SRC/zheev.f(3)

💜 SRC/zheev.f(3) — bestie's guide to ZHEEV 💜

ok so this page lives in the Library Functions Manual (yes it's giving "library functions" energy) and it's literally all about one subroutine. buckle up 🎀

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✨ NAME ✨

SRC/zheev.f — that's the file, that's the vibe, no notes 💅

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines

• subroutine zheev (jobz, uplo, n, a, lda, w, work, lwork, rwork, info) — ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices 🔥

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✨ Function/Subroutine Documentation ✨

subroutine zheev (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 info)

ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices 🦋

💖 Purpose:

!>
!> ZHEEV computes all eigenvalues and, optionally, eigenvectors of a
!> complex Hermitian matrix A.
!>

so yeah, ALL the eigenvalues, and if you ask nicely (aka JOBZ='V') you also get the eigenvectors of a complex Hermitian matrix A. main character energy fr fr 👑

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🌈 Parameters

• JOBZ — JOBZ is CHARACTER*1
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — N is INTEGER The order of the matrix A. Constraint: N >= 0. ✨
• A — A is COMPLEX*16 array, dimension (LDA, N) On entry, 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. 💀 yeah she gets wrecked, that's just how it is
• LDA — LDA is INTEGER The leading dimension of the array A. Constraint: LDA >= max(1,N).
• W — W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 🍓 (sorted, as a treat)
• WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 👑
• LWORK — LWORK is INTEGER The length of the array WORK. Constraint: LWORK >= max(1,2*N-1). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the blocksize for ZHETRD returned by ILAENV. slay ✨

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. (that last bit is the important part, ngl — no XERBLA yelling at you 🙈)

• RWORK — RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
• INFO — INFO is INTEGER
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. 😭 it literally didn't converge, sobbing

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🧚 Author

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

Definition at line 138 of file zheev.f. 📍

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⭐ Author

Generated automatically by Doxygen for LAPACK from the source code. (the robots wrote this one, not me 💅)

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LAPACK — Version 3.12.0 — SRC/zheev.f(3) 🫶

k that's the whole page, every single flag and constraint intact, go forth and diagonalize your Hermitian bestie 💖✨🦋