pinvh#
- scipy.linalg.pinvh(a, atol=None, rtol=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 complex Hermitian/real symmetric matrix using its eigenvalue decomposition and including all eigenvalues with ‘large’ absolute value. - The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details. - Parameters:
- a(N, N) array_like
- Real symmetric or complex hermetian matrix to be pseudo-inverted 
- atolfloat, optional
- Absolute threshold term, default value is 0. - Added in version 1.7.0. 
- rtolfloat, optional
- Relative threshold term, default value is - N * epswhere- epsis the machine precision value of the datatype of- a.- Added in version 1.7.0. 
- 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 algorithm does not converge. 
 
 - See also - pinv
- Moore-Penrose pseudoinverse of a matrix. 
 - Examples - For a more detailed example see - pinv.- >>> import numpy as np >>> from scipy.linalg import pinvh >>> rng = np.random.default_rng() >>> a = rng.standard_normal((9, 6)) >>> a = np.dot(a, a.T) >>> B = pinvh(a) >>> np.allclose(a, a @ B @ a) True >>> np.allclose(B, B @ a @ B) True