SRC/zhpev.f(3)

✨ SRC/zhpev.f ✨

okay bestie, buckle up, because we're diving into some LAPACK realness 💅

💖 SYNOPSIS 💖

Functions/Subroutines

subroutine zhpev (jobz, uplo, n, ap, w, z, ldz, work, rwork, info)

ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

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🎀 Function/Subroutine Documentation 🎀

subroutine zhpev (character jobz, character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

🦋 Purpose:

no cap, here's the tea:

ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage.

literally iconic ✨

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🌸 Parameters 🌸

• JOBZ

okay so JOBZ is CHARACTER*1 and it tells us what we're doing:

• = 'N': Compute eigenvalues only (just the vibes, no vectors);
• = 'V': Compute eigenvalues and eigenvectors (the whole package, periodt).

• UPLO

UPLO is CHARACTER*1, and it's giving "which triangle are we working with?" energy:

• = 'U': Upper triangle of A is stored;
• = 'L': Lower triangle of A is stored.

• N

N is INTEGER. It's the order of the matrix A. So like, N >= 0 bestie, don't come at me with negative numbers 🙈

• AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2). On entry, it's holding the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The way this works is:

The j-th column of A is stored in the array AP as follows:

• if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
• if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit though, AP is overwritten by values generated during the reduction to tridiagonal form 😭 like it gets a whole glow-up. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A. And if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A. So yeah, AP goes through some changes, iykyk.

• W

W is DOUBLE PRECISION array, dimension (N). If INFO = 0, it contains the eigenvalues in ascending order. slay.

• Z

Z is COMPLEX*16 array, dimension (LDZ, N). If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced — it's literally just vibing in the background, not invited to the party 🫶

• LDZ

LDZ is INTEGER. It's the leading dimension of the array Z. So like, LDZ >= 1, and if JOBZ = 'V', then LDZ >= max(1,N). Don't mess this up bestie.

• WORK

WORK is COMPLEX*16 array, dimension (max(1, 2*N-1)). It's doing its thing behind the scenes 💅

• RWORK

RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)). Same energy — just working hard so you don't have to.

• INFO

INFO is INTEGER, and it's giving "here's what happened" realness:

• = 0: successful exit — we ate and left no crumbs 👑
• < 0: if INFO = -i, the i-th argument had an illegal value — not me making a mistake 😭
• > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. it's giving "the vibes were off" 💀

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🌈 Author 🌈

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 136 of file zhpev.f.

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✨ Author (again, because she's iconic) ✨

Generated automatically by Doxygen for LAPACK from the source code. no cap, that's just how we do it around here 💖

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okay bestie, that's the whole manual page. you're now officially an expert on zhpev.f. go forth and compute those eigenvalues and eigenvectors like the main character you are 🦋✨

this masterpiece was generated by Doxygen for LAPACK from the source code, and it's serving LAPACK Version 3.12.0 realness. periodt. 💅🎀