# zlqt03.f - Man Page

TESTING/LIN/zlqt03.f

## Synopsis

### Functions/Subroutines

subroutine zlqt03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork, result)
ZLQT03

## Function/Subroutine Documentation

### subroutine zlqt03 (integer m, integer n, integer k, complex*16, dimension( lda, * ) af, complex*16, dimension( lda, * ) c, complex*16, dimension( lda, * ) cc, complex*16, dimension( lda, * ) q, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result)

ZLQT03

Purpose:

ZLQT03 tests ZUNMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.

ZLQT03 compares the results of a call to ZUNMLQ with the results of
forming Q explicitly by a call to ZUNGLQ and then performing matrix
multiplication by a call to ZGEMM.
Parameters

M

M is INTEGER
The number of rows or columns of the matrix C; C is n-by-m if
Q is applied from the left, or m-by-n if Q is applied from
the right.  M >= 0.

N

N is INTEGER
The order of the orthogonal matrix Q.  N >= 0.

K

K is INTEGER
The number of elementary reflectors whose product defines the
orthogonal matrix Q.  N >= K >= 0.

AF

AF is COMPLEX*16 array, dimension (LDA,N)
Details of the LQ factorization of an m-by-n matrix, as
returned by ZGELQF. See CGELQF for further details.

C

C is COMPLEX*16 array, dimension (LDA,N)

CC

CC is COMPLEX*16 array, dimension (LDA,N)

Q

Q is COMPLEX*16 array, dimension (LDA,N)

LDA

LDA is INTEGER
The leading dimension of the arrays AF, C, CC, and Q.

TAU

TAU is COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors corresponding
to the LQ factorization in AF.

WORK

WORK is COMPLEX*16 array, dimension (LWORK)

LWORK

LWORK is INTEGER
The length of WORK.  LWORK must be at least M, and should be
M*NB, where NB is the blocksize for this environment.

RWORK

RWORK is DOUBLE PRECISION array, dimension (M)

RESULT

RESULT is DOUBLE PRECISION array, dimension (4)
The test ratios compare two techniques for multiplying a
random matrix C by an n-by-n orthogonal matrix Q.
RESULT(1) = norm( Q*C - Q*C )  / ( N * norm(C) * EPS )
RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS )
RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 134 of file zlqt03.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlqt03(3) is an alias of zlqt03.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK