scipy.linalg.eigvalsh¶
- scipy.linalg.eigvalsh(a, b=None, lower=True, overwrite_a=False, overwrite_b=False, turbo=True, eigvals=None, type=1)¶
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 : array, shape (M, M)
A complex Hermitian or real symmetric matrix whose eigenvalues and eigenvectors will be computed.
b : array, shape (M, M)
A complex Hermitian or real symmetric definite positive matrix in. If omitted, identity matrix is assumed.
lower : boolean
Whether the pertinent array data is taken from the lower or upper triangle of a. (Default: lower)
turbo : boolean
Use divide and conquer algorithm (faster but expensive in memory, only for generalized eigenvalue problem and if eigvals=None)
eigvals : tuple (lo, hi)
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 :
- 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 : boolean
Whether to overwrite data in a (may improve performance)
overwrite_b : boolean
Whether to overwrite data in b (may improve performance)
Returns: w : real array, shape (N,)
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. :
