scipy.linalg.lapack.zhegvd#

scipy.linalg.lapack.zhegvd(a, b, itype=1, jobz='V', uplo='L', lwork=..., lrwork=..., liwork=..., overwrite_a=0, overwrite_b=0) = <flapack function zhegvd>#

Solve the generalized Hermitian-definite eigenproblem by divide-and-conquer (LAPACK zhegvd).

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.
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.
lworkint, optional: Default is n * (n + 2) when jobz is 'V', n + 1 otherwise.
lrworkint, optional: Size of the real workspace, which the real flavors do not have. Default is 2 * n ** 2 + 5 * n + 1 when jobz is 'V', n otherwise.
liworkint, optional: Default is 5 * n + 3 when jobz is 'V', 1 otherwise.
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.
vndarray: Eigenvectors as columns when jobz is 'V'.
infoint: 0 on success; if negative, the -info-th argument had an illegal value; if positive, the algorithm failed to converge.