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zgemqr.f(3) LAPACK zgemqr.f(3)

NAME

zgemqr.f

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

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Tue Nov 14 2017 Version 3.8.0