/home/abui.../slaswlq.f(3)

💅 NAME

okay so bestie, this page is about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slaswlq.f — a Fortran file in the LAPACK library, documented as a Library Functions Manual page 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines 🌸

• subroutine SLASWLQ (m, n, mb, nb, a, lda, t, ldt, work, lwork, info) — the one and only, the main character herself: SLASWLQ 👑

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🦋 Function/Subroutine Documentation 🦋

subroutine SLASWLQ (integer m, integer n, integer mb, integer nb, real,
    dimension( lda, * ) a, integer lda, real, dimension( ldt, *) t, integer
    ldt, real, dimension( * ) work, integer lwork, integer info)

SLASWLQ 💖

🎯 Purpose

!> !> SLASWLQ computes a blocked Tall-Skinny LQ factorization of !> a real M-by-N matrix A for M <= N: !> !> A = ( L 0 ) * Q, !> !> where: !> !> Q is a n-by-N orthogonal matrix, stored on exit in an implicit !> form in the elements above the diagonal of the array A and in !> the elements of the array T; !> L is a lower-triangular M-by-M matrix stored on exit in !> the elements on and below the diagonal of the array A. !> 0 is a M-by-(N-M) zero matrix, if M < N, and is not stored. !> !>

🌈 Parameters

• M

!> M is INTEGER !> The number of rows of the matrix A. M >= 0. !>

so like, how many rows A has. M >= 0, no negatives bestie 🚫

• N

!> N is INTEGER !> The number of columns of the matrix A. N >= M >= 0. !>

columns of A. note the judgment: N >= M >= 0 💅

• MB

!> MB is INTEGER !> The row block size to be used in the blocked QR. !> M >= MB >= 1 !>

the row block size for the blocked QR. M >= MB >= 1, fr fr.

• NB

!> NB is INTEGER !> The column block size to be used in the blocked QR. !> NB > 0. !>

the column block size for the blocked QR. NB > 0, periodt.

• A

!> A is REAL array, dimension (LDA,N) !> On entry, the M-by-N matrix A. !> On exit, the elements on and below the diagonal !> of the array contain the N-by-N lower triangular matrix L; !> the elements above the diagonal represent Q by the rows !> of blocked V (see Further Details). !> !>

a REAL array, dimension (LDA,N). on entry it's the M-by-N matrix A; on exit the on-and-below-diagonal bits hold the N-by-N lower triangular matrix L, and the above-diagonal bits represent Q via the rows of blocked V (see Further Details, bestie 👀).

• LDA

!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>

leading dimension of A. LDA >= max(1,M) — iconic constraint, no notes 💀

• T

!> T is REAL array, !> dimension (LDT, N * Number_of_row_blocks) !> where Number_of_row_blocks = CEIL((N-M)/(NB-M)) !> The blocked upper triangular block reflectors stored in compact form !> as a sequence of upper triangular blocks. !> See Further Details below. !>

a REAL array with dimension (LDT, N * Number_of_row_blocks), where Number_of_row_blocks = CEIL((N-M)/(NB-M)). it's the blocked upper triangular block reflectors, stored all compact as a sequence of upper triangular blocks. Further Details below, iykyk 🫶

• LDT

!> LDT is INTEGER !> The leading dimension of the array T. LDT >= MB. !>

leading dimension of T. LDT >= MB.

• WORK

!> (workspace) REAL array, dimension (MAX(1,LWORK)) !> !>

the workspace 💼 — REAL array, dimension (MAX(1,LWORK)).

• LWORK

!> LWORK is INTEGER !> The dimension of the array WORK. LWORK >= MB * M. !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> !>

dimension of WORK, and LWORK >= MB * M. and ooh, the fun part: if LWORK = -1 it assumes a workspace query — it only calculates the optimal size of the WORK array, returns that value as the first entry of the WORK array, and XERBLA issues no error message related to LWORK 😌✨

• INFO

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

• = 0: successful exit, slay 🎉
• < 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.

(the whole squad that brought you this 🫶)

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💜 Further Details

!> Short-Wide LQ (SWLQ) performs LQ by a sequence of orthogonal transformations, !> representing Q as a product of other orthogonal matrices !> Q = Q(1) * Q(2) * . . . * Q(k) !> where each Q(i) zeros out upper diagonal entries of a block of NB rows of A: !> Q(1) zeros out the upper diagonal entries of rows 1:NB of A !> Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A !> Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A !> . . . !> !> Q(1) is computed by GELQT, which represents Q(1) by Householder vectors !> stored under the diagonal of rows 1:MB of A, and by upper triangular !> block reflectors, stored in array T(1:LDT,1:N). !> For more information see Further Details in GELQT. !> !> Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors !> stored in columns [(i-1)(NB-M)+M+1:i(NB-M)+M] of A, and by upper triangular !> block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M). !> The last Q(k) may use fewer rows. !> For more information see Further Details in TPQRT. !> !> For more details of the overall algorithm, see the description of !> Sequential TSQR in Section 2.2 of [1]. !> !> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,” !> J. Demmel, L. Grigori, M. Hoemmen, J. Langou, !> SIAM J. Sci. Comput, vol. 34, no. 1, 2012 !>

Definition at line 165 of file slaswlq.f. 🧚

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💫 Author

Generated automatically by Doxygen for LAPACK from the source code.

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✨ and that's the whole thing! ✨ this little beauty lives in LAPACK, Version 3.12.0 — the doc page itself is /home/abui.../slaswlq.f(3). mwah, go forth and factorize responsibly 💖🦋🎀