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  4. dgemqr(3)

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dgemqr.f(3) LAPACK dgemqr.f(3)

NAME

dgemqr.f

SYNOPSIS

Functions/Subroutines


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

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)

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 unlikely not 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 171 of file dgemqr.f.

Author

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Tue Nov 14 2017 Version 3.8.0