DLAMTSQR(3)

DLAMTSQR(3) — okay bestie, this is the Library Functions Manual page for dlamtsqr.f from LAPACK 3.12.0, source chilling at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlamtsqr.f. Buckle up, we're doing blocked QR energy 💖✨

💅 NAME 💅

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlamtsqr.f — that's the file, and this page is giving DLAMTSQR(3) main character energy 🎀

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

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

🌸 Function/Subroutine Documentation 🌸

subroutine DLAMTSQR (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)

DLAMTSQR — yes bestie, that's the whole name, no cap 🫶

🎀 Purpose 🎀

DLAMTSQR 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 tall skinny QR factorization (DLATSQR). Iconic behavior, honestly 👑

💖 Parameters 💖

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

🧚 Further Details 🧚

Tall-Skinny QR (TSQR) performs QR 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 subdiagonal entries of a block of MB rows of A:

Q(1) zeros out the subdiagonal entries of rows 1:MB of A
Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
. . .

Q(1) is computed by GEQRT, 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 GEQRT.

Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N). 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 197 of file dlamtsqr.f.

🫶 Author (Doxygen's version) 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole vibe, bestie: the footer credits LAPACK Version 3.12.0 and the source path /home/abui.../dlamtsqr.f(3) — and the date slot is quiet in this copy, so I'm not inventing one. bye byeee 💖🦋🎀