# cgemqr.f - Man Page

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine cgemqr (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)

**Purpose:**

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

SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**H * C C * Q**H

where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by tall skinny QR factorization (CGEQR)

**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 array, dimension (LDA,K) Part of the data structure to represent Q as returned by CGEQR.

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

*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**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 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 CLATSQR or CGEQRT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, CGEQR will use either CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute the QR factorization. This version of CGEMQR will use either CLAMTSQR or CGEMQRT to multiply matrix Q by another matrix. Further Details in CLAMTSQR or CGEMQRT.

Definition at line 171 of file cgemqr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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