SRC/zlals0.f(3)

💖 NAME 💖

SRC/zlals0.f — that's the file this whole page is about, bestie, and it lives under the Library Functions Manual umbrella. 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines:

       subroutine zlals0 (icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm,
           givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c,
           s, rwork, info)
           ZLALS0 applies back multiplying factors in solving the least squares
           problem using divide and conquer SVD approach. Used by sgelsd.

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🦋 Function/Subroutine Documentation 🦋

Okay so here's the full signature, and yes, every type and dimension is staying exactly where it belongs:

   subroutine zlals0 (integer icompq, integer nl, integer nr, integer sqre,
       integer nrhs, complex*16, dimension( ldb, * ) b, integer ldb,
       complex*16, dimension( ldbx, * ) bx, integer ldbx, integer, dimension( *
       ) perm, integer givptr, integer, dimension( ldgcol, * ) givcol, integer
       ldgcol, double precision, dimension( ldgnum, * ) givnum, integer ldgnum,
       double precision, dimension( ldgnum, * ) poles, double precision,
       dimension( * ) difl, double precision, dimension( ldgnum, * ) difr,
       double precision, dimension( * ) z, integer k, double precision c,
       double precision s, double precision, dimension( * ) rwork, integer
       info)

And what does it do? ZLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd. Slay. 💅

🎀 Purpose 🎀

So picture this: ZLALS0 applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B while solving the least squares problem using the divide-and-conquer SVD approach. That's the whole vibe. ✨

For the left singular vector matrix, three types of orthogonal matrices are involved:

• (1L) Givens rotations: the number of such rotations is GIVPTR; the pairs of columns/rows they were applied to are stored in GIVCOL; and the C- and S-values of these rotations are stored in GIVNUM.
• (2L) Permutation. The (NL+1)-st row of B is to be moved to the first row, and for J=2:N, PERM(J)-th row of B is to be moved to the J-th row.
• (3L) The left singular vector matrix of the remaining matrix.

For the right singular vector matrix, four types of orthogonal matrices are involved:

• (1R) The right singular vector matrix of the remaining matrix.
• (2R) If SQRE = 1, one extra Givens rotation to generate the right null space.
• (3R) The inverse transformation of (2L).
• (4R) The inverse transformation of (1L).

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🍓 Parameters 🍓

Every single parameter, bestie, zero skips:

• ICOMPQ — INTEGER. Specifies whether singular vectors are to be computed in factored form: = 0: left singular vector matrix. = 1: right singular vector matrix.
• NL — INTEGER. The row dimension of the upper block. NL >= 1.
• NR — INTEGER. The row dimension of the lower block. NR >= 1.
• SQRE — INTEGER. = 0: the lower block is an NR-by-NR square matrix. = 1: the lower block is an NR-by-(NR+1) rectangular matrix. The bidiagonal matrix has row dimension N = NL + NR + 1, and column dimension M = N + SQRE.
• NRHS — INTEGER. The number of columns of B and BX. NRHS must be at least 1.
• B — COMPLEX*16 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 — INTEGER. The leading dimension of B. LDB must be at least max(1,MAX( M, N )).
• BX — COMPLEX*16 array, dimension ( LDBX, NRHS ).
• LDBX — INTEGER. The leading dimension of BX.
• PERM — INTEGER array, dimension ( N ). The permutations (from deflation and sorting) applied to the two blocks.
• GIVPTR — INTEGER. The number of Givens rotations which took place in this subproblem.
• GIVCOL — INTEGER array, dimension ( LDGCOL, 2 ). Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation.
• LDGCOL — INTEGER. The leading dimension of GIVCOL, must be at least N.
• GIVNUM — DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). Each number indicates the C or S value used in the corresponding Givens rotation.
• LDGNUM — INTEGER. The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K.
• POLES — DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). On entry, POLES(1:K, 1) contains the new singular values obtained from solving the secular equation, and POLES(1:K, 2) is an array containing the poles in the secular equation.
• DIFL — DOUBLE PRECISION array, dimension ( K ). On entry, DIFL(I) is the distance between I-th updated (undeflated) singular value and the I-th (undeflated) old singular value.
• DIFR — DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). On entry, DIFR(I, 1) contains the distances between I-th updated (undeflated) singular value and the I+1-th (undeflated) old singular value. And DIFR(I, 2) is the normalizing factor for the I-th right singular vector.
• Z — DOUBLE PRECISION array, dimension ( K ). Contain the components of the deflation-adjusted updating row vector.
• K — INTEGER. Contains the dimension of the non-deflated matrix, This is the order of the related secular equation. 1 <= K <=N.
• C — DOUBLE PRECISION. C contains garbage if SQRE =0 and the C-value of a Givens rotation related to the right null space if SQRE = 1.
• S — DOUBLE PRECISION. S contains garbage if SQRE =0 and the S-value of a Givens rotation related to the right null space if SQRE = 1.
• RWORK — DOUBLE PRECISION array, dimension ( K*(1+NRHS) + 2*NRHS ).
• INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

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👑 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 267 of file zlals0.f. ⭐

Yes bestie, the actual definition is at line 267 of file zlals0.f. 💖

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole entire page from SRC/zlals0.f(3), LAPACK Version 3.12.0 — no details left behind, periodt. 💖✨🦋