def pinv2(a, cond=None, rcond=None):
"""Compute the (Moore-Penrose) pseudo-inverse of a matrix.
Calculate a generalized inverse of a matrix using its
singular-value decomposition and including all 'large' singular
values.
Parameters
----------
a : array, shape (M, N)
Matrix to be pseudo-inverted
cond, rcond : float or None
Cutoff for 'small' singular values.
Singular values smaller than rcond*largest_singular_value are
considered zero.
If None or -1, suitable machine precision is used.
Returns
-------
B : array, shape (N, M)
Raises LinAlgError if SVD computation does not converge
Examples
--------
>>> from numpy import *
>>> a = random.randn(9, 6)
>>> B = linalg.pinv2(a)
>>> allclose(a, dot(a, dot(B, a)))
True
>>> allclose(B, dot(B, dot(a, B)))
True
"""
a = asarray_chkfinite(a)
u, s, vh = decomp_svd(a)
t = u.dtype.char
if rcond is not None:
cond = rcond
if cond in [None, -1]:
cond = {0: feps*1e3, 1: eps*1e6}[_array_precision[t]]
m, n = a.shape
cutoff = cond*numpy.maximum.reduce(s)
psigma = zeros((m, n), t)
for i in range(len(s)):
if s[i] > cutoff:
psigma[i, i] = 1.0/conjugate(s[i])
# XXX: use lapack/blas routines for dot
return transpose(conjugate(dot(dot(u, psigma), vh)))
def pinv2(a, cond=None, rcond=None):
"""Compute the (Moore-Penrose) pseudo-inverse of a matrix.
Calculate a generalized inverse of a matrix using its
singular-value decomposition and including all 'large' singular
values.
Parameters
----------
a : array, shape (M, N)
Matrix to be pseudo-inverted
cond, rcond : float or None
Cutoff for 'small' singular values.
Singular values smaller than rcond*largest_singular_value are
considered zero.
If None or -1, suitable machine precision is used.
Returns
-------
B : array, shape (N, M)
Raises LinAlgError if SVD computation does not converge
Examples
--------
>>> from numpy import *
>>> a = random.randn(9, 6)
>>> B = linalg.pinv2(a)
>>> allclose(a, dot(a, dot(B, a)))
True
>>> allclose(B, dot(B, dot(a, B)))
True
"""
a = asarray_chkfinite(a)
u, s, vh = decomp_svd(a)
t = u.dtype.char
if rcond is not None:
cond = rcond
if cond in [None, -1]:
cond = {0: feps * 1e3, 1: eps * 1e6}[_array_precision[t]]
m, n = a.shape
cutoff = cond * numpy.maximum.reduce(s)
psigma = zeros((m, n), t)
for i in range(len(s)):
if s[i] > cutoff:
psigma[i, i] = 1.0 / conjugate(s[i])
# XXX: use lapack/blas routines for dot
return transpose(conjugate(dot(dot(u, psigma), vh)))