heevd(3)

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version 3.12.1 · 9 versions
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heevd(3) — Library Functions Manual 🎀

✨ NAME ✨

heevd — {he,sy}evd: eig, divide and conquer. The whole Hermitian/symmetric eigenvalue squad, together in one manual page 💅

🌸 SYNOPSIS 🌸

🦋 Functions

  • cheevd — CHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices.
subroutine cheevd (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info)
  • dsyevd — DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices.
subroutine dsyevd (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork, info)
  • ssyevd — SSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices.
subroutine ssyevd (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork, info)
  • zheevd — ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices.
subroutine zheevd (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info)

💖 Detailed Description 💖

Okay so this is the function-by-function tea, bestie. Function Documentation is literally right below, no cap ✨

🎀 Function Documentation 🎀

🦋 subroutine cheevd

subroutine cheevd (character jobz, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) w, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

CHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices.

💜 Purpose

CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm. Iconic. 💅

🍓 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.
  • A — A is COMPLEX array, dimension (LDA, N). On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed. Gone. Periodt. 💀
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • W — W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
  • WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK — LWORK is INTEGER. The length of the array WORK.
    • If N <= 1, LWORK must be at least 1.
    • If JOBZ = 'N' and N > 1, LWORK must be at least N + 1.
    • If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2.
    • If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal 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 — RWORK is REAL array, dimension (MAX(1,LRWORK)). On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
  • LRWORK — LRWORK is INTEGER. The dimension of the 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 optimal 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 optimal LIWORK.
  • LIWORK — LIWORK is INTEGER. The dimension of the array IWORK.
    • If N <= 1, LIWORK must be at least 1.
    • If JOBZ = 'N' and 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 optimal 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 and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

💜 Author

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

🦋 Further Details

Modified description of INFO. Sven, 16 Feb 05.

🌸 Contributors

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 196 of file cheevd.f.

🦋 subroutine dsyevd

subroutine dsyevd (character jobz, character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) w, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices.

💜 Purpose

DSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm.

Because of large use of BLAS of level 3, DSYEVD needs N**2 more workspace than DSYEVX. She's hungry for workspace, bestie. 😭

🍓 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.
  • A — A is DOUBLE PRECISION array, dimension (LDA, N). On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed. Say bye to that triangle 👋💀
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • W — W is DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
  • WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK — LWORK is INTEGER. The dimension of the array WORK.
    • If N <= 1, LWORK must be at least 1.
    • If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1.
    • If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + 2*N**2.
    • If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.
  • IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

🍓 LIWORK

  • LIWORK (INTEGER) — the dimension of the IWORK array, i.e. how much integer scratch space you're handing over. The minimums are:
    • if N <= 1, LIWORK must be at least 1
    • if JOBZ = 'N' and N > 1, LIWORK must be at least 1
    • if JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N
🔮 and if LIWORK = -1, that's a workspace query bestie! The routine then only calculates the optimal sizes of the WORK and IWORK arrays, hands those values back as the first entries of the WORK and IWORK arrays, and XERBLA stays completely quiet — no error message related to LWORK or LIWORK gets thrown at you.
  • INFO (INTEGER) — the vibe report, aka did it work:
    • 0 — slay, successful exit 💅
    • < 0 — if INFO = -i, the i-th argument had an illegal value (you passed something cursed)
    • > 0 — if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero
    • > 0 — if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1)

🌸 Author 🌸

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

🫶 Contributors 🫶

  • Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
  • Modified by Francoise Tisseur, University of Tennessee
  • Modified description of INFO. Sven, 16 Feb 05.
📍 Definition at line 175 of file dsyevd.f.

✨ subroutine ssyevd ✨

subroutine ssyevd (character jobz, character uplo, integer n, real,
    dimension( lda, * ) a, integer lda, real, dimension( * ) w, real,
    dimension( * ) work, integer lwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

SSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices. Single precision edition, let's go 🎀

💜 Purpose 💜

okay so here's the whole point: SSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm. Fancy, iconic, we love her 🌈

Because of large use of BLAS of level 3, SSYEVD needs N**2 more workspace than SSYEVX. Not a glow-up that comes for free, bestie — that's the trade 💀

🎀 Parameters 🎀

  • JOBZ (CHARACTER1)* — what you actually want out of this:
    • 'N' — compute eigenvalues only
    • 'V' — compute eigenvalues and eigenvectors
  • UPLO (CHARACTER1)* — which triangle of A you've actually filled in:
    • 'U' — upper triangle of A is stored
    • 'L' — lower triangle of A is stored
  • N (INTEGER) — the order of the matrix A. N >= 0. (Zero is allowed, don't come for me.)
  • A (REAL array, dimension (LDA, N)) — the star of the show:
    • on entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A.
    • on exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A 🦋
    • if JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed 💀
⚠️ yeah, "destroyed" is the actual word in the docs. Your input matrix does not survive JOBZ = 'N'. Copy it first if you're attached to it.
  • LDA (INTEGER) — the leading dimension of the array A. LDA >= max(1,N).
  • W (REAL array, dimension (N)) — if INFO = 0, the eigenvalues in ascending order ⭐
  • WORK (REAL array, dimension (MAX(1,LWORK))) — on exit, if INFO = 0, WORK(1) returns the optimal LWORK 👑
  • LWORK (INTEGER) — the dimension of the array WORK:
    • if N <= 1, LWORK must be at least 1
    • if JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1
    • if JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + 2*N**2
🔮 if LWORK = -1, then a workspace query is assumed. The routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.
  • IWORK (INTEGER array, dimension (MAX(1,LIWORK))) — on exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
  • LIWORK (INTEGER) — the dimension of the array IWORK:
    • if N <= 1, LIWORK must be at least 1
    • if JOBZ = 'N' and N > 1, LIWORK must be at least 1
    • if JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N
🔮 and if LIWORK = -1, a workspace query is assumed again: the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns them as the first entries of the WORK and IWORK arrays, and XERBLA issues no error message related to LWORK or LIWORK.
  • INFO (INTEGER):
    • = 0 — successful exit ✅
    • < 0 — if INFO = -i, the i-th argument had an illegal value
    • > 0 — if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero
    • > 0 — if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1)

🌸 Author 🌸

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

🫶 Contributors 🫶

  • Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
  • Modified by Francoise Tisseur, University of Tennessee
  • Modified description of INFO. Sven, 16 Feb 05.
📍 Definition at line 173 of file ssyevd.f.

👑 subroutine zheevd 👑

subroutine zheevd (character jobz, character uplo, integer n, complex*16,
    dimension( lda, * ) a, integer lda, double precision, dimension( * ) w,
    complex*16, dimension( * ) work, integer lwork, double precision,
    dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices. Complex double precision, our most extra version yet 💅✨

💜 Purpose 💜

ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm. Same iconic energy as her siblings 🦋

🎀 Parameters 🎀

  • JOBZ (CHARACTER1)* — pick your fighter:
    • 'N' — compute eigenvalues only
    • 'V' — compute eigenvalues and eigenvectors
  • UPLO (CHARACTER1)*:
    • 'U' — upper triangle of A is stored
    • 'L' — lower triangle of A is stored
  • N (INTEGER) — the order of the matrix A. N >= 0.
  • A (COMPLEX16 array, dimension (LDA, N))*:
    • on entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A.
    • on exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A 🦋
    • if JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed 💀
  • LDA (INTEGER) — the leading dimension of the array A. LDA >= max(1,N).
  • W (DOUBLE PRECISION array, dimension (N)) — if INFO = 0, the eigenvalues in ascending order ⭐
  • WORK (COMPLEX16 array, dimension (MAX(1,LWORK)))* — on exit, if INFO = 0, WORK(1) returns the optimal LWORK 👑
  • LWORK (INTEGER) — the length of the array WORK:
    • if N <= 1, LWORK must be at least 1
    • if JOBZ = 'N' and N > 1, LWORK must be at least N + 1
    • if JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2
🔮 and if LWORK = -1, a workspace query is assumed: the routine only calculates the optimal 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. Three arrays, one query, no drama.
  • RWORK (DOUBLE PRECISION array, dimension (MAX(1,LRWORK))) — on exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
  • LRWORK (INTEGER) — the dimension of the 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, a workspace query is assumed; the routine only calculates the optimal 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

…and that's exactly where this chunk runs out, bestie — IWORK's whole breakdown picks up in the next part, don't go anywhere 🫶

  • IWORK — okay so this one is an INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. It's literally telling you what it wishes it had. 💖
  • LIWORK — INTEGER. It's the dimension of the array IWORK. The minimums are giving:
    • If N <= 1, LIWORK must be at least 1.
    • If JOBZ = 'N' and 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 optimal 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. Exit-status tea:
    • = 0: successful exit — periodt.
    • < 0: if INFO = -i, the i-th argument had an illegal value.
    • > 0: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

👑 Author

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

🔍 Further Details:

Modified description of INFO. Sven, 16 Feb 05.

🫶 Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

📌 Definition

Definition at line 196 of file zheevd.f.

🧚 Author

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Okay that's the whole heevd(3) page, bestie. 💖 Cute sign-off / footer vibe: source is LAPACK, version is Version 3.12.0, and the page is heevd(3) — that's the tea. 💅✨

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