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, rcond : float or None Cutoff for ‘small’ eigenvalues. Singular values smaller than rcond * largest_eigenvalue are considered zero. If None or -1, suitable machine precision is used. lower : bool Whether the pertinent array data is taken from the lower or upper triangle of a. (Default: lower) return_rank : bool, optional if True, return the effective rank of the matrix check_finite : boolean, optional Whether to check the input matrixes contain only finite numbers. Disabling may give a performance gain, but may result to problems (crashes, non-termination) if the inputs do contain infinities or NaNs. B : (N, N) ndarray The pseudo-inverse of matrix a. rank : int The effective rank of the matrix. Returned if return_rank == True LinAlgError : If eigenvalue does not converge

Examples

```>>> from numpy import *
>>> a = random.randn(9, 6)
>>> a = np.dot(a, a.T)
>>> B = pinvh(a)
>>> allclose(a, dot(a, dot(B, a)))
True
>>> allclose(B, dot(B, dot(a, B)))
True
```

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