DGESDD(3)

DGESDD(3) 🦋✨

okay so bestie, this page is from the Library Functions Manual, page dgesdd.f(3), and it's all about the LAPACK subroutine DGESDD — the singular value decomposition girlie. 💅

💖 NAME 💖

The source file for this whole slay is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/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

okay so DGESDD computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors. If singular vectors are desired, it uses a divide-and-conquer algorithm. literally the main character algorithm. 👑

The SVD is written:

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. yes bestie, it's transposed on purpose, don't come for her. 🙈

🌸 Parameters 🌸

JOBZ

JOBZ is 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

M is INTEGER The number of rows of the input matrix A. M >= 0.

N

N is INTEGER The number of columns of the input matrix A. N >= 0.

A

A is 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

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

S

S is DOUBLE PRECISION array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1).

U

U is 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

LDU is INTEGER The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.

VT

VT is 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

LDVT is 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

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. 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

IWORK is INTEGER array, dimension (8*min(M,N))

INFO

INFO is 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 🖨️

Generated automatically by Doxygen for LAPACK from the source code.

Source/version sign-off: LAPACK Version 3.12.0 and page /home/abui...RC/dgesdd.f(3). The original footer doesn't list a date, so I'm not inventing one — integrity, bestie. 💖✨