eigvals_banded(a_band, lower=False, overwrite_a_band=False, select='a', select_range=None, check_finite=True)
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.
The bands of the M by M matrix a.
Is the matrix in the lower form. (Default is upper form)
Discard data in a_band (may enhance performance)
Which eigenvalues to calculate
====== ======================================== select calculated ====== ======================================== 'a' All eigenvalues 'v' Eigenvalues in the interval (min, max] 'i' Eigenvalues with indices min <= i <= max ====== ========================================
Range of selected eigenvalues
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.
If eigenvalue computation does not converge.
The eigenvalues, in ascending order, each repeated according to its multiplicity.
Solve real symmetric or complex Hermitian band matrix eigenvalue problem.
eig
eigenvalues and right eigenvectors for non-symmetric arrays
eig_banded
eigenvalues and right eigenvectors for symmetric/Hermitian band matrices
eigh
eigenvalues and right eigenvectors for symmetric/Hermitian arrays
eigvals
eigenvalues of general arrays
eigvalsh_tridiagonal
eigenvalues of symmetric/Hermitian tridiagonal matrices
>>> from scipy.linalg import eigvals_bandedSee :
... 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])
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._decomp.eigvals
scipy.linalg._decomp.eigvals_banded
scipy.linalg._decomp.eigvalsh
scipy.linalg._decomp.eig_banded
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