SRC/clalsa.f(3)

okay bestie, this is the manual page for SRC/clalsa.f(3) — a whole LAPACK library functions manual moment. Buckle up, because CLALSA is doing compact-form SVD business and it is not here to be vague. 💖✨

NAME 🌸

SRC/clalsa.f — and yes, that's literally the whole name section. iconic minimalism.

SYNOPSIS ✨

Functions/Subroutines

subroutine clalsa (icompq, smlsiz, n, nrhs, b, ldb, bx, ldbx, u, ldu,
    vt, k, difl, difr, z, poles, givptr, givcol, ldgcol, perm, givnum,
    c, s, rwork, iwork, info)

CLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.

Function/Subroutine Documentation 💅

subroutine clalsa (integer icompq, integer smlsiz, integer n, integer nrhs,
    complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldbx, *
    ) bx, integer ldbx, 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( * ) rwork,
    integer, dimension( * ) iwork, integer info)

CLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.

Purpose: 🎯

Bestie, here's the whole plot: CLALSA is an intermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (the singular vectors are computed as products of simple orthogonal matrices). No cap.

If ICOMPQ = 0, CLALSA applies the inverse of the left singular vector matrix of an upper bidiagonal matrix to the right hand side; and if ICOMPQ = 1, CLALSA applies the right singular vector matrix to the right hand side. The singular vector matrices were generated in compact form by CLALSA. That last bit is important — it's the compact-form origin story. 🫶

Parameters 🧾

• ICOMPQ — ICOMPQ is INTEGER; specifies whether the left or the right singular vector matrix is involved. = 0: left singular vector matrix. = 1: right singular vector matrix.
• SMLSIZ — SMLSIZ is INTEGER; the maximum size of the subproblems at the bottom of the computation tree.
• N — N is INTEGER; the row and column dimensions of the upper bidiagonal matrix.
• NRHS — NRHS is INTEGER; the number of columns of B and BX. NRHS must be at least 1.
• B — B is COMPLEX array, dimension ( LDB, NRHS ). On input, B contains the right hand sides of the least squares problem in rows 1 through M. On output, B contains the solution X in rows 1 through N.
• LDB — LDB is INTEGER; the leading dimension of B in the calling subprogram. LDB must be at least max(1,MAX( M, N )).
• BX — BX is COMPLEX array, dimension ( LDBX, NRHS ). On exit, the result of applying the left or right singular vector matrix to B.
• LDBX — LDBX is INTEGER; the leading dimension of BX.
• U — U is REAL array, dimension ( LDU, SMLSIZ ). On entry, 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 ). On entry, VT**H contains the right singular vector matrices of all subproblems at the bottom level.
• K — K is INTEGER array, dimension ( N ).
• DIFL — DIFL is REAL array, dimension ( LDU, NLVL ), where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
• DIFR — DIFR is REAL array, dimension ( LDU, 2 * NLVL ). On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record distances between singular values on the I-th level and singular values on the (I -1)-th level, and DIFR(*, 2 * I) record the normalizing factors of the right singular vectors matrices of subproblems on I-th level.
• Z — Z is REAL array, dimension ( LDU, NLVL ). On entry, Z(1, I) contains 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 ). On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old singular values involved in the secular equations on the I-th level.
• GIVPTR — GIVPTR is INTEGER array, dimension ( N ). On entry, 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 ). On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records 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 ). On entry, PERM(*, I) records permutations done on the I-th level of the computation tree.
• GIVNUM — GIVNUM is REAL array, dimension ( LDU, 2 * NLVL ). On entry, GIVNUM(*, 2 *I -1 : 2 * I) records 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 ). On entry, if the I-th subproblem is not square, 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 ). On entry, if the I-th subproblem is not square, S( I ) contains the S-value of a Givens rotation related to the right null space of the I-th subproblem.
• RWORK — RWORK is REAL array, dimension at least MAX( (SMLSZ+1)*NRHS*3, N*(1+NRHS) + 2*NRHS ).
• IWORK — IWORK is INTEGER array, dimension (3*N).
• INFO — INFO is INTEGER; = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

Author 👑

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

Contributors: 🌸

• Ming Gu and Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA
• Osni Marques, LBNL/NERSC, USA

Definition at line 263 of file clalsa.f.

Author 💖

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okay bestie, that's the page: source SRC/clalsa.f(3), LAPACK version 3.12.0 — the footer didn't give a date, so no invented calendar lore here. periodt. 💅✨