eigvals_banded#
- scipy.linalg.eigvals_banded(a_band, lower=False, overwrite_a_band=False, select='a', select_range=None, check_finite=True)[source]#
- Solve real symmetric or complex Hermitian band matrix eigenvalue problem. - Find eigenvalues w 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. 
- lowerbool, optional
- Is the matrix in the lower form. (Default is upper form) 
- overwrite_a_bandbool, 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 
- check_finitebool, 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. 
 
- Raises:
- LinAlgError
- If eigenvalue computation does not converge. 
 
 - See also - eig_banded
- eigenvalues and right eigenvectors for symmetric/Hermitian band matrices 
- eigvalsh_tridiagonal
- eigenvalues of symmetric/Hermitian tridiagonal matrices 
- eigvals
- eigenvalues of general arrays 
- eigh
- eigenvalues and right eigenvectors for symmetric/Hermitian arrays 
- eig
- eigenvalues and right eigenvectors for non-symmetric arrays 
 - Examples - >>> import numpy as np >>> from scipy.linalg import eigvals_banded >>> A = np.array([[1, 5, 2, 0], [5, 2, 5, 2], [2, 5, 3, 5], [0, 2, 5, 4]]) >>> Ab = np.array([[1, 2, 3, 4], [5, 5, 5, 0], [2, 2, 0, 0]]) >>> w = eigvals_banded(Ab, lower=True) >>> w array([-4.26200532, -2.22987175, 3.95222349, 12.53965359])