# zgemqr.f - Man Page

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine zgemqr (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:**

ZGEMQR 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 (ZGEQR)

**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,K) Part of the data structure to represent Q as returned by ZGEQR.

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

*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 ZLATSQR or ZGEQRT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, ZGEQR will use either ZLATSQR (if the matrix is tall-and-skinny) or ZGEQRT to compute the QR factorization. This version of ZGEMQR will use either ZLAMTSQR or ZGEMQRT to multiply matrix Q by another matrix. Further Details in ZLAMTSQR or ZGEMQRT.

Definition at line 171 of file zgemqr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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