pinvh(a, atol=None, rtol=None, lower=True, return_rank=False, check_finite=True, cond=None, rcond=None)
Calculate a generalized inverse of a complex Hermitian/real symmetric matrix using its eigenvalue decomposition and including all eigenvalues with 'large' absolute value.
Real symmetric or complex hermetian matrix to be pseudo-inverted
Absolute threshold term, default value is 0.
Relative threshold term, default value is N * eps
where eps
is the machine precision value of the datatype of a
.
Whether the pertinent array data is taken from the lower or upper triangle of a. (Default: lower)
If True, return the effective rank of the matrix.
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.
In older versions, these values were meant to be used as atol
with rtol=0
. If both were given rcond
overwrote cond
and hence the code was not correct. Thus using these are strongly discouraged and the tolerances above are recommended instead. In fact, if provided, atol, rtol takes precedence over these keywords.
Deprecated in favor of rtol
and atol
parameters above and will be removed in future versions of SciPy.
Previously the default cutoff value was just eps*f
where f
was 1e3
for single precision and 1e6
for double precision.
If eigenvalue algorithm does not converge.
The pseudo-inverse of matrix a.
The effective rank of the matrix. Returned if :None:None:`return_rank` is True.
Compute the (Moore-Penrose) pseudo-inverse of a Hermitian matrix.
>>> 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) TrueSee :
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._basic.pinvh
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