def solve_gauss_seidel(A, b, x0=None, maxiter=100):
N = len(b)
L, D, U = lower_diag_upper(A)
E = -L
F = -U
x = parse_initial_cond(x0, N)
residual = 1
for _ in xrange(maxiter):
x = spsolve(D - E, (b + F * x))
residual = compute_normalized_linf_residual(A, x, b)
return x, residual
def solve_jacobi(A, b, x0=None, maxiter=100):
N = len(b)
L, D, U = lower_diag_upper(A)
E = - L
F = - U
D.data[:] = 1. / D.data[:]
D_inv = D
x = parse_initial_cond(x0, N)
for _ in xrange(maxiter):
x = D_inv * (b + (E + F) * x)
residual = compute_normalized_linf_residual(A, x, b)
return x, residual
def solve_ssor(A, b, x0=None, maxiter=100):
L, D, U = lower_diag_upper(A)
E = -L
F = -U
N = len(b)
x = parse_initial_cond(x0, N)
w = 1.24
residual = 1
for _ in xrange(maxiter):
x_gauss_seidel = spsolve(D - E, (b + F * x))
x = w * x_gauss_seidel + (1. - w) * x
x_gauss_seidel = spsolve(D - F, (b + E * x))
x = w * x_gauss_seidel + (1. - w) * x
residual = compute_normalized_l2_residual(A, x, b)
return x, residual
