scipy.linalg.lapack.chegvx#

scipy.linalg.lapack.chegvx(a, b, itype=1, jobz='V', range='A', uplo='L', vl=0.0, vu=1.0, il=1, iu=n, abstol=0.0, lwork=..., overwrite_a=0, overwrite_b=0) = <flapack function chegvx>#

Compute selected eigenvalues of the generalized Hermitian-definite problem (LAPACK chegvx).

Parameters:

andarray: Hermitian matrix of shape (n, n).
bndarray: Positive definite matrix of shape (n, n).
itypeint, optional: Which generalized problem to solve: 1 for a @ x = w * b @ x, 2 for a @ b @ x = w * x, 3 for b @ a @ x = w * x. Default is 1.
jobzstr, optional: 'V' to compute eigenvectors, 'N' for eigenvalues only. Default is 'V'. This family spells it as a letter where syev uses compute_v.
rangestr, optional: 'A' for all eigenvalues, 'V' for those in (vl, vu], 'I' for those indexed il through iu. Default is 'A'.
uplostr, optional: 'U' or 'L' for the triangle of a to reference. Default is 'L' – note that is the opposite of the lower=0 default elsewhere in this group, so the same matrix can give different answers between families.
vlfloat, optional: Lower bound of the interval; used only when range is 'V'. Default is 0.0.
vufloat, optional: Upper bound of the interval; used only when range is 'V'. Default is 1.0.
ilint, optional: Index of the smallest eigenvalue to return, 1-based; used only when range is 'I'. Default is 1.
iuint, optional: Index of the largest eigenvalue to return, 1-based; used only when range is 'I'. Default is n.
abstolfloat, optional: Absolute error tolerance for the eigenvalues. Default is 0.0.
lworkint, optional: Size of the workspace. Default is max(2 * n, 1). Use chegvx_lwork for the optimal value.
overwrite_aint, optional: If nonzero, a may be overwritten in place. Default is 0.
overwrite_bint, optional: If nonzero, b may be overwritten in place. Default is 0.

Returns:

wndarray: Eigenvalues in ascending order, length n. Real for every flavor.
zndarray: The m computed eigenvectors as columns, or empty when jobz is 'N'.
mint: Number of eigenvalues found.
ifailndarray: Indices of eigenvectors that failed to converge, 1-based.
infoint: 0 on success; if negative, the -info-th argument had an illegal value; if positive, the algorithm failed to converge.