SRC/dlamswlq.f(3)

💅 SRC/dlamswlq.f — LAPACK Library Functions Manual

okay so this is the SRC/dlamswlq.f(3) page from the LAPACK Library Functions Manual, and it's giving “short wide LQ but make it blocked” energy. Let's get into it, bestie 🫶.

💖 NAME

SRC/dlamswlq.f

✨ SYNOPSIS

🧚 Functions/Subroutines

subroutine dlamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c,
    ldc, work, lwork, info)
    DLAMSWLQ

🔥 Function/Subroutine Documentation

🌟 subroutine dlamswlq

subroutine dlamswlq (character side, character trans, integer m, integer n,
    integer k, integer mb, integer nb, double precision, dimension( lda, * )
    a, integer lda, double precision, dimension( ldt, * ) t, integer ldt,
    double precision, dimension( ldc, * ) c, integer ldc, double precision,
    dimension( * ) work, integer lwork, integer info)
    DLAMSWLQ

🎯 Purpose

DLAMSWLQ overwrites the general real M-by-N matrix C with:

                 SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'T':      Q**T * C       C * Q**T

where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (DLASWLQ). iconic behavior tbh 👑

🌸 Parameters

• SIDE — CHARACTER*1. = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.
• TRANS — CHARACTER*1. = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.
• M — INTEGER. The number of rows of the matrix C. M >=0.
• N — INTEGER. The number of columns of the matrix C. N >= 0.
• K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0;
• MB — INTEGER. The row block size to be used in the blocked LQ. M >= MB >= 1
• NB — INTEGER. The column block size to be used in the blocked LQ. NB > M.
• A — DOUBLE PRECISION array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R'. The i-th row must contain the vector which defines the blocked elementary reflector H(i), for i = 1,2,...,k, as returned by DLASWLQ in the first k rows of its array argument A.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,K).
• T — DOUBLE PRECISION array, dimension ( M * Number of blocks(CEIL(N-K/NB-K)),. The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.
• LDT — INTEGER. The leading dimension of the array T. LDT >= MB.
• C — DOUBLE PRECISION array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
• LDC — INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
• LWORK — INTEGER. The dimension of the array WORK. If MIN(M,N,K) = 0, LWORK >= 1. If SIDE = 'L', LWORK >= max(1,NB*MB). If SIDE = 'R', LWORK >= max(1,M*MB). If LWORK = -1, then a workspace query is assumed; the routine only calculates the minimal 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.
• INFO — INTEGER. = 0: successful exit. INFO < 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.

🔎 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 TPLQT.

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 198 of file dlamswlq.f.

📝 Author

Generated automatically by Doxygen for LAPACK from the source code.

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