clatsqr.f man page

clatsqr.f

Synopsis

Functions/Subroutines

subroutine clatsqr (M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, INFO)

Function/Subroutine Documentation

subroutine clatsqr (integer M, integer N, integer MB, integer NB, complex, dimension( lda, * ) A, integer LDA, complex, dimension(ldt, *) T, integer LDT, complex, dimension( * ) WORK, integer LWORK, integer INFO)

Purpose:

SLATSQR computes a blocked Tall-Skinny QR factorization of an M-by-N matrix A, where M >= N: A = Q * R .  

Parameters:

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 A. M >= N >= 0.

MB

          MB is INTEGER
          The row block size to be used in the blocked QR.
          MB > N.

NB

          NB is INTEGER
          The column block size to be used in the blocked QR.
          N >= NB >= 1.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and above the diagonal
          of the array contain the N-by-N upper triangular matrix R;
          the elements below the diagonal represent Q by the columns
          of blocked V (see Further Details).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

T

          T is COMPLEX array,
          dimension (LDT, N * Number_of_row_blocks)
          where Number_of_row_blocks = CEIL((M-N)/(MB-N))
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.
          See Further Details below.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= NB.

WORK

         (workspace) COMPLEX array, dimension (MAX(1,LWORK))

LWORK

          The dimension of the array WORK.  LWORK >= NB*N.
          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 151 of file clatsqr.f.

Author

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Referenced By

The man page clatsqr(3) is an alias of clatsqr.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK