SRC/dgesdd.f(3)

SRC/dgesdd.f(3) 💅✨

Okay bestie, this is the SRC/dgesdd.f(3) Library Functions Manual page, and it is so DGESDD — the divide-and-conquer SVD main character. We are keeping every flag, dimension, formula, and exit code fr fr, just with better vibes. 🫶

NAME

SRC/dgesdd.f

SYNOPSIS

Functions/Subroutines

subroutine dgesdd (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork,
    iwork, info)

DGESDD

Function/Subroutine Documentation 💖

subroutine dgesdd (character jobz, integer m, integer n, double precision,
    dimension( lda, * ) a, integer lda, double precision, dimension( * ) s,
    double precision, dimension( ldu, * ) u, integer ldu, double precision,
    dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * )
    work, integer lwork, integer, dimension( * ) iwork, integer info)

DGESDD

Purpose 🌸

Bestie, DGESDD computes the singular value decomposition (SVD) of a real M-by-N matrix A, and optionally computes the left and right singular vectors. If singular vectors are desired, it uses a divide-and-conquer algorithm. Iconic behavior, no cap.

The SVD is written as:

A = U * SIGMA * transpose(V)

where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A.

Note that the routine returns VT = V**T, not V. Not me forgetting the transpose, bestie. 🙈

Parameters 🎀

• JOBZ — CHARACTER*1. Specifies options for computing all or part of the matrix U:
  • = 'A': all M columns of U and all N rows of V**T are returned in the arrays U and VT;
  • = 'S': the first min(M,N) columns of U and the first min(M,N) rows of V**T are returned in the arrays U and VT;
  • = 'O': If M >= N, the first N columns of U are overwritten on the array A and all rows of V**T are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**T are overwritten in the array A;
  • = 'N': no columns of U or rows of V**T are computed.
• M — INTEGER. The number of rows of the input matrix A. M >= 0.
• N — INTEGER. The number of columns of the input matrix A. N >= 0.
• A — DOUBLE PRECISION array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit:
  • if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of V**T (the right singular vectors, stored rowwise) otherwise.
  • if JOBZ .ne. 'O', the contents of A are destroyed.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• S — DOUBLE PRECISION array, dimension (min(M,N)). The singular values of A, sorted so that S(i) >= S(i+1).
• U — DOUBLE PRECISION array, dimension (LDU,UCOL). UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'. If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M orthogonal matrix U; if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
• LDU — INTEGER. The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
• VT — DOUBLE PRECISION array, dimension (LDVT,N). If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S', VT contains the first min(M,N) rows of V**T (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
• LDVT — INTEGER. The leading dimension of the array VT. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N).
• WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — INTEGER. The dimension of the array WORK. LWORK >= 1. If LWORK = -1, a workspace query is assumed. The optimal size for the WORK array is calculated and stored in WORK(1), and no other work except argument checking is performed.

Let mx = max(M,N) and mn = min(M,N). If JOBZ = 'N', LWORK >= 3*mn + max( mx, 7*mn ). If JOBZ = 'O', LWORK >= 3*mn + max( mx, 5*mn*mn + 4*mn ). If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn. If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx. These are not tight minimums in all cases; see comments inside code. For good performance, LWORK should generally be larger; a query is recommended.

• IWORK — INTEGER array, dimension (8*min(M,N)).
• INFO — INTEGER:
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • = -4: if A had a NAN entry.
  • > 0: DBDSDC did not converge, updating process failed.
  • = 0: successful exit.

Author 🫶

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

Contributors: 🧚

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 211 of file dgesdd.f.

Author (the auto-generated footnote) 💅

Generated automatically by Doxygen for LAPACK from the source code.

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Catch you later, bestie 💖 — this page is from LAPACK Version 3.12.0, source SRC/dgesdd.f(3), auto-generated by Doxygen for LAPACK from the source code. Periodt. ✨