scipy.linalg.eigvalsh¶
- scipy.linalg.eigvalsh(a, b=None, lower=True, overwrite_a=False, overwrite_b=False, turbo=True, eigvals=None, type=1, check_finite=True)[source]¶
Solve an ordinary or generalized eigenvalue problem for a complex Hermitian or real symmetric matrix.
Find eigenvalues w of matrix a, where b is positive definite:
a v[:,i] = w[i] b v[:,i] v[i,:].conj() a v[:,i] = w[i] v[i,:].conj() b v[:,i] = 1
Parameters : a : (M, M) array_like
A complex Hermitian or real symmetric matrix whose eigenvalues and eigenvectors will be computed.
b : (M, M) array_like, optional
A complex Hermitian or real symmetric definite positive matrix in. If omitted, identity matrix is assumed.
lower : bool, optional
Whether the pertinent array data is taken from the lower or upper triangle of a. (Default: lower)
turbo : bool, optional
Use divide and conquer algorithm (faster but expensive in memory, only for generalized eigenvalue problem and if eigvals=None)
eigvals : tuple (lo, hi), optional
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.
type : integer, optional
Specifies the problem type to be solved:
type = 1: a v[:,i] = w[i] b v[:,i]
type = 2: a b v[:,i] = w[i] v[:,i]
type = 3: b a v[:,i] = w[i] v[:,i]
overwrite_a : bool, optional
Whether to overwrite data in a (may improve performance)
overwrite_b : bool, optional
Whether to overwrite data in b (may improve performance)
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.
Returns : w : (N,) float ndarray
The N (1<=N<=M) selected eigenvalues, in ascending order, each repeated according to its multiplicity.
Raises : LinAlgError : :
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 is reported but results will be wrong.
