LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zlqt01()

 subroutine zlqt01 ( integer M, integer N, complex*16, dimension( lda, * ) A, complex*16, dimension( lda, * ) AF, complex*16, dimension( lda, * ) Q, complex*16, dimension( lda, * ) L, integer LDA, complex*16, dimension( * ) TAU, complex*16, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * ) RWORK, double precision, dimension( * ) RESULT )

ZLQT01

Purpose:
``` ZLQT01 tests ZGELQF, which computes the LQ factorization of an m-by-n
matrix A, and partially tests ZUNGLQ which forms the n-by-n
orthogonal matrix Q.

ZLQT01 compares L with A*Q', and checks that Q is orthogonal.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The m-by-n matrix A.``` [out] AF ``` AF is COMPLEX*16 array, dimension (LDA,N) Details of the LQ factorization of A, as returned by ZGELQF. See ZGELQF for further details.``` [out] Q ``` Q is COMPLEX*16 array, dimension (LDA,N) The n-by-n orthogonal matrix Q.``` [out] L ` L is COMPLEX*16 array, dimension (LDA,max(M,N))` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= max(M,N).``` [out] TAU ``` TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by ZGELQF.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK.``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (max(M,N))` [out] RESULT ``` RESULT is DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS ) RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )```

Definition at line 124 of file zlqt01.f.

126*
127* -- LAPACK test routine --
128* -- LAPACK is a software package provided by Univ. of Tennessee, --
129* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*
131* .. Scalar Arguments ..
132 INTEGER LDA, LWORK, M, N
133* ..
134* .. Array Arguments ..
135 DOUBLE PRECISION RESULT( * ), RWORK( * )
136 COMPLEX*16 A( LDA, * ), AF( LDA, * ), L( LDA, * ),
137 \$ Q( LDA, * ), TAU( * ), WORK( LWORK )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 DOUBLE PRECISION ZERO, ONE
144 parameter( zero = 0.0d+0, one = 1.0d+0 )
145 COMPLEX*16 ROGUE
146 parameter( rogue = ( -1.0d+10, -1.0d+10 ) )
147* ..
148* .. Local Scalars ..
149 INTEGER INFO, MINMN
150 DOUBLE PRECISION ANORM, EPS, RESID
151* ..
152* .. External Functions ..
153 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY
154 EXTERNAL dlamch, zlange, zlansy
155* ..
156* .. External Subroutines ..
157 EXTERNAL zgelqf, zgemm, zherk, zlacpy, zlaset, zunglq
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC dble, dcmplx, max, min
161* ..
162* .. Scalars in Common ..
163 CHARACTER*32 SRNAMT
164* ..
165* .. Common blocks ..
166 COMMON / srnamc / srnamt
167* ..
168* .. Executable Statements ..
169*
170 minmn = min( m, n )
171 eps = dlamch( 'Epsilon' )
172*
173* Copy the matrix A to the array AF.
174*
175 CALL zlacpy( 'Full', m, n, a, lda, af, lda )
176*
177* Factorize the matrix A in the array AF.
178*
179 srnamt = 'ZGELQF'
180 CALL zgelqf( m, n, af, lda, tau, work, lwork, info )
181*
182* Copy details of Q
183*
184 CALL zlaset( 'Full', n, n, rogue, rogue, q, lda )
185 IF( n.GT.1 )
186 \$ CALL zlacpy( 'Upper', m, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
187*
188* Generate the n-by-n matrix Q
189*
190 srnamt = 'ZUNGLQ'
191 CALL zunglq( n, n, minmn, q, lda, tau, work, lwork, info )
192*
193* Copy L
194*
195 CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), l,
196 \$ lda )
197 CALL zlacpy( 'Lower', m, n, af, lda, l, lda )
198*
199* Compute L - A*Q'
200*
201 CALL zgemm( 'No transpose', 'Conjugate transpose', m, n, n,
202 \$ dcmplx( -one ), a, lda, q, lda, dcmplx( one ), l,
203 \$ lda )
204*
205* Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) .
206*
207 anorm = zlange( '1', m, n, a, lda, rwork )
208 resid = zlange( '1', m, n, l, lda, rwork )
209 IF( anorm.GT.zero ) THEN
210 result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
211 ELSE
212 result( 1 ) = zero
213 END IF
214*
215* Compute I - Q*Q'
216*
217 CALL zlaset( 'Full', n, n, dcmplx( zero ), dcmplx( one ), l, lda )
218 CALL zherk( 'Upper', 'No transpose', n, n, -one, q, lda, one, l,
219 \$ lda )
220*
221* Compute norm( I - Q*Q' ) / ( N * EPS ) .
222*
223 resid = zlansy( '1', 'Upper', n, l, lda, rwork )
224*
225 result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
226*
227 RETURN
228*
229* End of ZLQT01
230*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:173
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:115
subroutine zgelqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGELQF
Definition: zgelqf.f:143
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zunglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGLQ
Definition: zunglq.f:127
double precision function zlansy(NORM, UPLO, N, A, LDA, WORK)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansy.f:123
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