SGESVD(3)

💅 SGESVD — Library Functions Manual 💅

bestie, welcome to the sgesvd.f(3) page from the Library Functions Manual. Header path vibes: /home/abui...RC/sgesvd.f(3). This is the LAPACK routine for SVD, and yes she ate 💖✨

💖 NAME 💖

This page’s name is literally this exact path, no cap:

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

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine SGESVD (jobu, jobvt, m, n, a, lda, s, u, ldu, vt, ldvt, work,
    lwork, info)
     SGESVD computes the singular value decomposition (SVD) for GE
    matrices

🌸 Function/Subroutine Documentation 🌸

subroutine SGESVD (character jobu, character jobvt, 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 info)
     SGESVD computes the singular value decomposition (SVD) for GE matrices

🎀 Purpose 🎀

Okay so SGESVD computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors. The SVD is written like this, iconic behavior:

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 V**T, not V. That’s the whole tea.

🌈 Parameters 🌈

💜 JOBU

JOBU is CHARACTER*1 — specifies options for computing all or part of the matrix U:

• = 'A': all M columns of U are returned in array U:
• = 'S': the first min(m,n) columns of U (the left singular vectors) are returned in the array U;
• = 'O': the first min(m,n) columns of U (the left singular vectors) are overwritten on the array A;
• = 'N': no columns of U (no left singular vectors) are computed.

💜 JOBVT

JOBVT is CHARACTER*1 — specifies options for computing all or part of the matrix V**T:

• = 'A': all N rows of V**T are returned in the array VT;
• = 'S': the first min(m,n) rows of V**T (the right singular vectors) are returned in the array VT;
• = 'O': the first min(m,n) rows of V**T (the right singular vectors) are overwritten on the array A;
• = 'N': no rows of V**T (no right singular vectors) are computed.

🚨 Real talk: JOBVT and JOBU cannot both be 'O'.

💜 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 JOBU = 'O', A is overwritten with the first min(m,n) columns of U (the left singular vectors, stored columnwise);
  • if JOBVT = 'O', A is overwritten with the first min(m,n) rows of V**T (the right singular vectors, stored rowwise);
  • if JOBU .ne. 'O' and JOBVT .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) — (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.

• If JOBU = 'A', U contains the M-by-M orthogonal matrix U;
• if JOBU = 'S', U contains the first min(m,n) columns of U (the left singular vectors, stored columnwise);
• if JOBU = 'N' or 'O', U is not referenced.

💜 LDU

LDU is INTEGER — the leading dimension of the array U. LDU >= 1; if JOBU = 'S' or 'A', LDU >= M.

💜 VT

VT is REAL array, dimension (LDVT,N).

• If JOBVT = 'A', VT contains the N-by-N orthogonal matrix V**T;
• if JOBVT = 'S', VT contains the first min(m,n) rows of V**T (the right singular vectors, stored rowwise);
• if JOBVT = 'N' or 'O', VT is not referenced.

💜 LDVT

LDVT is INTEGER — the leading dimension of the array VT. LDVT >= 1; if JOBVT = 'A', LDVT >= N; if JOBVT = '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;
• if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged superdiagonal elements of an upper bidiagonal matrix B whose diagonal is in S (not necessarily sorted). B satisfies A = U * B * VT, so it has the same singular values as A, and singular vectors related by U and VT.

💜 LWORK

LWORK is INTEGER — the dimension of the array WORK.

LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code):

• PATH 1 (M much larger than N, JOBU='N')
• PATH 1t (N much larger than M, JOBVT='N')

LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)) for the other paths.

For good performance, LWORK should generally be larger.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

💜 INFO

INFO is INTEGER:

• = 0: successful exit.
• < 0: if INFO = -i, the i-th argument had an illegal value.
• > 0: if SBDSQR did not converge, INFO specifies how many superdiagonals of an intermediate bidiagonal form B did not converge to zero. See the description of WORK above for details.

💖 Author 💖

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

Definition at line 209 of file sgesvd.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off bestie: that’s the tea from LAPACK Version 3.12.0, and the page path is /home/abui...RC/sgesvd.f(3). Stay slay 💖✨🦋