ZHPEVD(3)

okay bestie, welcome to ZHPEVD(3) from the Library Functions Manual — the LAPACK page for the packed-storage complex Hermitian eigen routine. Buckle up, it’s giving “math but make it cute” 💅✨

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhpevd.f — yes, that’s the exact file path this page documents, no cap.

🌈 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

🦋 Function/Subroutine Documentation 🦋

Here’s the full typed signature, copied exactly because she is iconic and we do not mess with code:

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

✨ Purpose ✨

This absolute icon 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. And yes, the one-liner says it computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices — that’s the official vibe, fr fr.

🍓 Parameters 🍓

• JOBZ — CHARACTER*1. What do you want, bestie?
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• UPLO — CHARACTER*1. Which triangle are we storing?
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — INTEGER. The order of the matrix A. N >= 0.
• AP — 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.
• W — DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
• Z — 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 — INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — COMPLEX*16 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.
• RWORK — DOUBLE PRECISION 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.
• 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.
• INFO — 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.

Vibe check: an INFO > 0 is not a slay — it means the algorithm failed to converge, exactly as listed above. 💀

🌟 Author 🌟

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

Definition at line 192 of file zhpevd.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That’s the whole page, bestie — footer tea: source/version is LAPACK, Version 3.12.0, and the page path is /home/abui...RC/zhpevd.f(3). Mwah, go solve those Hermitian eigenvalues. 🫶