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from scipy import *
from weave import converters
from pylab import *
def norm(x):
return sqrt(abs(sum(x * conjugate(x))))
def rotmat(a, b):
# compute the Givens rotation matrix parameters for a and b
if (b==0.0):
c, s = 1.0, 0.0
elif (abs(b) > abs(a)):
##temp = a/b
temp = -a/b
s = 1.0 / sqrt(1.0 + temp**2)
c = temp * s
else:
##temp = b/a
temp = -b/a
c = 1.0 / sqrt(1.0 + temp**2)
s = temp * c
return c, s
def myGmresPython( A, x, b, M, restrt, max_it, tol ):
iter = 0 # initialization
flag = 0
bnrm2 = norm(b)
if ( bnrm2 == 0.0 ):
bnrm2 = 1.0
#r = M \ ( b-A*x );
r = b - matrixmultiply(A, x)
error = norm( r ) / bnrm2
if ( error < tol ):
return x, error, iter, flag
n = A.shape[0] # initialize workspace
m = restrt
V = zeros((n,m+1), Complex)
H = zeros((m+1, m), Complex)
cs, sn = zeros(m, Complex), zeros(m, Complex)
e1 = zeros(m+1, Complex)
e1[0] = 1.0
for iter in range(max_it):
#r = M \ ( b-A*x )
r = b - matrixmultiply(A, x)
V[:, 0] = r / norm( r )
#print 'sum(V[:, 0]) =', sum(V[:, 0])
s = norm( r )*e1
# construct orthonormal basis using Gram-Schmidt
for i in range(m):
#w = M \ matrixmultiply(A, V[:, i])
w = matrixmultiply(A, V[:, i])
for k in range(i+1):
H[k, i] = sum(w * conjugate(V[:, k]))
w = w - H[k, i] * V[:, k]
#print "sum(w) =", sum(w)
H[i+1, i] = norm( w )
V[:, i+1] = w / H[i+1, i]
#print "sum(V[:, i+1]) =", sum(V[:, i+1])
# apply Givens rotation
for k in range(i):
##temp = cs[k] * H[k, i] + sn[k] * H[k+1, i]
##H[k+1,i] = -sn[k] * H[k, i] + cs[k] * H[k+1, i]
temp = conjugate(cs[k]) * H[k, i] - conjugate(sn[k]) * H[k+1, i]
H[k+1,i] = sn[k] * H[k, i] + cs[k] * H[k+1, i]
H[k,i] = temp
# form i-th rotation matrix
cs[i], sn[i] = rotmat( H[i, i], H[i+1, i] )
##H[i, i] = cs[i]*H[i, i] + sn[i]*H[i+1, i]
H[i, i] = conjugate(cs[i])*H[i, i] - conjugate(sn[i])*H[i+1, i]
H[i+1,i] = 0.0
#print "sum(sum(H)) =", sum(sum(H))
# approximate residual norm
##temp = cs[i] * s[i]
temp = conjugate(cs[i]) * s[i] - conjugate(sn[i]) * s[i+1]
##s[i+1] = -sn[i] * s[i]
s[i+1] = sn[i] * s[i] + cs[i] * s[i+1]
s[i] = temp;
error = abs(s[i+1]) / bnrm2
#print "error =", error
# update approximation
if ( error <= tol ):
y = linalg.solve( H[:i+1, :i+1], s[:i+1] )
x = x + matrixmultiply(V[:, :i+1], y)
return x, error, iter, flag
if ( error <= tol ):
return x, error, iter, flag
y = linalg.solve( H[:m, :m], s[:m] )
#print "sum(y) =", sum(y)
x = x + matrixmultiply(V[:, :m], y) # update approximation
#print "sum(x) =", sum(x)
#r = M \ ( b-A*x ) # compute residual
r = b - matrixmultiply(A, x)
error = abs(s[i+1]) / bnrm2 # check convergence
#print "error =", error
if ( error <= tol ):
return x, error, iter, flag
if ( error > tol ):
flag = 1
return x, error, iter, flag
def myGmresC( A, x, b, M, restrt, max_it, tol ):
error = zeros(1, Float)
flag = zeros(1, Int)
iter = zeros(1, Int)
wrapping_code = """gmres(x, error(0), iter(0), flag(0), A, b, tol, restrt, max_it);"""
weave.inline(wrapping_code,
['x', 'error', 'iter', 'flag', 'A', 'b', 'tol', 'restrt', 'max_it'],
type_converters = converters.blitz,
include_dirs = ['./MoM/iterative/'],
library_dirs = ['./MoM/iterative/'],
libraries = ['ITERATIVE'],
headers = ['<iostream>','<complex>','"gmres.h"'],
compiler = 'gcc')
return x, error[0], iter[0], flag[0]
if __name__=="__main__":
ff = open('Z.txt', 'r')
Z = pickle.load(ff)
ff.close()
ff = open('V.txt', 'r')
V = pickle.load(ff)
ff.close()
N = V.shape[0]
Y = zeros(N, Complex)
X0 = zeros(N, Complex)
M = ones((N,N),Complex64)
restart = 3
tol = 1.e-3
maxiter = 50
# scipy linalg
I = matrixmultiply(linalg.inv(Z),V)
# myGmresPython
I2, error2, iteration2, info2 = myGmresPython( Z, X0, V, M, restart, maxiter, tol )
print "error2, iteration2, info2 =", error2, iteration2, info2
# myGmresC++
X0 = zeros(N, Complex)
I3, error3, iteration3, info3 = myGmresC( Z, X0, V, M, restart, maxiter, tol )
print "error3, iteration3, info3 =", error3, iteration3, info3
print sum(I), sum(I2), sum(I3)
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