SGESDD(3)

💅 SGESDD(3) — Library Functions Manual 🦋

okay bestie, welcome to the group chat where we learn the real SGESDD tea ☕✨. This page lives in the Library Functions Manual, and we are about to get into singular value decomposition like it's the main character.

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✨ NAME ✨

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

Literally the file path, bestie — that's the name on this one 💖.

🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

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

SGESDD

🦋 Function/Subroutine Documentation 🦋

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

SGESDD

💖 Purpose 💖

ok so SGESDD computes the singular value decomposition (SVD) of a real M-by-N matrix A, and it can optionally compute the left and right singular vectors too. If singular vectors are desired, it uses a divide-and-conquer algorithm. iconic behavior, no cap 💅

The SVD is written like this:

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. periodt 💀✨

🎀 Parameters 🎀

🍓 JOBZ 🍓

JOBZ is CHARACTER*1 and it 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 REAL 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 REAL array, dimension (min(M,N)).

The singular values of A, sorted so that S(i) >= S(i+1).

🍓 U 🍓

U is REAL 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 REAL 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 REAL 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. bestie, pls query, your future self will thank you 🫶

🍓 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: SBDSDC 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 sgesdd.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie! LAPACK Version 3.12.0, and the source/version footer says /home/abui...RC/sgesdd.f(3). Slay 💅✨