def faster_inverse(A):
b = np.identity(A.shape[1], dtype=A.dtype)
n_eq = A.shape[0]
n_rhs = A.shape[1]
pivots = np.zeros(n_eq, np.intc)
identity = np.eye(n_eq)
results = lapack_lite.zgesv(n_eq, n_rhs, A, n_eq, pivots, b, n_eq, 0)
if results['info'] > 0:
raise LinAlgError('Singular matrix')
return b
def regularized_inverse(A, lm):
"""
This computes the gereralized inverse of A through a
regularized solution: (Ah*A + lm^2*I)*C = Ah*I
use CBLAS to get the matrix product of (Ah*A + lm^2*I) in A2,
and then use LAPACK to solve for C.
Note: in column-major...
A is conj(Ah)
A2 is conj(Ah*A + lm^2*I) -- since A2 is hermitian symmetric
If conj(AhA + (lm^2)I)*C = conj(Ah), then conj(C) (the conjugate of
the LAPACK solution, which is in col-major) is the desired solution
in column-major. So the final answer in row-major is the hermitian
transpose of C.
"""
m, n = A.shape
# Ah is NxM
Ah = np.empty((n, m), A.dtype)
Ah[:] = A.transpose().conjugate()
# A2 is NxN
A2 = np.dot(Ah, A)
# add lm**2 to the diagonal (ie, A2 + (lm**2)*I)
A2.flat[0 : n * n : n + 1] += lm * lm
pivots = np.zeros(n, intc)
# A viewed as column major is considered to be NxNRHS (NxM)...
# the solution will be NxNRHS too, and is stored in A
results = lapack_lite.zgesv(n, m, A2, n, pivots, A, n, 0)
# put conjugate solution into row-major (MxN) by hermitian transpose
Ah[:] = A.transpose().conjugate()
return Ah
def regularized_inverse(A, lm):
"""
This computes the gereralized inverse of A through a
regularized solution: (Ah*A + lm^2*I)*C = Ah*I
use CBLAS to get the matrix product of (Ah*A + lm^2*I) in A2,
and then use LAPACK to solve for C.
Note: in column-major...
A is conj(Ah)
A2 is conj(Ah*A + lm^2*I) -- since A2 is hermitian symmetric
If conj(AhA + (lm^2)I)*C = conj(Ah), then conj(C) (the conjugate of
the LAPACK solution, which is in col-major) is the desired solution
in column-major. So the final answer in row-major is the hermitian
transpose of C.
"""
m, n = A.shape
# Ah is NxM
Ah = np.empty((n, m), A.dtype)
Ah[:] = A.transpose().conjugate()
# A2 is NxN
A2 = np.dot(Ah, A)
# add lm**2 to the diagonal (ie, A2 + (lm**2)*I)
A2.flat[0:n * n:n + 1] += (lm * lm)
pivots = np.zeros(n, intc)
# A viewed as column major is considered to be NxNRHS (NxM)...
# the solution will be NxNRHS too, and is stored in A
results = lapack_lite.zgesv(n, m, A2, n, pivots, A, n, 0)
# put conjugate solution into row-major (MxN) by hermitian transpose
Ah[:] = A.transpose().conjugate()
return Ah
