SRC/dsyevd.f(3)

💜 SRC/dsyevd.f — like, the LAPACK manual page, bestie

okay so this is a page from the LAPACK Library Functions Manual, and it's all about dsyevd — one little subroutine that does so much. Sit down, grab a strawberry 🍓, we're gonna go through it together, no cap.

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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 — that's the one-liner, and honestly? iconic.

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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. periodt. 💅

🎀 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 yeah — the algorithm is that girl (divide and conquer), but she charges rent in workspace. N² extra, bestie. budget accordingly. 😭

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🔥 Parameters 🔥

• JOBZ — it's CHARACTER*1, and here's the vibe check:
  • = 'N': compute eigenvalues only;
  • = 'V': compute eigenvalues and eigenvectors.
• UPLO — also CHARACTER*1, pick your triangle:
  • = 'U': upper triangle of A is stored;
  • = 'L': lower triangle of A is stored.
• N — INTEGER, the order of the matrix A. Constraint: N >= 0. (zero is fine, don't stress 🧚)
• A — DOUBLE PRECISION array, dimension (LDA, N). On entry, it's the symmetric matrix A: if UPLO = 'U', the leading N-by-N upper triangular part of A holds the upper triangular part of the matrix A; if UPLO = 'L', the leading N-by-N lower triangular part of A holds 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. deceased. 💀

• LDA — INTEGER, the leading dimension of the array A. Needs LDA >= max(1,N). respect the leading dimension, it's the main character.
• W — DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues come out in ascending order. cute and organized 🌸
• WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. she tells you the size she actually wanted. 🙈
• LWORK — INTEGER, the dimension of the array WORK. the lore:
  • 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 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. so yes, -1 is a legit move, it's the "just tell me the size bestie" flag. ✨

• 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, 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, different array 💅

• INFO — INTEGER, the receipts:
  • = 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).

😭 yeah. if you see a positive INFO, do the math above to find exactly which submatrix ghosted you.

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👑 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.

shoutout Sven for the INFO glow-up, fr fr 🫶

Definition at line 175 of file dsyevd.f.

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⭐ Author (again, but the auto-generated one) ⭐

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie — every flag, every boundary, every triangle, every -1 query, all of it. slay. 💖

LAPACK, Version 3.12.0, SRC/dsyevd.f(3) — mwah, that's the version and date, catch you in the next manpage 🌈✨🎀