eigvalsh(a, b=None, lower=True, overwrite_a=False, overwrite_b=False, turbo=True, eigvals=None, type=1, check_finite=True, subset_by_index=None, subset_by_value=None, driver=None)
Find eigenvalues array w
of array a
, where b
is positive definite such that for every eigenvalue λ (i-th entry of w) and its eigenvector vi (i-th column of v) satisfies:
a @ vi = λ * b @ vi vi.conj().T @ a @ vi = λ vi.conj().T @ b @ vi = 1
In the standard problem, b is assumed to be the identity matrix.
This function does not check the input array for being Hermitian/symmetric in order to allow for representing arrays with only their upper/lower triangular parts.
This function serves as a one-liner shorthand for scipy.linalg.eigh
with the option eigvals_only=True
to get the eigenvalues and not the eigenvectors. Here it is kept as a legacy convenience. It might be beneficial to use the main function to have full control and to be a bit more pythonic.
A complex Hermitian or real symmetric matrix whose eigenvalues will be computed.
A complex Hermitian or real symmetric definite positive matrix in. If omitted, identity matrix is assumed.
Whether the pertinent array data is taken from the lower or upper triangle of a
and, if applicable, b
. (Default: lower)
Whether to overwrite data in a
(may improve performance). Default is False.
Whether to overwrite data in b
(may improve performance). Default is False.
For the generalized problems, this keyword specifies the problem type to be solved for w
and v
(only takes 1, 2, 3 as possible inputs):
1 => a @ v = w @ b @ v 2 => a @ b @ v = w @ v 3 => b @ a @ v = w @ v
This keyword is ignored for standard problems.
Whether to check that the input matrices contain 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.
If provided, this two-element iterable defines the start and the end indices of the desired eigenvalues (ascending order and 0-indexed). To return only the second smallest to fifth smallest eigenvalues, [1, 4]
is used. [n-3, n-1]
returns the largest three. Only available with "evr", "evx", and "gvx" drivers. The entries are directly converted to integers via int()
.
If provided, this two-element iterable defines the half-open interval (a, b]
that, if any, only the eigenvalues between these values are returned. Only available with "evr", "evx", and "gvx" drivers. Use np.inf
for the unconstrained ends.
Defines which LAPACK driver should be used. Valid options are "ev", "evd", "evr", "evx" for standard problems and "gv", "gvd", "gvx" for generalized (where b is not None) problems. See the Notes section of scipy.linalg.eigh
.
Deprecated by ``driver=gvd`` option. Has no significant effect for eigenvalue computations since no eigenvectors are requested.
Deprecated by ``subset_by_index`` keyword. Indexes of the smallest and largest (in ascending order) eigenvalues and corresponding eigenvectors to be returned: 0 <= lo <= hi <= M-1. If omitted, all eigenvalues and eigenvectors are returned.
If eigenvalue computation does not converge, an error occurred, or b matrix is not definite positive. Note that if input matrices are not symmetric or Hermitian, no error will be reported but results will be wrong.
The N
( 1<=N<=M
) selected eigenvalues, in ascending order, each repeated according to its multiplicity.
Solves a standard or generalized eigenvalue problem for a complex Hermitian or real symmetric matrix.
eigh
eigenvalues and right eigenvectors for symmetric/Hermitian arrays
eigvals
eigenvalues of general arrays
eigvals_banded
eigenvalues for symmetric/Hermitian band matrices
eigvalsh_tridiagonal
eigenvalues of symmetric/Hermitian tridiagonal matrices
For more examples see scipy.linalg.eigh
.
>>> from scipy.linalg import eigvalshSee :
... A = np.array([[6, 3, 1, 5], [3, 0, 5, 1], [1, 5, 6, 2], [5, 1, 2, 2]])
... w = eigvalsh(A)
... w array([-3.74637491, -0.76263923, 6.08502336, 12.42399079])
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._decomp.eigvals
scipy.linalg._decomp.eigvalsh
scipy.linalg._decomp.eigh
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