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slamtsqr.f(3) LAPACK slamtsqr.f(3)

NAME

slamtsqr.f -

SYNOPSIS

Functions/Subroutines


subroutine slamtsqr (SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
 

Function/Subroutine Documentation

subroutine slamtsqr (characterSIDE, characterTRANS, integerM, integerN, integerK, integerMB, integerNB, real, dimension( lda, * )A, integerLDA, real, dimension( ldt, * )T, integerLDT, real, dimension(ldc, * )C, integerLDC, real, dimension( * )WORK, integerLWORK, integerINFO)

Purpose:
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 (DLATSQR)
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. M >= N >= 0.
K 
          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          N >= K >= 0;
MB 
          MB is INTEGER
          The block size to be used in the blocked QR.
          MB > N. (must be the same as DLATSQR)
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 DLATSQR 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

Author

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