eigvalsh_tridiagonal(d, e, select='a', select_range=None, check_finite=True, tol=0.0, lapack_driver='auto')
Find eigenvalues w
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
.
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 lapack_driver='stebz'
). 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. 'sterf' and '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.
Solve eigenvalue problem for a real symmetric tridiagonal matrix.
eigh_tridiagonal
eigenvalues and right eiegenvectors for symmetric/Hermitian tridiagonal matrices
>>> from scipy.linalg import eigvalsh_tridiagonal, eigvalshSee :
... d = 3*np.ones(4)
... e = -1*np.ones(3)
... w = eigvalsh_tridiagonal(d, e)
... A = np.diag(d) + np.diag(e, k=1) + np.diag(e, k=-1)
... w2 = eigvalsh(A) # Verify with other eigenvalue routines
... np.allclose(w - w2, np.zeros(4)) True
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._decomp.eigh_tridiagonal
scipy.linalg._decomp.eigvalsh
scipy.linalg._decomp.eigvals_banded
scipy.linalg._decomp.eigvals
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