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authorEugeniy Mikhailov <evgmik@gmail.com>2012-09-25 10:03:13 -0400
committerEugeniy Mikhailov <evgmik@gmail.com>2012-09-25 10:11:06 -0400
commit75f540e90acae010bec47622411f5fc419222e6b (patch)
tree229faead5634331cdee17734b30c95272f6395b4
parentc46fe7ea99c3e7602024a1c1272178859b6a92e9 (diff)
downloadNresonances-75f540e90acae010bec47622411f5fc419222e6b.tar.gz
Nresonances-75f540e90acae010bec47622411f5fc419222e6b.zip
added test files for simulations
Diffstat
-rw-r--r--xmds2/realistic_Rb/Makefile3
-rwxr-xr-xxmds2/realistic_Rb/tests/run_tests.py350
-rw-r--r--xmds2/realistic_Rb/tests/testsuite/realistic_Rb.xmds667
-rw-r--r--xmds2/realistic_Rb/tests/testsuite/realistic_Rb_expected.xsil699
-rw-r--r--xmds2/realistic_Rb/tests/testsuite/realistic_Rb_expected_mg0.datbin0 -> 3240832 bytes
5 files changed, 1719 insertions, 0 deletions
diff --git a/xmds2/realistic_Rb/Makefile b/xmds2/realistic_Rb/Makefile
index e088e15..34d73e1 100644
--- a/xmds2/realistic_Rb/Makefile
+++ b/xmds2/realistic_Rb/Makefile
@@ -46,6 +46,9 @@ $(png_targets): %.png : %.pdf
pdf: $(pdf_targets)
+test:
+ cd tests; ./run_tests.py
+
$(pdf_targets): %.pdf : %.eps
cat $< | ps2eps -B > __tt.eps
epspdf __tt.eps $@
diff --git a/xmds2/realistic_Rb/tests/run_tests.py b/xmds2/realistic_Rb/tests/run_tests.py
new file mode 100755
index 0000000..61f4eea
--- /dev/null
+++ b/xmds2/realistic_Rb/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())
diff --git a/xmds2/realistic_Rb/tests/testsuite/realistic_Rb.xmds b/xmds2/realistic_Rb/tests/testsuite/realistic_Rb.xmds
new file mode 100644
index 0000000..8963ae5
--- /dev/null
+++ b/xmds2/realistic_Rb/tests/testsuite/realistic_Rb.xmds
@@ -0,0 +1,667 @@
+<?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</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 then 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;
+ // proportional to splitting ratios sqrt(6) , sqrt(3), sqrt(2)
+ const double rt6 = 2.449489742783178;
+ const double rt3 = 1.7320508075688772;
+ const double rt2 = 1.4142135623730951;
+
+
+ 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;
+
+ const double Gamma_super=6*(2*M_PI*1e6); // characteristic decay rate of upper level used for eta calculations expressed in [1/s]
+ // eta will be calculated in the <arguments> section
+ double eta = 0; // eta constant in the wave equation for Rabi frequency. Units are [1/(m s)]
+ double eta1=0, eta2=0, eta3=0;
+
+ // --------- 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);
+
+ // Natural linewidth of j's level in [1/s]
+ const double g1 = 3.612847284945266e7;
+ const double g2 = 3.8117309832741246e7;
+
+ // levels energy
+ const double ha0 = 2.1471788680034824e10;
+ const double ha1 = 2.558764384495815e9;
+ const double ha2 = 5.323020344462938e8;
+ const double hb2 = 7.85178251911697e7;
+
+ // Larmor frequency
+ double WL=0;
+
+
+
+ complex E1ac, E2ac, E3ac, E4ac; // Complex conjugated Rabi frequencies
+
+ // density matrix elements which calculated via Hermitian property r_ij=conj(r_ji)
+ complex
+ r1301,
+ r1402,
+ r0903,
+ r1503,
+ r1004,
+ r1604,
+ r1105,
+ r0206,
+ r1406,
+ r0307,
+ r0907,
+ r1507,
+ r0408,
+ r1008,
+ r1608,
+ r1509,
+ r1610;
+
+
+ // 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="E1o" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+ <argument name="E2o" type="real" default_value="0.05*(2*M_PI*1e6)" />
+ <argument name="E3o" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+ <argument name="E4o" 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;
+
+ // eta constant in the wave equation for Rabi frequency. Units are [1/(m s)]
+ eta = 3*lambda*lambda*Ndens*Gamma_super/8.0/M_PI;
+ // !FIXME over simplification: we should use relevant levels linewidths
+ eta1 = eta;
+ eta2 = eta;
+ eta3 = eta;
+ ]]>
+ </arguments>
+ <bing />
+ <diagnostics />
+ <fftw plan="estimate" 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">
+ <components>E1 E2 E3 E4</components>
+ <initialisation>
+ <![CDATA[
+ // Initial (at starting 'z' position) electromagnetic field does not depend on detuning
+ // as well as time
+ E1=E1o;
+ E2=E2o*exp(-pow( ((t-0.0)/Pwidth),2) );
+ E3=E3o;
+ E4=E4o;
+ ]]>
+ </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>E1a E2a E3a E4a</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;
+ E1a=E1*prob_v_normalized;
+ E2a=E2*prob_v_normalized;
+ E3a=E3*prob_v_normalized;
+ E4a=E4*prob_v_normalized;
+ ]]>
+ </evaluation>
+ </computed_vector>
+
+ <!-- Averaged across Maxwell distribution density matrix components -->
+ <computed_vector name="density_matrix_averaged" dimensions="t" type="complex">
+ <components>
+ r0101a
+ r0113a
+ r0202a
+ r0214a
+ r0303a
+ r0309a
+ r0315a
+ r0404a
+ r0410a
+ r0416a
+ r0505a
+ r0511a
+ r0602a
+ r0606a
+ r0614a
+ r0703a
+ r0707a
+ r0709a
+ r0715a
+ r0804a
+ r0808a
+ r0810a
+ r0816a
+ r0909a
+ r0915a
+ r1010a
+ r1016a
+ r1111a
+ r1313a
+ r1414a
+ r1515a
+ r1616a
+ </components>
+ <evaluation>
+ <dependencies basis="v">density_matrix Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm</dependencies>
+ <![CDATA[
+ double prob_v_normalized=probability_v/probability_v_norm;
+
+ r0101a = r0101*prob_v_normalized;
+ r0113a = r0113*prob_v_normalized;
+ r0202a = r0202*prob_v_normalized;
+ r0214a = r0214*prob_v_normalized;
+ r0303a = r0303*prob_v_normalized;
+ r0309a = r0309*prob_v_normalized;
+ r0315a = r0315*prob_v_normalized;
+ r0404a = r0404*prob_v_normalized;
+ r0410a = r0410*prob_v_normalized;
+ r0416a = r0416*prob_v_normalized;
+ r0505a = r0505*prob_v_normalized;
+ r0511a = r0511*prob_v_normalized;
+ r0602a = r0602*prob_v_normalized;
+ r0606a = r0606*prob_v_normalized;
+ r0614a = r0614*prob_v_normalized;
+ r0703a = r0703*prob_v_normalized;
+ r0707a = r0707*prob_v_normalized;
+ r0709a = r0709*prob_v_normalized;
+ r0715a = r0715*prob_v_normalized;
+ r0804a = r0804*prob_v_normalized;
+ r0808a = r0808*prob_v_normalized;
+ r0810a = r0810*prob_v_normalized;
+ r0816a = r0816*prob_v_normalized;
+ r0909a = r0909*prob_v_normalized;
+ r0915a = r0915*prob_v_normalized;
+ r1010a = r1010*prob_v_normalized;
+ r1016a = r1016*prob_v_normalized;
+ r1111a = r1111*prob_v_normalized;
+ r1313a = r1313*prob_v_normalized;
+ r1414a = r1414*prob_v_normalized;
+ r1515a = r1515*prob_v_normalized;
+ r1616a = r1616*prob_v_normalized;
+ ]]>
+ </evaluation>
+ </computed_vector>
+
+
+ <vector name="density_matrix" type="complex" initial_space="t">
+ <components>
+ 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
+ </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
+ 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;
+ ]]>
+ </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 then 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[
+ E1ac = conj(E1a);
+ E2ac = conj(E2a);
+ E3ac = conj(E3a);
+ E4ac = conj(E4a);
+
+ // Density matrix is Hermitian so we use r_ij=conj(r_ji)
+
+ r1301 = conj(r0113);
+ r1402 = conj(r0214);
+ r0903 = conj(r0309);
+ r1503 = conj(r0315);
+ r1004 = conj(r0410);
+ r1604 = conj(r0416);
+ r1105 = conj(r0511);
+ r0206 = conj(r0602);
+ r1406 = conj(r0614);
+ r0307 = conj(r0703);
+ r0907 = conj(r0709);
+ r1507 = conj(r0715);
+ r0408 = conj(r0804);
+ r1008 = conj(r0810);
+ r1608 = conj(r0816);
+ r1509 = conj(r0915);
+ r1610 = conj(r1016);
+
+ // Equations of motions according to Simon's mathematica code
+ dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1313)/6. - i*((r0113*E4a)/(4.*rt6) - (r1301*E4ac)/(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*E4ac)/(4.*rt6) - (r1313*E4ac)/(4.*rt6));
+ dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1313)/12. + (g2*r1414)/4. - i*((r0214*E4a)/8. - (r1402*E4ac)/8.);
+ dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*((WL*r0214)/2. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 - (r0206*E3ac)/(8.*rt3) + (r0202*E4ac)/8. - (r1414*E4ac)/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. - (r0903*E1ac)/(4.*rt6) - (r1503*E4ac)/8.);
+ dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*(-((-WL/6. - delta1 - v*Kvec1)*r0309) + (r0303*E1ac)/(4.*rt6) - (r0909*E1ac)/(4.*rt6) - (r0307*E2ac)/(4.*rt6) - (r1509*E4ac)/8.);
+ dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(((-2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0315) - (r0915*E1ac)/(4.*rt6) - (r0307*E3ac)/8. + (r0303*E4ac)/8. - (r1515*E4ac)/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) - (r1004*E1ac)/(4.*rt2) - (r1604*E4ac)/(4.*rt6));
+ dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(WL*r0410)/2. + (delta1 + v*Kvec1)*r0410 + (r0404*E1ac)/(4.*rt2) - (r1010*E1ac)/(4.*rt2) - (r0408*E2ac)/(4.*rt6) - (r1610*E4ac)/(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*E1ac)/(4.*rt2) - (r0408*E3ac)/(4.*rt2) + (r0404*E4ac)/(4.*rt6) - (r1616*E4ac)/(4.*rt6));
+ dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((r0511*E1a)/4. - (r1105*E1ac)/4.);
+ dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(WL*r0511) - (WL/6. - delta1 - v*Kvec1)*r0511 + (r0505*E1ac)/4. - (r1111*E1ac)/4.);
+ dr0602_dt = -(gt*r0602) - i*(-(WL*r0602)/2. + (-WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0602 + (r0614*E4a)/8. + (r1402*E3ac)/(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) + (r1406*E3ac)/(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*E3ac)/(8.*rt3) + (r1414*E3ac)/(8.*rt3) + (r0602*E4ac)/8.);
+ dr0703_dt = -(gt*r0703) - i*((-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 + (r0709*E1a)/(4.*rt6) + (r0715*E4a)/8. + (r0903*E2ac)/(4.*rt6) + (r1503*E3ac)/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. + (r0907*E2ac)/(4.*rt6) + (r1507*E3ac)/8.);
+ dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*(-((-WL/6. - delta1 - v*Kvec1)*r0709) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0709 + (r0703*E1ac)/(4.*rt6) - (r0707*E2ac)/(4.*rt6) + (r0909*E2ac)/(4.*rt6) + (r1509*E3ac)/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*E2ac)/(4.*rt6) - (r0707*E3ac)/8. + (r1515*E3ac)/8. + (r0703*E4ac)/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) + (r1004*E2ac)/(4.*rt6) + (r1604*E3ac)/(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) + (r1008*E2ac)/(4.*rt6) + (r1608*E3ac)/(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*E1ac)/(4.*rt2) - (r0808*E2ac)/(4.*rt6) + (r1010*E2ac)/(4.*rt6) + (r1610*E3ac)/(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*E2ac)/(4.*rt6) - (r0808*E3ac)/(4.*rt2) + (r1616*E3ac)/(4.*rt2) + (r0804*E4ac)/(4.*rt6));
+ dr0909_dt = -((gt + g1)*r0909) - i*(-(r0309*E1a)/(4.*rt6) + (r0709*E2a)/(4.*rt6) + (r0903*E1ac)/(4.*rt6) - (r0907*E2ac)/(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) - (r0907*E3ac)/8. + (r0903*E4ac)/8.);
+ dr1010_dt = -((gt + g1)*r1010) - i*(-(r0410*E1a)/(4.*rt2) + (r0810*E2a)/(4.*rt6) + (r1004*E1ac)/(4.*rt2) - (r1008*E2ac)/(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) - (r1008*E3ac)/(4.*rt2) + (r1004*E4ac)/(4.*rt6));
+ dr1111_dt = -((gt + g1)*r1111) - i*(-(r0511*E1a)/4. + (r1105*E1ac)/4.);
+ dr1313_dt = -((gt + g2)*r1313) - i*(-(r0113*E4a)/(4.*rt6) + (r1301*E4ac)/(4.*rt6));
+ dr1414_dt = -((gt + g2)*r1414) - i*((r0614*E3a)/(8.*rt3) - (r0214*E4a)/8. - (r1406*E3ac)/(8.*rt3) + (r1402*E4ac)/8.);
+ dr1515_dt = -((gt + g2)*r1515) - i*((r0715*E3a)/8. - (r0315*E4a)/8. - (r1507*E3ac)/8. + (r1503*E4ac)/8.);
+ dr1616_dt = -((gt + g2)*r1616) - i*((r0816*E3a)/(4.*rt2) - (r0416*E4a)/(4.*rt6) - (r1608*E3ac)/(4.*rt2) + (r1604*E4ac)/(4.*rt6));
+ ]]>
+ </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[
+ // Density matrix is Hermitian so we use r_ij=conj(r_ji)
+ r1301 = conj(r0113);
+ r1402 = conj(r0214);
+ r0903 = conj(r0309);
+ r1503 = conj(r0315);
+ r1004 = conj(r0410);
+ r1604 = conj(r0416);
+ r1105 = conj(r0511);
+ r0206 = conj(r0602);
+ r1406 = conj(r0614);
+ r0307 = conj(r0703);
+ r0907 = conj(r0709);
+ r1507 = conj(r0715);
+ r0408 = conj(r0804);
+ r1008 = conj(r0810);
+ r1608 = conj(r0816);
+ r1509 = conj(r0915);
+ r1610 = conj(r1016);
+
+ dE1_dz = 0.16666666666666666*i*eta1*(2.449489742783178*r0903 + 4.242640687119286*r1004 + 6.*r1105) - Lt[E1];
+ dE2_dz = -0.4082482904638631*i*eta1*(r0907 + r1008) - Lt[E2];
+ dE3_dz = -0.3333333333333333*i*eta2*(1.7320508075688772*r1406 + 3.*r1507 + 4.242640687119286*r1608) - Lt[E3];
+ dE4_dz = (i*eta2*(2.449489742783178*r1301 + 3*r1402 + 3*r1503 + 2.449489742783178*r1604))/3. - Lt[E4];
+ ]]>
+ </operators>
+ </integrate>
+ </sequence>
+
+
+
+ <!-- The output to generate -->
+ <output format="binary" filename="realistic_Rb.xsil">
+ <group>
+ <sampling basis="t(1000) " initial_sample="yes">
+ <dependencies>E_field_avgd</dependencies>
+ <moments>I1_out I2_out I3_out I4_out</moments>
+ <![CDATA[
+ I1_out = mod2(E1a);
+ I2_out = mod2(E2a);
+ I3_out = mod2(E3a);
+ I4_out = mod2(E4a);
+ ]]>
+ </sampling>
+ </group>
+
+ <!--
+ <group>
+ <sampling basis="t(100) v(10)" initial_sample="yes">
+ <dependencies>density_matrix_averaged</dependencies>
+ <moments>
+ r11_out r22_out r33_out r44_out
+ r12_re_out r12_im_out r13_re_out r13_im_out r14_re_out r14_im_out
+ r23_re_out r23_im_out r24_re_out r24_im_out
+ r34_re_out r34_im_out
+ </moments>
+ <![CDATA[
+ // populations output
+ r11_out = r11a.Re();
+ r22_out = r22a.Re();
+ r33_out = r33a.Re();
+ r44_out = r44a.Re();
+ // coherences output
+ r12_re_out = r12a.Re();
+ r12_im_out = r12a.Im();
+ r13_re_out = r13a.Re();
+ r13_im_out = r13a.Im();
+ r14_re_out = r14a.Re();
+ r14_im_out = r14a.Im();
+ r23_re_out = r23a.Re();
+ r23_im_out = r23a.Im();
+ r24_re_out = r24a.Re();
+ r24_im_out = r24a.Im();
+ r34_re_out = r34a.Re();
+ r34_im_out = r34a.Im();
+ ]]>
+ </sampling>
+ </group>
+ -->
+
+ <!-- use the following two groups only for debuging
+ otherwise they are quite useless and have to much information
+ in 3D space (z,t,v) -->
+ <!--
+ <group>
+ <sampling basis="t(100) v(10)" initial_sample="yes">
+ <dependencies>E_field</dependencies>
+ <moments>I1_out_v I2_out_v I3_out_v I4_out_v</moments>
+ <![CDATA[
+ // light field intensity distribution in velocity subgroups
+ I1_out_v = mod2(E1);
+ I2_out_v = mod2(E2);
+ I3_out_v = mod2(E3);
+ I4_out_v = mod2(E4);
+ ]]>
+ </sampling>
+ </group>
+
+ <group>
+ <sampling basis="t(100) v(10)" initial_sample="yes">
+ <dependencies>density_matrix</dependencies>
+ <moments>
+ r11_out_v r22_out_v r33_out_v r44_out_v
+ r12_re_out_v r12_im_out_v r13_re_out_v r13_im_out_v r14_re_out_v r14_im_out_v
+ r23_re_out_v r23_im_out_v r24_re_out_v r24_im_out_v
+ r34_re_out_v r34_im_out_v
+ </moments>
+ <![CDATA[
+ // density matrix distribution in velocity subgroups
+ // populations output
+ r11_out_v = r11.Re();
+ r22_out_v = r22.Re();
+ r33_out_v = r33.Re();
+ r44_out_v = r44.Re();
+ // coherences output
+ r12_re_out_v = r12.Re();
+ r12_im_out_v = r12.Im();
+ r13_re_out_v = r13.Re();
+ r13_im_out_v = r13.Im();
+ r14_re_out_v = r14.Re();
+ r14_im_out_v = r14.Im();
+ r23_re_out_v = r23.Re();
+ r23_im_out_v = r23.Im();
+ r24_re_out_v = r24.Re();
+ r24_im_out_v = r24.Im();
+ r34_re_out_v = r34.Re();
+ r34_im_out_v = r34.Im();
+ ]]>
+ </sampling>
+ </group>
+ -->
+
+ </output>
+
+</simulation>
+
+<!--
+vim: ts=2 sw=2 foldmethod=indent:
+-->
diff --git a/xmds2/realistic_Rb/tests/testsuite/realistic_Rb_expected.xsil b/xmds2/realistic_Rb/tests/testsuite/realistic_Rb_expected.xsil
new file mode 100644
index 0000000..409374d
--- /dev/null
+++ b/xmds2/realistic_Rb/tests/testsuite/realistic_Rb_expected.xsil
@@ -0,0 +1,699 @@
+<?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</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 then 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;
+ // proportional to splitting ratios sqrt(6) , sqrt(3), sqrt(2)
+ const double rt6 = 2.449489742783178;
+ const double rt3 = 1.7320508075688772;
+ const double rt2 = 1.4142135623730951;
+
+
+ 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;
+
+ const double Gamma_super=6*(2*M_PI*1e6); // characteristic decay rate of upper level used for eta calculations expressed in [1/s]
+ // eta will be calculated in the <arguments> section
+ double eta = 0; // eta constant in the wave equation for Rabi frequency. Units are [1/(m s)]
+ double eta1=0, eta2=0, eta3=0;
+
+ // --------- 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);
+
+ // Natural linewidth of j's level in [1/s]
+ const double g1 = 3.612847284945266e7;
+ const double g2 = 3.8117309832741246e7;
+
+ // levels energy
+ const double ha0 = 2.1471788680034824e10;
+ const double ha1 = 2.558764384495815e9;
+ const double ha2 = 5.323020344462938e8;
+ const double hb2 = 7.85178251911697e7;
+
+ // Larmor frequency
+ double WL=0;
+
+
+
+ complex E1ac, E2ac, E3ac, E4ac; // Complex conjugated Rabi frequencies
+
+ // density matrix elements which calculated via Hermitian property r_ij=conj(r_ji)
+ complex
+ r1301,
+ r1402,
+ r0903,
+ r1503,
+ r1004,
+ r1604,
+ r1105,
+ r0206,
+ r1406,
+ r0307,
+ r0907,
+ r1507,
+ r0408,
+ r1008,
+ r1608,
+ r1509,
+ r1610;
+
+
+ // 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="E1o" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+ <argument name="E2o" type="real" default_value="0.05*(2*M_PI*1e6)" />
+ <argument name="E3o" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+ <argument name="E4o" 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;
+
+ // eta constant in the wave equation for Rabi frequency. Units are [1/(m s)]
+ eta = 3*lambda*lambda*Ndens*Gamma_super/8.0/M_PI;
+ // !FIXME over simplification: we should use relevant levels linewidths
+ eta1 = eta;
+ eta2 = eta;
+ eta3 = eta;
+ ]]>
+ </arguments>
+ <bing />
+ <diagnostics />
+ <fftw plan="estimate" 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">
+ <components>E1 E2 E3 E4</components>
+ <initialisation>
+ <![CDATA[
+ // Initial (at starting 'z' position) electromagnetic field does not depend on detuning
+ // as well as time
+ E1=E1o;
+ E2=E2o*exp(-pow( ((t-0.0)/Pwidth),2) );
+ E3=E3o;
+ E4=E4o;
+ ]]>
+ </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>E1a E2a E3a E4a</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;
+ E1a=E1*prob_v_normalized;
+ E2a=E2*prob_v_normalized;
+ E3a=E3*prob_v_normalized;
+ E4a=E4*prob_v_normalized;
+ ]]>
+ </evaluation>
+ </computed_vector>
+
+ <!-- Averaged across Maxwell distribution density matrix components -->
+ <computed_vector name="density_matrix_averaged" dimensions="t" type="complex">
+ <components>
+ r0101a
+ r0113a
+ r0202a
+ r0214a
+ r0303a
+ r0309a
+ r0315a
+ r0404a
+ r0410a
+ r0416a
+ r0505a
+ r0511a
+ r0602a
+ r0606a
+ r0614a
+ r0703a
+ r0707a
+ r0709a
+ r0715a
+ r0804a
+ r0808a
+ r0810a
+ r0816a
+ r0909a
+ r0915a
+ r1010a
+ r1016a
+ r1111a
+ r1313a
+ r1414a
+ r1515a
+ r1616a
+ </components>
+ <evaluation>
+ <dependencies basis="v">density_matrix Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm</dependencies>
+ <![CDATA[
+ double prob_v_normalized=probability_v/probability_v_norm;
+
+ r0101a = r0101*prob_v_normalized;
+ r0113a = r0113*prob_v_normalized;
+ r0202a = r0202*prob_v_normalized;
+ r0214a = r0214*prob_v_normalized;
+ r0303a = r0303*prob_v_normalized;
+ r0309a = r0309*prob_v_normalized;
+ r0315a = r0315*prob_v_normalized;
+ r0404a = r0404*prob_v_normalized;
+ r0410a = r0410*prob_v_normalized;
+ r0416a = r0416*prob_v_normalized;
+ r0505a = r0505*prob_v_normalized;
+ r0511a = r0511*prob_v_normalized;
+ r0602a = r0602*prob_v_normalized;
+ r0606a = r0606*prob_v_normalized;
+ r0614a = r0614*prob_v_normalized;
+ r0703a = r0703*prob_v_normalized;
+ r0707a = r0707*prob_v_normalized;
+ r0709a = r0709*prob_v_normalized;
+ r0715a = r0715*prob_v_normalized;
+ r0804a = r0804*prob_v_normalized;
+ r0808a = r0808*prob_v_normalized;
+ r0810a = r0810*prob_v_normalized;
+ r0816a = r0816*prob_v_normalized;
+ r0909a = r0909*prob_v_normalized;
+ r0915a = r0915*prob_v_normalized;
+ r1010a = r1010*prob_v_normalized;
+ r1016a = r1016*prob_v_normalized;
+ r1111a = r1111*prob_v_normalized;
+ r1313a = r1313*prob_v_normalized;
+ r1414a = r1414*prob_v_normalized;
+ r1515a = r1515*prob_v_normalized;
+ r1616a = r1616*prob_v_normalized;
+ ]]>
+ </evaluation>
+ </computed_vector>
+
+
+ <vector name="density_matrix" type="complex" initial_space="t">
+ <components>
+ 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
+ </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
+ 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;
+ ]]>
+ </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 then 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[
+ E1ac = conj(E1a);
+ E2ac = conj(E2a);
+ E3ac = conj(E3a);
+ E4ac = conj(E4a);
+
+ // Density matrix is Hermitian so we use r_ij=conj(r_ji)
+
+ r1301 = conj(r0113);
+ r1402 = conj(r0214);
+ r0903 = conj(r0309);
+ r1503 = conj(r0315);
+ r1004 = conj(r0410);
+ r1604 = conj(r0416);
+ r1105 = conj(r0511);
+ r0206 = conj(r0602);
+ r1406 = conj(r0614);
+ r0307 = conj(r0703);
+ r0907 = conj(r0709);
+ r1507 = conj(r0715);
+ r0408 = conj(r0804);
+ r1008 = conj(r0810);
+ r1608 = conj(r0816);
+ r1509 = conj(r0915);
+ r1610 = conj(r1016);
+
+ // Equations of motions according to Simon's mathematica code
+ dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1313)/6. - i*((r0113*E4a)/(4.*rt6) - (r1301*E4ac)/(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*E4ac)/(4.*rt6) - (r1313*E4ac)/(4.*rt6));
+ dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1313)/12. + (g2*r1414)/4. - i*((r0214*E4a)/8. - (r1402*E4ac)/8.);
+ dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*((WL*r0214)/2. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 - (r0206*E3ac)/(8.*rt3) + (r0202*E4ac)/8. - (r1414*E4ac)/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. - (r0903*E1ac)/(4.*rt6) - (r1503*E4ac)/8.);
+ dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*(-((-WL/6. - delta1 - v*Kvec1)*r0309) + (r0303*E1ac)/(4.*rt6) - (r0909*E1ac)/(4.*rt6) - (r0307*E2ac)/(4.*rt6) - (r1509*E4ac)/8.);
+ dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(((-2*WL)/3. - delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0315) - (r0915*E1ac)/(4.*rt6) - (r0307*E3ac)/8. + (r0303*E4ac)/8. - (r1515*E4ac)/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) - (r1004*E1ac)/(4.*rt2) - (r1604*E4ac)/(4.*rt6));
+ dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(WL*r0410)/2. + (delta1 + v*Kvec1)*r0410 + (r0404*E1ac)/(4.*rt2) - (r1010*E1ac)/(4.*rt2) - (r0408*E2ac)/(4.*rt6) - (r1610*E4ac)/(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*E1ac)/(4.*rt2) - (r0408*E3ac)/(4.*rt2) + (r0404*E4ac)/(4.*rt6) - (r1616*E4ac)/(4.*rt6));
+ dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((r0511*E1a)/4. - (r1105*E1ac)/4.);
+ dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(WL*r0511) - (WL/6. - delta1 - v*Kvec1)*r0511 + (r0505*E1ac)/4. - (r1111*E1ac)/4.);
+ dr0602_dt = -(gt*r0602) - i*(-(WL*r0602)/2. + (-WL/2. - delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0602 + (r0614*E4a)/8. + (r1402*E3ac)/(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) + (r1406*E3ac)/(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*E3ac)/(8.*rt3) + (r1414*E3ac)/(8.*rt3) + (r0602*E4ac)/8.);
+ dr0703_dt = -(gt*r0703) - i*((-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 + (r0709*E1a)/(4.*rt6) + (r0715*E4a)/8. + (r0903*E2ac)/(4.*rt6) + (r1503*E3ac)/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. + (r0907*E2ac)/(4.*rt6) + (r1507*E3ac)/8.);
+ dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*(-((-WL/6. - delta1 - v*Kvec1)*r0709) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0709 + (r0703*E1ac)/(4.*rt6) - (r0707*E2ac)/(4.*rt6) + (r0909*E2ac)/(4.*rt6) + (r1509*E3ac)/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*E2ac)/(4.*rt6) - (r0707*E3ac)/8. + (r1515*E3ac)/8. + (r0703*E4ac)/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) + (r1004*E2ac)/(4.*rt6) + (r1604*E3ac)/(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) + (r1008*E2ac)/(4.*rt6) + (r1608*E3ac)/(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*E1ac)/(4.*rt2) - (r0808*E2ac)/(4.*rt6) + (r1010*E2ac)/(4.*rt6) + (r1610*E3ac)/(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*E2ac)/(4.*rt6) - (r0808*E3ac)/(4.*rt2) + (r1616*E3ac)/(4.*rt2) + (r0804*E4ac)/(4.*rt6));
+ dr0909_dt = -((gt + g1)*r0909) - i*(-(r0309*E1a)/(4.*rt6) + (r0709*E2a)/(4.*rt6) + (r0903*E1ac)/(4.*rt6) - (r0907*E2ac)/(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) - (r0907*E3ac)/8. + (r0903*E4ac)/8.);
+ dr1010_dt = -((gt + g1)*r1010) - i*(-(r0410*E1a)/(4.*rt2) + (r0810*E2a)/(4.*rt6) + (r1004*E1ac)/(4.*rt2) - (r1008*E2ac)/(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) - (r1008*E3ac)/(4.*rt2) + (r1004*E4ac)/(4.*rt6));
+ dr1111_dt = -((gt + g1)*r1111) - i*(-(r0511*E1a)/4. + (r1105*E1ac)/4.);
+ dr1313_dt = -((gt + g2)*r1313) - i*(-(r0113*E4a)/(4.*rt6) + (r1301*E4ac)/(4.*rt6));
+ dr1414_dt = -((gt + g2)*r1414) - i*((r0614*E3a)/(8.*rt3) - (r0214*E4a)/8. - (r1406*E3ac)/(8.*rt3) + (r1402*E4ac)/8.);
+ dr1515_dt = -((gt + g2)*r1515) - i*((r0715*E3a)/8. - (r0315*E4a)/8. - (r1507*E3ac)/8. + (r1503*E4ac)/8.);
+ dr1616_dt = -((gt + g2)*r1616) - i*((r0816*E3a)/(4.*rt2) - (r0416*E4a)/(4.*rt6) - (r1608*E3ac)/(4.*rt2) + (r1604*E4ac)/(4.*rt6));
+ ]]>
+ </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[
+ // Density matrix is Hermitian so we use r_ij=conj(r_ji)
+ r1301 = conj(r0113);
+ r1402 = conj(r0214);
+ r0903 = conj(r0309);
+ r1503 = conj(r0315);
+ r1004 = conj(r0410);
+ r1604 = conj(r0416);
+ r1105 = conj(r0511);
+ r0206 = conj(r0602);
+ r1406 = conj(r0614);
+ r0307 = conj(r0703);
+ r0907 = conj(r0709);
+ r1507 = conj(r0715);
+ r0408 = conj(r0804);
+ r1008 = conj(r0810);
+ r1608 = conj(r0816);
+ r1509 = conj(r0915);
+ r1610 = conj(r1016);
+
+ dE1_dz = 0.16666666666666666*i*eta1*(2.449489742783178*r0903 + 4.242640687119286*r1004 + 6.*r1105) - Lt[E1];
+ dE2_dz = -0.4082482904638631*i*eta1*(r0907 + r1008) - Lt[E2];
+ dE3_dz = -0.3333333333333333*i*eta2*(1.7320508075688772*r1406 + 3.*r1507 + 4.242640687119286*r1608) - Lt[E3];
+ dE4_dz = (i*eta2*(2.449489742783178*r1301 + 3*r1402 + 3*r1503 + 2.449489742783178*r1604))/3. - Lt[E4];
+ ]]>
+ </operators>
+ </integrate>
+ </sequence>
+
+
+
+ <!-- The output to generate -->
+ <output format="binary" filename="realistic_Rb.xsil">
+ <group>
+ <sampling basis="t(1000) " initial_sample="yes">
+ <dependencies>E_field_avgd</dependencies>
+ <moments>I1_out I2_out I3_out I4_out</moments>
+ <![CDATA[
+ I1_out = mod2(E1a);
+ I2_out = mod2(E2a);
+ I3_out = mod2(E3a);
+ I4_out = mod2(E4a);
+ ]]>
+ </sampling>
+ </group>
+
+ <!--
+ <group>
+ <sampling basis="t(100) v(10)" initial_sample="yes">
+ <dependencies>density_matrix_averaged</dependencies>
+ <moments>
+ r11_out r22_out r33_out r44_out
+ r12_re_out r12_im_out r13_re_out r13_im_out r14_re_out r14_im_out
+ r23_re_out r23_im_out r24_re_out r24_im_out
+ r34_re_out r34_im_out
+ </moments>
+ <![CDATA[
+ // populations output
+ r11_out = r11a.Re();
+ r22_out = r22a.Re();
+ r33_out = r33a.Re();
+ r44_out = r44a.Re();
+ // coherences output
+ r12_re_out = r12a.Re();
+ r12_im_out = r12a.Im();
+ r13_re_out = r13a.Re();
+ r13_im_out = r13a.Im();
+ r14_re_out = r14a.Re();
+ r14_im_out = r14a.Im();
+ r23_re_out = r23a.Re();
+ r23_im_out = r23a.Im();
+ r24_re_out = r24a.Re();
+ r24_im_out = r24a.Im();
+ r34_re_out = r34a.Re();
+ r34_im_out = r34a.Im();
+ ]]>
+ </sampling>
+ </group>
+ -->
+
+ <!-- use the following two groups only for debuging
+ otherwise they are quite useless and have to much information
+ in 3D space (z,t,v) -->
+ <!--
+ <group>
+ <sampling basis="t(100) v(10)" initial_sample="yes">
+ <dependencies>E_field</dependencies>
+ <moments>I1_out_v I2_out_v I3_out_v I4_out_v</moments>
+ <![CDATA[
+ // light field intensity distribution in velocity subgroups
+ I1_out_v = mod2(E1);
+ I2_out_v = mod2(E2);
+ I3_out_v = mod2(E3);
+ I4_out_v = mod2(E4);
+ ]]>
+ </sampling>
+ </group>
+
+ <group>
+ <sampling basis="t(100) v(10)" initial_sample="yes">
+ <dependencies>density_matrix</dependencies>
+ <moments>
+ r11_out_v r22_out_v r33_out_v r44_out_v
+ r12_re_out_v r12_im_out_v r13_re_out_v r13_im_out_v r14_re_out_v r14_im_out_v
+ r23_re_out_v r23_im_out_v r24_re_out_v r24_im_out_v
+ r34_re_out_v r34_im_out_v
+ </moments>
+ <![CDATA[
+ // density matrix distribution in velocity subgroups
+ // populations output
+ r11_out_v = r11.Re();
+ r22_out_v = r22.Re();
+ r33_out_v = r33.Re();
+ r44_out_v = r44.Re();
+ // coherences output
+ r12_re_out_v = r12.Re();
+ r12_im_out_v = r12.Im();
+ r13_re_out_v = r13.Re();
+ r13_im_out_v = r13.Im();
+ r14_re_out_v = r14.Re();
+ r14_im_out_v = r14.Im();
+ r23_re_out_v = r23.Re();
+ r23_im_out_v = r23.Im();
+ r24_re_out_v = r24.Re();
+ r24_im_out_v = r24.Im();
+ r34_re_out_v = r34.Re();
+ r34_im_out_v = r34.Im();
+ ]]>
+ </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 E1o = 0.000000e+00
+ Command line argument E2o = 1.000000e+02
+ Command line argument E3o = 0.000000e+00
+ Command line argument E4o = 0.000000e+00
+ 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 Temperature = 1.000000e-03
+</info>
+
+<XSIL Name="moment_group_1">
+ <Param Name="n_independent">2</Param>
+ <Array Name="variables" Type="Text">
+ <Dim>6</Dim>
+ <Stream><Metalink Format="Text" Delimiter=" \n"/>
+z t I1_out I2_out I3_out I4_out
+ </Stream>
+ </Array>
+ <Array Name="data" Type="double">
+ <Dim>101</Dim>
+ <Dim>1000</Dim>
+ <Dim>6</Dim>
+ <Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="LittleEndian"/>
+realistic_Rb_expected_mg0.dat
+ </Stream>
+ </Array>
+</XSIL>
+</simulation>
diff --git a/xmds2/realistic_Rb/tests/testsuite/realistic_Rb_expected_mg0.dat b/xmds2/realistic_Rb/tests/testsuite/realistic_Rb_expected_mg0.dat
new file mode 100644
index 0000000..ff30ab5
--- /dev/null
+++ b/xmds2/realistic_Rb/tests/testsuite/realistic_Rb_expected_mg0.dat
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generated by cgit v1.2.3 (git 2.39.1) at 2024-11-16 07:37:21 +0000