DSYEVD(3)

💖 DSYEVD 💖

okay bestie, so this page is from dsyevd.f(3) — it lives in the LAPACK Library Functions Manual and the file path is /home/abui...RC/dsyevd.f(3). Yes the header is a whole path, don't ask, it's giving build-system realness 😭

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsyevd.f

that's it. that's the name. it's literally just the file path and honestly? iconic. 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine DSYEVD (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork,
    info)

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

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🎀 Function/Subroutine Documentation 🎀

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.
!>

so like — it does ALL the eigenvalues, and if you want the eigenvectors too it'll hand them over, and it's out here using a divide and conquer algorithm for the eigenvector part (main character energy fr fr 👑). and heads up: because it's out here using BLAS level 3 heavily, DSYEVD needs N**2 more workspace than DSYEVX does. that's the tradeoff bestie, no cap 🫶

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🌈 Parameters 🌈

JOBZ

!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors.
!>

JOBZ is CHARACTER*1 — it's literally the "what do you want from me" switch 🎀

• 'N' — eigenvalues only, keep it light
• 'V' — eigenvalues and eigenvectors, give me everything

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

UPLO is CHARACTER*1 — which triangle of A are we actually storing, bestie? 🤔

• '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.
!>

N is INTEGER, it's the order of the matrix A, and N >= 0 — no negative girlies allowed 🙈

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.
!>

A is a DOUBLE PRECISION array, dimension (LDA, N) — this is the moment, the actual matrix 🦋

On entry: it's 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.

⚠️ but 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. deleted. she's not coming back 💀 so don't come crying to me if you needed that data, bestie.

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

LDA is INTEGER — the leading dimension of the array A, and LDA >= max(1,N) ⭐

W

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

W is a DOUBLE PRECISION array, dimension (N) — if INFO = 0, this is where the eigenvalues come out, in ascending order 🎀 she's organized, she's tidy, we love her.

WORK

!>          WORK is DOUBLE PRECISION array,
!>                                         dimension (LWORK)
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>

WORK is a DOUBLE PRECISION array, dimension (LWORK). On exit, if INFO = 0, WORK(1) returns the optimal LWORK 🌸 (yes, position 1 of the workspace array is secretly a little note-to-self about how much workspace you should've used, iykyk)

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.
!>

LWORK is INTEGER — the dimension of the array WORK. here's the size chart bestie, memorize it 🧚

• 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.

and here's the fun part 🎉 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. it's the "just tell me how much room I need, I'm not doing the math yet" option and honestly? relatable 💅

IWORK

!>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
!>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
!>

IWORK is an 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 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.
!>

LIWORK is INTEGER — the dimension of the array IWORK. the integer-flavored size chart 🍓

• 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 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. same deal as LWORK = -1, she's just doing recon 🔥

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).
!>

INFO is INTEGER — the vibe report 😭

• = 0 — successful exit, we ate, no notes 👑
• < 0 — if INFO = -i, the i-th argument had an illegal value (you passed something cursed, bestie)
• > 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. and 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) 🧚 (yes it's telling you exactly which submatrix ghosted you, very thoughtful of her)

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🦋 Author 🦋

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

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💐 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.

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⭐ Definition at line 176 of file dsyevd.f. ⭐

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🌷 Author 🌷

Generated automatically by Doxygen for LAPACK from the source code. (she didn't write herself, a robot did, and we respect her for it 🤖💖)

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🫶 and that's the whole page bestie! LAPACK, Version 3.12.0, dated /home/abui...RC/dsyevd.f(3) — mwah, go forth and diagonalize 💅✨🌸