# cgemlq.f - Man Page

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

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

**CGEMLQ**

**Purpose:**

CGEMLQ 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 (CGELQ)

**Parameters***SIDE*SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right.

*TRANS*TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**H.

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

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

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

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

*C*C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

*LDC*LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).

*WORK*(workspace) COMPLEX 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 CLASWQR or CGELQT Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, CGELQ will use either CLASWLQ (if the matrix is wide-and-short) or CGELQT to compute the LQ factorization. This version of CGEMLQ will use either CLAMSWLQ or CGEMLQT to multiply matrix Q by another matrix. Further Details in CLAMSWLQ or CGEMLQT.

Definition at line 168 of file cgemlq.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Mon Jun 28 2021 Version 3.10.0 LAPACK