SRC/slasda.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

🌸 NAME 🌸

SRC/slasda.f — this is the page for our Unix/Linux bestie in the Library Functions Manual. The header calls it SRC/slasda.f(3), and we are absolutely reading it together 💖.

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine slasda (icompq, smlsiz, n, sqre, d, e, u, ldu, vt, k, difl,
    difr, z, poles, givptr, givcol, ldgcol, perm, givnum, c, s, work,
    iwork, info)

SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

💫 Function/Subroutine Documentation 💫

subroutine slasda (integer icompq, integer smlsiz, integer n, integer sqre,
    real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, *
    ) u, integer ldu, real, dimension( ldu, * ) vt, integer, dimension( * )
    k, real, dimension( ldu, * ) difl, real, dimension( ldu, * ) difr, real,
    dimension( ldu, * ) z, real, dimension( ldu, * ) poles, integer,
    dimension( * ) givptr, integer, dimension( ldgcol, * ) givcol, integer
    ldgcol, integer, dimension( ldgcol, * ) perm, real, dimension( ldu, * )
    givnum, real, dimension( * ) c, real, dimension( * ) s, real, dimension(
    * ) work, integer, dimension( * ) iwork, integer info)

SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

🌟 Purpose 🌟

Using a divide and conquer approach, SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE. The algorithm computes the singular values in the SVD B = U * S * VT. The orthogonal matrices U and VT are optionally computed in compact form.

A related subroutine, SLASD0, computes the singular values and the singular vectors in explicit form.

Bestie, that is the whole vibe: divide and conquer, compact form optional, and SLASD0 is the related subroutine doing the explicit-form thing 💅.

🎀 Parameters 🎀

  • ICOMPQ — ICOMPQ is INTEGER. Specifies whether singular vectors are to be computed in compact form, as follows: = 0: Compute singular values only. = 1: Compute singular vectors of upper bidiagonal matrix in compact form.
  • SMLSIZ — SMLSIZ is INTEGER. The maximum size of the subproblems at the bottom of the computation tree.
  • N — N is INTEGER. The row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array D.
  • SQRE — SQRE is INTEGER. Specifies the column dimension of the bidiagonal matrix. = 0: The bidiagonal matrix has column dimension M = N; = 1: The bidiagonal matrix has column dimension M = N + 1.
  • D — D is REAL array, dimension ( N ). On entry D contains the main diagonal of the bidiagonal matrix. On exit D, if INFO = 0, contains its singular values.
  • E — E is REAL array, dimension ( M-1 ). Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed.
  • U — U is REAL array, dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left singular vector matrices of all subproblems at the bottom level.
  • LDU — LDU is INTEGER, LDU = > N. The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z.
  • VT — VT is REAL array, dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right singular vector matrices of all subproblems at the bottom level.
  • K — K is INTEGER array, dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th secular equation on the computation tree.
  • DIFL — DIFL is REAL array, dimension ( LDU, NLVL ), where NLVL = floor(log_2 (N/SMLSIZ))).
  • DIFR — DIFR is REAL array, dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and dimension ( N ) if ICOMPQ = 0. If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) record distances between singular values on the I-th level and singular values on the (I -1)-th level, and DIFR(1:N, 2 * I ) contains the normalizing factors for the right singular vector matrix. See SLASD8 for details.
  • Z — Z is REAL array, dimension ( LDU, NLVL ) if ICOMPQ = 1 and dimension ( N ) if ICOMPQ = 0. The first K elements of Z(1, I) contain the components of the deflation-adjusted updating row vector for subproblems on the I-th level.
  • POLES — POLES is REAL array, dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and POLES(1, 2*I) contain the new and old singular values involved in the secular equations on the I-th level.
  • GIVPTR — GIVPTR is INTEGER array, dimension ( N ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records the number of Givens rotations performed on the I-th problem on the computation tree.
  • GIVCOL — GIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations of Givens rotations performed on the I-th level on the computation tree.
  • LDGCOL — LDGCOL is INTEGER, LDGCOL = > N. The leading dimension of arrays GIVCOL and PERM.
  • PERM — PERM is INTEGER array, dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records permutations done on the I-th level of the computation tree.
  • GIVNUM — GIVNUM is REAL array, dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-values of Givens rotations performed on the I-th level on the computation tree.
  • C — C is REAL array, dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 and the I-th subproblem is not square, on exit, C( I ) contains the C-value of a Givens rotation related to the right null space of the I-th subproblem.
  • S — S is REAL array, dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 and the I-th subproblem is not square, on exit, S( I ) contains the S-value of a Givens rotation related to the right null space of the I-th subproblem.
  • WORK — WORK is REAL array, dimension (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).
  • IWORK — IWORK is INTEGER array, dimension (7*N).
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = 1, a singular value 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 at line 270 of file slasda.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

Okay bestie, that’s the whole page 💖. The footer has no date listed, but it does say LAPACK Version 3.12.0 and SRC/slasda.f(3) — and it was generated automatically by Doxygen for LAPACK from the source code. Slay, we got every detail 🎀✨

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