Initial import from https://statweb.stanford.edu/~candes/software/l1magic/v1.11

Additional Clean up of Mac dirs and tex generated files

1 files changed, 76 insertions, 0 deletions

diff --git a/Optimization/cgsolve.m b/Optimization/cgsolve.m
new file mode 100644
index 0000000..dbbc4d8
--- /dev/null
+++ b/Optimization/cgsolve.m
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+% cgsolve.m
+%
+% Solve a symmetric positive definite system Ax = b via conjugate gradients.
+%
+% Usage: [x, res, iter] = cgsolve(A, b, tol, maxiter, verbose)
+%
+% A - Either an NxN matrix, or a function handle.
+%
+% b - N vector
+%
+% tol - Desired precision.  Algorithm terminates when 
+%    norm(Ax-b)/norm(b) < tol .
+%
+% maxiter - Maximum number of iterations.
+%
+% verbose - If 0, do not print out progress messages.
+%    If and integer greater than 0, print out progress every 'verbose' iters.
+%
+% Written by: Justin Romberg, Caltech
+% Email: jrom@acm.caltech.edu
+% Created: October 2005
+%
+
+function [x, res, iter] = cgsolve(A, b, tol, maxiter, verbose)
+
+if (nargin < 5), verbose = 1; end
+
+implicit = isa(A,'function_handle');
+
+x = zeros(length(b),1);
+r = b;
+d = r;
+delta = r'*r;
+delta0 = b'*b;
+numiter = 0;
+bestx = x;
+bestres = sqrt(delta/delta0); 
+while ((numiter < maxiter) && (delta > tol^2*delta0))
+
+  % q = A*d
+  if (implicit), q = A(d);  else  q = A*d;  end
+ 
+  alpha = delta/(d'*q);
+  x = x + alpha*d;
+  
+  if (mod(numiter+1,50) == 0)
+    % r = b - Aux*x
+    if (implicit), r = b - A(x);  else  r = b - A*x;  end
+  else
+    r = r - alpha*q;
+  end
+  
+  deltaold = delta;
+  delta = r'*r;
+  beta = delta/deltaold;
+  d = r + beta*d;
+  numiter = numiter + 1;
+  if (sqrt(delta/delta0) < bestres)
+    bestx = x;
+    bestres = sqrt(delta/delta0);
+  end    
+  
+  if ((verbose) && (mod(numiter,verbose)==0))
+    disp(sprintf('cg: Iter = %d, Best residual = %8.3e, Current residual = %8.3e', ...
+      numiter, bestres, sqrt(delta/delta0)));
+  end
+  
+end
+
+if (verbose)
+  disp(sprintf('cg: Iterations = %d, best residual = %14.8e', numiter, bestres));
+end
+x = bestx;
+res = bestres;
+iter = numiter;
+