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assembInt.py
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assembInt.py
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#!/usr/bin/env python
# coding: utf8
debug = True
if debug:
print('Debug: {}'.format(debug))
from time import time
import numpy as np
import scipy.linalg as la
import scipy.sparse as sp
import scipy.sparse.linalg as spla
import bempp.api as bem
from domains import *
debug = True
meshname = "./geo/sphere-disjoint.msh"
#meshname = "./geo/ellipse-concentric.msh"
# domains = Domains(generate_disjoint_Domains(2))
# wl = 6.0
# kRef = 2 * np.pi / wl
kRef = 0.1 * np.pi
# dd = [
# { 'name': '0',
# 'phys': 1,
# 'union': [-10, -100],
# },
# { 'name': 'A',
# 'phys': 2,
# 'union': 10,
# },
# { 'name': 'B',
# 'phys': 5,
# 'union': 100,
# }
# ]
# domains = Domains(dd)
dd = [
{ 'name': '0',
'phys': 1,
'union': [-1, -2, 3],
},
{ 'name': 'A',
'phys': 2,
'union': 1,
},
{ 'name': 'B',
'phys': 3,
'union': 2,
},
{ 'name': 'C',
'phys': 4,
'union': -3,
}
]
domains = Domains(dd)
# dd = [
# { 'name': '0',
# 'phys': 1,
# 'union': [-1],
# },
# { 'name': 'A',
# 'phys': 2,
# 'union': [1, -2],
# },
# { 'name': 'B',
# 'phys': 1,
# 'union': [2, -3],
# },
# { 'name': 'C',
# 'phys': 1,
# 'union': 3,
# }
# ]
# domains = Domains(dd)
if debug:
print('Debug: {}'.format(debug))
# ??
# bem.enable_console_logging()
# print('Dense')
# bem.global_parameters.assembly.boundary_operator_assembly_type = 'dense'
# bem.global_parameters.assembly.boundary_operator_assembly_type = 'hmat'
#pass
# bem.global_parameters.assembly.boundary_operator_assembly_type = 'dense'
print(bem.global_parameters.assembly.boundary_operator_assembly_type)
grid = bem.import_grid(meshname)
# opM = bem.BlockedOperator(len(domains), len(domains))
opA = bem.BlockedOperator(len(domains), len(domains))
opX = bem.BlockedOperator(len(domains), len(domains))
opI = bem.BlockedOperator(len(domains), len(domains))
opZ = bem.BlockedOperator(len(domains), len(domains))
opY = bem.BlockedOperator(len(domains), len(domains))
kind_d = ("P", 1)
kind_n = ("P", 1)
funK = bem.operators.boundary.helmholtz.double_layer
funV = bem.operators.boundary.helmholtz.single_layer
funQ = bem.operators.boundary.helmholtz.adjoint_double_layer
funW = bem.operators.boundary.helmholtz.hypersingular
funI = bem.operators.boundary.sparse.identity
# kind_d = ("RT", 0)
# kind_n = ("RT", 0)
# funK = bem.operators.boundary.maxwell.magnetic_field
# funV = bem.operators.boundary.maxwell.electric_field
# funQ = bem.operators.boundary.maxwell.magnetic_field
# funW = bem.operators.boundary.maxwell.electric_field
# funI = bem.operators.boundary.sparse.maxwell_identity
tinit = time()
print('\n=Collecting all the blocks')
for dom in domains:
me = dom['name']
ii = domains.getIndexDom(me)
print('==Domain: {0}'.format(me))
print('===Diag: Block #({0}, {0})'.format(ii))
eps, alpha, beta = dom['phys']
k = kRef * np.sqrt(eps)
opAA = bem.BlockedOperator(2, 2)
opII = bem.BlockedOperator(2, 2)
bem_space = bem.function_space
Nints = len(dom['interfaces'])
opK = bem.BlockedOperator(Nints, Nints)
opV = bem.BlockedOperator(Nints, Nints)
opW = bem.BlockedOperator(Nints, Nints)
opQ = bem.BlockedOperator(Nints, Nints)
opId = bem.BlockedOperator(Nints, Nints)
opIn = bem.BlockedOperator(Nints, Nints)
for facei, signi in zip(dom['interfaces'], dom['signs']):
i = domains.getIndexInt(me, facei)
space_test_d = bem_space(grid, kind_d[0], kind_d[1], domains=[facei])
space_test_n = bem_space(grid, kind_n[0], kind_n[1], domains=[facei])
space_range_d = bem_space(grid, kind_d[0], kind_d[1], domains=[facei])
space_range_n = bem_space(grid, kind_n[0], kind_d[1], domains=[facei])
for facej, signj in zip(dom['interfaces'], dom['signs']):
j = domains.getIndexInt(me, facej)
print('====Interface: ({0}, {1}) #({2}, {3})'.format(facei, facej,
i, j))
space_trial_d = bem_space(grid, kind_d[0], kind_d[1], domains=[facej])
space_trial_n = bem_space(grid, kind_n[0], kind_n[1], domains=[facej])
opKK = funK(space_trial_d, space_range_d, space_test_d, k)
opVV = funV(space_trial_n, space_range_d, space_test_d, k)
opWW = funW(space_trial_d, space_range_n, space_test_n, k)
opQQ = funQ(space_trial_n, space_range_n, space_test_n, k)
opK[i, j] = signj * opKK
opV[i, j] = opVV
opW[i, j] = opWW
opQ[i, j] = signi * opQQ
opIId = funI(space_trial_d, space_range_d, space_test_d)
opIIn = funI(space_trial_n, space_range_n, space_test_n)
opId[i, j] = opIId
opIn[i, j] = opIIn
opAA[0, 0] = - opK
opAA[0, 1] = opV
opAA[1, 0] = opW
opAA[1, 1] = opQ
opII[0, 0] = opId
opII[1, 1] = opIn
opA[ii, ii] = opAA
opI[ii, ii] = opII
for d in domains.getNeighborOf(dom['name']):
other = d['name']
jj = domains.getIndexDom(other)
print('===Coupling {0} with {1}: Block #({2}, {3})'.format(other,
domains.getName(jj),
ii, jj))
NintsMe, NintsOther = len(dom['interfaces']), len(d['interfaces'])
opXXd = bem.BlockedOperator(NintsMe, NintsOther)
opXXn = bem.BlockedOperator(NintsMe, NintsOther)
for facei, signi in zip(dom['interfaces'], dom['signs']):
i = domains.getIndexInt(me, facei)
space_test_d = bem_space(grid, kind_d[0], kind_d[1], domains=[facei])
space_test_n = bem_space(grid, kind_n[0], kind_n[1], domains=[facei])
space_range_d = bem_space(grid, kind_d[0], kind_d[1], domains=[facei])
space_range_n = bem_space(grid, kind_n[0], kind_d[1], domains=[facei])
for facej, signj in zip(d['interfaces'], d['signs']):
j = domains.getIndexInt(other, facej)
print('====Interface: ({0}, {1}) #({2}, {3})'.format(facei, facej,
i, j))
space_trial_d = bem_space(grid, kind_d[0], kind_d[1], domains=[facej])
space_trial_n = bem_space(grid, kind_n[0], kind_n[1], domains=[facej])
opXd = funI(space_trial_d, space_range_d, space_test_d)
opXn = funI(space_trial_n, space_range_n, space_test_n)
opXXd[i, j] = opXd
opXXn[i, j] = -opXn
opXX = bem.BlockedOperator(2, 2)
opXX[0, 0] = opXXd
opXX[1, 1] = opXXn
opX[ii, jj] = opXX
#
##done
print('\n=Collecting DtN/NtD')
for dom in domains:
me = dom['name']
ii = domains.getIndexDom(me)
print('==Domain: {0}'.format(me))
print('===Diag: Block #({0}, {0})'.format(ii))
bem_space = bem.function_space
Nints = len(dom['interfaces'])
opmId = bem.BlockedOperator(Nints, Nints)
opmIn = bem.BlockedOperator(Nints, Nints)
opmNtD = bem.BlockedOperator(Nints, Nints)
opmDtN = bem.BlockedOperator(Nints, Nints)
for d in domains.getNeighborOf(dom['name']):
other = d['name']
jj = domains.getIndexDom(other)
NintsMe, NintsOther = len(dom['interfaces']), len(d['interfaces'])
opoId = bem.BlockedOperator(NintsMe, NintsOther)
opoIn = bem.BlockedOperator(NintsMe, NintsOther)
opoNtD = bem.BlockedOperator(NintsMe, NintsOther)
opoDtN = bem.BlockedOperator(NintsMe, NintsOther)
for facei, signi in zip(dom['interfaces'], dom['signs']):
i = domains.getIndexInt(me, facei)
space_test_d = bem_space(grid, kind_d[0], kind_d[1], domains=[facei])
space_test_n = bem_space(grid, kind_n[0], kind_n[1], domains=[facei])
space_range_d = bem_space(grid, kind_d[0], kind_d[1], domains=[facei])
space_range_n = bem_space(grid, kind_n[0], kind_d[1], domains=[facei])
mspace_trial_d = bem_space(grid, kind_d[0], kind_d[1], domains=[facei])
mspace_trial_n = bem_space(grid, kind_n[0], kind_d[1], domains=[facei])
for facej, signj in zip(d['interfaces'], d['signs']):
j = domains.getIndexInt(other, facej)
ospace_trial_d = bem_space(grid, kind_d[0], kind_d[1], domains=[facej])
ospace_trial_n = bem_space(grid, kind_n[0], kind_n[1], domains=[facej])
opmi_dd = funI(mspace_trial_d, space_range_d, space_test_d)
opmi_dn = funI(mspace_trial_d, space_range_n, space_test_n)
opmi_nn = funI(mspace_trial_n, space_range_n, space_test_n)
opmi_nd = funI(mspace_trial_n, space_range_d, space_test_d)
opoi_dd = funI(ospace_trial_d, space_range_d, space_test_d)
opoi_dn = funI(ospace_trial_d, space_range_d, space_test_n)
opoi_nn = funI(ospace_trial_n, space_range_n, space_test_n)
opoi_nd = funI(ospace_trial_n, space_range_n, space_test_d)
opoId[i, j] = opoi_dd
opoIn[i, j] = opoi_nn
opmId[i, i] = opmi_dd
opmIn[i, i] = opmi_nn
epsi, epsj = dom['phys'], d['phys']
ki, kj = kRef * np.sqrt(epsi), kRef * np.sqrt(epsj),
ntd_i = 1.0 / (1j * ki)
dtn_j = 1j * kj
opoNtD[i, j] = - ntd_i * opoi_nd
opoDtN[i, j] = - dtn_j * opoi_dn
opmNtD[i, i] = - ntd_i * opmi_nd
opmDtN[i, i] = - dtn_j * opmi_dn
opYY = bem.BlockedOperator(2, 2)
opYY[0, 0] = opoId
opYY[0, 1] = - 1.0 * opoNtD
opYY[1, 0] = -1.0 * opoDtN
opYY[1, 1] = -1.0 * opoIn
opY[ii, jj] = opYY
opZZ = bem.BlockedOperator(2, 2)
opZZ[0, 0] = opmId
opZZ[0, 1] = opmNtD
opZZ[1, 0] = - 1.0 * opmDtN
opZZ[1, 1] = opmIn
opZ[ii, ii] = opZZ
print('\n=RHS')
def evalIncDirichletTrace(x, normal, dom_ind, result):
result[0] = -np.exp( 1j * kRef * x[1])
def evalIncNeumannTrace(x, normal, dom_ind, result):
result[0] = -1j * normal[1] * kRef * np.exp( 1j * kRef * x[1])
def evalZeros(point, normal, dom_ind, result):
result[0] = 0. + 1j * 0.
inf = '0'
rhss = [] * len(domains)
rhs = [] * len(domains)
neighbors = domains.getNeighborOf(inf)
for ii in range(len(domains)):
name = domains.getName(ii)
dom = domains.getEntry(name)
jj = domains.getIndexDom(dom['name'])
print('==Domain: {0} #{1}'.format(dom['name'], ii))
space_d = bem.function_space(grid, kind_d[0], kind_d[1], domains=dom['interfaces'])
space_n = bem.function_space(grid, kind_n[0], kind_n[1], domains=dom['interfaces'])
if dom['name'] == inf:
IncDirichletTrace = bem.GridFunction(space_d, fun=evalIncDirichletTrace)
IncNeumannTrace = bem.GridFunction(space_n, fun=evalIncNeumannTrace)
idir, ineu = IncDirichletTrace, - IncNeumannTrace
elif dom in neighbors:
IncDirichletTrace = bem.GridFunction(space_d, fun=evalIncDirichletTrace)
IncNeumannTrace = bem.GridFunction(space_n, fun=evalIncNeumannTrace)
idir, ineu = - IncDirichletTrace, - IncNeumannTrace
else:
IncDirichletTrace = bem.GridFunction(space_d, fun=evalZeros)
IncNeumannTrace = bem.GridFunction(space_n, fun=evalZeros)
idir, ineu = IncDirichletTrace, IncNeumannTrace
rhs.append(idir)
rhs.append(ineu)
tt = time()
print('==Assembling RHS (projections)')
b = np.array([], dtype=complex)
for r in rhs:
b = np.concatenate((b, r.projections()))
trhs = time() - tt
print('#time Assembling RHS: {}'.format(trhs))
##
tAssemb = time()
print('\n=Assembling all the matrices')
print('==BlockDiag assembling: A (be patient)')
for ii in range(len(domains)):
tt = time()
print('===Block: #({0}, {0})'.format(ii), end=' ')
opp = opA[ii, ii]
for i, j, who in zip([0, 0, 1, 1], [0, 1, 0, 1], ['K', 'V', 'W', 'Q']):
print(who, end=' ', flush=True)
op = opp[i, j]
a = op.weak_form()
print(' time: {}'.format(time() - tt))
# if something is missing... to be sure !
Aw = opA.weak_form()
print('==Coupling assembling: X')
Xw = opX.weak_form()
print('==MTF assembling: M ')
#########################
opMTF = opA - 0.5 * opX
########################
MTFw = opMTF.weak_form()
bmtf = 0.5 * b
print('==Identity assembling: J')
Jw = opI.weak_form()
tAssemb = time() - tAssemb
#
print('')
print('#total time Assembling: {}'.format(tAssemb))
print('')
#
tt = time()
Jcsc = sp.lil_matrix(Jw.shape, dtype=complex)
row_start, col_start = 0, 0
row_end, col_end = 0, 0
for ii in range(len(domains)):
Jb = Jw[ii, ii]
Jd, Jn = Jb[0, 0], Jb[1, 1]
mat = bem.as_matrix(Jd)
mat = sp.lil_matrix(mat)
r, c = mat.shape
row_end += r
col_end += c
Jcsc[row_start:row_end, col_start:col_end] = mat
row_start, col_start = row_end, col_end
mat = bem.as_matrix(Jn)
mat = sp.lil_matrix(mat)
r, c = mat.shape
row_end += r
col_end += c
Jcsc[row_start:row_end, col_start:col_end] = mat
row_start, col_start = row_end, col_end
Jcsc = Jcsc.tocsc()
print('##time convert Identity to CSC: {}'.format(time() - tt))
tt = time()
iJlu = spla.splu(Jcsc)
print('##time sparse J=LU: {}'.format(time() - tt))
tt = time()
Ecsc = sp.lil_matrix(Xw.shape, dtype=complex)
row_start, row_end = 0, 0
for r in range(len(domains)):
row, col = 0, 0
col_start, col_end = 0, 0
first = True
for c in range(len(domains)):
if first:
op = opI[r, r]
row, _ = op.weak_form().shape
row_end += row
first = False
op = opX[r, c]
if not op is None:
mat = bem.as_matrix(op.weak_form())
mat = sp.lil_matrix(mat)
_ , col = mat.shape
else:
opp = opI[c, c]
_ , col = opp.weak_form().shape
col_end += col
if c > r and (op is not None):
Ecsc[row_start:row_end, col_start:col_end] = mat
col_start = col_end
row_start = row_end
Ecsc = Ecsc.tocsc()
print('##time to build E: {}'.format(time() - tt))
tpro = time() - tinit
#
print('')
print('#total time all processing: {}'.format(tpro))
print('')
#
print('=Size: {}'.format(MTFw.shape))
#
print('')
print(' ## All assembling done ! ##')
print(" == LET'S GO !! ==")
print('')
#
#################################################
#################################################
#################################################
###############################
opA2 = opA * opA
opC = 0.5 * opI + opA
opC2 = opC * opC
# print('assembling and inverting in BEM++ (remove this part) [checking]')
# A2w = opA2.weak_form()
# Cw = opC.weak_form()
# C2w = opC2.weak_form()
#################################
norm = np.linalg.norm
shape = MTFw.shape
MTF = spla.LinearOperator(shape, matvec=MTFw.matvec, dtype=complex)
J = spla.LinearOperator(shape, matvec=Jw.matvec, dtype=complex)
iJ = spla.LinearOperator(shape, matvec=iJlu.solve, dtype=complex)
At = spla.LinearOperator(shape, matvec=Aw.matvec, dtype=complex)
X = spla.LinearOperator(shape, matvec=Xw.matvec, dtype=complex)
E = spla.LinearOperator(shape, matvec=Ecsc.dot, dtype=complex)
#####################################
#####################################
A = 2.0 * At
M = A - X
#####################################
#####################################
A2 = A * iJ * A
Ce = 0.5 * J - At
Ci = 0.5 * J + At
Ce2 = Ce * iJ * Ce
Ci2 = Ci * iJ * Ci
x = np.random.rand(shape[0])
print('\n=Checking', flush=True)
print('==check: M = A - X')
t0 = time()
y = M(x)
t1 = time() - t0
t0 = time()
z = A(x) - X(x)
t2 = time() - t0
print('#time: {0} {1} {2}'.format(t1, t2, t1 - t2))
e = la.norm(y - z)
print(e)
print('==check: A2 = J')
t0 = time()
y2 = A2(x)
t1 = time() - t0
t0 = time()
z2 = J(x)
t2 = time() - t0
print('#time: {0} {1} {2}'.format(t1, t2, t1 - t2))
e2 = la.norm(y2 - z2)
print(e2)
# #######################
# y = A2w.matvec(x)
# z = 0.25 * Jw.matvec(x)
# e = norm(y - z)
# print(e)
# #######################
print('==check exterior Proj.')
t0 = time()
yy = Ce2(x)
t1 = time() - t0
t0 = time()
zz = Ce(x)
t2 = time() - t0
print('#time: {0} {1} {2}'.format(t1, t2, t1 - t2))
ee = la.norm(yy - zz)
print(ee)
# #######################
# y = C2w.matvec(x)
# z = Cw.matvec(x)
# e = norm(y - z)
# print(e)
# #######################
print('==check interior Proj.')
t0 = time()
yy = Ci2(x)
t1 = time() - t0
t0 = time()
zz = Ci(x)
t2 = time() - t0
print('#time: {0} {1} {2}'.format(t1, t2, t1 - t2))
ee = la.norm(yy - zz)
print(ee)
print('==Error-Calderon with random [no-sense]')
t0 = time()
y = A(x)
t1 = time() - t0
t0 = time()
z = J(x)
t2 = time() - t0
print('#time: {0} {1} {2}'.format(t1, t2, t1 - t2))
e = la.norm(y - z)
print(e)
#################################################
#################################################
#################################################
from krylov import gmres
#################################################
#################################################
#################################################
iA = iJ * A * iJ
#################################################
print('==Error-inv A')
t0 = time()
y = iA(A(x))
t1 = time() - t0
t0 = time()
z = x
t2 = time() - t0
print('#time: {0} {1} {2}'.format(t1, t2, t1 - t2))
e = la.norm(y - z)
print(e)
t0 = time()
y = A(iA(x))
t1 = time() - t0
t0 = time()
z = x
t2 = time() - t0
print('#time: {0} {1} {2}'.format(t1, t2, t1 - t2))
e = la.norm(y - z)
print(e)
#################################################
Pjac = iA
Pgs = iA + iA * E * iA
Malpha = lambda alpha: (1.0 - alpha) * (A - J) + alpha * (J - X)
# Msigma = lambda sigma: A - J + sigma - sigma * iJ * X
# Mtau = lambda tau: tau * iJ * A - tau + J - X
Msigma = lambda sigma: (A - J) + sigma * (J - X)
Mtau = lambda tau: tau * (A - J) + J - X
#################################################
#################################################
# Yw = opY.weak_form()
# Zw = opZ.weak_form()
# Y = spla.LinearOperator(shape, matvec=Yw.matvec, dtype=complex)
# Z = spla.LinearOperator(shape, matvec=Zw.matvec, dtype=complex)
# Msp = (A - J) + (Z - Y)
# Mspp = (A - J) + Z * (J - X)
# Msppp = (A - J) + Z * iJ * (J - X)
#################################################
#################################################
# F = 2.0 * At + 0.5 * X - X * At
CCi = iJ * (0.5 * J + At)
CCe = (0.5 * J - At)
B = J - X
F = B * CCi + CCe
#################################################
#################################################
#################################################
tol = 1e-6
res = []
restart = 20
if restart is None: scale = 1
else: scale = restart
maxiter = int((M.shape[0] / scale) * 0.1)
if maxiter < 50: maxiter = 50
norm_b = la.norm(b)
#################################################
#################################################
#################################################
def rescaleRes(res, P, b):
scale = 1.0 / la.norm(P(b))
new_res = scale * res
return new_res
#################################################
print('\nWO restart={0} maxiter={1}'.format(restart, maxiter))
del res
res = []
tt = time()
xx, info = gmres(M, b,
orthog='mgs',
tol=tol,
residuals=res,
restrt=restart,
maxiter=maxiter)
tt = time() - tt
print(info, len(res))
oResWO = np.array(res)
ResWO = rescaleRes(oResWO, lambda x: x, b)
print('#time: {}'.format(tt))
#sol = xx
print('=Error-Calderon WO')
y = A(xx)
z = J(xx)
e = la.norm(y - z)
ee = la.norm(xx)
print(e, ee, norm_b)
print('-')
y = Ce(xx)
e = la.norm(y)
y = Ci(xx)
z = J(xx)
ee = la.norm(y - z)
y = CCi(xx)
z = xx
eee = la.norm(y - z)
print(e, eee)
print('\nJac restart={0} maxiter={1}'.format(restart, maxiter))
del res
res = []
tt = time()
xx, info = gmres(M, b,
M = Pjac,
orthog='mgs',
tol=tol,
residuals=res,
restrt=restart,
maxiter=maxiter)
tt = time() - tt
print(info, len(res))
oResJac = np.array(res)
ResJac = rescaleRes(oResJac, Pjac, b)
print('#time: {}'.format(tt))
print('=Error-Calderon Jacobi')
y = A(xx)
z = J(xx)
e = la.norm(y - z)
ee = la.norm(xx)
print(e, ee, norm_b)
print('\nGS restart={0} maxiter={1}'.format(restart, maxiter))
del res
res = []
tt = time()
xx, info = gmres(M, b,
M = Pgs,
orthog='mgs',
tol=tol,
residuals=res,
restrt=restart,
maxiter=maxiter)
tt = time() - tt
print(info, len(res))
oResGS = np.array(res)
ResGS = rescaleRes(oResGS, Pgs, b)
print('#time: {}'.format(tt))
sol = xx
print('=Error-Calderon GS')
y = A(xx)
z = J(xx)
e = la.norm(y - z)
ee = la.norm(xx)
print(e, ee, norm_b)
sigma = -0.5
print('\nSigmaWO restart={0} maxiter={1}'.format(restart, maxiter))
del res
res = []
Ms, bs = Msigma(sigma), sigma * b
tt = time()
xx, info = gmres(Ms, bs,
orthog='mgs',
tol=tol,
residuals=res,
restrt=restart,
maxiter=maxiter)
tt = time() - tt
print(info, len(res))
oResSigWO = np.array(res)
ResSigJWO = rescaleRes(oResSigWO, lambda x: x, bs)
print('#time: {}'.format(tt))
print('=Error-Calderon Sigma WO')
y = A(xx)
z = J(xx)
e = la.norm(y - z)
ee = la.norm(xx)
print(e, ee, norm_b)
print('\nSigmaJac restart={0} maxiter={1}'.format(restart, maxiter))
del res
res = []
Ms, bs = Msigma(sigma), sigma * b
tt = time()
xx, info = gmres(Ms, bs,
M = Pjac,
orthog='mgs',
tol=tol,
residuals=res,
restrt=restart,
maxiter=maxiter)
tt = time() - tt
print(info, len(res))
oResSigJac = np.array(res)
ResSigJJac = rescaleRes(oResSigJac, Pjac, bs)
print('#time: {}'.format(tt))
print('=Error-Calderon Sigma Jacobi')
y = A(xx)
z = J(xx)
e = la.norm(y - z)
print(e)
print('\nSigmaGS restart={0} maxiter={1}'.format(restart, maxiter))
del res
res = []
Ms, bs = Msigma(sigma), sigma * b
tt = time()
xx, info = gmres(Ms, bs,
M = Pgs,
orthog='mgs',
tol=tol,
residuals=res,
restrt=restart,
maxiter=maxiter)
tt = time() - tt
print(info, len(res))
oResSigGS = np.array(res)
ResSigJGS = rescaleRes(oResSigGS, Pgs, bs)
print('#time: {}'.format(tt))
print('=Error-Calderon Sigma GS')
y = A(xx)
z = J(xx)
e = la.norm(y - z)
print(e)
# ####################################
# ####################################
#tau = -X * iJ * (J + A)
tau = -0.5
print('\nTauWO restart={0} maxiter={1}'.format(restart, maxiter))
del res
res = []
Ms, bs = Mtau(tau), b
tt = time()
xx, info = gmres(Ms, bs,
orthog='mgs',
tol=tol,
residuals=res,
restrt=restart,
maxiter=maxiter)
tt = time() - tt
print(info, len(res))
oResTauWO = np.array(res)
ResTauWO = rescaleRes(oResTauWO, lambda x: x, bs)
print('#time: {}'.format(tt))
print('=Error-Calderon Tau WO')
y = A(xx)
z = J(xx)
e = la.norm(y - z)
ee = la.norm(xx)
print(e, ee, norm_b)
# ####################################
# ####################################
print('\nBD WO restart={0} maxiter={1}'.format(restart, maxiter))
del res
res = []
Ms, bs = F, b
tt = time()
xx, info = gmres(Ms, bs,
orthog='mgs',
tol=tol,
residuals=res,
restrt=restart,
maxiter=maxiter)
xx = CCi(xx)
tt = time() - tt
print(info, len(res))
oResFWO = np.array(res)
ResFWO = rescaleRes(oResFWO, lambda x: x, bs)
print('#time: {}'.format(tt))
u = xx
print('=Error-Calderon BD WO')
y = A(xx)
z = J(xx)
e = la.norm(y - z)
ee = la.norm(xx)
print(e, ee, norm_b)
print('-')
y = At(xx)
z = 0.5 * J(xx)
e = la.norm(y - z)
y = Ce(xx)
ee = la.norm(y)
y = Ci(xx)
z = J(xx)
eee = la.norm(y - z)
y = CCi(xx)
z = xx
eeee = la.norm(y - z)
eeeee = la.norm(B(xx) - b)
print(e, ee, eee, eeee, eeeee)
# ####################################
# ####################################
# print('\nSP WO restart={0} maxiter={1}'.format(restart, maxiter))
# del res
# res = []
# Ms, bs = Msp, Z(b)
# tt = time()
# xx, info = gmres(Ms, bs,
# orthog='mgs',
# tol=tol,
# residuals=res,
# restrt=restart,
# maxiter=maxiter)
# tt = time() - tt
# print(info, len(res))
# oResSPWO = np.array(res)
# ResSPWO = rescaleRes(oResSPWO, lambda x: x, bs)
# print('#time: {}'.format(tt))
# print('=Error-Calderon SP WO')
# y = A(xx)
# z = J(xx)
# e = la.norm(y - z)
# ee = la.norm(xx)
# print(e, ee, norm_b)
# print('-')
# y = At(xx)
# z = 0.5 * J(xx)
# e = la.norm(y - z)
# y = Ce(xx)
# ee = la.norm(y)