def _debug_chebyshev_polynomial_basis_generator(self):
step_val=5
cheby_generator = ChebyshevPolynomial()
eigen_estimator = GerschgorinCircleTheoremEigenvalueEstimator()
max_eigen, min_eigen = eigen_estimator.csr_mat_extreme_eigenvalue_estimation(self._mat)
print("max:{}, min:{}\n".format(max_eigen,min_eigen))
res = cheby_generator.basis_generation_with_eigenvalue_shifting_and_scaling_single_vec(\
self._mat, self._B, step_val, max_eigen, min_eigen)
print(res)
def bcbcg_solver_least_square_eigen_param(self, mat, RHS, init_X, step_val,
tol, maxiter, whichcol,
max_eigenvalue, min_eigenvalue):
#gerschgorin_estimator = GerschgorinCircleTheoremEigenvalueEstimator()
#max_eigenvalue, min_eigenvalue = gerschgorin_estimator.csr_mat_extreme_eigenvalue_estimation(mat)
chebyshev_basis_generator = ChebyshevPolynomial()
op_A = linalg.aslinearoperator(mat)
m_R = RHS - op_A(init_X)
m_X = init_X.copy()
R_to_RHS_norm_ratio = lambda x: np.linalg.norm(
m_R[:, x]) / np.linalg.norm(RHS[:, x])
residual_ratio_hist = [R_to_RHS_norm_ratio(whichcol)]
print("max and min eigen which are going to be used ... ",
max_eigenvalue, " , ", min_eigenvalue)
for itercounter in range(1, maxiter + 1):
m_chebyshev_basis = \
chebyshev_basis_generator.basis_generation_with_eigenvalue_shifting_and_scaling_block_vecs(\
mat, m_R, step_val, max_eigenvalue, min_eigenvalue)
#print("basis rank",np.linalg.matrix_rank(m_chebyshev_basis))
#return
if itercounter == 1:
m_Q = m_chebyshev_basis
else:
m_AQ_trans_mul_chebyshev_basis = np.matmul(
m_AQ.T, m_chebyshev_basis)
#m_B = np.matmul(m_Q_trans_AQ_inverse , m_AQ_trans_mul_chebyshev_basis)
m_B = np.linalg.lstsq(m_Q_trans_AQ,
m_AQ_trans_mul_chebyshev_basis)[0]
m_Q = m_chebyshev_basis - np.matmul(m_Q, m_B)
m_AQ = op_A.matmat(m_Q)
m_Q_trans_AQ = np.matmul(m_Q.T, m_AQ)
#m_Q_trans_AQ_inverse = np.linalg.inv(m_Q_trans_AQ)
#m_alpha = np.matmul( m_Q_trans_AQ_inverse, np.matmul(m_Q.T, m_R) )
m_alpha = np.linalg.lstsq(m_Q_trans_AQ, np.matmul(m_Q.T, m_R))[0]
m_X += np.matmul(m_Q, m_alpha)
m_R -= np.matmul(m_AQ, m_alpha)
residual_ratio_hist.append(R_to_RHS_norm_ratio(whichcol))
print(itercounter, ": ", R_to_RHS_norm_ratio(whichcol))
if residual_ratio_hist[-1] <= tol:
return m_X, m_R, residual_ratio_hist
return m_X, m_R, residual_ratio_hist
def _debug_chebyshev_polynomial_basis_generator(self):
step_val = 5
cheby_generator = ChebyshevPolynomial()
eigen_estimator = GerschgorinCircleTheoremEigenvalueEstimator()
max_eigen, min_eigen = eigen_estimator.csr_mat_extreme_eigenvalue_estimation(
self._mat)
print("max:{}, min:{}\n".format(max_eigen, min_eigen))
res = cheby_generator.basis_generation_with_eigenvalue_shifting_and_scaling_single_vec(\
self._mat, self._B, step_val, max_eigen, min_eigen)
print(res)
def cbcg_solver_least_square_eigen_param(self, mat, rhs, init_x, step_val,
tol, maxiter, max_eigenvalue,
min_eigenvalue):
"""get the inverse matrix by least square method"""
#gerschgorin_estimator = GerschgorinCircleTheoremEigenvalueEstimator()
#max_eigenvalue, min_eigenvalue = gerschgorin_estimator.csr_mat_extreme_eigenvalue_estimation(mat)
chebyshev_basis_generator = ChebyshevPolynomial()
op_A = linalg.aslinearoperator(mat)
v_r = rhs - op_A(init_x)
v_x = init_x.copy()
s_normb = np.linalg.norm(rhs)
residual_ratio_hist = [np.linalg.norm(v_r) / s_normb]
print("max and min eigen which are going to be used ... ",
max_eigenvalue, " , ", min_eigenvalue)
for itercounter in range(1, maxiter + 1):
m_chebyshev_basis = \
chebyshev_basis_generator.basis_generation_with_eigenvalue_shifting_and_scaling_single_vec(\
mat, v_r, step_val, max_eigenvalue, min_eigenvalue)
if itercounter == 1:
m_Q = m_chebyshev_basis
else:
#op_AQ_trans = linalg.aslinearoperator(m_AQ.transpose())
#AQ_trans_mul_chebyshev_basis = op_AQ_trans.matmat(m_chebyshev_basis)
#m_B = linalg.aslinearoperator(Q_trans_AQ_inverse).matmat (AQ_trans_mul_chebyshev_basis)
m_AQ_trans_mul_chebyshev_basis = np.matmul(
m_AQ.T, m_chebyshev_basis)
#m_B = np.matmul(m_Q_trans_AQ_inverse , m_AQ_trans_mul_chebyshev_basis)
m_B = np.linalg.lstsq(m_Q_trans_AQ,
m_AQ_trans_mul_chebyshev_basis)[0]
m_Q = m_chebyshev_basis - np.matmul(m_Q, m_B)
m_AQ = op_A.matmat(m_Q)
#m_Q_trans_AQ = linalg.aslinearoperator(m_Q.transpose())(m_AQ)
m_Q_trans_AQ = np.matmul(m_Q.T, m_AQ)
#m_Q_trans_AQ_inverse = np.linalg.inv(m_Q_trans_AQ)
#v_alpha = np.matmul( m_Q_trans_AQ_inverse, np.matmul(m_Q.T, v_r) )
v_alpha = np.linalg.lstsq(m_Q_trans_AQ, np.matmul(m_Q.T, v_r))[0]
v_x += np.matmul(m_Q, v_alpha)
v_r -= np.matmul(m_AQ, v_alpha)
residual_ratio_hist.append(np.linalg.norm(v_r) / s_normb)
print(itercounter, ": ", np.linalg.norm(v_r) / s_normb)
if residual_ratio_hist[-1] <= tol:
return v_x, v_r, residual_ratio_hist
return v_x, v_r, residual_ratio_hist
def bcbcg_solver_least_square_eigen_param(self, mat, RHS, init_X, step_val, tol, maxiter,whichcol, max_eigenvalue, min_eigenvalue):
#gerschgorin_estimator = GerschgorinCircleTheoremEigenvalueEstimator()
#max_eigenvalue, min_eigenvalue = gerschgorin_estimator.csr_mat_extreme_eigenvalue_estimation(mat)
chebyshev_basis_generator = ChebyshevPolynomial()
op_A = linalg.aslinearoperator(mat)
m_R = RHS - op_A(init_X)
m_X = init_X.copy()
R_to_RHS_norm_ratio = lambda x: np.linalg.norm(m_R[:,x])/np.linalg.norm(RHS[:,x])
residual_ratio_hist = [R_to_RHS_norm_ratio(whichcol)]
print ("max and min eigen which are going to be used ... ", max_eigenvalue, " , ", min_eigenvalue)
for itercounter in range(1, maxiter+1):
m_chebyshev_basis = \
chebyshev_basis_generator.basis_generation_with_eigenvalue_shifting_and_scaling_block_vecs(\
mat, m_R, step_val, max_eigenvalue, min_eigenvalue)
#print("basis rank",np.linalg.matrix_rank(m_chebyshev_basis))
#return
if itercounter == 1:
m_Q = m_chebyshev_basis
else:
m_AQ_trans_mul_chebyshev_basis = np.matmul(m_AQ.T , m_chebyshev_basis)
#m_B = np.matmul(m_Q_trans_AQ_inverse , m_AQ_trans_mul_chebyshev_basis)
m_B = np.linalg.lstsq(m_Q_trans_AQ, m_AQ_trans_mul_chebyshev_basis)[0]
m_Q = m_chebyshev_basis - np.matmul(m_Q, m_B)
m_AQ = op_A.matmat(m_Q)
m_Q_trans_AQ = np.matmul(m_Q.T, m_AQ)
#m_Q_trans_AQ_inverse = np.linalg.inv(m_Q_trans_AQ)
#m_alpha = np.matmul( m_Q_trans_AQ_inverse, np.matmul(m_Q.T, m_R) )
m_alpha = np.linalg.lstsq( m_Q_trans_AQ, np.matmul(m_Q.T, m_R) )[0]
m_X += np.matmul(m_Q,m_alpha)
m_R -= np.matmul(m_AQ, m_alpha)
residual_ratio_hist.append(R_to_RHS_norm_ratio(whichcol))
print(itercounter, ": ", R_to_RHS_norm_ratio(whichcol))
if residual_ratio_hist[-1] <= tol:
return m_X, m_R, residual_ratio_hist
return m_X, m_R, residual_ratio_hist
def cbcg_solver_least_square_eigen_param(self, mat, rhs, init_x, step_val, tol, maxiter, max_eigenvalue, min_eigenvalue):
"""get the inverse matrix by least square method"""
#gerschgorin_estimator = GerschgorinCircleTheoremEigenvalueEstimator()
#max_eigenvalue, min_eigenvalue = gerschgorin_estimator.csr_mat_extreme_eigenvalue_estimation(mat)
chebyshev_basis_generator = ChebyshevPolynomial()
op_A = linalg.aslinearoperator(mat)
v_r = rhs - op_A(init_x)
v_x = init_x.copy()
s_normb = np.linalg.norm(rhs)
residual_ratio_hist = [np.linalg.norm(v_r)/s_normb]
print ("max and min eigen which are going to be used ... ", max_eigenvalue, " , ", min_eigenvalue)
for itercounter in range(1, maxiter+1):
m_chebyshev_basis = \
chebyshev_basis_generator.basis_generation_with_eigenvalue_shifting_and_scaling_single_vec(\
mat, v_r, step_val, max_eigenvalue, min_eigenvalue)
if itercounter == 1:
m_Q = m_chebyshev_basis
else:
#op_AQ_trans = linalg.aslinearoperator(m_AQ.transpose())
#AQ_trans_mul_chebyshev_basis = op_AQ_trans.matmat(m_chebyshev_basis)
#m_B = linalg.aslinearoperator(Q_trans_AQ_inverse).matmat (AQ_trans_mul_chebyshev_basis)
m_AQ_trans_mul_chebyshev_basis = np.matmul(m_AQ.T , m_chebyshev_basis)
#m_B = np.matmul(m_Q_trans_AQ_inverse , m_AQ_trans_mul_chebyshev_basis)
m_B = np.linalg.lstsq(m_Q_trans_AQ, m_AQ_trans_mul_chebyshev_basis)[0]
m_Q = m_chebyshev_basis - np.matmul(m_Q, m_B)
m_AQ = op_A.matmat(m_Q)
#m_Q_trans_AQ = linalg.aslinearoperator(m_Q.transpose())(m_AQ)
m_Q_trans_AQ = np.matmul(m_Q.T, m_AQ)
#m_Q_trans_AQ_inverse = np.linalg.inv(m_Q_trans_AQ)
#v_alpha = np.matmul( m_Q_trans_AQ_inverse, np.matmul(m_Q.T, v_r) )
v_alpha = np.linalg.lstsq(m_Q_trans_AQ, np.matmul(m_Q.T, v_r))[0]
v_x += np.matmul(m_Q,v_alpha)
v_r -= np.matmul(m_AQ, v_alpha)
residual_ratio_hist.append( np.linalg.norm(v_r)/s_normb)
print(itercounter, ": ", np.linalg.norm(v_r)/s_normb)
if residual_ratio_hist[-1] <= tol:
return v_x, v_r, residual_ratio_hist
return v_x, v_r, residual_ratio_hist