# zgemlq.f - Man Page

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine zgemlq (character SIDE, character TRANS, integer M, integer N, integer K, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) T, integer TSIZE, complex*16, dimension( ldc, * ) C, integer LDC, complex*16, dimension( * ) WORK, integer LWORK, integer INFO)

**Purpose:**

ZGEMLQ overwrites the general real M-by-N matrix C with

SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (ZGELQ)

**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 COMPLEX*16 array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' Part of the data structure to represent Q as returned by ZGELQ.

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

*T*T is COMPLEX*16 array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by ZGELQ.

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

*C*C is COMPLEX*16 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) COMPLEX*16 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 ZLASWLQ or ZGELQT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, ZGELQ will use either ZLASWLQ (if the matrix is wide-and-short) or ZGELQT to compute the LQ factorization. This version of ZGEMLQ will use either ZLAMSWLQ or ZGEMLQT to multiply matrix Q by another matrix. Further Details in ZLAMSWLQ or ZGEMLQT.

Definition at line 168 of file zgemlq.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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