source: inundation/ga/storm_surge/pyvolution/cg_solve.py @ 438

import exceptions
class VectorShapeError(exceptions.Exception): pass


def conjugate_gradient(A,b,x0,imax=2000,tol=1.0e-8,iprint=0):
   """
   Try to solve linear equation Ax = b using
   conjugate gradient method
   
   Input
   A: matrix or function which applies a matrix, assumed symmetric
   b: right hand side
   x0: inital guess
   imax: max number of iterations
   tol: tolerance used for residual
   
   Output
   x: approximate solution
   """

   #if nargin<3
   #   x0 = zeros(b);
   #end

   from Numeric import dot, asarray, Float
   #from operator import mod

   b  = asarray(b, typecode=Float)
   x0 = asarray(x0, typecode=Float)
   #A = asarray(A, typecode=Float)

   #print "A shape",A.shape
   #print "b shape",len(b.shape)
   #print "x0 shape",x0.shape[0]

   if len(b.shape) != 1 :
      raise VectorShapeError, 'input vector should consist of only one column'

   if iprint == 0:
      iprint = imax
      
   i=1
   x = x0
   r = b - A*x
   d = r
   rTr = dot(r,r)
   rTr0 = rTr

   while (i<imax and rTr>tol**2*rTr0):
       q = A*d
       alpha = rTr/dot(d,q)
       x = x + alpha*d
       if i%50 :
           r = b - A*x
       else:
           r = r - alpha*q
       rTrOld = rTr
       rTr = dot(r,r)
       bt = rTr/rTrOld

       d = r + bt*d
       i = i+1
       if i%iprint == 0 :
          print 'i = %g rTr = %20.15e'% (i,rTr)

          
   if i==imax:
     print 'max number of iterations attained'

   return x