coding utf-8 from numpy import dot as mul from precondition import imp

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# coding=utf-8
from numpy import dot as mul
from precondition import *
import numpy as np
from numpy.random import randn as random_matrix
from random import randint
from numpy import linalg
import scipy
"""
2 lab
=================
PCG
полиномиальное ускорение
фиксируется число шагов
MZ = R
трёхчленная реккурентная формула(через полиномы чебышёва и лежандра)
http://www.wikiwand.com/en/Symmetric_successive_overrelaxation ssor
https://github.com/pyamg/pyamg/tree/master/pyamg/relaxation тут и Чёбышев есть
"""
n = 50
epsilon = 0.01
steps = 100
def pcg(A, S, b):
S_t = np.transpose(S)
eig_values, eig_vectros = linalg.eig(A)
M = max(eig_values) + 0.001
m = min(eig_values) - 0.001
x = [None for _ in xrange(0, steps)]
r = [None for _ in xrange(0, steps)]
z = [None for _ in xrange(0, steps)]
d = [1 for _ in xrange(0, steps)]
betta = [None for _ in xrange(0, steps)]
p = [None for _ in xrange(0, steps)]
alpha = [None for _ in xrange(0, steps)]
x[0] = random_matrix(n, 1)
r[0] = b - mul(A, x[0])
betta[1] = 0
for k in xrange(0, steps - 1):
#z[k] = mul(mul(S_t, S), r[k])
E = np.zeros([n, n])
E[np.diag_indices_from(E)] = [1 for i in xrange(n)]
z[k+1] = (2/(M-m)) * (d[k]/d[k+1])*((2*S - (m+M)*E)*z[k] + 2*r[k])- (d[k-1])/(d[k+1])*z[k-1]
if k >= 1:
betta[k+1] = sum((z[k][0] * r[k])[0]) / sum((z[k-1], r[k-1])[0])
p[k+1] = z[k] + betta[k+1][0] * p[k]
d[k+1] = 2*(2-m-M)/(M-m)*d[k]-d[k-1]
else:
p[1] = z[0]
y = mul(A, p[k+1])
alpha[k+1] = sum(z[k] * r[k])[0] / sum(mul(A, p[k+1]) * p[k+1])[0]
x[k+1] = x[k] + alpha[k+1] * p[k+1]
r[k+1] = r[k] - alpha[k+1] * mul(A, p[k+1])
if k == 40:
return x[k+1]
"""
# array: [k-1, k, k+1]
x = [None, random_matrix(n, 1), None]
r = [b - mul(A, x[1]), b - mul(A, x[1]), None]
z = [mul(mul(S_t, S), r[1]), mul(mul(S_t, S), r[1]), None]
betta = [None, 0, 0]
p = [None, z[1], None]
alpha = [None, None, None]
for k in xrange(1, steps):
z[1] = mul(mul(S_t, S), r[1])
betta[2] = sum(z[1] * r[1])[0] / sum(z[0], r[0])[0]
p[2] = z[1] + betta[2][0] * p[1] # TODO error
alpha[2] = sum(z[1] * r[1])[0] / sum(mul(A, p[2]) * p[2])[0]
x[2] = x[1] + alpha[2] * p[2]
r[2] = r[1] - alpha[2] * mul(A, p[2])
print sum(r[2] * r[2])[0]
if sum(r[2] * r[2])[0] <= epsilon:
print 'k: {d}'.format(k)
return x[2]
# тут массивы сдвигаем на 1 влево:)
x[:-1], r[:-1], z[:-1], betta[:-1], p[:-1], alpha[:-1] = x[1:], r[1:], z[1:], betta[1:], p[1:], alpha[1:]
"""
# [:-1] [1:]
"""
x_k = random_matrix(n, 1)
r_k = b - mul(A, x_k)
betta = 0
k = 0
z_k = mul(mul(S_t, S), r_k)
while sum(r_k * r_k) >= epsilon:
z_1, r_1 = z_k, r_k
z_k = mul(mul(S_t, S), r_k)
if k >= 1:
betta = sum(z_k * r_k) / sum(z_1, r_1)
p_k = z_k + betta * p_k
else:
p_k = z_1
p_k = z_k + betta * p_k
alpha = sum(z_k * r_k) / sum(mul(A, p_k), p_k)
x_k = x_k + alpha * p_k
r_k = r_k - alpha * mul(A, p_k)
k += 1
"""
def main():
# A, S = jacobi_precondition(n=n)
A, S = ssor_precondition(w=1.0, n=n)
b = random_matrix(n, 1)
print pcg(A, S, b)
print linalg.solve(A,b)
if __name__ == '__main__':
main()