hpev(3)

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version 3.12.1 · 9 versions
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hpev(3): eig, QR iteration ✨

okay bestie, this is the hpev(3) page from the Library Functions Manual, and it's giving packed-matrix LAPACK realness 💅. We're talking eigenvalues, eigenvectors, and a whole little family of routines: chpev, dspev, sspev, and zhpev. Buckle up 🎀

💖 NAME 💖

hpev — {hp,sp}ev: eig, QR iteration

🌸 SYNOPSIS 🌸

Functions

  • chpev — 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
  • dspev — subroutine dspev (jobz, uplo, n, ap, w, z, ldz, work, info) — DSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
  • sspev — subroutine sspev (jobz, uplo, n, ap, w, z, ldz, work, info) — SSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
  • zhpev — subroutine zhpev (jobz, uplo, n, ap, w, z, ldz, work, rwork, info) — ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

🦋 Detailed Description 🦋

This section is basically a title card in the original page, so no extra technical tea here, bestie. The actual function lore lives under Function Documentation 👇

👑 Function Documentation 👑

💜 chpev 💜

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 is the complex Hermitian, packed-storage routine: it computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage. Iconic behavior, honestly 💅

🎀 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, this is 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 AP like this:

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. If UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A. So yeah, your input gets absolutely redecorated 🫠

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. She's off duty 💀

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.
Converge or explain yourself, bestie 😭 The INFO > 0 case means the algorithm did not fully converge.

🌟 Author 🌟

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

Definition at line 136 of file chpev.f.

💙 dspev 💙

subroutine dspev (character jobz, character uplo, integer n, double
       precision, dimension( * ) ap, double precision, dimension( * ) w, double
       precision, dimension( ldz, * ) z, integer ldz, double precision,
       dimension( * ) work, integer info)

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

✨ Purpose ✨

DSPEV computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage. Double precision, packed storage, main character energy 🔥

🎀 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 DOUBLE PRECISION array, dimension (N*(N+1)/2)

On entry, the upper or lower triangle of the symmetric 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. If UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A. Same vibe: your packed triangle is getting a whole new look ✨

W — W is DOUBLE PRECISION array, dimension (N)

If INFO = 0, the eigenvalues in ascending order.

Z — Z is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (3*N)

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.

🌟 Author 🌟

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

Definition at line 129 of file dspev.f.

💚 sspev 💚

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

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

✨ Purpose ✨

SSPEV computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage. Real symmetric, packed, single precision — she's serving exactly what the name says 🍓

🎀 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 REAL array, dimension (N*(N+1)/2)

On entry, the upper or lower triangle of the symmetric 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. If UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A. The packed triangle gets a glow-up and you just have to live with it 💅

W — W is REAL array, dimension (N)

If INFO = 0, the eigenvalues in ascending order.

Z — Z is REAL 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 REAL array, dimension (3*N)

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.

🌟 Author 🌟

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

Definition at line 129 of file sspev.f.

💖 subroutine zhpev 💖

   subroutine zhpev (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,
       double precision, dimension( * ) rwork, integer info)

okay bestie, the doc's one-liner is literally: “ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices.” Not me adding “OTHER” — that's the text. 💅

✨ Purpose ✨

ZHPEV computes all the eigenvalues and, optionally, the eigenvectors of a complex Hermitian matrix in packed storage. That's the whole assignment. ✨

🎀 Parameters 🎀

  • JOBZ — CHARACTER*1. The switch for what you actually want:
    • = 'N': Compute eigenvalues only;
    • = 'V': Compute eigenvalues and eigenvectors.
  • UPLO — CHARACTER*1. Tells it which triangle of A you packed:
    • = '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, this is 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 AP like this:
    • 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 yeah, your input gets ate. 💀

  • W — DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order. Slay, sorted. ✨
  • 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. Don't even look at it, bestie. 🙈
  • 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, 2*N-1)). Workspace. It's giving backstage crew. 🫶
  • RWORK — DOUBLE PRECISION array, dimension (max(1, 3*N-2)). More workspace. 💅
  • INFO — INTEGER. The vibe check at the end:
    • = 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.

🌸 Author 🌸

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

📌 Definition at line 136 of file zhpev.f.

Author Generated automatically by Doxygen for LAPACK from the source code.

💖 and that's the whole hpev(3) moment, bestie — brought to you by LAPACK Version 3.12.0, page hpev(3). Footer vibes only, no cap. 🎀✨

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