dgemqr.f - Man Page

Synopsis

Functions/Subroutines

subroutine dgemqr (SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, C, LDC, WORK, LWORK, INFO)
DGEMQR

Function/Subroutine Documentation

subroutine dgemqr (character SIDE, character TRANS, integer M, integer N, integer K, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) T, integer TSIZE, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) WORK, integer LWORK, integer INFO)

DGEMQR

Purpose:

 DGEMQR 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 (DGEQR)
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. N >= 0.

K

          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,K)
          Part of the data structure to represent Q as returned by DGEQR.

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 DOUBLE PRECISION array, dimension (MAX(5,TSIZE)).
          Part of the data structure to represent Q as returned by DGEQR.

TSIZE

          TSIZE is INTEGER
          The dimension of the array T. TSIZE >= 5.

C

          C is DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (MAX(1,LWORK))

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1, then a workspace query is assumed. The routine
          only calculates the size of the WORK array, returns this
          value as WORK(1), and no error message related to WORK 
          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

 These details are particular for this LAPACK implementation. Users should not 
 take them for granted. These details may change in the future, and are not likely
 true for another LAPACK implementation. These details are relevant if one wants
 to try to understand the code. They are not part of the interface.

 In this version,

          T(2): row block size (MB)
          T(3): column block size (NB)
          T(6:TSIZE): data structure needed for Q, computed by
                           DLATSQR or DGEQRT

  Depending on the matrix dimensions M and N, and row and column
  block sizes MB and NB returned by ILAENV, DGEQR will use either
  DLATSQR (if the matrix is tall-and-skinny) or DGEQRT to compute
  the QR factorization.
  This version of DGEMQR will use either DLAMTSQR or DGEMQRT to 
  multiply matrix Q by another matrix.
  Further Details in DLATMSQR or DGEMQRT.

Definition at line 170 of file dgemqr.f.

Author

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Referenced By

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

Thu Apr 1 2021 Version 3.9.1 LAPACK