SRC/slals0.f(3)

Hey bestie 💖 welcome to the SRC/slals0.f(3) page from the Library Functions Manual. This is the LAPACK internal that applies back multiplying factors while solving the least squares problem with the divide-and-conquer SVD approach, and it's used by sgelsd. It's giving very specific linear algebra, no cap. ✨

✨ NAME ✨

SRC/slals0.f — yes, that's the whole name. Iconic. 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine slals0 (icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm,
    givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c,
    s, work, info)

SLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd. 🫶

💫 Function/Subroutine Documentation 💫

Okay so here's the actual function documentation. Buckle up, bestie — it's detailed but honestly kind of iconic.

subroutine slals0 (integer icompq, integer nl, integer nr, integer sqre,
       integer nrhs, real, dimension( ldb, * ) b, integer ldb, real, dimension(
       ldbx, * ) bx, integer ldbx, integer, dimension( * ) perm, integer
       givptr, integer, dimension( ldgcol, * ) givcol, integer ldgcol, real,
       dimension( ldgnum, * ) givnum, integer ldgnum, real, dimension( ldgnum,
       * ) poles, real, dimension( * ) difl, real, dimension( ldgnum, * ) difr,
       real, dimension( * ) z, integer k, real c, real s, real, dimension( * )
       work, integer info)

SLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd. 🧚

🎀 Purpose 🎀

SLALS0 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 in solving the least squares problem using the divide-and-conquer SVD approach. 🌸

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, the 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). 💜

🍓 Parameters 🍓

• ICOMPQ — INTEGER. Specifies whether singular vectors are to be computed in factored form: = 0 means left singular vector matrix; = 1 means 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 — REAL 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 — REAL 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 — REAL 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 — REAL 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 — REAL 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 — REAL 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 — REAL array, dimension ( K ). Contains 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 — REAL. C contains garbage if SQRE =0 and the C-value of a Givens rotation related to the right null space if SQRE = 1. 💀
• S — REAL. S contains garbage if SQRE =0 and the S-value of a Givens rotation related to the right null space if SQRE = 1. 💀
• WORK — REAL array, dimension ( K ). ✨
• INFO — 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 265 of file slals0.f. 🎀

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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Alright bestie, that's the whole SRC/slals0.f(3) situation. Cute little sign-off: LAPACK Version 3.12.0, generated automatically by Doxygen for LAPACK from the source code — and no separate date is listed in the footer, so we're not inventing one. Stay slay, and may your least-squares problems stay solved. 💖✨