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clatsqr.f(3) LAPACK clatsqr.f(3)

NAME

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

Author

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