ZHEEVD(3)

💖 ZHEEVD(3) 💖 — LAPACK Library Functions Manual

okay bestie, welcome to the LAPACK Library Functions Manual page for ZHEEVD(3). This is the tea on a complex Hermitian eigenvalue solver that's lowkey iconic. ✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zheevd.f

That's the file path, bestie — not me making it up. 💅

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine ZHEEVD (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork,
    iwork, liwork, info)
     ZHEEVD computes the eigenvalues and, optionally, the left and/or
    right eigenvectors for HE matrices

🦋 Function/Subroutine Documentation 🦋

subroutine ZHEEVD (character jobz, character uplo, integer n, complex*16,
    dimension( lda, * ) a, integer lda, double precision, dimension( * ) w,
    complex*16, dimension( * ) work, integer lwork, double precision,
    dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices. Periodt. 💫

🎀 Purpose 🎀

okay so the source comment is literally:

!>
!> ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
!> complex Hermitian matrix A.  If eigenvectors are desired, it uses a
!> divide and conquer algorithm.
!>
!>

Translation: it computes all eigenvalues of a complex Hermitian matrix A, and if you want eigenvectors too, it uses a divide and conquer algorithm. Obsessed. 💜

💅 Parameters 💅

🔥 JOBZ

JOBZ is CHARACTER*1 — the vibe selector:

= 'N':  Compute eigenvalues only;
= 'V':  Compute eigenvalues and eigenvectors.

So 'N' means eigenvalues only, 'V' means eigenvalues + eigenvectors. Slay. 🎀

🔥 UPLO

UPLO is CHARACTER*1 — tells it which triangle of A is stored:

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

'U' = upper triangle of A is stored; 'L' = lower triangle of A is stored. Pick your fighter. 💅

🔥 N

N is INTEGER — the order of the matrix A. And the rule is N >= 0. No cap. 🫶

🔥 A

A is COMPLEX*16 array, dimension (LDA, N).

On entry, it's the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A.

On exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed. So yes, bestie, that triangle gets demolished — protect your data. 😭

🔥 LDA

LDA is INTEGER — the leading dimension of the array A. The rule: LDA >= max(1,N). Keep it cute and legal. ✨

🔥 W

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

🔥 WORK

WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. Iconic workspace behavior. 👑

🔥 LWORK

LWORK is INTEGER — the length of the array WORK. The minimums are:

If N <= 1,                LWORK must be at least 1.
If JOBZ  = 'N' and N > 1, LWORK must be at least N + 1.
If JOBZ  = 'V' and N > 1, LWORK must be at least 2*N + N**2.

And if LWORK = -1, then a workspace query is assumed: the routine only calculates the optimal sizes of the WORK, RWORK, and IWORK arrays, returns these values as the first entries of the WORK, RWORK, and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. That's the whole tea. 💅

🔥 RWORK

RWORK is DOUBLE PRECISION array, dimension (LRWORK). On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. 🌈

🔥 LRWORK

LRWORK is INTEGER — the dimension of the array RWORK. Minimums:

If N <= 1,                LRWORK must be at least 1.
If JOBZ  = 'N' and N > 1, LRWORK must be at least N.
If JOBZ  = 'V' and N > 1, LRWORK must be at least
                         1 + 5*N + 2*N**2.

If LRWORK = -1, then a workspace query is assumed: the routine only calculates the optimal sizes of the WORK, RWORK, and IWORK arrays, returns these values as the first entries of the WORK, RWORK, and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. Same query energy. ✨

🔥 IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. 🦋

🔥 LIWORK

LIWORK is INTEGER — the dimension of the array IWORK. Minimums:

If N <= 1,                LIWORK must be at least 1.
If JOBZ  = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed: the routine only calculates the optimal sizes of the WORK, RWORK, and IWORK arrays, returns these values as the first entries of the WORK, RWORK, and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. Query queen. 👑

🔥 INFO

INFO is INTEGER — the status report:

= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i and JOBZ = 'N', then the algorithm failed
      to converge; i off-diagonal elements of an intermediate
      tridiagonal form did not converge to zero;
      if INFO = i and JOBZ = 'V', then the algorithm failed
      to compute an eigenvalue while working on the submatrix
      lying in rows and columns INFO/(N+1) through
      mod(INFO,N+1).

So = 0 is a clean win 🎉, < 0 means an argument was illegal, and > 0 is the algorithm-failed-to-converge situation. Not me being dramatic — that's literally the source. 💀

🌟 Author 🌟

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

🌈 Further Details: 🌈

Modified description of INFO. Sven, 16 Feb 05.

👑 Contributors: 👑

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

📍 Definition 📍

Definition at line 197 of file zheevd.f.

💫 Author (generated) 💫

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page! LAPACK Version 3.12.0 and the path /home/abui...RC/zheevd.f(3) — keep those in mind. Bye, love you, stan ZHEEVD. 💖✨🎀