SRC/clamswlq.f(3)

🦋 SRC/clamswlq.f(3) — Library Functions Manual 🦋

💖 NAME 💖

SRC/clamswlq.f — bestie, this is the page for the clamswlq routine, and it’s honestly giving main-character energy in the LAPACK lineup. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

🫶 Function/Subroutine Documentation 🫶

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

CLAMSWLQ — okay so this is the whole signature, and yes, every single argument is about to get its moment. ✨

🌸 Purpose 🌸

CLAMSWLQ overwrites the general complex M-by-N matrix C with:

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

where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (CLASWLQ). No cap, that’s the whole vibe. 🦋

💅 Parameters 💅

Okay bestie, these are the args, and literally none of them are skippable. 👑

• SIDE — SIDE is CHARACTER*1
  • = 'L': apply Q or Q**H from the Left;
  • = 'R': apply Q or Q**H from the Right.
• TRANS — TRANS is CHARACTER*1
  • = 'N': No transpose, apply Q;
  • = 'C': Conjugate transpose, apply Q**H.
• M — M is INTEGER: the number of rows of the matrix C. 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 row block size to be used in the blocked LQ. M >= MB >= 1
• NB — NB is INTEGER: the column block size to be used in the blocked LQ. NB > M.
• A — A is COMPLEX 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 CLASWLQ in the first k rows of its array argument A.
• LDA — LDA is INTEGER: the leading dimension of the array A. LDA => max(1,K).
• T — T is COMPLEX 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 — LDT is INTEGER: the leading dimension of the array T. LDT >= MB.
• C — C is COMPLEX array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
• LDC — LDC is INTEGER: the leading dimension of the array C. LDC >= max(1,M).
• WORK — (workspace) COMPLEX 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,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 — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

👑 Author 👑

The author squad, periodt:

• 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 unitary transformations, representing Q as a product of other unitary 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 clamswlq.f.

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

---

k bye bestie — this page is from LAPACK, Version 3.12.0, source file SRC/clamswlq.f(3). mwah 💋✨