SRC/slamtsqr.f(3)

✨ NAME ✨

SRC/slamtsqr.f — bestie, this is the SRC/slamtsqr.f(3) page from the Library Functions Manual, and it's all about the SLAMTSQR subroutine. 💅

🌸 SYNOPSIS 🌸

🦋 Functions/Subroutines 🦋

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

💖 Function/Subroutine Documentation 💖

subroutine slamtsqr (character side, character trans, integer m, integer n,
    integer k, integer mb, integer nb, real, dimension( lda, * ) a, integer
    lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * )
    c, integer ldc, real, dimension( * ) work, integer lwork, integer info)
    SLAMTSQR

Okay so this is SLAMTSQR, and here's its whole deal, no cap. 🫶

🎀 Purpose 🎀

SLAMTSQR overwrites the general real M-by-N matrix C with the exact matrix tea shown here:

!>
!>      SLAMTSQR 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 (SLATSQR)
!>

💅 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 SLATSQR)
• NB — NB is INTEGER. The column block size to be used in the blocked QR. N >= NB >= 1.
• A — A is REAL 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 SLATSQR 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 REAL 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 REAL 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) REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
• LWORK — LWORK is INTEGER. The dimension of the array WORK. If MIN(M,N,K) = 0, LWORK >= 1. 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 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 — INFO is 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.

🔥 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 199 of file slamtsqr.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that's the whole page, bestie — LAPACK Version 3.12.0, source SRC/slamtsqr.f(3), and yes the Doxygen auto-gen credit is up there. bye 💖