SRC/zlamtsqr.f(3)

📦
version 3.12.1 · 5 versions
, in arch rolling

Hey bestie! 💖 Welcome to the manual page for SRC/zlamtsqr.f, served fresh from the Library Functions Manual. This one is all about ZLAMTSQR, and we're gonna keep every single detail, no cap. 🫶

💖 NAME 💖

SRC/zlamtsqr.f — that's the file, bestie. ✨

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

  • subroutine zlamtsqr (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info) — ZLAMTSQR 👑

🔥 Function/Subroutine Documentation 🔥

subroutine zlamtsqr (character side, character trans, integer m, integer n,
    integer k, integer mb, integer nb, complex*16, dimension( lda, * ) a,
    integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16,
    dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work,
    integer lwork, integer info)

ZLAMTSQR is the main character here. 💅

🎯 Purpose 🎯

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

              SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'C':      Q**H * C       C * Q**H

where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by tall skinny QR factorization (ZLATSQR). 🦋

🧾 Parameters 🧾

  • SIDE — SIDE is CHARACTER*1. Pick a side, bestie: = '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 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 ZLATSQR). 🔥
  • NB — NB is INTEGER. The column block size to be used in the blocked QR. N >= NB >= 1. 🎀
  • A — A is COMPLEX*16 array, dimension (LDA,K). The i-th column must contain the vector which defines the blocked elementary reflector H(i), for i = 1,2,...,k, as returned by ZLATSQR 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 COMPLEX*16 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 COMPLEX*16 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*16 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 unitary transformations, representing Q as a product of other unitary 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 zlamtsqr.f. 🌸

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. 🫶

💖 That’s the whole page, bestie! LAPACK Version 3.12.0, SRC/zlamtsqr.f(3), signing off. 🎀

📦 where this page comes from