SRC/zhpevd.f(3)

💖 SRC/zhpevd.f 💖

okay bestie, this is a page from the Library Functions Manual and it's all about zhpevd.f, a LAPACK routine that literally eats Hermitian matrices for breakfast and spits out eigenvalues (and eigenvectors if you ask nicely). no cap, it's iconic 🎀

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🌸 NAME 🌸

SRC/zhpevd.f

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🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

• subroutine zhpevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info) — ZHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 💅

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💅 Function/Subroutine Documentation 💅

🎀 subroutine zhpevd 🎀

subroutine zhpevd (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,
    integer lwork, double precision, dimension( * ) rwork, integer lrwork,
    integer, dimension( * ) iwork, integer liwork, integer info)

ZHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 🦋

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✨ Purpose ✨

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

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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. N >= 0. ✨
• AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. 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, AP is overwritten by values generated during the reduction to tridiagonal form. 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. 💀 (like, it literally replaces your matrix, so don't come crying later)

• W — W is DOUBLE PRECISION array, dimension (N); if INFO = 0, the eigenvalues in ascending order. 🌈
• 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. 🎀
• LDZ — LDZ is INTEGER; the leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). 👑
• WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)); on exit, if INFO = 0, WORK(1) returns the required LWORK. ⭐
• LWORK — LWORK is INTEGER; the dimension of array WORK.
  • If N <= 1, LWORK must be at least 1.
  • If JOBZ = 'N' and N > 1, LWORK must be at least N.
  • If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the required 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. 🧚 (workspace query slay)

• RWORK — RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)); on exit, if INFO = 0, RWORK(1) returns the required LRWORK. 💜
• LRWORK — LRWORK is INTEGER; the dimension of array RWORK.
  • 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 required 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. 🌸

• IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)); on exit, if INFO = 0, IWORK(1) returns the required LIWORK. 🍓
• LIWORK — LIWORK is INTEGER; the dimension of array IWORK.
  • If JOBZ = 'N' or 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 required 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. 🙈

• 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. 💀 (like, it tried and it literally couldn't, no cap)

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👑 Author 👑

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

Definition at line 192 of file zhpevd.f. ✨

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🌟 Author (the meta one) 🌟

Generated automatically by Doxygen for LAPACK from the source code. 🤖 (not me writing my own manpage, periodt)

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okay bestie that's the whole thing, every single flag and value accounted for, and honestly? it ate. 🫶💖

LAPACK — Version 3.12.0 — that's the footer, bestie, and this page was brought to you by SRC/zhpevd.f(3), signing off with main character energy. 💅✨🎀