eigh_tridiagonal(d, e, eigvals_only=False, select='a', select_range=None, check_finite=True, tol=0.0, lapack_driver='auto')
Find eigenvalues w
and optionally right eigenvectors v
of a
:
a v[:,i] = w[i] v[:,i] v.H v = identity
For a real symmetric matrix a
with diagonal elements d
and off-diagonal elements e
.
This function makes use of LAPACK S/DSTEMR
routines.
The diagonal elements of the array.
The off-diagonal elements of the array.
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.
The absolute tolerance to which each eigenvalue is required (only used when 'stebz' is the :None:None:`lapack_driver`
). An eigenvalue (or cluster) is considered to have converged if it lies in an interval of this width. If <= 0. (default), the value eps*|a|
is used where eps is the machine precision, and |a|
is the 1-norm of the matrix a
.
LAPACK function to use, can be 'auto', 'stemr', 'stebz', 'sterf', or 'stev'. When 'auto' (default), it will use 'stemr' if select='a'
and 'stebz' otherwise. When 'stebz' is used to find the eigenvalues and eigvals_only=False
, then a second LAPACK call (to ?STEIN
) is used to find the corresponding eigenvectors. 'sterf' can only be used when eigvals_only=True
and select='a'
. 'stev' can only be used when select='a'
.
If eigenvalue computation does not converge.
The eigenvalues, in ascending order, each repeated according to its multiplicity.
The normalized eigenvector corresponding to the eigenvalue w[i]
is the column v[:,i]
.
Solve eigenvalue problem for a real symmetric tridiagonal matrix.
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
eigvalsh_tridiagonal
eigenvalues of symmetric/Hermitian tridiagonal matrices
>>> from scipy.linalg import eigh_tridiagonalSee :
... d = 3*np.ones(4)
... e = -1*np.ones(3)
... w, v = eigh_tridiagonal(d, e)
... A = np.diag(d) + np.diag(e, k=1) + np.diag(e, k=-1)
... np.allclose(A @ v - v @ np.diag(w), np.zeros((4, 4))) True
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._decomp.eig_banded
scipy.linalg._decomp.eigvalsh_tridiagonal
scipy.linalg._decomp.eig
scipy.linalg._decomp.eigh
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