.*rt2) + (Em2a*r0616)/(4.*rt6) - (Ep2a*r0816)/(4.*rt6) - (delta1 + v*Kvec1)*r1016 - r1015*((2*WLx)/3. - (2*i*WLy)/3.) + r0916*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1116*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1016*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr1109_dt = -((gt + g1)*r1109) - i*(-(conj(Em1a)*conj(r0111))/4. - (conj(Ep1a)*conj(r0311))/(4.*rt6) + (conj(Ep2a)*conj(r0711))/(4.*rt6) + (Em1a*r0309)/(4.*rt6) + (Ep1a*r0509)/4. + (Em2a*r0709)/(4.*rt6) + r1009*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-delta1 - v*Kvec1 - WLz/6.) + r1109*(-delta1 - v*Kvec1 + WLz/6.));
+dr1110_dt = -((gt + g1)*r1110) - i*(-(conj(Em1a)*conj(r0211))/(4.*rt2) - (conj(Ep1a)*conj(r0411))/(4.*rt2) - (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep2a)*conj(r0811))/(4.*rt6) + (Em1a*r0310)/(4.*rt6) + (Ep1a*r0510)/4. + (Em2a*r0710)/(4.*rt6) + (delta1 + v*Kvec1)*r1110 + r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-delta1 - v*Kvec1 + WLz/6.));
+dr1111_dt = -((gt + g1)*r1111) - i*(-(conj(Em1a)*conj(r0311))/(4.*rt6) - (conj(Ep1a)*conj(r0511))/4. - (conj(Em2a)*conj(r0711))/(4.*rt6) + (Em1a*r0311)/(4.*rt6) + (Ep1a*r0511)/4. + (Em2a*r0711)/(4.*rt6) + conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1112_dt = (-((gt + g1)*r1112) - (gt + g2)*r1112)/2. - i*(-(conj(Ep4a)*conj(r0211))/(4.*rt6) - (conj(Ep3a)*conj(r0611))/(4.*rt2) + (Em1a*r0312)/(4.*rt6) + (Ep1a*r0512)/4. + (Em2a*r0712)/(4.*rt6) - r1113*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-delta1 - v*Kvec1 + WLz/6.) - r1112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1113_dt = (-((gt + g1)*r1113) - (gt + g2)*r1113)/2. - i*((conj(Em4a)*conj(r0111))/(4.*rt6) - (conj(Ep4a)*conj(r0311))/8. - (conj(Ep3a)*conj(r0711))/8. + (Em1a*r0313)/(4.*rt6) + (Ep1a*r0513)/4. + (Em2a*r0713)/(4.*rt6) - r1112*((2*WLx)/3. - (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-delta1 - v*Kvec1 + WLz/6.) - r1113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1114_dt = (-((gt + g1)*r1114) - (gt + g2)*r1114)/2. - i*((conj(Em4a)*conj(r0211))/8. - (conj(Ep4a)*conj(r0411))/8. - (conj(Em3a)*conj(r0611))/(8.*rt3) - (conj(Ep3a)*conj(r0811))/(8.*rt3) + (Em1a*r0314)/(4.*rt6) + (Ep1a*r0514)/4. + (Em2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1114 - r1113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-delta1 - v*Kvec1 + WLz/6.));
+dr1115_dt = (-((gt + g1)*r1115) - (gt + g2)*r1115)/2. - i*((conj(Em4a)*conj(r0311))/8. - (conj(Ep4a)*conj(r0511))/(4.*rt6) - (conj(Em3a)*conj(r0711))/8. + (Em1a*r0315)/(4.*rt6) + (Ep1a*r0515)/4. + (Em2a*r0715)/(4.*rt6) - r1116*((2*WLx)/3. + (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r1115*(-delta1 - v*Kvec1 + WLz/6.));
+dr1116_dt = (-((gt + g1)*r1116) - (gt + g2)*r1116)/2. - i*((conj(Em4a)*conj(r0411))/(4.*rt6) - (conj(Em3a)*conj(r0811))/(4.*rt2) + (Em1a*r0316)/(4.*rt6) + (Ep1a*r0516)/4. + (Em2a*r0716)/(4.*rt6) - r1115*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r1116*(-delta1 - v*Kvec1 + WLz/6.));
+dr1212_dt = -((gt + g2)*r1212) - i*(-(conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Ep3a)*conj(r0612))/(4.*rt2) + (Ep4a*r0212)/(4.*rt6) + (Ep3a*r0612)/(4.*rt2) + r1312*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.));
+dr1312_dt = -((gt + g2)*r1312) - i*(-(conj(Ep4a)*conj(r0213))/(4.*rt6) - (conj(Ep3a)*conj(r0613))/(4.*rt2) - (Em4a*r0112)/(4.*rt6) + (Ep4a*r0312)/8. + (Ep3a*r0712)/8. + r1212*((2*WLx)/3. + (2*i*WLy)/3.) - r1313*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1313_dt = -((gt + g2)*r1313) - i*((conj(Em4a)*conj(r0113))/(4.*rt6) - (conj(Ep4a)*conj(r0313))/8. - (conj(Ep3a)*conj(r0713))/8. - (Em4a*r0113)/(4.*rt6) + (Ep4a*r0313)/8. + (Ep3a*r0713)/8. - r1312*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1412_dt = -((gt + g2)*r1412) - i*(-(conj(Ep4a)*conj(r0214))/(4.*rt6) - (conj(Ep3a)*conj(r0614))/(4.*rt2) - (Em4a*r0212)/8. + (Ep4a*r0412)/8. + (Em3a*r0612)/(8.*rt3) + (Ep3a*r0812)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1412 - r1413*((2*WLx)/3. + (2*i*WLy)/3.) + r1512*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1413_dt = -((gt + g2)*r1413) - i*((conj(Em4a)*conj(r0114))/(4.*rt6) - (conj(Ep4a)*conj(r0314))/8. - (conj(Ep3a)*conj(r0714))/8. - (Em4a*r0213)/8. + (Ep4a*r0413)/8. + (Em3a*r0613)/(8.*rt3) + (Ep3a*r0813)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1413 - r1412*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1313*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1414_dt = -((gt + g2)*r1414) - i*((conj(Em4a)*conj(r0214))/8. - (conj(Ep4a)*conj(r0414))/8. - (conj(Em3a)*conj(r0614))/(8.*rt3) - (conj(Ep3a)*conj(r0814))/(8.*rt3) - (Em4a*r0214)/8. + (Ep4a*r0414)/8. + (Em3a*r0614)/(8.*rt3) + (Ep3a*r0814)/(8.*rt3) - r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1512_dt = -((gt + g2)*r1512) - i*(-(conj(Ep4a)*conj(r0215))/(4.*rt6) - (conj(Ep3a)*conj(r0615))/(4.*rt2) - (Em4a*r0312)/8. + (Ep4a*r0512)/(4.*rt6) + (Em3a*r0712)/8. + r1612*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1513_dt = -((gt + g2)*r1513) - i*((conj(Em4a)*conj(r0115))/(4.*rt6) - (conj(Ep4a)*conj(r0315))/8. - (conj(Ep3a)*conj(r0715))/8. - (Em4a*r0313)/8. + (Ep4a*r0513)/(4.*rt6) + (Em3a*r0713)/8. - r1512*((2*WLx)/3. - (2*i*WLy)/3.) + r1613*((2*WLx)/3. - (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1514_dt = -((gt + g2)*r1514) - i*((conj(Em4a)*conj(r0215))/8. - (conj(Ep4a)*conj(r0415))/8. - (conj(Em3a)*conj(r0615))/(8.*rt3) - (conj(Ep3a)*conj(r0815))/(8.*rt3) - (Em4a*r0314)/8. + (Ep4a*r0514)/(4.*rt6) + (Em3a*r0714)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1514 + r1614*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1514*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1515_dt = -((gt + g2)*r1515) - i*((conj(Em4a)*conj(r0315))/8. - (conj(Ep4a)*conj(r0515))/(4.*rt6) - (conj(Em3a)*conj(r0715))/8. - (Em4a*r0315)/8. + (Ep4a*r0515)/(4.*rt6) + (Em3a*r0715)/8. + r1615*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.) - r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1612_dt = -((gt + g2)*r1612) - i*(-(conj(Ep4a)*conj(r0216))/(4.*rt6) - (conj(Ep3a)*conj(r0616))/(4.*rt2) - (Em4a*r0412)/(4.*rt6) + (Em3a*r0812)/(4.*rt2) + r1512*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*((2*WLx)/3. + (2*i*WLy)/3.) + r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1613_dt = -((gt + g2)*r1613) - i*((conj(Em4a)*conj(r0116))/(4.*rt6) - (conj(Ep4a)*conj(r0316))/8. - (conj(Ep3a)*conj(r0716))/8. - (Em4a*r0413)/(4.*rt6) + (Em3a*r0813)/(4.*rt2) - r1612*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1614_dt = -((gt + g2)*r1614) - i*((conj(Em4a)*conj(r0216))/8. - (conj(Ep4a)*conj(r0416))/8. - (conj(Em3a)*conj(r0616))/(8.*rt3) - (conj(Ep3a)*conj(r0816))/(8.*rt3) - (Em4a*r0414)/(4.*rt6) + (Em3a*r0814)/(4.*rt2) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1614 + r1514*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1614*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr1615_dt = -((gt + g2)*r1615) - i*((conj(Em4a)*conj(r0316))/8. - (conj(Ep4a)*conj(r0516))/(4.*rt6) - (conj(Em3a)*conj(r0716))/8. - (Em4a*r0415)/(4.*rt6) + (Em3a*r0815)/(4.*rt2) + r1515*((2*WLx)/3. + (2*i*WLy)/3.) - r1616*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1616_dt = -((gt + g2)*r1616) - i*((conj(Em4a)*conj(r0416))/(4.*rt6) - (conj(Em3a)*conj(r0816))/(4.*rt2) - (Em4a*r0416)/(4.*rt6) + (Em3a*r0816)/(4.*rt2) - r1615*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.));
+//---------------- RbEquations.cdata ends  ------------------
+]]>
diff --git a/xmds2/realistic_Rb_and_fields/RbInits.cdata b/xmds2/realistic_Rb_and_fields/RbInits.cdata
new file mode 100644
index 0000000..0e04ec5
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/RbInits.cdata
@@ -0,0 +1,140 @@
+<![CDATA[
+//---------------- RbInits.cdata starts ------------------
+r0101 = 0.125;
+r0109 = 0;
+r0110 = 0;
+r0111 = 0;
+r0112 = 0;
+r0113 = 0;
+r0114 = 0;
+r0115 = 0;
+r0116 = 0;
+r0201 = 0;
+r0202 = 0.125;
+r0209 = 0;
+r0210 = 0;
+r0211 = 0;
+r0212 = 0;
+r0213 = 0;
+r0214 = 0;
+r0215 = 0;
+r0216 = 0;
+r0301 = 0;
+r0302 = 0;
+r0303 = 0.125;
+r0309 = 0;
+r0310 = 0;
+r0311 = 0;
+r0312 = 0;
+r0313 = 0;
+r0314 = 0;
+r0315 = 0;
+r0316 = 0;
+r0401 = 0;
+r0402 = 0;
+r0403 = 0;
+r0404 = 0.125;
+r0409 = 0;
+r0410 = 0;
+r0411 = 0;
+r0412 = 0;
+r0413 = 0;
+r0414 = 0;
+r0415 = 0;
+r0416 = 0;
+r0501 = 0;
+r0502 = 0;
+r0503 = 0;
+r0504 = 0;
+r0505 = 0.125;
+r0509 = 0;
+r0510 = 0;
+r0511 = 0;
+r0512 = 0;
+r0513 = 0;
+r0514 = 0;
+r0515 = 0;
+r0516 = 0;
+r0601 = 0;
+r0602 = 0;
+r0603 = 0;
+r0604 = 0;
+r0605 = 0;
+r0606 = 0.125;
+r0609 = 0;
+r0610 = 0;
+r0611 = 0;
+r0612 = 0;
+r0613 = 0;
+r0614 = 0;
+r0615 = 0;
+r0616 = 0;
+r0701 = 0;
+r0702 = 0;
+r0703 = 0;
+r0704 = 0;
+r0705 = 0;
+r0706 = 0;
+r0707 = 0.125;
+r0709 = 0;
+r0710 = 0;
+r0711 = 0;
+r0712 = 0;
+r0713 = 0;
+r0714 = 0;
+r0715 = 0;
+r0716 = 0;
+r0801 = 0;
+r0802 = 0;
+r0803 = 0;
+r0804 = 0;
+r0805 = 0;
+r0806 = 0;
+r0807 = 0;
+r0808 = 0.125;
+r0809 = 0;
+r0810 = 0;
+r0811 = 0;
+r0812 = 0;
+r0813 = 0;
+r0814 = 0;
+r0815 = 0;
+r0816 = 0;
+r0909 = 0;
+r0912 = 0;
+r0913 = 0;
+r0914 = 0;
+r0915 = 0;
+r0916 = 0;
+r1009 = 0;
+r1010 = 0;
+r1012 = 0;
+r1013 = 0;
+r1014 = 0;
+r1015 = 0;
+r1016 = 0;
+r1109 = 0;
+r1110 = 0;
+r1111 = 0;
+r1112 = 0;
+r1113 = 0;
+r1114 = 0;
+r1115 = 0;
+r1116 = 0;
+r1212 = 0;
+r1312 = 0;
+r1313 = 0;
+r1412 = 0;
+r1413 = 0;
+r1414 = 0;
+r1512 = 0;
+r1513 = 0;
+r1514 = 0;
+r1515 = 0;
+r1612 = 0;
+r1613 = 0;
+r1614 = 0;
+r1615 = 0;
+r1616 = 0;
+//---------------- RbInits.cdata ends  ------------------
+]]>
diff --git a/xmds2/realistic_Rb_and_fields/RbInits.h b/xmds2/realistic_Rb_and_fields/RbInits.h
deleted file mode 100644
index a52ec17..0000000
--- a/xmds2/realistic_Rb_and_fields/RbInits.h
+++ /dev/null
@@ -1,138 +0,0 @@
-//---------------- RbInits.h starts ------------------
-r0101 = 0.125;
-r0109 = 0;
-r0110 = 0;
-r0111 = 0;
-r0112 = 0;
-r0113 = 0;
-r0114 = 0;
-r0115 = 0;
-r0116 = 0;
-r0201 = 0;
-r0202 = 0.125;
-r0209 = 0;
-r0210 = 0;
-r0211 = 0;
-r0212 = 0;
-r0213 = 0;
-r0214 = 0;
-r0215 = 0;
-r0216 = 0;
-r0301 = 0;
-r0302 = 0;
-r0303 = 0.125;
-r0309 = 0;
-r0310 = 0;
-r0311 = 0;
-r0312 = 0;
-r0313 = 0;
-r0314 = 0;
-r0315 = 0;
-r0316 = 0;
-r0401 = 0;
-r0402 = 0;
-r0403 = 0;
-r0404 = 0.125;
-r0409 = 0;
-r0410 = 0;
-r0411 = 0;
-r0412 = 0;
-r0413 = 0;
-r0414 = 0;
-r0415 = 0;
-r0416 = 0;
-r0501 = 0;
-r0502 = 0;
-r0503 = 0;
-r0504 = 0;
-r0505 = 0.125;
-r0509 = 0;
-r0510 = 0;
-r0511 = 0;
-r0512 = 0;
-r0513 = 0;
-r0514 = 0;
-r0515 = 0;
-r0516 = 0;
-r0601 = 0;
-r0602 = 0;
-r0603 = 0;
-r0604 = 0;
-r0605 = 0;
-r0606 = 0.125;
-r0609 = 0;
-r0610 = 0;
-r0611 = 0;
-r0612 = 0;
-r0613 = 0;
-r0614 = 0;
-r0615 = 0;
-r0616 = 0;
-r0701 = 0;
-r0702 = 0;
-r0703 = 0;
-r0704 = 0;
-r0705 = 0;
-r0706 = 0;
-r0707 = 0.125;
-r0709 = 0;
-r0710 = 0;
-r0711 = 0;
-r0712 = 0;
-r0713 = 0;
-r0714 = 0;
-r0715 = 0;
-r0716 = 0;
-r0801 = 0;
-r0802 = 0;
-r0803 = 0;
-r0804 = 0;
-r0805 = 0;
-r0806 = 0;
-r0807 = 0;
-r0808 = 0.125;
-r0809 = 0;
-r0810 = 0;
-r0811 = 0;
-r0812 = 0;
-r0813 = 0;
-r0814 = 0;
-r0815 = 0;
-r0816 = 0;
-r0909 = 0;
-r0912 = 0;
-r0913 = 0;
-r0914 = 0;
-r0915 = 0;
-r0916 = 0;
-r1009 = 0;
-r1010 = 0;
-r1012 = 0;
-r1013 = 0;
-r1014 = 0;
-r1015 = 0;
-r1016 = 0;
-r1109 = 0;
-r1110 = 0;
-r1111 = 0;
-r1112 = 0;
-r1113 = 0;
-r1114 = 0;
-r1115 = 0;
-r1116 = 0;
-r1212 = 0;
-r1312 = 0;
-r1313 = 0;
-r1412 = 0;
-r1413 = 0;
-r1414 = 0;
-r1512 = 0;
-r1513 = 0;
-r1514 = 0;
-r1515 = 0;
-r1612 = 0;
-r1613 = 0;
-r1614 = 0;
-r1615 = 0;
-r1616 = 0;
-//---------------- RbInits.h ends  ------------------
diff --git a/xmds2/realistic_Rb_and_fields/RbPropEquations.cdata b/xmds2/realistic_Rb_and_fields/RbPropEquations.cdata
new file mode 100644
index 0000000..f098f3d
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/RbPropEquations.cdata
@@ -0,0 +1,12 @@
+<![CDATA[
+//---------------- RbPropEquations.cdata starts ------------------
+dEp1_dz = -((i*Ndens*(rt2*conj(r0309) + rt6*(conj(r0410) + rt2*conj(r0511)))*eta1)/(rt2*rt6)) - Lt[Ep1];
+dEm1_dz = -((i*Ndens*(rt2*rt6*conj(r0109) + rt6*conj(r0210) + rt2*conj(r0311))*eta1)/(rt2*rt6)) - Lt[Em1];
+dEp2_dz = (i*Ndens*(conj(r0709) + conj(r0810))*eta1)/rt6 - Lt[Ep2];
+dEm2_dz = -((i*Ndens*(conj(r0610) + conj(r0711))*eta1)/rt6) - Lt[Em2];
+dEp3_dz = -((i*Ndens*(rt2*rt3*conj(r0612) + rt3*conj(r0713) + conj(r0814))*eta2)/rt3) - Lt[Ep3];
+dEm3_dz = -((i*Ndens*(conj(r0614) + rt3*(conj(r0715) + rt2*conj(r0816)))*eta2)/rt3) - Lt[Em3];
+dEp4_dz = -((i*Ndens*(rt2*conj(r0212) + rt3*conj(r0313) + rt3*conj(r0414) + rt2*conj(r0515))*eta2)/rt3) - Lt[Ep4];
+dEm4_dz = (i*Ndens*(rt2*conj(r0113) + rt3*conj(r0214) + rt3*conj(r0315) + rt2*conj(r0416))*eta2)/rt3 - Lt[Em4];
+//---------------- RbPropEquations.cdata ends  ------------------
+]]>
diff --git a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
index d10dbad..33f7918 100644
--- a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
+++ b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
@@ -1,8 +1,12 @@
 <?xml version="1.0"?>
-<!--Below text defines necessary included files and references to them-->
+<!-- Below text defines necessary includes files generated by mathematica 
+		 and references to them -->
 <!DOCTYPE simulation [
+<!ENTITY RbAtomConstantsFile SYSTEM "RbAtomConstants.cdata" >
 <!ENTITY RbChosenRhoFile SYSTEM "RbChosenRho.txt" >
-<!ENTITY RbEquationsFile SYSTEM "RbEquations.txt" >
+<!ENTITY RbInitsFile SYSTEM "RbInits.cdata" >
+<!ENTITY RbEquationsFile SYSTEM "RbEquations.cdata" >
+<!ENTITY RbPropEquationsFile SYSTEM "RbPropEquations.cdata" >
 ]>
 <simulation xmds-version="2">
 	<testing>
@@ -54,14 +58,14 @@
 
 	<features>
 		<globals>
+			<!--atom related constants-->
+			<!--read from Mathematica generated RbAtomConstants.cdata-->
+			&RbAtomConstantsFile;
+
 			<![CDATA[
 				// Some numerical constants
 				const double pi = M_PI; 
 
-				// atom related constants
-				//read from Mathematica generated RbAtomConstants.h
-				#include "RbAtomConstants.h"
-
 				const double c=3.e8;
 				const double k_boltzmann= 1.3806505e-23; // Boltzmann knostant in [J/K]
 				const double lambda=794.7e-9; //wavelength in m
@@ -86,7 +90,6 @@
 
 				// inner use variables 
 				double probability_v; // will be used as p(v) in Maxwell distribution
-
 			]]>
 		</globals>
 		<validation kind="run-time"/> <!--allows to put ranges as variables-->
@@ -232,9 +235,7 @@
 	<vector name="density_matrix" type="complex" initial_space="t">
 		<components>
 			<!-- read from Mathematica generated RbChosenRho.txt -->
-<!-- ############### RbChosenRho.txt starts ################ -->
-r0101 r0109 r0110 r0111 r0112 r0113 r0114 r0115 r0116 r0201 r0202 r0209 r0210 r0211 r0212 r0213 r0214 r0215 r0216 r0301 r0302 r0303 r0309 r0310 r0311 r0312 r0313 r0314 r0315 r0316 r0401 r0402 r0403 r0404 r0409 r0410 r0411 r0412 r0413 r0414 r0415 r0416 r0501 r0502 r0503 r0504 r0505 r0509 r0510 r0511 r0512 r0513 r0514 r0515 r0516 r0601 r0602 r0603 r0604 r0605 r0606 r0609 r0610 r0611 r0612 r0613 r0614 r0615 r0616 r0701 r0702 r0703 r0704 r0705 r0706 r0707 r0709 r0710 r0711 r0712 r0713 r0714 r0715 r0716 r0801 r0802 r0803 r0804 r0805 r0806 r0807 r0808 r0809 r0810 r0811 r0812 r0813 r0814 r0815 r0816 r0909 r0912 r0913 r0914 r0915 r0916 r1009 r1010 r1012 r1013 r1014 r1015 r1016 r1109 r1110 r1111 r1112 r1113 r1114 r1115 r1116 r1212 r1312 r1313 r1412 r1413 r1414 r1512 r1513 r1514 r1515 r1612 r1613 r1614 r1615 r1616 
-<!-- ############### RbChosenRho.txt ends  ################# -->
+			&RbChosenRhoFile;
 		</components>
 		<initialisation>
 			<!--This sets boundary condition at all times and left border of z (i.e. z=0)-->
@@ -248,10 +249,9 @@ r0101 r0109 r0110 r0111 r0112 r0113 r0114 r0115 r0116 r0201 r0202 r0209 r0210 r0
 			// TODO: Fix above. Make the equation of motion for r11 
 			//       and express other level, let's say r44
 			//       through population normalization
-
-			//read from Mathematica generated RbInits.h
-			#include "RbInits.h"
 			]]>
+			<!--read from Mathematica generated RbInits.cdata-->
+			&RbInitsFile;
 		</initialisation>
 	</vector>
 
@@ -288,149 +288,9 @@ r0101 r0109 r0110 r0111 r0112 r0113 r0114 r0115 r0116 r0201 r0202 r0209 r0210 r0
             ]]>
 						-->
           </boundary_condition>
-					<![CDATA[
-						// Equations of motions according to Simon's mathematica code
-						//read from Mathematica generated RbEquations.txt
-//---------------- RbEquations.txt starts ------------------
-dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1212)/3. + (g2*r1313)/6. - i*((conj(Em1a)*conj(r0109))/4. - (conj(Em4a)*conj(r0113))/(4.*rt6) - (Em1a*r0109)/4. + (Em4a*r0113)/(4.*rt6) + r0201*(WLx/2. - (i*WLy)/2.) - conj(r0201)*(WLx/2. + (i*WLy)/2.));
-dr0109_dt = (-(gt*r0109) - (gt + g1)*r0109)/2. - i*(-(conj(Ep1a)*conj(r0301))/(4.*rt6) + (conj(Ep2a)*conj(r0701))/(4.*rt6) - (conj(Em4a)*conj(r0913))/(4.*rt6) - (conj(Em1a)*r0101)/4. + (conj(Em1a)*r0909)/4. + r0209*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-delta1 - v*Kvec1 - WLz/6.) + r0109*WLz);
-dr0110_dt = (-(gt*r0110) - (gt + g1)*r0110)/2. - i*(-(conj(Em1a)*conj(r0201))/(4.*rt2) - (conj(Ep1a)*conj(r0401))/(4.*rt2) - (conj(Em2a)*conj(r0601))/(4.*rt6) + (conj(Ep2a)*conj(r0801))/(4.*rt6) + (conj(Em1a)*conj(r1009))/4. - (conj(Em4a)*conj(r1013))/(4.*rt6) + (delta1 + v*Kvec1)*r0110 + r0210*(WLx/2. - (i*WLy)/2.) - r0111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0110*WLz);
-dr0111_dt = (-(gt*r0111) - (gt + g1)*r0111)/2. - i*(-(conj(Em1a)*conj(r0301))/(4.*rt6) - (conj(Ep1a)*conj(r0501))/4. - (conj(Em2a)*conj(r0701))/(4.*rt6) + (conj(Em1a)*conj(r1109))/4. - (conj(Em4a)*conj(r1113))/(4.*rt6) + r0211*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0111*(-delta1 - v*Kvec1 + WLz/6.) + r0111*WLz);
-dr0112_dt = (-(gt*r0112) - (gt + g2)*r0112)/2. - i*(-(conj(Ep4a)*conj(r0201))/(4.*rt6) - (conj(Ep3a)*conj(r0601))/(4.*rt2) + (conj(Em1a)*r0912)/4. - (conj(Em4a)*r1312)/(4.*rt6) + r0212*(WLx/2. - (i*WLy)/2.) - r0113*((2*WLx)/3. + (2*i*WLy)/3.) + r0112*WLz - r0112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0113_dt = (-(gt*r0113) - (gt + g2)*r0113)/2. - i*(-(conj(Ep4a)*conj(r0301))/8. - (conj(Ep3a)*conj(r0701))/8. + (conj(Em4a)*r0101)/(4.*rt6) + (conj(Em1a)*r0913)/4. - (conj(Em4a)*r1313)/(4.*rt6) - r0112*((2*WLx)/3. - (2*i*WLy)/3.) + r0213*(WLx/2. - (i*WLy)/2.) - r0114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + r0113*WLz);
-dr0114_dt = (-(gt*r0114) - (gt + g2)*r0114)/2. - i*((conj(Em4a)*conj(r0201))/8. - (conj(Ep4a)*conj(r0401))/8. - (conj(Em3a)*conj(r0601))/(8.*rt3) - (conj(Ep3a)*conj(r0801))/(8.*rt3) - (conj(Em4a)*conj(r1413))/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0114 + (conj(Em1a)*r0914)/4. + r0214*(WLx/2. - (i*WLy)/2.) - r0113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0114*WLz);
-dr0115_dt = (-(gt*r0115) - (gt + g2)*r0115)/2. - i*((conj(Em4a)*conj(r0301))/8. - (conj(Ep4a)*conj(r0501))/(4.*rt6) - (conj(Em3a)*conj(r0701))/8. - (conj(Em4a)*conj(r1513))/(4.*rt6) + (conj(Em1a)*r0915)/4. + r0215*(WLx/2. - (i*WLy)/2.) - r0116*((2*WLx)/3. + (2*i*WLy)/3.) - r0114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0115*WLz);
-dr0116_dt = (-(gt*r0116) - (gt + g2)*r0116)/2. - i*((conj(Em4a)*conj(r0401))/(4.*rt6) - (conj(Em3a)*conj(r0801))/(4.*rt2) - (conj(Em4a)*conj(r1613))/(4.*rt6) + (conj(Em1a)*r0916)/4. - r0115*((2*WLx)/3. - (2*i*WLy)/3.) + r0216*(WLx/2. - (i*WLy)/2.) - r0116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0116*WLz);
-dr0201_dt = -(gt*r0201) + (g1*r1009)/(2.*rt2) + (g2*r1312)/6. + (g2*r1413)/(2.*rt6) - i*((conj(Em1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0112))/(4.*rt6) - (conj(Em4a)*conj(r0114))/8. - (Em1a*r0209)/4. + (Em4a*r0213)/(4.*rt6) + r0101*(WLx/2. + (i*WLy)/2.) - r0202*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0201*WLz)/2.);
-dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1212)/6. + (g2*r1313)/12. + (g2*r1414)/4. - i*((conj(Em1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Em4a)*conj(r0214))/8. - (Em1a*r0210)/(4.*rt2) - (Ep4a*r0212)/(4.*rt6) + (Em4a*r0214)/8. - r0201*(WLx/2. - (i*WLy)/2.) + conj(r0201)*(WLx/2. + (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
-dr0209_dt = (-(gt*r0209) - (gt + g1)*r0209)/2. - i*(-(conj(Ep1a)*conj(r0302))/(4.*rt6) + (conj(Ep2a)*conj(r0702))/(4.*rt6) + (conj(Ep4a)*conj(r0912))/(4.*rt6) - (conj(Em4a)*conj(r0914))/8. - (conj(Em1a)*r0201)/4. + (conj(Em1a)*r1009)/(4.*rt2) + r0109*(WLx/2. + (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-delta1 - v*Kvec1 - WLz/6.) + (r0209*WLz)/2.);
-dr0210_dt = (-(gt*r0210) - (gt + g1)*r0210)/2. - i*(-(conj(Ep1a)*conj(r0402))/(4.*rt2) - (conj(Em2a)*conj(r0602))/(4.*rt6) + (conj(Ep2a)*conj(r0802))/(4.*rt6) + (conj(Ep4a)*conj(r1012))/(4.*rt6) - (conj(Em4a)*conj(r1014))/8. - (conj(Em1a)*r0202)/(4.*rt2) + (delta1 + v*Kvec1)*r0210 + (conj(Em1a)*r1010)/(4.*rt2) + r0110*(WLx/2. + (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0211*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + (r0210*WLz)/2.);
-dr0211_dt = (-(gt*r0211) - (gt + g1)*r0211)/2. - i*(-(conj(Em1a)*conj(r0302))/(4.*rt6) - (conj(Ep1a)*conj(r0502))/4. - (conj(Em2a)*conj(r0702))/(4.*rt6) + (conj(Em1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1112))/(4.*rt6) - (conj(Em4a)*conj(r1114))/8. + r0111*(WLx/2. + (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0211*(-delta1 - v*Kvec1 + WLz/6.) + (r0211*WLz)/2.);
-dr0212_dt = (-(gt*r0212) - (gt + g2)*r0212)/2. - i*(-(conj(Ep3a)*conj(r0602))/(4.*rt2) - (conj(Ep4a)*r0202)/(4.*rt6) + (conj(Em1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1212)/(4.*rt6) - (conj(Em4a)*r1412)/8. + r0112*(WLx/2. + (i*WLy)/2.) - r0213*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0212*WLz)/2. - r0212*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0213_dt = (-(gt*r0213) - (gt + g2)*r0213)/2. - i*(-(conj(Ep4a)*conj(r0302))/8. - (conj(Ep3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1312))/(4.*rt6) + (conj(Em4a)*r0201)/(4.*rt6) + (conj(Em1a)*r1013)/(4.*rt2) - (conj(Em4a)*r1413)/8. - r0212*((2*WLx)/3. - (2*i*WLy)/3.) + r0113*(WLx/2. + (i*WLy)/2.) - r0214*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0213*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + (r0213*WLz)/2.);
-dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*(-(conj(Ep4a)*conj(r0402))/8. - (conj(Em3a)*conj(r0602))/(8.*rt3) - (conj(Ep3a)*conj(r0802))/(8.*rt3) + (conj(Ep4a)*conj(r1412))/(4.*rt6) + (conj(Em4a)*r0202)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 + (conj(Em1a)*r1014)/(4.*rt2) - (conj(Em4a)*r1414)/8. + r0114*(WLx/2. + (i*WLy)/2.) - r0213*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0215*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0214*WLz)/2.);
-dr0215_dt = (-(gt*r0215) - (gt + g2)*r0215)/2. - i*((conj(Em4a)*conj(r0302))/8. - (conj(Ep4a)*conj(r0502))/(4.*rt6) - (conj(Em3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1512))/(4.*rt6) - (conj(Em4a)*conj(r1514))/8. + (conj(Em1a)*r1015)/(4.*rt2) + r0115*(WLx/2. + (i*WLy)/2.) - r0216*((2*WLx)/3. + (2*i*WLy)/3.) - r0214*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0215*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + (r0215*WLz)/2.);
-dr0216_dt = (-(gt*r0216) - (gt + g2)*r0216)/2. - i*((conj(Em4a)*conj(r0402))/(4.*rt6) - (conj(Em3a)*conj(r0802))/(4.*rt2) + (conj(Ep4a)*conj(r1612))/(4.*rt6) - (conj(Em4a)*conj(r1614))/8. + (conj(Em1a)*r1016)/(4.*rt2) - r0215*((2*WLx)/3. - (2*i*WLy)/3.) + r0116*(WLx/2. + (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0216*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + (r0216*WLz)/2.);
-dr0301_dt = -(gt*r0301) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0109))/(4.*rt6) + (conj(Em1a)*conj(r0111))/(4.*rt6) + (conj(Ep4a)*conj(r0113))/8. - (conj(Em4a)*conj(r0115))/8. - (Em1a*r0309)/4. + (Em4a*r0313)/(4.*rt6) - r0302*(WLx/2. + (i*WLy)/2.) + r0401*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0201*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0301*WLz);
-dr0302_dt = -(gt*r0302) + (g1*r1009)/(2.*rt3) + (g1*r1110)/(4.*rt3) + (g2*r1312)/(2.*rt6) + (g2*r1514)/4. - i*((conj(Ep1a)*conj(r0209))/(4.*rt6) + (conj(Em1a)*conj(r0211))/(4.*rt6) + (conj(Ep4a)*conj(r0213))/8. - (conj(Em4a)*conj(r0215))/8. - (Em1a*r0310)/(4.*rt2) - (Ep4a*r0312)/(4.*rt6) + (Em4a*r0314)/8. - r0301*(WLx/2. - (i*WLy)/2.) + r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0202*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0302*WLz)/2.);
-dr0303_dt = gt/8. - gt*r0303 + (g1*r0909)/12. + (g1*r1010)/3. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1515)/4. - i*((conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Em1a)*conj(r0311))/(4.*rt6) + (conj(Ep4a)*conj(r0313))/8. - (conj(Em4a)*conj(r0315))/8. - (Ep1a*r0309)/(4.*rt6) - (Em1a*r0311)/(4.*rt6) - (Ep4a*r0313)/8. + (Em4a*r0315)/8. - r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
-dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*((conj(Ep2a)*conj(r0703))/(4.*rt6) + (conj(Ep4a)*conj(r0913))/8. - (conj(Em4a)*conj(r0915))/8. - (conj(Em1a)*r0301)/4. - (conj(Ep1a)*r0303)/(4.*rt6) + (conj(Ep1a)*r0909)/(4.*rt6) + (conj(Em1a)*r1109)/(4.*rt6) + r0409*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0209*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-delta1 - v*Kvec1 - WLz/6.));
-dr0310_dt = (-(gt*r0310) - (gt + g1)*r0310)/2. - i*(-(conj(Ep1a)*conj(r0403))/(4.*rt2) - (conj(Em2a)*conj(r0603))/(4.*rt6) + (conj(Ep2a)*conj(r0803))/(4.*rt6) + (conj(Ep1a)*conj(r1009))/(4.*rt6) + (conj(Ep4a)*conj(r1013))/8. - (conj(Em4a)*conj(r1015))/8. - (conj(Em1a)*r0302)/(4.*rt2) + (delta1 + v*Kvec1)*r0310 + (conj(Em1a)*r1110)/(4.*rt6) + r0410*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0210*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0311*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
-dr0311_dt = (-(gt*r0311) - (gt + g1)*r0311)/2. - i*(-(conj(Ep1a)*conj(r0503))/4. - (conj(Em2a)*conj(r0703))/(4.*rt6) + (conj(Ep1a)*conj(r1109))/(4.*rt6) + (conj(Ep4a)*conj(r1113))/8. - (conj(Em4a)*conj(r1115))/8. - (conj(Em1a)*r0303)/(4.*rt6) + (conj(Em1a)*r1111)/(4.*rt6) + r0411*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0211*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0311*(-delta1 - v*Kvec1 + WLz/6.));
-dr0312_dt = (-(gt*r0312) - (gt + g2)*r0312)/2. - i*(-(conj(Ep3a)*conj(r0603))/(4.*rt2) - (conj(Ep4a)*r0302)/(4.*rt6) + (conj(Ep1a)*r0912)/(4.*rt6) + (conj(Em1a)*r1112)/(4.*rt6) + (conj(Ep4a)*r1312)/8. - (conj(Em4a)*r1512)/8. - r0313*((2*WLx)/3. + (2*i*WLy)/3.) + r0412*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0212*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0313_dt = (-(gt*r0313) - (gt + g2)*r0313)/2. - i*(-(conj(Ep3a)*conj(r0703))/8. + (conj(Em4a)*r0301)/(4.*rt6) - (conj(Ep4a)*r0303)/8. + (conj(Ep1a)*r0913)/(4.*rt6) + (conj(Em1a)*r1113)/(4.*rt6) + (conj(Ep4a)*r1313)/8. - (conj(Em4a)*r1513)/8. - r0312*((2*WLx)/3. - (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0413*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0213*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0313*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr0314_dt = (-(gt*r0314) - (gt + g2)*r0314)/2. - i*(-(conj(Ep4a)*conj(r0403))/8. - (conj(Em3a)*conj(r0603))/(8.*rt3) - (conj(Ep3a)*conj(r0803))/(8.*rt3) + (conj(Ep4a)*conj(r1413))/8. + (conj(Em4a)*r0302)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0314 + (conj(Ep1a)*r0914)/(4.*rt6) + (conj(Em1a)*r1114)/(4.*rt6) - (conj(Em4a)*r1514)/8. - r0313*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0315*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0414*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0214*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
-dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(conj(Ep4a)*conj(r0503))/(4.*rt6) - (conj(Em3a)*conj(r0703))/8. + (conj(Ep4a)*conj(r1513))/8. + (conj(Em4a)*r0303)/8. + (conj(Ep1a)*r0915)/(4.*rt6) + (conj(Em1a)*r1115)/(4.*rt6) - (conj(Em4a)*r1515)/8. - r0316*((2*WLx)/3. + (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0415*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0215*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0315*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
-dr0316_dt = (-(gt*r0316) - (gt + g2)*r0316)/2. - i*((conj(Em4a)*conj(r0403))/(4.*rt6) - (conj(Em3a)*conj(r0803))/(4.*rt2) + (conj(Ep4a)*conj(r1613))/8. - (conj(Em4a)*conj(r1615))/8. + (conj(Ep1a)*r0916)/(4.*rt6) + (conj(Em1a)*r1116)/(4.*rt6) - r0315*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0216*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0316*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
-dr0401_dt = -(gt*r0401) - (g2*r1512)/6. + (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0114))/8. - (conj(Em4a)*conj(r0116))/(4.*rt6) - (Em1a*r0409)/4. + (Em4a*r0413)/(4.*rt6) + r0501*(WLx/2. - (i*WLy)/2.) - r0402*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0401*WLz)/2.);
-dr0402_dt = -(gt*r0402) + (g1*r1109)/4. + (g2*r1412)/(2.*rt6) - (g2*r1513)/12. + (g2*r1614)/(2.*rt6) - i*((conj(Ep1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0214))/8. - (conj(Em4a)*conj(r0216))/(4.*rt6) - (Em1a*r0410)/(4.*rt2) - (Ep4a*r0412)/(4.*rt6) + (Em4a*r0414)/8. - r0401*(WLx/2. - (i*WLy)/2.) + r0502*(WLx/2. - (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0402*WLz);
-dr0403_dt = -(gt*r0403) + (g1*r1009)/(4.*rt3) + (g1*r1110)/(2.*rt3) + (g2*r1413)/4. + (g2*r1615)/(2.*rt6) - i*((conj(Ep1a)*conj(r0310))/(4.*rt2) + (conj(Ep4a)*conj(r0314))/8. - (conj(Em4a)*conj(r0316))/(4.*rt6) - (Ep1a*r0409)/(4.*rt6) - (Em1a*r0411)/(4.*rt6) - (Ep4a*r0413)/8. + (Em4a*r0415)/8. + r0503*(WLx/2. - (i*WLy)/2.) - r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0404*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0403*WLz)/2.);
-dr0404_dt = gt/8. - gt*r0404 + (g1*r1010)/4. + (g1*r1111)/4. + (g2*r1414)/4. + (g2*r1515)/12. + (g2*r1616)/6. - i*((conj(Ep1a)*conj(r0410))/(4.*rt2) + (conj(Ep4a)*conj(r0414))/8. - (conj(Em4a)*conj(r0416))/(4.*rt6) - (Ep1a*r0410)/(4.*rt2) - (Ep4a*r0414)/8. + (Em4a*r0416)/(4.*rt6) + r0504*(WLx/2. - (i*WLy)/2.) - conj(r0504)*(WLx/2. + (i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
-dr0409_dt = (-(gt*r0409) - (gt + g1)*r0409)/2. - i*((conj(Ep2a)*conj(r0704))/(4.*rt6) + (conj(Ep4a)*conj(r0914))/8. - (conj(Em4a)*conj(r0916))/(4.*rt6) - (conj(Em1a)*r0401)/4. - (conj(Ep1a)*r0403)/(4.*rt6) + (conj(Ep1a)*r1009)/(4.*rt2) + r0509*(WLx/2. - (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-delta1 - v*Kvec1 - WLz/6.) - (r0409*WLz)/2.);
-dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(conj(Em2a)*conj(r0604))/(4.*rt6) + (conj(Ep2a)*conj(r0804))/(4.*rt6) + (conj(Ep4a)*conj(r1014))/8. - (conj(Em4a)*conj(r1016))/(4.*rt6) - (conj(Em1a)*r0402)/(4.*rt2) - (conj(Ep1a)*r0404)/(4.*rt2) + (delta1 + v*Kvec1)*r0410 + (conj(Ep1a)*r1010)/(4.*rt2) + r0510*(WLx/2. - (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0411*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - (r0410*WLz)/2.);
-dr0411_dt = (-(gt*r0411) - (gt + g1)*r0411)/2. - i*(-(conj(Ep1a)*conj(r0504))/4. - (conj(Em2a)*conj(r0704))/(4.*rt6) + (conj(Ep1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1114))/8. - (conj(Em4a)*conj(r1116))/(4.*rt6) - (conj(Em1a)*r0403)/(4.*rt6) + r0511*(WLx/2. - (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0411*(-delta1 - v*Kvec1 + WLz/6.) - (r0411*WLz)/2.);
-dr0412_dt = (-(gt*r0412) - (gt + g2)*r0412)/2. - i*(-(conj(Ep3a)*conj(r0604))/(4.*rt2) - (conj(Ep4a)*r0402)/(4.*rt6) + (conj(Ep1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1412)/8. - (conj(Em4a)*r1612)/(4.*rt6) + r0512*(WLx/2. - (i*WLy)/2.) - r0413*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0412*WLz)/2. - r0412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0413_dt = (-(gt*r0413) - (gt + g2)*r0413)/2. - i*(-(conj(Ep3a)*conj(r0704))/8. + (conj(Em4a)*r0401)/(4.*rt6) - (conj(Ep4a)*r0403)/8. + (conj(Ep1a)*r1013)/(4.*rt2) + (conj(Ep4a)*r1413)/8. - (conj(Em4a)*r1613)/(4.*rt6) - r0412*((2*WLx)/3. - (2*i*WLy)/3.) + r0513*(WLx/2. - (i*WLy)/2.) - r0414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - (r0413*WLz)/2.);
-dr0414_dt = (-(gt*r0414) - (gt + g2)*r0414)/2. - i*(-(conj(Em3a)*conj(r0604))/(8.*rt3) - (conj(Ep3a)*conj(r0804))/(8.*rt3) + (conj(Em4a)*r0402)/8. - (conj(Ep4a)*r0404)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0414 + (conj(Ep1a)*r1014)/(4.*rt2) + (conj(Ep4a)*r1414)/8. - (conj(Em4a)*r1614)/(4.*rt6) + r0514*(WLx/2. - (i*WLy)/2.) - r0413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0415*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0414*WLz)/2.);
-dr0415_dt = (-(gt*r0415) - (gt + g2)*r0415)/2. - i*(-(conj(Ep4a)*conj(r0504))/(4.*rt6) - (conj(Em3a)*conj(r0704))/8. + (conj(Ep4a)*conj(r1514))/8. + (conj(Em4a)*r0403)/8. + (conj(Ep1a)*r1015)/(4.*rt2) - (conj(Em4a)*r1615)/(4.*rt6) + r0515*(WLx/2. - (i*WLy)/2.) - r0416*((2*WLx)/3. + (2*i*WLy)/3.) - r0414*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0415*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - (r0415*WLz)/2.);
-dr0416_dt = (-(gt*r0416) - (gt + g2)*r0416)/2. - i*(-(conj(Em3a)*conj(r0804))/(4.*rt2) + (conj(Ep4a)*conj(r1614))/8. + (conj(Em4a)*r0404)/(4.*rt6) + (conj(Ep1a)*r1016)/(4.*rt2) - (conj(Em4a)*r1616)/(4.*rt6) - r0415*((2*WLx)/3. - (2*i*WLy)/3.) + r0516*(WLx/2. - (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0416*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - (r0416*WLz)/2.);
-dr0501_dt = -(gt*r0501) - (g2*r1612)/3. - i*((conj(Ep1a)*conj(r0111))/4. + (conj(Ep4a)*conj(r0115))/(4.*rt6) - (Em1a*r0509)/4. + (Em4a*r0513)/(4.*rt6) + r0401*(WLx/2. + (i*WLy)/2.) - r0502*(WLx/2. + (i*WLy)/2.) - 2*r0501*WLz);
-dr0502_dt = -(gt*r0502) + (g2*r1512)/6. - (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0211))/4. + (conj(Ep4a)*conj(r0215))/(4.*rt6) - (Em1a*r0510)/(4.*rt2) - (Ep4a*r0512)/(4.*rt6) + (Em4a*r0514)/8. - r0501*(WLx/2. - (i*WLy)/2.) + r0402*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0502*WLz)/2.);
-dr0503_dt = -(gt*r0503) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0311))/4. + (conj(Ep4a)*conj(r0315))/(4.*rt6) - (Ep1a*r0509)/(4.*rt6) - (Em1a*r0511)/(4.*rt6) - (Ep4a*r0513)/8. + (Em4a*r0515)/8. + r0403*(WLx/2. + (i*WLy)/2.) - r0502*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0504*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0503*WLz);
-dr0504_dt = -(gt*r0504) + (g1*r1110)/(2.*rt2) + (g2*r1514)/(2.*rt6) + (g2*r1615)/6. - i*((conj(Ep1a)*conj(r0411))/4. + (conj(Ep4a)*conj(r0415))/(4.*rt6) - (Ep1a*r0510)/(4.*rt2) - (Ep4a*r0514)/8. + (Em4a*r0516)/(4.*rt6) + r0404*(WLx/2. + (i*WLy)/2.) - r0505*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0504*WLz)/2.);
-dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((conj(Ep1a)*conj(r0511))/4. + (conj(Ep4a)*conj(r0515))/(4.*rt6) - (Ep1a*r0511)/4. - (Ep4a*r0515)/(4.*rt6) - r0504*(WLx/2. - (i*WLy)/2.) + conj(r0504)*(WLx/2. + (i*WLy)/2.));
-dr0509_dt = (-(gt*r0509) - (gt + g1)*r0509)/2. - i*((conj(Ep2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r0915))/(4.*rt6) - (conj(Em1a)*r0501)/4. - (conj(Ep1a)*r0503)/(4.*rt6) + (conj(Ep1a)*r1109)/4. + r0409*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-delta1 - v*Kvec1 - WLz/6.) - r0509*WLz);
-dr0510_dt = (-(gt*r0510) - (gt + g1)*r0510)/2. - i*(-(conj(Em2a)*conj(r0605))/(4.*rt6) + (conj(Ep2a)*conj(r0805))/(4.*rt6) + (conj(Ep4a)*conj(r1015))/(4.*rt6) - (conj(Em1a)*r0502)/(4.*rt2) - (conj(Ep1a)*r0504)/(4.*rt2) + (delta1 + v*Kvec1)*r0510 + (conj(Ep1a)*r1110)/4. + r0410*(WLx/2. + (i*WLy)/2.) - r0511*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0510*WLz);
-dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(conj(Em2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r1115))/(4.*rt6) - (conj(Em1a)*r0503)/(4.*rt6) - (conj(Ep1a)*r0505)/4. + (conj(Ep1a)*r1111)/4. + r0411*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0511*(-delta1 - v*Kvec1 + WLz/6.) - r0511*WLz);
-dr0512_dt = (-(gt*r0512) - (gt + g2)*r0512)/2. - i*(-(conj(Ep3a)*conj(r0605))/(4.*rt2) - (conj(Ep4a)*r0502)/(4.*rt6) + (conj(Ep1a)*r1112)/4. + (conj(Ep4a)*r1512)/(4.*rt6) + r0412*(WLx/2. + (i*WLy)/2.) - r0513*((2*WLx)/3. + (2*i*WLy)/3.) - r0512*WLz - r0512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0513_dt = (-(gt*r0513) - (gt + g2)*r0513)/2. - i*(-(conj(Ep3a)*conj(r0705))/8. + (conj(Em4a)*r0501)/(4.*rt6) - (conj(Ep4a)*r0503)/8. + (conj(Ep1a)*r1113)/4. + (conj(Ep4a)*r1513)/(4.*rt6) - r0512*((2*WLx)/3. - (2*i*WLy)/3.) + r0413*(WLx/2. + (i*WLy)/2.) - r0514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r0513*WLz);
-dr0514_dt = (-(gt*r0514) - (gt + g2)*r0514)/2. - i*(-(conj(Em3a)*conj(r0605))/(8.*rt3) - (conj(Ep3a)*conj(r0805))/(8.*rt3) + (conj(Em4a)*r0502)/8. - (conj(Ep4a)*r0504)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0514 + (conj(Ep1a)*r1114)/4. + (conj(Ep4a)*r1514)/(4.*rt6) + r0414*(WLx/2. + (i*WLy)/2.) - r0513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0514*WLz);
-dr0515_dt = (-(gt*r0515) - (gt + g2)*r0515)/2. - i*(-(conj(Em3a)*conj(r0705))/8. + (conj(Em4a)*r0503)/8. - (conj(Ep4a)*r0505)/(4.*rt6) + (conj(Ep1a)*r1115)/4. + (conj(Ep4a)*r1515)/(4.*rt6) + r0415*(WLx/2. + (i*WLy)/2.) - r0516*((2*WLx)/3. + (2*i*WLy)/3.) - r0514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r0515*WLz);
-dr0516_dt = (-(gt*r0516) - (gt + g2)*r0516)/2. - i*(-(conj(Em3a)*conj(r0805))/(4.*rt2) + (conj(Ep4a)*conj(r1615))/(4.*rt6) + (conj(Em4a)*r0504)/(4.*rt6) + (conj(Ep1a)*r1116)/4. - r0515*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*(WLx/2. + (i*WLy)/2.) - r0516*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r0516*WLz);
-dr0601_dt = -(gt*r0601) - i*((conj(Em2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0112))/(4.*rt2) + (conj(Em3a)*conj(r0114))/(8.*rt3) - (Em1a*r0609)/4. + (Em4a*r0613)/(4.*rt6) - r0602*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0601*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0601*WLz);
-dr0602_dt = -(gt*r0602) - i*((conj(Em2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0212))/(4.*rt2) + (conj(Em3a)*conj(r0214))/(8.*rt3) - (Em1a*r0610)/(4.*rt2) - (Ep4a*r0612)/(4.*rt6) + (Em4a*r0614)/8. - r0601*(WLx/2. - (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0602*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - (r0602*WLz)/2.);
-dr0603_dt = -(gt*r0603) - i*((conj(Em2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0312))/(4.*rt2) + (conj(Em3a)*conj(r0314))/(8.*rt3) - (Ep1a*r0609)/(4.*rt6) - (Em1a*r0611)/(4.*rt6) - (Ep4a*r0613)/8. + (Em4a*r0615)/8. - r0602*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0604*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0603*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
-dr0604_dt = -(gt*r0604) - i*((conj(Em2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0412))/(4.*rt2) + (conj(Em3a)*conj(r0414))/(8.*rt3) - (Ep1a*r0610)/(4.*rt2) - (Ep4a*r0614)/8. + (Em4a*r0616)/(4.*rt6) - r0605*(WLx/2. + (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0604*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + (r0604*WLz)/2.);
-dr0605_dt = -(gt*r0605) - i*((conj(Em2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0512))/(4.*rt2) + (conj(Em3a)*conj(r0514))/(8.*rt3) - (Ep1a*r0611)/4. - (Ep4a*r0615)/(4.*rt6) - r0604*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0605*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0605*WLz);
-dr0606_dt = gt/8. - gt*r0606 + (g1*r0909)/12. + (g1*r1010)/12. + (g2*r1212)/2. + (g2*r1313)/4. + (g2*r1414)/12. - i*((conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0612))/(4.*rt2) + (conj(Em3a)*conj(r0614))/(8.*rt3) - (Em2a*r0610)/(4.*rt6) - (Ep3a*r0612)/(4.*rt2) - (Em3a*r0614)/(8.*rt3) - conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
-dr0609_dt = (-(gt*r0609) - (gt + g1)*r0609)/2. - i*((conj(Ep2a)*conj(r0706))/(4.*rt6) + (conj(Ep3a)*conj(r0912))/(4.*rt2) + (conj(Em3a)*conj(r0914))/(8.*rt3) - (conj(Em1a)*r0601)/4. - (conj(Ep1a)*r0603)/(4.*rt6) + (conj(Em2a)*r1009)/(4.*rt6) - r0610*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0709*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0609*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0609*(-delta1 - v*Kvec1 - WLz/6.));
-dr0610_dt = (-(gt*r0610) - (gt + g1)*r0610)/2. - i*((conj(Ep2a)*conj(r0806))/(4.*rt6) + (conj(Ep3a)*conj(r1012))/(4.*rt2) + (conj(Em3a)*conj(r1014))/(8.*rt3) - (conj(Em1a)*r0602)/(4.*rt2) - (conj(Ep1a)*r0604)/(4.*rt2) - (conj(Em2a)*r0606)/(4.*rt6) + (delta1 + v*Kvec1)*r0610 + (conj(Em2a)*r1010)/(4.*rt6) - r0611*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0609*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0710*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0610*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
-dr0611_dt = (-(gt*r0611) - (gt + g1)*r0611)/2. - i*(-(conj(Em2a)*conj(r0706))/(4.*rt6) + (conj(Em2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1112))/(4.*rt2) + (conj(Em3a)*conj(r1114))/(8.*rt3) - (conj(Em1a)*r0603)/(4.*rt6) - (conj(Ep1a)*r0605)/4. - r0610*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0711*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0611*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0611*(-delta1 - v*Kvec1 + WLz/6.));
-dr0612_dt = (-(gt*r0612) - (gt + g2)*r0612)/2. - i*(-(conj(Ep4a)*r0602)/(4.*rt6) - (conj(Ep3a)*r0606)/(4.*rt2) + (conj(Em2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1212)/(4.*rt2) + (conj(Em3a)*r1412)/(8.*rt3) - r0613*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0612*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0613_dt = (-(gt*r0613) - (gt + g2)*r0613)/2. - i*(-(conj(Ep3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1312))/(4.*rt2) + (conj(Em4a)*r0601)/(4.*rt6) - (conj(Ep4a)*r0603)/8. + (conj(Em2a)*r1013)/(4.*rt6) + (conj(Em3a)*r1413)/(8.*rt3) - r0612*((2*WLx)/3. - (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0613*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr0614_dt = (-(gt*r0614) - (gt + g2)*r0614)/2. - i*(-(conj(Ep3a)*conj(r0806))/(8.*rt3) + (conj(Ep3a)*conj(r1412))/(4.*rt2) + (conj(Em4a)*r0602)/8. - (conj(Ep4a)*r0604)/8. - (conj(Em3a)*r0606)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0614 + (conj(Em2a)*r1014)/(4.*rt6) + (conj(Em3a)*r1414)/(8.*rt3) - r0613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0614*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
-dr0615_dt = (-(gt*r0615) - (gt + g2)*r0615)/2. - i*(-(conj(Em3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1512))/(4.*rt2) + (conj(Em3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0603)/8. - (conj(Ep4a)*r0605)/(4.*rt6) + (conj(Em2a)*r1015)/(4.*rt6) - r0616*((2*WLx)/3. + (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0615*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
-dr0616_dt = (-(gt*r0616) - (gt + g2)*r0616)/2. - i*(-(conj(Em3a)*conj(r0806))/(4.*rt2) + (conj(Ep3a)*conj(r1612))/(4.*rt2) + (conj(Em3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0604)/(4.*rt6) + (conj(Em2a)*r1016)/(4.*rt6) - r0615*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0616*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0616*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
-dr0701_dt = -(gt*r0701) - i*(-(conj(Ep2a)*conj(r0109))/(4.*rt6) + (conj(Em2a)*conj(r0111))/(4.*rt6) + (conj(Ep3a)*conj(r0113))/8. + (conj(Em3a)*conj(r0115))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0701 - (Em1a*r0709)/4. + (Em4a*r0713)/(4.*rt6) - r0702*(WLx/2. + (i*WLy)/2.) + r0601*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0701*WLz);
-dr0702_dt = -(gt*r0702) - i*(-(conj(Ep2a)*conj(r0209))/(4.*rt6) + (conj(Em2a)*conj(r0211))/(4.*rt6) + (conj(Ep3a)*conj(r0213))/8. + (conj(Em3a)*conj(r0215))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0702 - (Em1a*r0710)/(4.*rt2) - (Ep4a*r0712)/(4.*rt6) + (Em4a*r0714)/8. - r0701*(WLx/2. - (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0602*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - (r0702*WLz)/2.);
-dr0703_dt = -(gt*r0703) - i*(-(conj(Ep2a)*conj(r0309))/(4.*rt6) + (conj(Em2a)*conj(r0311))/(4.*rt6) + (conj(Ep3a)*conj(r0313))/8. + (conj(Em3a)*conj(r0315))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 - (Ep1a*r0709)/(4.*rt6) - (Em1a*r0711)/(4.*rt6) - (Ep4a*r0713)/8. + (Em4a*r0715)/8. - r0702*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0704*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0603*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
-dr0704_dt = -(gt*r0704) - i*(-(conj(Ep2a)*conj(r0409))/(4.*rt6) + (conj(Em2a)*conj(r0411))/(4.*rt6) + (conj(Ep3a)*conj(r0413))/8. + (conj(Em3a)*conj(r0415))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0704 - (Ep1a*r0710)/(4.*rt2) - (Ep4a*r0714)/8. + (Em4a*r0716)/(4.*rt6) - r0705*(WLx/2. + (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0604*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + (r0704*WLz)/2.);
-dr0705_dt = -(gt*r0705) - i*(-(conj(Ep2a)*conj(r0509))/(4.*rt6) + (conj(Em2a)*conj(r0511))/(4.*rt6) + (conj(Ep3a)*conj(r0513))/8. + (conj(Em3a)*conj(r0515))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0705 - (Ep1a*r0711)/4. - (Ep4a*r0715)/(4.*rt6) - r0704*(WLx/2. - (i*WLy)/2.) + r0605*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0705*WLz);
-dr0706_dt = -(gt*r0706) + (g1*r1110)/12. + (g2*r1312)/(2.*rt2) + (g2*r1413)/(2.*rt3) + (g2*r1514)/(4.*rt3) - i*(-(conj(Ep2a)*conj(r0609))/(4.*rt6) + (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep3a)*conj(r0613))/8. + (conj(Em3a)*conj(r0615))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0706 - (Em2a*r0710)/(4.*rt6) - (Ep3a*r0712)/(4.*rt2) - (Em3a*r0714)/(8.*rt3) + r0606*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0706*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
-dr0707_dt = gt/8. - gt*r0707 + (g1*r0909)/12. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1414)/3. + (g2*r1515)/4. - i*(-(conj(Ep2a)*conj(r0709))/(4.*rt6) + (conj(Em2a)*conj(r0711))/(4.*rt6) + (conj(Ep3a)*conj(r0713))/8. + (conj(Em3a)*conj(r0715))/8. + (Ep2a*r0709)/(4.*rt6) - (Em2a*r0711)/(4.*rt6) - (Ep3a*r0713)/8. - (Em3a*r0715)/8. + conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
-dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*((conj(Ep3a)*conj(r0913))/8. + (conj(Em3a)*conj(r0915))/8. - (conj(Em1a)*r0701)/4. - (conj(Ep1a)*r0703)/(4.*rt6) + (conj(Ep2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0709 - (conj(Ep2a)*r0909)/(4.*rt6) + (conj(Em2a)*r1109)/(4.*rt6) + r0609*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0809*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0709*(-delta1 - v*Kvec1 - WLz/6.));
-dr0710_dt = (-(gt*r0710) - (gt + g1)*r0710)/2. - i*((conj(Ep2a)*conj(r0807))/(4.*rt6) - (conj(Ep2a)*conj(r1009))/(4.*rt6) + (conj(Ep3a)*conj(r1013))/8. + (conj(Em3a)*conj(r1015))/8. - (conj(Em1a)*r0702)/(4.*rt2) - (conj(Ep1a)*r0704)/(4.*rt2) - (conj(Em2a)*r0706)/(4.*rt6) + (delta1 + v*Kvec1)*r0710 + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0710 + (conj(Em2a)*r1110)/(4.*rt6) + r0610*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0711*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0709*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
-dr0711_dt = (-(gt*r0711) - (gt + g1)*r0711)/2. - i*(-(conj(Ep2a)*conj(r1109))/(4.*rt6) + (conj(Ep3a)*conj(r1113))/8. + (conj(Em3a)*conj(r1115))/8. - (conj(Em1a)*r0703)/(4.*rt6) - (conj(Ep1a)*r0705)/4. - (conj(Em2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0711 + (conj(Em2a)*r1111)/(4.*rt6) + r0611*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0811*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0711*(-delta1 - v*Kvec1 + WLz/6.));
-dr0712_dt = (-(gt*r0712) - (gt + g2)*r0712)/2. - i*(-(conj(Ep4a)*r0702)/(4.*rt6) - (conj(Ep3a)*r0706)/(4.*rt2) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0712 - (conj(Ep2a)*r0912)/(4.*rt6) + (conj(Em2a)*r1112)/(4.*rt6) + (conj(Ep3a)*r1312)/8. + (conj(Em3a)*r1512)/8. - r0713*((2*WLx)/3. + (2*i*WLy)/3.) + r0612*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0712*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0713_dt = (-(gt*r0713) - (gt + g2)*r0713)/2. - i*((conj(Em4a)*r0701)/(4.*rt6) - (conj(Ep4a)*r0703)/8. - (conj(Ep3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0713 - (conj(Ep2a)*r0913)/(4.*rt6) + (conj(Em2a)*r1113)/(4.*rt6) + (conj(Ep3a)*r1313)/8. + (conj(Em3a)*r1513)/8. - r0712*((2*WLx)/3. - (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0613*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0713*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr0714_dt = (-(gt*r0714) - (gt + g2)*r0714)/2. - i*(-(conj(Ep3a)*conj(r0807))/(8.*rt3) + (conj(Ep3a)*conj(r1413))/8. + (conj(Em4a)*r0702)/8. - (conj(Ep4a)*r0704)/8. - (conj(Em3a)*r0706)/(8.*rt3) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0714 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0714 - (conj(Ep2a)*r0914)/(4.*rt6) + (conj(Em2a)*r1114)/(4.*rt6) + (conj(Em3a)*r1514)/8. - r0713*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0715*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0614*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
-dr0715_dt = (-(gt*r0715) - (gt + g2)*r0715)/2. - i*((conj(Ep3a)*conj(r1513))/8. + (conj(Em4a)*r0703)/8. - (conj(Ep4a)*r0705)/(4.*rt6) - (conj(Em3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0715 - (conj(Ep2a)*r0915)/(4.*rt6) + (conj(Em2a)*r1115)/(4.*rt6) + (conj(Em3a)*r1515)/8. - r0716*((2*WLx)/3. + (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0615*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0815*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0715*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
-dr0716_dt = (-(gt*r0716) - (gt + g2)*r0716)/2. - i*(-(conj(Em3a)*conj(r0807))/(4.*rt2) + (conj(Ep3a)*conj(r1613))/8. + (conj(Em3a)*conj(r1615))/8. + (conj(Em4a)*r0704)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0716 - (conj(Ep2a)*r0916)/(4.*rt6) + (conj(Em2a)*r1116)/(4.*rt6) - r0715*((2*WLx)/3. - (2*i*WLy)/3.) + r0616*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0816*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0716*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
-dr0801_dt = -(gt*r0801) - i*(-(conj(Ep2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0114))/(8.*rt3) + (conj(Em3a)*conj(r0116))/(4.*rt2) - (Em1a*r0809)/4. + (Em4a*r0813)/(4.*rt6) - r0802*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0801*WLz);
-dr0802_dt = -(gt*r0802) - i*(-(conj(Ep2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0214))/(8.*rt3) + (conj(Em3a)*conj(r0216))/(4.*rt2) - (Em1a*r0810)/(4.*rt2) - (Ep4a*r0812)/(4.*rt6) + (Em4a*r0814)/8. - r0801*(WLx/2. - (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - (r0802*WLz)/2.);
-dr0803_dt = -(gt*r0803) - i*(-(conj(Ep2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0314))/(8.*rt3) + (conj(Em3a)*conj(r0316))/(4.*rt2) - (Ep1a*r0809)/(4.*rt6) - (Em1a*r0811)/(4.*rt6) - (Ep4a*r0813)/8. + (Em4a*r0815)/8. - r0802*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0804*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
-dr0804_dt = -(gt*r0804) - i*(-(conj(Ep2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0414))/(8.*rt3) + (conj(Em3a)*conj(r0416))/(4.*rt2) - (Ep1a*r0810)/(4.*rt2) - (Ep4a*r0814)/8. + (Em4a*r0816)/(4.*rt6) - r0805*(WLx/2. + (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + (r0804*WLz)/2.);
-dr0805_dt = -(gt*r0805) - i*(-(conj(Ep2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0514))/(8.*rt3) + (conj(Em3a)*conj(r0516))/(4.*rt2) - (Ep1a*r0811)/4. - (Ep4a*r0815)/(4.*rt6) - r0804*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + r0805*WLz);
-dr0806_dt = -(gt*r0806) - (g1*r1109)/12. + (g2*r1412)/(2.*rt6) + (g2*r1513)/4. + (g2*r1614)/(2.*rt6) - i*(-(conj(Ep2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0614))/(8.*rt3) + (conj(Em3a)*conj(r0616))/(4.*rt2) - (Em2a*r0810)/(4.*rt6) - (Ep3a*r0812)/(4.*rt2) - (Em3a*r0814)/(8.*rt3) + r0706*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
-dr0807_dt = -(gt*r0807) + (g1*r1009)/12. + (g2*r1413)/(4.*rt3) + (g2*r1514)/(2.*rt3) + (g2*r1615)/(2.*rt2) - i*(-(conj(Ep2a)*conj(r0710))/(4.*rt6) + (conj(Ep3a)*conj(r0714))/(8.*rt3) + (conj(Em3a)*conj(r0716))/(4.*rt2) - (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0807 + (Ep2a*r0809)/(4.*rt6) - (Em2a*r0811)/(4.*rt6) - (Ep3a*r0813)/8. - (Em3a*r0815)/8. + r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0808*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
-dr0808_dt = gt/8. - gt*r0808 + (g1*r1010)/12. + (g1*r1111)/12. + (g2*r1414)/12. + (g2*r1515)/4. + (g2*r1616)/2. - i*(-(conj(Ep2a)*conj(r0810))/(4.*rt6) + (conj(Ep3a)*conj(r0814))/(8.*rt3) + (conj(Em3a)*conj(r0816))/(4.*rt2) + (Ep2a*r0810)/(4.*rt6) - (Ep3a*r0814)/(8.*rt3) - (Em3a*r0816)/(4.*rt2) + conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
-dr0809_dt = (-(gt*r0809) - (gt + g1)*r0809)/2. - i*((conj(Ep3a)*conj(r0914))/(8.*rt3) + (conj(Em3a)*conj(r0916))/(4.*rt2) - (conj(Em1a)*r0801)/4. - (conj(Ep1a)*r0803)/(4.*rt6) + (conj(Ep2a)*r0807)/(4.*rt6) - (conj(Ep2a)*r1009)/(4.*rt6) + r0709*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-delta1 - v*Kvec1 - WLz/6.) + r0809*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
-dr0810_dt = (-(gt*r0810) - (gt + g1)*r0810)/2. - i*((conj(Ep3a)*conj(r1014))/(8.*rt3) + (conj(Em3a)*conj(r1016))/(4.*rt2) - (conj(Em1a)*r0802)/(4.*rt2) - (conj(Ep1a)*r0804)/(4.*rt2) - (conj(Em2a)*r0806)/(4.*rt6) + (conj(Ep2a)*r0808)/(4.*rt6) + (delta1 + v*Kvec1)*r0810 - (conj(Ep2a)*r1010)/(4.*rt6) + r0710*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0811*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
-dr0811_dt = (-(gt*r0811) - (gt + g1)*r0811)/2. - i*(-(conj(Ep2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1114))/(8.*rt3) + (conj(Em3a)*conj(r1116))/(4.*rt2) - (conj(Em1a)*r0803)/(4.*rt6) - (conj(Ep1a)*r0805)/4. - (conj(Em2a)*r0807)/(4.*rt6) + r0711*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0811*(-delta1 - v*Kvec1 + WLz/6.) + r0811*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
-dr0812_dt = (-(gt*r0812) - (gt + g2)*r0812)/2. - i*(-(conj(Ep4a)*r0802)/(4.*rt6) - (conj(Ep3a)*r0806)/(4.*rt2) - (conj(Ep2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1412)/(8.*rt3) + (conj(Em3a)*r1612)/(4.*rt2) - r0813*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0812*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0813_dt = (-(gt*r0813) - (gt + g2)*r0813)/2. - i*((conj(Em4a)*r0801)/(4.*rt6) - (conj(Ep4a)*r0803)/8. - (conj(Ep3a)*r0807)/8. - (conj(Ep2a)*r1013)/(4.*rt6) + (conj(Ep3a)*r1413)/(8.*rt3) + (conj(Em3a)*r1613)/(4.*rt2) - r0812*((2*WLx)/3. - (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0813*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr0814_dt = (-(gt*r0814) - (gt + g2)*r0814)/2. - i*((conj(Em4a)*r0802)/8. - (conj(Ep4a)*r0804)/8. - (conj(Em3a)*r0806)/(8.*rt3) - (conj(Ep3a)*r0808)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0814 - (conj(Ep2a)*r1014)/(4.*rt6) + (conj(Ep3a)*r1414)/(8.*rt3) + (conj(Em3a)*r1614)/(4.*rt2) - r0813*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0815*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
-dr0815_dt = (-(gt*r0815) - (gt + g2)*r0815)/2. - i*((conj(Ep3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0803)/8. - (conj(Ep4a)*r0805)/(4.*rt6) - (conj(Em3a)*r0807)/8. - (conj(Ep2a)*r1015)/(4.*rt6) + (conj(Em3a)*r1615)/(4.*rt2) - r0816*((2*WLx)/3. + (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0815*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0815*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
-dr0816_dt = (-(gt*r0816) - (gt + g2)*r0816)/2. - i*((conj(Ep3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0804)/(4.*rt6) - (conj(Em3a)*r0808)/(4.*rt2) - (conj(Ep2a)*r1016)/(4.*rt6) + (conj(Em3a)*r1616)/(4.*rt2) - r0815*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0816*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0816*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
-dr0909_dt = -((gt + g1)*r0909) - i*(-(conj(Em1a)*conj(r0109))/4. - (conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Ep2a)*conj(r0709))/(4.*rt6) + (Em1a*r0109)/4. + (Ep1a*r0309)/(4.*rt6) - (Ep2a*r0709)/(4.*rt6) - conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
-dr0912_dt = (-((gt + g1)*r0912) - (gt + g2)*r0912)/2. - i*(-(conj(Ep4a)*conj(r0209))/(4.*rt6) - (conj(Ep3a)*conj(r0609))/(4.*rt2) + (Em1a*r0112)/4. + (Ep1a*r0312)/(4.*rt6) - (Ep2a*r0712)/(4.*rt6) - r0913*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0912*(-delta1 - v*Kvec1 - WLz/6.) - r0912*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr0913_dt = (-((gt + g1)*r0913) - (gt + g2)*r0913)/2. - i*((conj(Em4a)*conj(r0109))/(4.*rt6) - (conj(Ep4a)*conj(r0309))/8. - (conj(Ep3a)*conj(r0709))/8. + (Em1a*r0113)/4. + (Ep1a*r0313)/(4.*rt6) - (Ep2a*r0713)/(4.*rt6) - r0912*((2*WLx)/3. - (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0913*(-delta1 - v*Kvec1 - WLz/6.) - r0913*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr0914_dt = (-((gt + g1)*r0914) - (gt + g2)*r0914)/2. - i*((conj(Em4a)*conj(r0209))/8. - (conj(Ep4a)*conj(r0409))/8. - (conj(Em3a)*conj(r0609))/(8.*rt3) - (conj(Ep3a)*conj(r0809))/(8.*rt3) + (Em1a*r0114)/4. + (Ep1a*r0314)/(4.*rt6) - (Ep2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0914 - r0913*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0915*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0914*(-delta1 - v*Kvec1 - WLz/6.));
-dr0915_dt = (-((gt + g1)*r0915) - (gt + g2)*r0915)/2. - i*((conj(Em4a)*conj(r0309))/8. - (conj(Ep4a)*conj(r0509))/(4.*rt6) - (conj(Em3a)*conj(r0709))/8. + (Em1a*r0115)/4. + (Ep1a*r0315)/(4.*rt6) - (Ep2a*r0715)/(4.*rt6) - r0916*((2*WLx)/3. + (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0915*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0915*(-delta1 - v*Kvec1 - WLz/6.));
-dr0916_dt = (-((gt + g1)*r0916) - (gt + g2)*r0916)/2. - i*((conj(Em4a)*conj(r0409))/(4.*rt6) - (conj(Em3a)*conj(r0809))/(4.*rt2) + (Em1a*r0116)/4. + (Ep1a*r0316)/(4.*rt6) - (Ep2a*r0716)/(4.*rt6) - r0915*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0916*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0916*(-delta1 - v*Kvec1 - WLz/6.));
-dr1009_dt = -((gt + g1)*r1009) - i*(-(conj(Em1a)*conj(r0110))/4. - (conj(Ep1a)*conj(r0310))/(4.*rt6) + (conj(Ep2a)*conj(r0710))/(4.*rt6) + (Em1a*r0209)/(4.*rt2) + (Ep1a*r0409)/(4.*rt2) + (Em2a*r0609)/(4.*rt6) - (Ep2a*r0809)/(4.*rt6) - (delta1 + v*Kvec1)*r1009 + r0909*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1009*(-delta1 - v*Kvec1 - WLz/6.));
-dr1010_dt = -((gt + g1)*r1010) - i*(-(conj(Em1a)*conj(r0210))/(4.*rt2) - (conj(Ep1a)*conj(r0410))/(4.*rt2) - (conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep2a)*conj(r0810))/(4.*rt6) + (Em1a*r0210)/(4.*rt2) + (Ep1a*r0410)/(4.*rt2) + (Em2a*r0610)/(4.*rt6) - (Ep2a*r0810)/(4.*rt6) + conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
-dr1012_dt = (-((gt + g1)*r1012) - (gt + g2)*r1012)/2. - i*(-(conj(Ep4a)*conj(r0210))/(4.*rt6) - (conj(Ep3a)*conj(r0610))/(4.*rt2) + (Em1a*r0212)/(4.*rt2) + (Ep1a*r0412)/(4.*rt2) + (Em2a*r0612)/(4.*rt6) - (Ep2a*r0812)/(4.*rt6) - (delta1 + v*Kvec1)*r1012 - r1013*((2*WLx)/3. + (2*i*WLy)/3.) + r0912*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1012*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1013_dt = (-((gt + g1)*r1013) - (gt + g2)*r1013)/2. - i*((conj(Em4a)*conj(r0110))/(4.*rt6) - (conj(Ep4a)*conj(r0310))/8. - (conj(Ep3a)*conj(r0710))/8. + (Em1a*r0213)/(4.*rt2) + (Ep1a*r0413)/(4.*rt2) + (Em2a*r0613)/(4.*rt6) - (Ep2a*r0813)/(4.*rt6) - (delta1 + v*Kvec1)*r1013 - r1012*((2*WLx)/3. - (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0913*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1013*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr1014_dt = (-((gt + g1)*r1014) - (gt + g2)*r1014)/2. - i*((conj(Em4a)*conj(r0210))/8. - (conj(Ep4a)*conj(r0410))/8. - (conj(Em3a)*conj(r0610))/(8.*rt3) - (conj(Ep3a)*conj(r0810))/(8.*rt3) + (Em1a*r0214)/(4.*rt2) + (Ep1a*r0414)/(4.*rt2) + (Em2a*r0614)/(4.*rt6) - (Ep2a*r0814)/(4.*rt6) - (delta1 + v*Kvec1)*r1014 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1014 - r1013*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1015*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0914*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
-dr1015_dt = (-((gt + g1)*r1015) - (gt + g2)*r1015)/2. - i*((conj(Em4a)*conj(r0310))/8. - (conj(Ep4a)*conj(r0510))/(4.*rt6) - (conj(Em3a)*conj(r0710))/8. + (Em1a*r0215)/(4.*rt2) + (Ep1a*r0415)/(4.*rt2) + (Em2a*r0615)/(4.*rt6) - (Ep2a*r0815)/(4.*rt6) - (delta1 + v*Kvec1)*r1015 - r1016*((2*WLx)/3. + (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0915*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1115*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1015*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
-dr1016_dt = (-((gt + g1)*r1016) - (gt + g2)*r1016)/2. - i*((conj(Em4a)*conj(r0410))/(4.*rt6) - (conj(Em3a)*conj(r0810))/(4.*rt2) + (Em1a*r0216)/(4.*rt2) + (Ep1a*r0416)/(4.*rt2) + (Em2a*r0616)/(4.*rt6) - (Ep2a*r0816)/(4.*rt6) - (delta1 + v*Kvec1)*r1016 - r1015*((2*WLx)/3. - (2*i*WLy)/3.) + r0916*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1116*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1016*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
-dr1109_dt = -((gt + g1)*r1109) - i*(-(conj(Em1a)*conj(r0111))/4. - (conj(Ep1a)*conj(r0311))/(4.*rt6) + (conj(Ep2a)*conj(r0711))/(4.*rt6) + (Em1a*r0309)/(4.*rt6) + (Ep1a*r0509)/4. + (Em2a*r0709)/(4.*rt6) + r1009*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-delta1 - v*Kvec1 - WLz/6.) + r1109*(-delta1 - v*Kvec1 + WLz/6.));
-dr1110_dt = -((gt + g1)*r1110) - i*(-(conj(Em1a)*conj(r0211))/(4.*rt2) - (conj(Ep1a)*conj(r0411))/(4.*rt2) - (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep2a)*conj(r0811))/(4.*rt6) + (Em1a*r0310)/(4.*rt6) + (Ep1a*r0510)/4. + (Em2a*r0710)/(4.*rt6) + (delta1 + v*Kvec1)*r1110 + r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-delta1 - v*Kvec1 + WLz/6.));
-dr1111_dt = -((gt + g1)*r1111) - i*(-(conj(Em1a)*conj(r0311))/(4.*rt6) - (conj(Ep1a)*conj(r0511))/4. - (conj(Em2a)*conj(r0711))/(4.*rt6) + (Em1a*r0311)/(4.*rt6) + (Ep1a*r0511)/4. + (Em2a*r0711)/(4.*rt6) + conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
-dr1112_dt = (-((gt + g1)*r1112) - (gt + g2)*r1112)/2. - i*(-(conj(Ep4a)*conj(r0211))/(4.*rt6) - (conj(Ep3a)*conj(r0611))/(4.*rt2) + (Em1a*r0312)/(4.*rt6) + (Ep1a*r0512)/4. + (Em2a*r0712)/(4.*rt6) - r1113*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-delta1 - v*Kvec1 + WLz/6.) - r1112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1113_dt = (-((gt + g1)*r1113) - (gt + g2)*r1113)/2. - i*((conj(Em4a)*conj(r0111))/(4.*rt6) - (conj(Ep4a)*conj(r0311))/8. - (conj(Ep3a)*conj(r0711))/8. + (Em1a*r0313)/(4.*rt6) + (Ep1a*r0513)/4. + (Em2a*r0713)/(4.*rt6) - r1112*((2*WLx)/3. - (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-delta1 - v*Kvec1 + WLz/6.) - r1113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr1114_dt = (-((gt + g1)*r1114) - (gt + g2)*r1114)/2. - i*((conj(Em4a)*conj(r0211))/8. - (conj(Ep4a)*conj(r0411))/8. - (conj(Em3a)*conj(r0611))/(8.*rt3) - (conj(Ep3a)*conj(r0811))/(8.*rt3) + (Em1a*r0314)/(4.*rt6) + (Ep1a*r0514)/4. + (Em2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1114 - r1113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-delta1 - v*Kvec1 + WLz/6.));
-dr1115_dt = (-((gt + g1)*r1115) - (gt + g2)*r1115)/2. - i*((conj(Em4a)*conj(r0311))/8. - (conj(Ep4a)*conj(r0511))/(4.*rt6) - (conj(Em3a)*conj(r0711))/8. + (Em1a*r0315)/(4.*rt6) + (Ep1a*r0515)/4. + (Em2a*r0715)/(4.*rt6) - r1116*((2*WLx)/3. + (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r1115*(-delta1 - v*Kvec1 + WLz/6.));
-dr1116_dt = (-((gt + g1)*r1116) - (gt + g2)*r1116)/2. - i*((conj(Em4a)*conj(r0411))/(4.*rt6) - (conj(Em3a)*conj(r0811))/(4.*rt2) + (Em1a*r0316)/(4.*rt6) + (Ep1a*r0516)/4. + (Em2a*r0716)/(4.*rt6) - r1115*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r1116*(-delta1 - v*Kvec1 + WLz/6.));
-dr1212_dt = -((gt + g2)*r1212) - i*(-(conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Ep3a)*conj(r0612))/(4.*rt2) + (Ep4a*r0212)/(4.*rt6) + (Ep3a*r0612)/(4.*rt2) + r1312*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.));
-dr1312_dt = -((gt + g2)*r1312) - i*(-(conj(Ep4a)*conj(r0213))/(4.*rt6) - (conj(Ep3a)*conj(r0613))/(4.*rt2) - (Em4a*r0112)/(4.*rt6) + (Ep4a*r0312)/8. + (Ep3a*r0712)/8. + r1212*((2*WLx)/3. + (2*i*WLy)/3.) - r1313*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1313_dt = -((gt + g2)*r1313) - i*((conj(Em4a)*conj(r0113))/(4.*rt6) - (conj(Ep4a)*conj(r0313))/8. - (conj(Ep3a)*conj(r0713))/8. - (Em4a*r0113)/(4.*rt6) + (Ep4a*r0313)/8. + (Ep3a*r0713)/8. - r1312*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
-dr1412_dt = -((gt + g2)*r1412) - i*(-(conj(Ep4a)*conj(r0214))/(4.*rt6) - (conj(Ep3a)*conj(r0614))/(4.*rt2) - (Em4a*r0212)/8. + (Ep4a*r0412)/8. + (Em3a*r0612)/(8.*rt3) + (Ep3a*r0812)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1412 - r1413*((2*WLx)/3. + (2*i*WLy)/3.) + r1512*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1413_dt = -((gt + g2)*r1413) - i*((conj(Em4a)*conj(r0114))/(4.*rt6) - (conj(Ep4a)*conj(r0314))/8. - (conj(Ep3a)*conj(r0714))/8. - (Em4a*r0213)/8. + (Ep4a*r0413)/8. + (Em3a*r0613)/(8.*rt3) + (Ep3a*r0813)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1413 - r1412*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1313*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr1414_dt = -((gt + g2)*r1414) - i*((conj(Em4a)*conj(r0214))/8. - (conj(Ep4a)*conj(r0414))/8. - (conj(Em3a)*conj(r0614))/(8.*rt3) - (conj(Ep3a)*conj(r0814))/(8.*rt3) - (Em4a*r0214)/8. + (Ep4a*r0414)/8. + (Em3a*r0614)/(8.*rt3) + (Ep3a*r0814)/(8.*rt3) - r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
-dr1512_dt = -((gt + g2)*r1512) - i*(-(conj(Ep4a)*conj(r0215))/(4.*rt6) - (conj(Ep3a)*conj(r0615))/(4.*rt2) - (Em4a*r0312)/8. + (Ep4a*r0512)/(4.*rt6) + (Em3a*r0712)/8. + r1612*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1513_dt = -((gt + g2)*r1513) - i*((conj(Em4a)*conj(r0115))/(4.*rt6) - (conj(Ep4a)*conj(r0315))/8. - (conj(Ep3a)*conj(r0715))/8. - (Em4a*r0313)/8. + (Ep4a*r0513)/(4.*rt6) + (Em3a*r0713)/8. - r1512*((2*WLx)/3. - (2*i*WLy)/3.) + r1613*((2*WLx)/3. - (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr1514_dt = -((gt + g2)*r1514) - i*((conj(Em4a)*conj(r0215))/8. - (conj(Ep4a)*conj(r0415))/8. - (conj(Em3a)*conj(r0615))/(8.*rt3) - (conj(Ep3a)*conj(r0815))/(8.*rt3) - (Em4a*r0314)/8. + (Ep4a*r0514)/(4.*rt6) + (Em3a*r0714)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1514 + r1614*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1514*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
-dr1515_dt = -((gt + g2)*r1515) - i*((conj(Em4a)*conj(r0315))/8. - (conj(Ep4a)*conj(r0515))/(4.*rt6) - (conj(Em3a)*conj(r0715))/8. - (Em4a*r0315)/8. + (Ep4a*r0515)/(4.*rt6) + (Em3a*r0715)/8. + r1615*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.) - r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
-dr1612_dt = -((gt + g2)*r1612) - i*(-(conj(Ep4a)*conj(r0216))/(4.*rt6) - (conj(Ep3a)*conj(r0616))/(4.*rt2) - (Em4a*r0412)/(4.*rt6) + (Em3a*r0812)/(4.*rt2) + r1512*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*((2*WLx)/3. + (2*i*WLy)/3.) + r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
-dr1613_dt = -((gt + g2)*r1613) - i*((conj(Em4a)*conj(r0116))/(4.*rt6) - (conj(Ep4a)*conj(r0316))/8. - (conj(Ep3a)*conj(r0716))/8. - (Em4a*r0413)/(4.*rt6) + (Em3a*r0813)/(4.*rt2) - r1612*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
-dr1614_dt = -((gt + g2)*r1614) - i*((conj(Em4a)*conj(r0216))/8. - (conj(Ep4a)*conj(r0416))/8. - (conj(Em3a)*conj(r0616))/(8.*rt3) - (conj(Ep3a)*conj(r0816))/(8.*rt3) - (Em4a*r0414)/(4.*rt6) + (Em3a*r0814)/(4.*rt2) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1614 + r1514*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1614*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
-dr1615_dt = -((gt + g2)*r1615) - i*((conj(Em4a)*conj(r0316))/8. - (conj(Ep4a)*conj(r0516))/(4.*rt6) - (conj(Em3a)*conj(r0716))/8. - (Em4a*r0415)/(4.*rt6) + (Em3a*r0815)/(4.*rt2) + r1515*((2*WLx)/3. + (2*i*WLy)/3.) - r1616*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
-dr1616_dt = -((gt + g2)*r1616) - i*((conj(Em4a)*conj(r0416))/(4.*rt6) - (conj(Em3a)*conj(r0816))/(4.*rt2) - (Em4a*r0416)/(4.*rt6) + (Em3a*r0816)/(4.*rt2) - r1615*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.));
-//---------------- RbEquations.txt ends  ------------------
-					]]>
-
+					<!-- Equations of motions according to Simon's mathematica code -->
+					<!-- read from Mathematica generated RbEquations.cdata -->
+					&RbEquationsFile;
         </operator>
 				<!--
 							 According to xmds2 docs operator kind="ip" should be faster
@@ -446,19 +306,8 @@ dr1616_dt = -((gt + g2)*r1616) - i*((conj(Em4a)*conj(r0416))/(4.*rt6) - (conj(Em
 				</operator>
         <integration_vectors>E_field</integration_vectors>
 				<dependencies>density_matrix</dependencies>
-				<![CDATA[
-				//read from Mathematica generated RbPropEquations.txt
-//---------------- RbPropEquations.txt starts ------------------
-dEp1_dz = -((i*Ndens*(rt2*conj(r0309) + rt6*(conj(r0410) + rt2*conj(r0511)))*eta1)/(rt2*rt6)) - Lt[Ep1];
-dEm1_dz = -((i*Ndens*(rt2*rt6*conj(r0109) + rt6*conj(r0210) + rt2*conj(r0311))*eta1)/(rt2*rt6)) - Lt[Em1];
-dEp2_dz = (i*Ndens*(conj(r0709) + conj(r0810))*eta1)/rt6 - Lt[Ep2];
-dEm2_dz = -((i*Ndens*(conj(r0610) + conj(r0711))*eta1)/rt6) - Lt[Em2];
-dEp3_dz = -((i*Ndens*(rt2*rt3*conj(r0612) + rt3*conj(r0713) + conj(r0814))*eta2)/rt3) - Lt[Ep3];
-dEm3_dz = -((i*Ndens*(conj(r0614) + rt3*(conj(r0715) + rt2*conj(r0816)))*eta2)/rt3) - Lt[Em3];
-dEp4_dz = -((i*Ndens*(rt2*conj(r0212) + rt3*conj(r0313) + rt3*conj(r0414) + rt2*conj(r0515))*eta2)/rt3) - Lt[Ep4];
-dEm4_dz = (i*Ndens*(rt2*conj(r0113) + rt3*conj(r0214) + rt3*conj(r0315) + rt2*conj(r0416))*eta2)/rt3 - Lt[Em4];
-//---------------- RbPropEquations.txt ends  ------------------
-				]]>
+				<!-- read from Mathematica generated RbPropEquations.cdata-->
+				&RbPropEquationsFile;
 			</operators>
 		</integrate>
 	</sequence>
-- 
cgit v1.2.3


From f2891fa6f6ea67b9fd6a3fbec4cc6344debfba64 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Wed, 28 Nov 2012 23:28:39 -0500
Subject: typo in makefile

---
 xmds2/realistic_Rb/Makefile            |  3 ++-
 xmds2/realistic_Rb_and_fields/Makefile | 25 ++++++++++++++++++-------
 2 files changed, 20 insertions(+), 8 deletions(-)

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb/Makefile b/xmds2/realistic_Rb/Makefile
index 583bc6a..1f5c4fd 100644
--- a/xmds2/realistic_Rb/Makefile
+++ b/xmds2/realistic_Rb/Makefile
@@ -16,7 +16,8 @@ M_FILES = $(patsubst %.xmds,%.m,$(XMDS_FILES))
 
 test_dir = tests
 test_result_dir = $(test_dir)/testsuite_results
-XMDS_INCLUDES_misc  = RbChosenRho.txt RbInits.cdata RbEquations.cdata RbAtomConstans.cdata
+XMDS_INCLUDES_misc  = RbChosenRho.txt RbInits.cdata RbEquations.cdata \
+		      RbAtomConstants.cdata RbPropEquations.cdata
 XMDS_INCLUDES_xmds_in_target_dir = $(XMDS_INCLUDES_misc:%=$(test_dir)/%)
 XMDS_INCLUDES_cdata_in_target_dir = $(XMDS_INCLUDES_misc:%=$(test_result_dir)/%)
 
diff --git a/xmds2/realistic_Rb_and_fields/Makefile b/xmds2/realistic_Rb_and_fields/Makefile
index d485891..1f5c4fd 100644
--- a/xmds2/realistic_Rb_and_fields/Makefile
+++ b/xmds2/realistic_Rb_and_fields/Makefile
@@ -1,9 +1,11 @@
 ###  -*- make -*-
 ### This file is part of the Debian xmds package
 ### Copyright (C) 2006 Rafael Laboissiere
-### This file is relased under the GNU General Public License
+### This file is released under the GNU General Public License
 ### NO WARRANTIES!
 
+INSTALL = install --mode=664 -D 
+
 ### This makefile can be used to build and run the XMDS examples
 
 XMDS_FILES = $(shell ls *.xmds)
@@ -12,14 +14,19 @@ CC_FILES = $(patsubst %.xmds,%.cc,$(XMDS_FILES))
 XSIL_FILES = $(patsubst %.xmds,%.xsil,$(XMDS_FILES))
 M_FILES = $(patsubst %.xmds,%.m,$(XMDS_FILES))
 
-XMDS_INCLUDES = RbAtomConstants.h RbInits.h
+test_dir = tests
+test_result_dir = $(test_dir)/testsuite_results
+XMDS_INCLUDES_misc  = RbChosenRho.txt RbInits.cdata RbEquations.cdata \
+		      RbAtomConstants.cdata RbPropEquations.cdata
+XMDS_INCLUDES_xmds_in_target_dir = $(XMDS_INCLUDES_misc:%=$(test_dir)/%)
+XMDS_INCLUDES_cdata_in_target_dir = $(XMDS_INCLUDES_misc:%=$(test_result_dir)/%)
 
 XMDS = xmds2
 XSIL2GRAPHICS = xsil2graphics
 
 all: $(RUN_FILES) 
 
-%.run: %.xmds $(XMDS_INCLUDES)
+%.run: %.xmds
 	$(XMDS) $<
 	mv $(patsubst %.xmds,%,$<) $@
 
@@ -48,10 +55,14 @@ $(png_targets): %.png : %.pdf
 
 pdf: $(pdf_targets) 
 
-test:
-	cp $(XMDS_FILES) tests/testsuite/
-	mkdir -p tests/testsuite_results
-	cp $(XMDS_INCLUDES) tests/testsuite_results/
+$(XMDS_INCLUDES_cdata_in_target_dir): $(test_result_dir)/% : %
+	$(INSTALL) $< $@
+
+$(XMDS_INCLUDES_xmds_in_target_dir): $(test_dir)/% : %
+	$(INSTALL) $< $@
+
+test: $(XMDS_INCLUDES_cdata_in_target_dir) $(XMDS_INCLUDES_xmds_in_target_dir)
+	$(INSTALL) $(XMDS_FILES) tests/testsuite/
 	cd tests; ./run_tests.py
 
 test_from_scratch:
-- 
cgit v1.2.3


From aeeeb3a41ba3df163dede45c37efe74c6ce71ca3 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Wed, 28 Nov 2012 23:36:08 -0500
Subject: completed move of mathematica generated files to includes

---
 xmds2/realistic_Rb/RbAtomConstans.cdata  | 18 ------------------
 xmds2/realistic_Rb/RbAtomConstants.cdata | 18 ++++++++++++++++++
 xmds2/realistic_Rb/RbPropEquations.cdata |  8 ++++++++
 xmds2/realistic_Rb/realistic_Rb.xmds     | 16 +++++-----------
 4 files changed, 31 insertions(+), 29 deletions(-)
 delete mode 100644 xmds2/realistic_Rb/RbAtomConstans.cdata
 create mode 100644 xmds2/realistic_Rb/RbAtomConstants.cdata
 create mode 100644 xmds2/realistic_Rb/RbPropEquations.cdata

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb/RbAtomConstans.cdata b/xmds2/realistic_Rb/RbAtomConstans.cdata
deleted file mode 100644
index 040d3c9..0000000
--- a/xmds2/realistic_Rb/RbAtomConstans.cdata
+++ /dev/null
@@ -1,18 +0,0 @@
-<![CDATA[
-//---------------- RbAtomConstans.cdata starts ------------------
-const double ha0 = 2.1471788680034824e10;
-const double ha1 = 2.558764384495815e9;
-const double g1 = 3.612847284945266e7;
-const double ha2 = 5.323020344462938e8;
-const double hb2 = 7.85178251911697e7;
-const double g2 = 3.8117309832741246e7;
-const double lambda1 = 7.949788511562656e-7;
-const double lambda2 = 7.802412096860509e-7;
-const double eta1 = 5.450949336831401e-6;
-const double eta2 = 5.5397657647874e-6;
-const double rt6 = 2.449489742783178;
-const double rt3 = 1.7320508075688772;
-const double rt2 = 1.4142135623730951;
-//---------------- RbAtomConstans.cdata ends   ------------------
-]]>
-
diff --git a/xmds2/realistic_Rb/RbAtomConstants.cdata b/xmds2/realistic_Rb/RbAtomConstants.cdata
new file mode 100644
index 0000000..040d3c9
--- /dev/null
+++ b/xmds2/realistic_Rb/RbAtomConstants.cdata
@@ -0,0 +1,18 @@
+<![CDATA[
+//---------------- RbAtomConstans.cdata starts ------------------
+const double ha0 = 2.1471788680034824e10;
+const double ha1 = 2.558764384495815e9;
+const double g1 = 3.612847284945266e7;
+const double ha2 = 5.323020344462938e8;
+const double hb2 = 7.85178251911697e7;
+const double g2 = 3.8117309832741246e7;
+const double lambda1 = 7.949788511562656e-7;
+const double lambda2 = 7.802412096860509e-7;
+const double eta1 = 5.450949336831401e-6;
+const double eta2 = 5.5397657647874e-6;
+const double rt6 = 2.449489742783178;
+const double rt3 = 1.7320508075688772;
+const double rt2 = 1.4142135623730951;
+//---------------- RbAtomConstans.cdata ends   ------------------
+]]>
+
diff --git a/xmds2/realistic_Rb/RbPropEquations.cdata b/xmds2/realistic_Rb/RbPropEquations.cdata
new file mode 100644
index 0000000..2a30be4
--- /dev/null
+++ b/xmds2/realistic_Rb/RbPropEquations.cdata
@@ -0,0 +1,8 @@
+<![CDATA[
+//---------------- RbPropEquations.cdata starts ------------------
+dE1_dz = 0.16666666666666666*i*Ndens*(2.449489742783178*conj(r0309) + 4.242640687119286*conj(r0410) + 6.*conj(r0511))*eta1 - Lt[E1];
+dE2_dz = -0.4082482904638631*i*Ndens*(conj(r0709) + conj(r0810))*eta1 - Lt[E2];
+dE3_dz = -0.3333333333333333*i*Ndens*(1.7320508075688772*conj(r0614) + 3.*conj(r0715) + 4.242640687119286*conj(r0816))*eta2 - Lt[E3];
+dE4_dz = (i*Ndens*(2.449489742783178*conj(r0113) + 3*conj(r0214) + 3*conj(r0315) + 2.449489742783178*conj(r0416))*eta2)/3. - Lt[E4];
+//---------------- RbPropEquations.cdata ends  ------------------
+]]>
diff --git a/xmds2/realistic_Rb/realistic_Rb.xmds b/xmds2/realistic_Rb/realistic_Rb.xmds
index 7744dd8..e3a5367 100644
--- a/xmds2/realistic_Rb/realistic_Rb.xmds
+++ b/xmds2/realistic_Rb/realistic_Rb.xmds
@@ -1,10 +1,11 @@
 <?xml version="1.0"?>
 <!--Below text defines necessary included files and references to them-->
 <!DOCTYPE simulation [
-<!ENTITY RbAtomConstansFile SYSTEM "RbAtomConstans.cdata" >
+<!ENTITY RbAtomConstantsFile SYSTEM "RbAtomConstants.cdata" >
 <!ENTITY RbChosenRhoFile SYSTEM "RbChosenRho.txt" >
 <!ENTITY RbInitsFile SYSTEM "RbInits.cdata" >
 <!ENTITY RbEquationsFile SYSTEM "RbEquations.cdata" >
+<!ENTITY RbPropEquationsFile SYSTEM "RbPropEquations.cdata" >
 ]>
 <simulation xmds-version="2">
 	<testing>
@@ -57,7 +58,7 @@
 	<features>
 		<globals>
 			<!-- read from Mathematica generated RbAtomConstans.cdata-->
-			&RbAtomConstansFile;
+			&RbAtomConstantsFile;
 			<![CDATA[
 				// Some numerical constants
 				const double pi = M_PI; 
@@ -291,15 +292,8 @@
 				</operator>
         <integration_vectors>E_field</integration_vectors>
 				<dependencies>density_matrix</dependencies>
-				<![CDATA[
-				//read from Mathematica generated RbPropEquations.txt
-//---------------- RbPropEquations.txt starts ------------------
-dE1_dz = 0.16666666666666666*i*Ndens*(2.449489742783178*conj(r0309) + 4.242640687119286*conj(r0410) + 6.*conj(r0511))*eta1 - Lt[E1];
-dE2_dz = -0.4082482904638631*i*Ndens*(conj(r0709) + conj(r0810))*eta1 - Lt[E2];
-dE3_dz = -0.3333333333333333*i*Ndens*(1.7320508075688772*conj(r0614) + 3.*conj(r0715) + 4.242640687119286*conj(r0816))*eta2 - Lt[E3];
-dE4_dz = (i*Ndens*(2.449489742783178*conj(r0113) + 3*conj(r0214) + 3*conj(r0315) + 2.449489742783178*conj(r0416))*eta2)/3. - Lt[E4];
-//---------------- RbPropEquations.txt ends  ------------------
-				]]>
+				<!-- read from Mathematica generated RbPropEquations.cdata-->
+				&RbPropEquationsFile;
 			</operators>
 		</integrate>
 	</sequence>
-- 
cgit v1.2.3


From dd093133de2a1328dcdaaf03765b5d15835ed0f9 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Wed, 28 Nov 2012 23:37:56 -0500
Subject: added auxiliary makefiles

---
 xmds2/realistic_Rb_and_fields/Makefile.fig | 39 +++++++++++++++++++++++++
 xmds2/realistic_Rb_and_fields/Makefile.par | 41 ++++++++++++++++++++++++++
 xmds2/realistic_Rb_and_fields/Makefile.pp  | 47 ++++++++++++++++++++++++++++++
 3 files changed, 127 insertions(+)
 create mode 100644 xmds2/realistic_Rb_and_fields/Makefile.fig
 create mode 100644 xmds2/realistic_Rb_and_fields/Makefile.par
 create mode 100644 xmds2/realistic_Rb_and_fields/Makefile.pp

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/Makefile.fig b/xmds2/realistic_Rb_and_fields/Makefile.fig
new file mode 100644
index 0000000..71fba31
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/Makefile.fig
@@ -0,0 +1,39 @@
+###  -*- make -*-
+### This makefile can be used to build and run the XMDS examples
+
+GNUPLOT_FILES = $(wildcard *.gp)
+
+SCRIPTS_DIR = .
+
+
+eps_targets  = $(wildcard *.eps)
+eps_bb_targets  =  $(eps_targets:%.eps=%.bb)
+pdf_targets  = $(eps_targets:%.eps=%.pdf)	
+png_targets  = $(pdf_targets:%.pdf=%.png)
+
+fig: png
+
+pdf: $(pdf_targets) 
+
+# fix bounding box
+$(eps_bb_targets): %.bb : %.eps
+	@cat $< | ps2eps -q -B > $@
+
+$(pdf_targets): %.pdf : %.bb
+	epspdf $< $@
+
+png: $(png_targets) 
+
+$(png_targets): %.png : %.pdf
+	convert -density 300 $< $@
+
+clean:
+	rm -f *.pdf
+	rm -f *.eps
+	rm -f *.bb
+
+real_clean: clean
+	rm -f *.png
+
+.PRECIOUS: %.run %.xsil %.m
+.PHONY: all clean
diff --git a/xmds2/realistic_Rb_and_fields/Makefile.par b/xmds2/realistic_Rb_and_fields/Makefile.par
new file mode 100644
index 0000000..5fddce1
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/Makefile.par
@@ -0,0 +1,41 @@
+###  -*- make -*-
+### This file is part of the Debian xmds package
+### Copyright (C) 2006 Rafael Laboissiere
+### This file is relased under the GNU General Public License
+### NO WARRANTIES!
+
+### This makefile can be used to build and run the XMDS examples
+
+
+XMDS_FILES = $(wildcard *.xmds)
+BASE_NAME = $(patsubst %.xmds,%,$(XMDS_FILES))
+RUN_FILES = $(patsubst %.xmds,%.run,$(XMDS_FILES))
+XSIL_FILES = $(patsubst %.xmds,%.xsil,$(XMDS_FILES))
+PARAMS_FILES = $(wildcard *.params)
+PP_DIR = $(PARAMS_FILES:%.params=%)
+CALC_XSIL_FILES = $(PARAMS_FILES:%.params=%/$(BASE_NAME).xsil)
+
+default: $(CALC_XSIL_FILES) 
+
+$(CALC_XSIL_FILES): %/$(BASE_NAME).xsil : %  %.params  
+	echo processing $$(dirname $(@)) dir
+	$(MAKE) -C $$(dirname $(@)) \
+		-f ../Makefile.pp \
+		SCRIPTS_DIR=../ \
+		PARAMS_FILE=../$<.params \
+		XSIL_FILES=$(XSIL_FILES) \
+		RUN_FILES=$(RUN_FILES)
+
+$(PP_DIR): % : %.params
+	echo need to make dir
+	[ -d $@ ] ||  mkdir -p  $@
+
+clean:
+	for d in $(PP_DIR); \
+	do $(MAKE) -C $$d SCRIPTS_DIR=../ -f ../Makefile.pp $@; done
+
+real_clean:
+	for d in $(PP_DIR); \
+	do $(MAKE) -C $$d SCRIPTS_DIR=../ -f ../Makefile.pp $@; done
+
+.PHONY: all clean
diff --git a/xmds2/realistic_Rb_and_fields/Makefile.pp b/xmds2/realistic_Rb_and_fields/Makefile.pp
new file mode 100644
index 0000000..e24107e
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/Makefile.pp
@@ -0,0 +1,47 @@
+###  -*- make -*-
+### This makefile can be used to build and run the XMDS examples
+
+
+GNUPLOT_FILES = $(wildcard *.gp)
+XSIL_FILES = $(wildcard *.xsil)
+RUN_FILES = $(patsubst %.xsil,%.run,$(XSIL_FILES))
+M_FILES = $(patsubst %.xsil,%.m,$(XSIL_FILES))
+
+SCRIPTS_DIR = ..
+
+XSIL2GRAPHICS = xsil2graphics
+
+include $(PARAMS_FILE)
+
+all: $(XSIL_FILES)  $(M_FILES) plot fig
+
+$(XSIL_FILES): ../$(RUN_FILES) $(PARAMS_FILE)
+	$< $(PARAMS) | grep "Time elapsed for simulation is:" > exact_analysis_execution_time.txt
+
+%.m: %.xsil
+	$(XSIL2GRAPHICS) $<
+
+fig: pp_I2.stamp
+	$(MAKE) -f $(SCRIPTS_DIR)/Makefile.fig $@
+
+
+pretty_plots: pp_I2.stamp $(GNUPLOT_FILES)
+	gnuplot $(SCRIPTS_DIR)/plot_fields_propagation_I2.gp
+	gnuplot $(SCRIPTS_DIR)/plot_fields_propagation_I4.gp
+
+plot: pp_I2.stamp
+
+pp_I2.stamp: $(XSIL_FILES) $(M_FILES)
+	octave -q $(SCRIPTS_DIR)/pp_I2.m
+
+clean:
+	rm -f pp_I2.stamp
+	$(MAKE) -f $(SCRIPTS_DIR)/Makefile.fig $@
+
+real_clean: clean
+	rm -f $(M_FILES) $(XSIL_FILES) *.dat octave-core 
+	$(MAKE) -f $(SCRIPTS_DIR)/Makefile.fig $@
+	rm -f exact_analysis_execution_time.txt
+
+.PRECIOUS: %.run %.xsil %.m
+.PHONY: all clean
-- 
cgit v1.2.3


From 48d6b0e778ddcb822298b963f81024211a8a7069 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Wed, 28 Nov 2012 23:39:42 -0500
Subject: added needed run_tests.py to the test dir

---
 xmds2/realistic_Rb_and_fields/tests/run_tests.py | 350 +++++++++++++++++++++++
 1 file changed, 350 insertions(+)
 create mode 100755 xmds2/realistic_Rb_and_fields/tests/run_tests.py

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/tests/run_tests.py b/xmds2/realistic_Rb_and_fields/tests/run_tests.py
new file mode 100755
index 0000000..61f4eea
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/tests/run_tests.py
@@ -0,0 +1,350 @@
+#!/usr/bin/env python
+# encoding: utf-8
+"""
+run_tests.py
+
+Created by Graham Dennis on 2008-06-15.
+
+Copyright (c) 2008-2012, Graham Dennis
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+"""
+
+import xpdeint.Python24Support
+
+import os
+import re
+import sys
+import getopt
+import shutil
+import hashlib
+import unittest
+import subprocess
+
+from xml.dom import minidom
+import xpdeint.minidom_extras
+from xpdeint import CodeParser
+
+from xpdeint.XSILFile import XSILFile
+
+import numpy
+
+help_message = '''
+The help message goes here.
+'''
+
+
+class Usage(Exception):
+  def __init__(self, msg):
+    self.msg = msg
+
+def pass_nan_test(array1, array2):
+    """Return `True` if isNaN(`array1`) == isNaN(`array2`)"""
+    # NaN test. array2 is allowed to be NaN at an index if array1 is also NaN there.
+    nanTestPassed = numpy.equal(numpy.isnan(array1), numpy.isnan(array2)).all()
+    return nanTestPassed
+
+def array_approx_equal(array1, array2, absTol, relTol):
+  """Return `True` if all of (`array1` - `array2`) <= `absTol` or (`array1` - `array2`) <= `relTol` * `array2`"""
+  diff = array1-array2
+  # NaN values would fail this test. So we have to exclude them. But only exclude them if array2 (the expected results)
+  # have a NaN
+  return numpy.logical_or(numpy.logical_or(numpy.abs(diff) <= 0.5 * relTol * (numpy.abs(array2) + numpy.abs(array1)), numpy.abs(diff) <= absTol), numpy.isnan(array2)).all()
+
+def scriptTestingFunction(root, scriptName, testDir, absPath, self):
+  if not os.path.exists(testDir):
+    os.makedirs(testDir)
+  
+  proc = subprocess.Popen('xmds2 --no-version ' + absPath,
+                          shell=True,
+                          stdout=subprocess.PIPE,
+                          stderr=subprocess.PIPE,
+                          cwd=testDir)
+  (stdout, stderr) = proc.communicate()
+  returnCode = proc.wait()
+  
+  message = ''.join(["\n%(handleName)s:\n%(content)s" % locals() for handleName, content in [('stdout', stdout), ('stderr', stderr)] if content])
+  
+  # A few tests require XMDS1. If XMDS1 isn't present we should just
+  # skip that test rather than failing.
+  # The skip functionality for the unittest class is only available
+  # in python 2.7 and later, so check for that too.
+  if returnCode != 0 and sys.version_info[:2] >= (2, 7):
+    if re.search(r'^The missing \w+ feature\(s\) were: .*xmds.*', message, re.MULTILINE):
+      self.skipTest("Skipping test as XMDS1 is required and not installed")
+
+  # A few tests require specific features.  If it isn't available, skip the test
+  # rather than failing.
+  # The skip functionality for the unittest class is only available
+  # in python 2.7 and later, so check for that too.
+  if returnCode != 0 and sys.version_info[:2] >= (2, 7):
+    if re.search(r'^The missing \w+ feature\(s\) were:', message, re.MULTILINE):
+      self.skipTest("Skipping test as feature required is not installed")
+
+  self.assert_(returnCode == 0, ("Failed to compile." % locals()) + message)
+  
+  xmlDocument = minidom.parse(absPath)
+  simulationElement = xmlDocument.getChildElementByTagName('simulation')
+  nameElement = simulationElement.getChildElementByTagName('name')
+  testingElement = simulationElement.getChildElementByTagName('testing')
+  
+  simulationName = nameElement.innerText()
+  
+  # If the source is the same as the last known good, then we don't need to compile or execute the simulation.
+  sourceFilePath = os.path.join(testDir, simulationName + '.cc')
+  checksumFilePath = os.path.join(testDir, simulationName + '_last_known_good.checksum')
+  sourceContents = file(sourceFilePath).read()
+  h = hashlib.sha1()
+  h.update(sourceContents)
+  currentChecksum = h.hexdigest()
+  
+  if os.path.exists(checksumFilePath):
+    lastKnownGoodChecksum = file(checksumFilePath).read()
+    
+    if lastKnownGoodChecksum == currentChecksum:
+      # The checksums check out, so we don't need to go any further
+      return
+  
+  # Now we have compiled, we need to copy any input data needed and then run the simulation
+  inputXSILElements = testingElement.getChildElementsByTagName('input_xsil_file', optional=True)
+  
+  filesToCopy = []
+  
+  for inputXSILElement in inputXSILElements:
+    name = inputXSILElement.getAttribute('name').strip()
+    filesToCopy.append(name)
+    inputXSILFile = XSILFile(os.path.join(os.path.split(absPath)[0], name), loadData=False)
+    filesToCopy.extend([os.path.join(os.path.split(name)[0], xsil.data.filename) for xsil in inputXSILFile.xsilObjects if hasattr(xsil.data, 'filename')])
+  
+  for fileToCopy in filesToCopy:
+    sourceFile = os.path.join(os.path.split(absPath)[0], fileToCopy)
+    shutil.copy(sourceFile, testDir)
+  
+  # Allow command-line arguments to be specified for the simulation
+  commandLineElement = testingElement.getChildElementByTagName('command_line', optional=True)
+  argumentsElement = testingElement.getChildElementByTagName('arguments', optional=True)
+  commandLineString = './' + simulationName
+  if commandLineElement:
+    # The command line element overrides the prefix
+    commandLineString = commandLineElement.innerText().strip()
+  if argumentsElement:
+    commandLineString += ' ' + argumentsElement.innerText().strip()
+  
+  simulationProc = subprocess.Popen(commandLineString,
+                                    shell=True,
+                                    stdout=subprocess.PIPE,
+                                    stderr=subprocess.PIPE,
+                                    cwd=testDir)
+  (stdout, stderr) = simulationProc.communicate()
+  returnCode = simulationProc.wait()
+  
+  self.assert_(returnCode == 0, "Failed to execute compiled simulation correctly." % locals())
+  
+  # The next thing to check is that the generated data agrees with the expected data to within the set error margins.
+  xsilFileElements = testingElement.getChildElementsByTagName('xsil_file', optional=True)
+  for xsilFileElement in xsilFileElements:
+    sourceFile = xsilFileElement.getAttribute('name').strip()
+    expectedResultsFile = xsilFileElement.getAttribute('expected').strip()
+    # Defaults
+    absoluteTolerance = 0 
+    relativeTolerance = 1e-9
+    
+    if xsilFileElement.hasAttribute('absolute_tolerance'):
+      absoluteTolerance = float(xsilFileElement.getAttribute('absolute_tolerance'))
+    if xsilFileElement.hasAttribute('relative_tolerance'):
+      relativeTolerance = float(xsilFileElement.getAttribute('relative_tolerance'))
+    
+    resultsFullPath = os.path.join(testDir, sourceFile)
+    results = XSILFile(resultsFullPath)
+    expectedResultsFullPath = os.path.join(os.path.split(absPath)[0], expectedResultsFile)
+    if not os.path.exists(expectedResultsFullPath):
+      print >> sys.stderr, "Expected results file '%(expectedResultsFile)s' missing. Using current. " % locals()
+      
+      # If there are any NaN's in the results, issue a warning.
+      for mgNum, o in enumerate(results.xsilObjects):
+        for v in o.independentVariables:
+          if numpy.isnan(v['array']).any():
+            print >> sys.stderr, "Warning: Coordinate '%s' in moment group %i of file '%s' contains a NaN." % (v['name'], mgNum+1, sourceFile)
+        for v in o.dependentVariables:
+          if numpy.isnan(v['array']).any():
+            print >> sys.stderr, "Warning: Dependent variable '%s' in moment group %i of file '%s' contains a NaN." % (v['name'], mgNum+1, sourceFile)
+      
+      resultsFileContents = file(resultsFullPath).read()
+      
+      for xsilObject in results.xsilObjects:
+        if hasattr(xsilObject.data, 'filename'):
+          # If the moment group has a data file name, then we need to copy it to the expected results file
+          newDataFilename = xsilObject.data.filename.replace(os.path.splitext(sourceFile)[0], os.path.splitext(expectedResultsFile)[0], 1)
+          
+          resultsFileContents = resultsFileContents.replace(xsilObject.data.filename, newDataFilename)
+          
+          shutil.copyfile(os.path.join(testDir, xsilObject.data.filename),
+                          os.path.join(os.path.split(absPath)[0], newDataFilename))
+      
+      file(expectedResultsFullPath, 'w').write(resultsFileContents)
+    else:
+      expectedResults = XSILFile(expectedResultsFullPath)
+      
+      self.assert_(len(results.xsilObjects) == len(expectedResults.xsilObjects))
+      
+      momentGroupElements = xsilFileElement.getChildElementsByTagName('moment_group', optional=True)
+      if momentGroupElements:
+        self.assert_(len(momentGroupElements) == len(results.xsilObjects))
+      else:
+        momentGroupElements = [None]*len(results.xsilObjects)
+      
+      for mgNum, (o1, o2, mgElem) in enumerate(zip(results.xsilObjects, expectedResults.xsilObjects, momentGroupElements)):
+        currentAbsoluteTolerance = absoluteTolerance
+        currentRelativeTolerance = relativeTolerance
+        self.assert_(len(o1.independentVariables) == len(o2.independentVariables),
+                     "The number of independent variables in moment group %(mgNum)i doesn't match." % locals())
+        self.assert_(len(o1.dependentVariables) == len(o2.dependentVariables),
+                     "The number of dependent variables in moment group %(mgNum)i doesn't match." % locals())
+        
+        if mgElem:
+          if mgElem.hasAttribute('absolute_tolerance'):
+            currentAbsoluteTolerance = float(mgElem.getAttribute('absolute_tolerance'))
+          if mgElem.hasAttribute('relative_tolerance'):
+            currentRelativeTolerance = float(mgElem.getAttribute('relative_tolerance'))
+        
+        self.assert_(currentAbsoluteTolerance != None and currentRelativeTolerance != None, "An absolute and a relative tolerance must be specified.")
+        
+        for v1, v2 in zip(o1.independentVariables, o2.independentVariables):
+          self.assert_(v1['name'] == v2['name'])
+          self.assert_(v1['length'] == v2['length'])
+          # These are the coordinates, we just specify a constant absolute and relative tolerance.
+          # No-one should need to change these
+          self.assert_(array_approx_equal(v1['array'], v2['array'], 1e-7, 1e-6),
+                      "Coordinate '%s' in moment group %i of file '%s' didn't pass tolerance criteria." % (v1['name'], mgNum+1, sourceFile))
+        
+        for v1, v2 in zip(o1.dependentVariables, o2.dependentVariables):
+          self.assert_(v1['name'] == v2['name'])
+          self.assert_(pass_nan_test(v1['array'], v2['array']),
+                       "Dependent variable '%s' in moment group %i of file '%s' had a NaN where the expected results didn't (or vice-versa)." % (v1['name'], mgNum+1, sourceFile))
+          self.assert_(array_approx_equal(v1['array'], v2['array'], currentAbsoluteTolerance, currentRelativeTolerance),
+                       "Dependent variable '%s' in moment group %i of file '%s' failed to pass tolerance criteria." % (v1['name'], mgNum+1, sourceFile))
+  
+  # Test has succeeded, so save our checksum for the source file and copy the source file
+  file(checksumFilePath, 'w').write(currentChecksum)
+  
+  lastKnownGoodSourcePath = os.path.join(testDir, simulationName + '_last_known_good.cc')
+  file(lastKnownGoodSourcePath, 'w').write(sourceContents)
+
+def partial(func, *args, **keywords):
+  def newfunc(*fargs, **fkeywords):
+    newkeywords = keywords.copy()
+    newkeywords.update(fkeywords)
+    return func(*(args + fargs), **newkeywords)
+  return newfunc
+
+
+def main(argv=None):
+  if argv is None:
+    argv = sys.argv
+  try:
+    try:
+      opts, args = getopt.getopt(argv[1:], "ho:v", ["help", "output="])
+    except getopt.error, msg:
+      raise Usage(msg)
+  
+    # option processing
+    for option, value in opts:
+      if option == "-v":
+        verbose = True
+      if option in ("-h", "--help"):
+        raise Usage(help_message)
+      if option in ("-o", "--output"):
+        output = value
+  
+  except Usage, err:
+    print >> sys.stderr, sys.argv[0].split("/")[-1] + ": " + str(err.msg)
+    print >> sys.stderr, "\t for help use --help"
+    return 2
+  
+  basePath = os.path.dirname(__file__)
+  
+  resultsPath = os.path.join(basePath, 'testsuite_results')
+  if not os.path.exists(resultsPath):
+    os.mkdir(resultsPath)
+  resultsPath = os.path.abspath(resultsPath)
+  
+  print "Saving test results in %(resultsPath)s" % locals()
+  
+  testsuites = {}
+  baseSuiteName = 'testsuite'
+  baseSuitePath = os.path.join(basePath, baseSuiteName)
+  
+  for root, dirs, files in os.walk(baseSuitePath):
+    # First remove directories we don't want to traverse
+    for dirName in ['.svn']:
+      if dirName in dirs:
+        dirs.remove(dirName)
+    # Remove the 'testsuite/' part of the path
+    dirRelativeToBase = root[(len(baseSuitePath)+1):]
+    if dirRelativeToBase:
+      testSuiteName = os.path.join(baseSuiteName, dirRelativeToBase)
+    else:
+      testSuiteName = baseSuiteName
+    
+    # If we have .xmds files in this path, then create a TestCase subclass
+    xmdsTestScripts = [filename for filename in files if os.path.splitext(filename)[1].lower() == '.xmds']
+    
+    if xmdsTestScripts:
+      class ScriptTestCase(unittest.TestCase):
+        # Create test functions for each test script using 'scriptTestingFunction'
+        # These test function names are of the form 'test_ScriptName'
+        for scriptName in xmdsTestScripts:
+          prefix = os.path.splitext(scriptName)[0]
+          absPath = os.path.abspath(os.path.join(root, scriptName))
+          testDir = os.path.join(resultsPath, dirRelativeToBase)
+          locals()['test_' + prefix] = partial(scriptTestingFunction, root, scriptName, testDir, absPath)
+          locals()['test_' + prefix].__doc__ = os.path.join(dirRelativeToBase, scriptName)
+      
+      # Create a TestSuite from that class
+      suite = unittest.defaultTestLoader.loadTestsFromTestCase(ScriptTestCase)
+      testsuites[testSuiteName] = suite
+    
+    if not testSuiteName in testsuites:
+      testsuites[testSuiteName] = unittest.TestSuite()
+    
+    suite = testsuites[testSuiteName]
+    # Add our TestSuite as a sub-suite of all parent suites
+    head = testSuiteName
+    while True:
+      head, tail = os.path.split(head)
+      if not head or not tail:
+        break
+      testsuites[head].addTest(suite)
+  
+  
+  suitesToRun = list()
+  if len(args):
+    for suiteName in args:
+      fullSuiteName = os.path.join(baseSuiteName, suiteName)
+      if fullSuiteName in testsuites:
+        suitesToRun.append(testsuites[fullSuiteName])
+      else:
+        print >> sys.stderr, "Unable to find test '%(suiteName)s'" % locals()
+  else:
+    suitesToRun.append(testsuites[baseSuiteName])
+  suitesToRun.append(unittest.defaultTestLoader.loadTestsFromModule(CodeParser))
+  
+  fullSuite = unittest.TestSuite(tests=suitesToRun)
+  
+  return not unittest.TextTestRunner().run(fullSuite).wasSuccessful()
+
+
+if __name__ == "__main__":
+  sys.exit(main())
-- 
cgit v1.2.3


From f53644c51b5bb8b6bff66ac327d65111077a2544 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Thu, 29 Nov 2012 13:24:03 -0500
Subject: added target to copy mathematica files

---
 xmds2/realistic_Rb_and_fields/Makefile | 6 ++++++
 1 file changed, 6 insertions(+)

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/Makefile b/xmds2/realistic_Rb_and_fields/Makefile
index 1f5c4fd..bc7cf13 100644
--- a/xmds2/realistic_Rb_and_fields/Makefile
+++ b/xmds2/realistic_Rb_and_fields/Makefile
@@ -21,6 +21,8 @@ XMDS_INCLUDES_misc  = RbChosenRho.txt RbInits.cdata RbEquations.cdata \
 XMDS_INCLUDES_xmds_in_target_dir = $(XMDS_INCLUDES_misc:%=$(test_dir)/%)
 XMDS_INCLUDES_cdata_in_target_dir = $(XMDS_INCLUDES_misc:%=$(test_result_dir)/%)
 
+MATHEMATICA_DIR = ../../mathemathica_fwm
+
 XMDS = xmds2
 XSIL2GRAPHICS = xsil2graphics
 
@@ -68,6 +70,10 @@ test: $(XMDS_INCLUDES_cdata_in_target_dir) $(XMDS_INCLUDES_xmds_in_target_dir)
 test_from_scratch:
 	rm -r tests/testsuite_results
 
+$(XMDS_INCLUDES_misc): %: $(MATHEMATICA_DIR)/%
+	cp $< $@
+
+copy_mathematica_generated_files: $(XMDS_INCLUDES_misc)
 
 $(pdf_targets): %.pdf : %.eps
 	cat $< | ps2eps -B > __tt.eps
-- 
cgit v1.2.3


From 30d082e4ea50244839fd5537483822e559db8a18 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Fri, 30 Nov 2012 17:17:09 -0500
Subject: added post processing script and sample case parameters

---
 xmds2/realistic_Rb_and_fields/pp_I2.m              | 82 ++++++++++++++++++++++
 .../two_field_circular_eit_cold.params             | 10 +++
 2 files changed, 92 insertions(+)
 create mode 100644 xmds2/realistic_Rb_and_fields/pp_I2.m
 create mode 100644 xmds2/realistic_Rb_and_fields/two_field_circular_eit_cold.params

(limited to 'xmds2')

diff --git a/xmds2/realistic_Rb_and_fields/pp_I2.m b/xmds2/realistic_Rb_and_fields/pp_I2.m
new file mode 100644
index 0000000..c3c6932
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/pp_I2.m
@@ -0,0 +1,82 @@
+% suppress output of plots on display
+set (0, "defaultfigurevisible", "off") 
+
+realistic_Rb_and_fields
+
+%% field I2  propagation
+z_1=z_1*100; % z in cm
+t_1=t_1*1e6; % time now measured in uS
+figure(1)
+%set(gca,'fontsize',20); 
+imagesc(z_1, t_1, Ip2_out_1); colorbar
+tmin=-0.4;
+tmax= 0.4;
+ylim([tmin,tmax],'manual');	
+xlabel('z (cm)')
+ylabel('t (uS)')
+zlabel('I_p2')
+title('I_p2')
+print('-color','-depsc2', '-tight', '-S200,120', 'fields_propagation_Ip2.eps')
+
+figure(1)
+%set(gca,'fontsize',20); 
+imagesc(z_1, t_1, Im2_out_1); colorbar
+tmin=-0.4;
+tmax= 0.4;
+ylim([tmin,tmax],'manual');	
+xlabel('z (cm)')
+ylabel('t (uS)')
+zlabel('I_m2')
+title('I_m2')
+print('-color','-depsc2', '-tight', '-S200,120', 'fields_propagation_Im2.eps')
+
+
+%% field I4  propagation
+figure(3)
+
+imagesc(z_1, t_1, Ip4_out_1); colorbar
+tmin=-0.4;
+tmax= 0.4;
+ylim([tmin,tmax],'manual');	
+xlabel('z (cm)')
+ylabel('t (uS)')
+zlabel('I_p4')
+title('I_p4')
+print('-color','-depsc2', '-tight', '-S200,120', 'fields_propagation_Ip4.eps')
+
+figure(4)
+
+imagesc(z_1, t_1, Im4_out_1); colorbar
+tmin=-0.4;
+tmax= 0.4;
+ylim([tmin,tmax],'manual');	
+xlabel('z (cm)')
+ylabel('t (uS)')
+zlabel('I_m4')
+title('I_m4')
+print('-color','-depsc2', '-tight', '-S200,120', 'fields_propagation_Im4.eps')
+
+
+
+
+
+%% fields before and after the cell
+figure(5)
+%set(gca,'fontsize',30); 
+plot( ...
+	 t_1,Ip2_out_1(:,1),'.-;I_p2 before;', "linewidth", 4  ...
+	,t_1,Im2_out_1(:,1),'.-;I_m2 before;', "linewidth", 4  ...
+	,t_1,Ip2_out_1(:,end), '-;I_p2 after;', "linewidth", 4 ...
+	,t_1,Im2_out_1(:,end), '-;I_m2 after;', "linewidth", 4 ...
+	,t_1,Ip4_out_1(:,end), '-;I_p4 after;', "linewidth", 4 ...
+	,t_1,Im4_out_1(:,end), '-;I_m after;', "linewidth", 4 ...
+	)
+xlabel('t (uS)')
+ylabel('I (1/s)^2')
+title('Fields before and after cell')
+legend('location', 'northeast');
+print('-color','-depsc2', 'fields_before_after_cell.eps')
+
+
+fid_stamp=fopen ("pp_I2.stamp", "a+");
+fclose (fid_stamp);
diff --git a/xmds2/realistic_Rb_and_fields/two_field_circular_eit_cold.params b/xmds2/realistic_Rb_and_fields/two_field_circular_eit_cold.params
new file mode 100644
index 0000000..325be02
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/two_field_circular_eit_cold.params
@@ -0,0 +1,10 @@
+
+PARAMS =  \
+	  --Ndens=1e15 \
+	  --Lcell=10.0e-2 \
+	  --Temperature=1e-3 \
+          --WLx=0 --WLy=0 --WLz=0 \
+	  --Pwidth=0.4e-6 \
+	  --delta1=0 --delta2=0 --delta3=0 \
+          --Ep1o=5e7 --Ep2o=1e2 --Ep3o=0 --Ep4o=0 --Em1o=0 --Em2o=0 --Em3o=0 --Em4o=0
+
-- 
cgit v1.2.3