scipy.linalg.pinvh¶
-
scipy.linalg.
pinvh
(a, cond=None, rcond=None, lower=True, return_rank=False, check_finite=True)[source]¶ Compute the (Moore-Penrose) pseudo-inverse of a Hermitian matrix.
Calculate a generalized inverse of a Hermitian or real symmetric matrix using its eigenvalue decomposition and including all eigenvalues with ‘large’ absolute value.
- Parameters
- a(N, N) array_like
Real symmetric or complex hermetian matrix to be pseudo-inverted
- cond, rcondfloat or None
Cutoff for ‘small’ singular values; singular values smaller than this value are considered as zero. If both are omitted, the default
max(M,N)*largest_eigenvalue*eps
is used whereeps
is the machine precision value of the datatype ofa
.Changed in version 1.3.0: Previously the default cutoff value was just
eps*f
wheref
was1e3
for single precision and1e6
for double precision.- lowerbool, optional
Whether the pertinent array data is taken from the lower or upper triangle of a. (Default: lower)
- return_rankbool, optional
If True, return the effective rank of the matrix.
- check_finitebool, optional
Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.
- Returns
- B(N, N) ndarray
The pseudo-inverse of matrix a.
- rankint
The effective rank of the matrix. Returned if return_rank is True.
- Raises
- LinAlgError
If eigenvalue does not converge
Examples
>>> from scipy.linalg import pinvh >>> a = np.random.randn(9, 6) >>> a = np.dot(a, a.T) >>> B = pinvh(a) >>> np.allclose(a, np.dot(a, np.dot(B, a))) True >>> np.allclose(B, np.dot(B, np.dot(a, B))) True