scipy.linalg.eig_banded¶
- scipy.linalg.eig_banded(a_band, lower=False, eigvals_only=False, overwrite_a_band=False, select='a', select_range=None, max_ev=0, check_finite=True)[source]¶
Solve real symmetric or complex hermitian band matrix eigenvalue problem.
Find eigenvalues w and optionally right eigenvectors v of a:
a v[:,i] = w[i] v[:,i] v.H v = identity
The matrix a is stored in a_band either in lower diagonal or upper diagonal ordered form:
a_band[u + i - j, j] == a[i,j] (if upper form; i <= j) a_band[ i - j, j] == a[i,j] (if lower form; i >= j)where u is the number of bands above the diagonal.
Example of a_band (shape of a is (6,6), u=2):
upper form: * * a02 a13 a24 a35 * a01 a12 a23 a34 a45 a00 a11 a22 a33 a44 a55 lower form: a00 a11 a22 a33 a44 a55 a10 a21 a32 a43 a54 * a20 a31 a42 a53 * *
Cells marked with * are not used.
Parameters: a_band : (u+1, M) array_like
The bands of the M by M matrix a.
lower : bool, optional
Is the matrix in the lower form. (Default is upper form)
eigvals_only : bool, optional
Compute only the eigenvalues and no eigenvectors. (Default: calculate also eigenvectors)
overwrite_a_band : bool, optional
Discard data in a_band (may enhance performance)
select : {‘a’, ‘v’, ‘i’}, optional
Which eigenvalues to calculate
select calculated ‘a’ All eigenvalues ‘v’ Eigenvalues in the interval (min, max] ‘i’ Eigenvalues with indices min <= i <= max select_range : (min, max), optional
Range of selected eigenvalues
max_ev : int, optional
For select==’v’, maximum number of eigenvalues expected. For other values of select, has no meaning.
In doubt, leave this parameter untouched.
check_finite : bool, optional
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.
Returns: w : (M,) ndarray
The eigenvalues, in ascending order, each repeated according to its multiplicity.
v : (M, M) float or complex ndarray
The normalized eigenvector corresponding to the eigenvalue w[i] is the column v[:,i].
Raises LinAlgError if eigenvalue computation does not converge