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  4. sgemlq(3)

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sgemlq.f(3) LAPACK sgemlq.f(3)

NAME

sgemlq.f

SYNOPSIS

Functions/Subroutines


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

Function/Subroutine Documentation

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

Purpose:

SGEMLQ 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 short wide LQ factorization (SGELQ)

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 REAL array, dimension


                               (LDA,M) if SIDE = 'L',


                               (LDA,N) if SIDE = 'R'


          Part of the data structure to represent Q as returned by DGELQ.

LDA



          LDA is INTEGER


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

T



          T is REAL array, dimension (MAX(5,TSIZE)).


          Part of the data structure to represent Q as returned by SGELQ.

TSIZE



          TSIZE is INTEGER


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

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 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 SLASWLQ or SGELQT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, SGELQ will use either SLASWLQ (if the matrix is wide-and-short) or SGELQT to compute the LQ factorization. This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to multiply matrix Q by another matrix. Further Details in SLAMSWLQ or SGEMLQT.

Definition at line 169 of file sgemlq.f.

Author

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Tue Nov 14 2017 Version 3.8.0