DLASDA(3)

okay so bestie, this page is from the Library Functions Manual, and the header path is /home/abui...RC/dlasda.f(3) — yes, it’s truncated like that, iconic 💅. Buckle up, because DLASDA is a whole LAPACK subroutine and we are keeping every single detail.

---

💖 NAME 💖

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

That’s the file, bestie. That’s the NAME section. No cap.

---

✨ SYNOPSIS ✨

Functions/Subroutines

Here’s the call signature, verbatim, because we do not mess with code:

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

• subroutine DLASDA — DLASDA 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 🌸

Here’s the full signature again with all the types and dimensions, exactly:

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

DLASDA 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, DLASDA 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, DLASD0, computes the singular values and the singular vectors in explicit form.

Parameters 📋

Every parameter, every value, no skipping:

• 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension ( M-1 ). Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed.
• U — U is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension ( LDU, NLVL ), where NLVL = floor(log_2 (N/SMLSIZ))).
• DIFR — DIFR is DOUBLE PRECISION 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 DLASD8 for details.
• Z — Z is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 dlasda.f.

---

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bestie, that’s the whole page — the footer says LAPACK, Version 3.12.0, and the path /home/abui...RC/dlasda.f(3). You ate this, fr fr 💅✨