SLALS0(3)

🌸 NAME 🌸

okay bestie, welcome to the SLALS0(3) page from the Library Functions Manual. The page is literally named by this path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slals0.f

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✨ 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.

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💅 Function/Subroutine Documentation 💅

🦋 subroutine SLALS0 🦋

   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

Okay so here's the whole vibe: 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, 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 — ICOMPQ is INTEGER. Specifies whether singular vectors are to be computed in factored form: = 0: Left singular vector matrix. = 1: Right singular vector matrix.
• NL — NL is INTEGER. The row dimension of the upper block. NL >= 1.
• NR — NR is INTEGER. The row dimension of the lower block. NR >= 1.
• SQRE — SQRE is 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 — NRHS is INTEGER. The number of columns of B and BX. NRHS must be at least 1.
• B — B is 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 — LDB is INTEGER. The leading dimension of B. LDB must be at least max(1,MAX( M, N )).
• BX — BX is REAL array, dimension ( LDBX, NRHS ).
• LDBX — LDBX is INTEGER. The leading dimension of BX.
• PERM — PERM is INTEGER array, dimension ( N ). The permutations (from deflation and sorting) applied to the two blocks.
• GIVPTR — GIVPTR is INTEGER. The number of Givens rotations which took place in this subproblem.
• GIVCOL — GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ). Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation.
• LDGCOL — LDGCOL is INTEGER. The leading dimension of GIVCOL, must be at least N.
• GIVNUM — GIVNUM is REAL array, dimension ( LDGNUM, 2 ). Each number indicates the C or S value used in the corresponding Givens rotation.
• LDGNUM — LDGNUM is INTEGER. The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K.
• POLES — POLES is 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 — DIFL is 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 — DIFR is 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 — Z is REAL array, dimension ( K ). Contain the components of the deflation-adjusted updating row vector.
• K — K is INTEGER. Contains the dimension of the non-deflated matrix, This is the order of the related secular equation. 1 <= K <=N.
• C — C is 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 — S is 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 — WORK is REAL array, dimension ( K ).
• INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

Bestie, note the garbage-vibes warnings on C and S: if SQRE =0, those values are literally garbage. Do not trust them, periodt.

👑 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. 🔥

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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💖 cute sign-off time: the footer is giving LAPACK Version 3.12.0 and the page path /home/abui...RC/slals0.f(3). The date slot is literally not in this footer, so no fake date from me, bestie. Byeeee, go slay those singular vectors! 💅✨