SRC/chpev.f(3)

✨ SRC/chpev.f ✨

okay so bestie, this is a page from the LAPACK manual — that's the Library Functions Manual, iykyk — and it's literally all about one little subroutine. buckle up 💅

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🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines

• subroutine chpev (jobz, uplo, n, ap, w, z, ldz, work, rwork, info) — CHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices ✨

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💖 Function/Subroutine Documentation 💖

subroutine chpev (character jobz, character uplo, integer n, complex,
    dimension( * ) ap, real, dimension( * ) w, complex, dimension( ldz, * )
    z, integer ldz, complex, dimension( * ) work, real, dimension( * )
    rwork, integer info)

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

🦋 Purpose

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

so yeah — all the eigenvalues, and eigenvectors too if you ask nicely, of a complex Hermitian matrix in packed storage. that's the whole gig 🫶

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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 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.
!>

⚠️ heads up bestie: AP gets overwritten on exit — the reduction to tridiagonal form T just moves right on in and takes over those elements. no cap, your input triangle is gone 🙈

🍓 W

!>          W is REAL array, dimension (N)
!>          If INFO = 0, the eigenvalues in ascending order.
!>

🍓 Z

!>          Z is 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.
!>

🍓 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 array, dimension (max(1, 2*N-1))
!>

🍓 RWORK

!>          RWORK is REAL 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.
!>

💀 INFO > 0 means the algorithm failed to converge — specifically, i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. not the slay you wanted, but at least you know exactly what went down.

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👑 Author

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

Definition at line 136 of file chpev.f. 📍

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💜 Author

Generated automatically by Doxygen for LAPACK from the source code. (yes bestie, a robot wrote this and it still ate 🤖✨)

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LAPACK · Version 3.12.0 · SRC/chpev.f(3)

that's the page, fr fr — go forth and diagonalize 🧚‍♀️💖