def solve_block_jacobi(A, b, n_partitions=2, x0=None, maxiter=100):
assert A.shape[0] == A.shape[1], "Square matrix required"
N = len(b)
x = parse_initial_cond(x0, N)
A_sub = partition_mat_by_num(A, n_partitions)
x_sub_old = partition_vec_by_num(x, n_partitions)
b_sub = partition_vec_by_num(b, n_partitions)
rhs_sub = dict()
x_sub = dict()
residual = 0.0
for _ in xrange(maxiter):
for i in xrange(n_partitions): # Go through row blocks
sum_mat_vec_results = np.zeros(len(b_sub[i]))
for j in xrange(n_partitions):
if i == j:
continue
sum_mat_vec_results += A_sub[i, j] * x_sub_old[j]
rhs_sub[i] = b_sub[i] - sum_mat_vec_results
x_sub[i] = spsolve(A_sub[i, i], rhs_sub[i])
for i in xrange(n_partitions):
x_sub_old[i][:] = x_sub[i][:]
x = reconstruct_vec_from_sub_vectors(x_sub)
residual = compute_normalized_linf_residual(A, x, b)
return x, residual
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