SRC/chpevd.f(3)

✨ SRC/chpevd.f — Library Functions Manual ✨

okay bestie, welcome to SRC/chpevd.f(3) 💅 this is a whole LAPACK situation and it's genuinely iconic, so let's get into it. 🎀

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🌸 NAME 🌸

SRC/chpevd.f — literally the file name, that's it, that's the name 🫶

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines

subroutine chpevd (jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork,
    lrwork, iwork, liwork, info)

CHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices — ok so that's what it does, and yes, "OTHER matrices" is exactly what the manpage says, no cap. 💀

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💖 Function/Subroutine Documentation 💖

🌈 subroutine chpevd

subroutine chpevd (character jobz, character uplo, integer n, complex,
    dimension( * ) ap, real, dimension( * ) w, complex, dimension( ldz, * )
    z, integer ldz, complex, dimension( * ) work, integer lwork, real,
    dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

CHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices — same energy as the synopsis, and honestly it ate. 🔥

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👑 Purpose

CHPEVD 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.

so like, all the eigenvalues, optionally eigenvectors, complex Hermitian matrix A, packed storage. and if you want the eigenvectors it goes full divide and conquer which is very main character energy. 🧚✨

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🎀 Parameters

• JOBZ — this one is CHARACTER*1 💅
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• UPLO — also CHARACTER*1, cute 🦋
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — INTEGER. The order of the matrix A. N >= 0. periodt.
• AP — COMPLEX 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. 👀 so yes, your input gets rewritten, that's the vibe.

• W — REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order. sorted, slay. ⭐
• Z — COMPLEX 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. 🙈 ignored, honestly relatable.
• LDZ — INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the required LWORK.
• LWORK — 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. 🫶 peek before you commit, honestly iconic behaviour.

• RWORK — REAL array, dimension (MAX(1,LRWORK)). On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
• LRWORK — 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. literally same deal as LWORK bestie 💖

• IWORK — INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
• LIWORK — 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. (yes, that's three for three, the workspace query trio ate 🍓)

• INFO — INTEGER. the vibe check of the whole operation:
  • = 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. 💀 dramatic but true.

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🧚 Author

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

Definition at line 192 of file chpevd.f. 📍

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💜 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. not a human, just vibes 🤖✨

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ok that's the whole page bestie, every flag, every array dimension, every XERBLA warning — nothing skipped, we keep the facts exact and the energy immaculate. 💅

LAPACK · Version 3.12.0 · SRC/chpevd.f(3) — mwah, that's the footer, signing off 🫶🌸