# dgemlq.f - Man Page

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine dgemlq (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:**

DGEMLQ 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 (DGELQ)

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

*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 DLASWLQ or DGELQT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, DGELQ will use either DLASWLQ (if the matrix is wide-and-short) or DGELQT to compute the LQ factorization. This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to multiply matrix Q by another matrix. Further Details in DLAMSWLQ or DGEMLQT.

Definition at line 170 of file dgemlq.f.

## Author

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## Referenced By

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