SLAMTSQR(3)

💖 SLAMTSQR(3) — Library Functions Manual 💖

okay bestie, welcome to the glow-up of the SLAMTSQR(3) page from the Library Functions Manual. The header was literally serving /home/abui.../slamtsqr.f(3) twice, which is iconic in a mysterious-path way. We are keeping every deet, just with more sparkle. ✨

🌸 NAME 🌸

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

✨ 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

🎯 Purpose

so here’s the whole vibe: 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 Q**T from the Left;
• = 'R': apply Q or Q**T 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)

bestie this one has to match SLATSQR, no cap.

🧚 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))

💫 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

👑 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 slamtsqr.f.

💌 Author

Generated automatically by Doxygen for LAPACK from the source code.

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