SRC/slasdq.f(3)

💖 SRC/slasdq.f(3) 💖

okay so bestie, this is a page from the Library Functions Manual and it's serving pure LAPACK energy 🫶. The whole thing is literally about SRC/slasdq.f, no cap.

✨ NAME ✨

SRC/slasdq.f

✨ SYNOPSIS ✨

🌈 Functions/Subroutines

subroutine slasdq (uplo, sqre, n, ncvt, nru, ncc, d, e, vt, ldvt, u,
           ldu, c, ldc, work, info)

The summary is giving: SLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

✨ Function/Subroutine Documentation ✨

🎀 subroutine slasdq

subroutine slasdq (character uplo, integer sqre, integer n, integer ncvt,
       integer nru, integer ncc, real, dimension( * ) d, real, dimension( * )
       e, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( ldu, *
       ) u, integer ldu, real, dimension( ldc, * ) c, integer ldc, real,
       dimension( * ) work, integer info)

SLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc. That's the main character energy of this whole page, fr fr.

🦋 Purpose

okay so here's the tea: SLASDQ computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired. Letting B denote the input bidiagonal matrix, the algorithm computes orthogonal matrices Q and P such that:

B = Q * S * P**T

where P**T denotes the transpose of P. The singular values S are overwritten on D. Obsessed with that.

The input matrix U is changed to U * Q if desired.

The input matrix VT is changed to P**T * VT if desired.

The input matrix C is changed to Q**T * C if desired.

It also points at J. Demmel and W. Kahan, LAPACK Working Note #3, for a detailed description of the algorithm. iykyk 🧚

🌸 Parameters

• UPLO — CHARACTER*1. On entry, UPLO specifies whether the input bidiagonal matrix is upper or lower bidiagonal, and whether it is square are not.
  • UPLO = 'U' or 'u' → B is upper bidiagonal.
  • UPLO = 'L' or 'l' → B is lower bidiagonal.
• SQRE — INTEGER.
  • = 0: then the input matrix is N-by-N.
  • = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and (N+1)-by-N if UPLU = 'L'.
  • The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE >= N columns.
• N — INTEGER. On entry, N specifies the number of rows and columns in the matrix. N must be at least 0.
• NCVT — INTEGER. On entry, NCVT specifies the number of columns of the matrix VT. NCVT must be at least 0.
• NRU — INTEGER. On entry, NRU specifies the number of rows of the matrix U. NRU must be at least 0.
• NCC — INTEGER. On entry, NCC specifies the number of columns of the matrix C. NCC must be at least 0.
• D — REAL array, dimension (N). On entry, D contains the diagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in ascending order.
• E — REAL array. dimension is (N-1) if SQRE = 0 and N if SQRE = 1. On entry, the entries of E contain the offdiagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, E will contain 0. If the algorithm does not converge, D and E will contain the diagonal and superdiagonal entries of a bidiagonal matrix orthogonally equivalent to the one given as input.
• VT — REAL array, dimension (LDVT, NCVT). On entry, contains a matrix which on exit has been premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0).
• LDVT — INTEGER. On entry, LDVT specifies the leading dimension of VT as declared in the calling (sub) program. LDVT must be at least 1. If NCVT is nonzero LDVT must also be at least N.
• U — REAL array, dimension (LDU, N). On entry, contains a matrix which on exit has been postmultiplied by Q, dimension NRU-by-N if SQRE = 0 and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0).
• LDU — INTEGER. On entry, LDU specifies the leading dimension of U as declared in the calling (sub) program. LDU must be at least max( 1, NRU ) .
• C — REAL array, dimension (LDC, NCC). On entry, contains an N-by-NCC matrix which on exit has been premultiplied by Q**T dimension N-by-NCC if SQRE = 0 and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0).
• LDC — INTEGER. On entry, LDC specifies the leading dimension of C as declared in the calling (sub) program. LDC must be at least 1. If NCC is nonzero, LDC must also be at least N.
• WORK — REAL array, dimension (4*N). Workspace. Only referenced if one of NCVT, NRU, or NCC is nonzero, and if N is at least 2.
• INFO — INTEGER. On exit, a value of 0 indicates a successful exit. If INFO < 0, argument number -INFO is illegal. If INFO > 0, the algorithm did not converge, and INFO specifies how many superdiagonals did not converge.

👑 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

Definition at line 209 of file slasdq.f.

💻 Author

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and that's the whole page, bestie 💅 — source/version vibes from LAPACK Version 3.12.0, on SRC/slasdq.f(3). mwah 💖