 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ clqt01()

 subroutine clqt01 ( integer M, integer N, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) L, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT )

CLQT01

Purpose:
``` CLQT01 tests CGELQF, which computes the LQ factorization of an m-by-n
matrix A, and partially tests CUNGLQ which forms the n-by-n
orthogonal matrix Q.

CLQT01 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 array, dimension (LDA,N) The m-by-n matrix A.``` [out] AF ``` AF is COMPLEX array, dimension (LDA,N) Details of the LQ factorization of A, as returned by CGELQF. See CGELQF for further details.``` [out] Q ``` Q is COMPLEX array, dimension (LDA,N) The n-by-n orthogonal matrix Q.``` [out] L ` L is COMPLEX 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 array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by CGELQF.``` [out] WORK ` WORK is COMPLEX array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK.``` [out] RWORK ` RWORK is REAL array, dimension (max(M,N))` [out] RESULT ``` RESULT is REAL 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 clqt01.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 REAL RESULT( * ), RWORK( * )
136 COMPLEX A( LDA, * ), AF( LDA, * ), L( LDA, * ),
137 \$ Q( LDA, * ), TAU( * ), WORK( LWORK )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 REAL ZERO, ONE
144 parameter( zero = 0.0e+0, one = 1.0e+0 )
145 COMPLEX ROGUE
146 parameter( rogue = ( -1.0e+10, -1.0e+10 ) )
147* ..
148* .. Local Scalars ..
149 INTEGER INFO, MINMN
150 REAL ANORM, EPS, RESID
151* ..
152* .. External Functions ..
153 REAL CLANGE, CLANSY, SLAMCH
154 EXTERNAL clange, clansy, slamch
155* ..
156* .. External Subroutines ..
157 EXTERNAL cgelqf, cgemm, cherk, clacpy, claset, cunglq
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC cmplx, max, min, real
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 = slamch( 'Epsilon' )
172*
173* Copy the matrix A to the array AF.
174*
175 CALL clacpy( 'Full', m, n, a, lda, af, lda )
176*
177* Factorize the matrix A in the array AF.
178*
179 srnamt = 'CGELQF'
180 CALL cgelqf( m, n, af, lda, tau, work, lwork, info )
181*
182* Copy details of Q
183*
184 CALL claset( 'Full', n, n, rogue, rogue, q, lda )
185 IF( n.GT.1 )
186 \$ CALL clacpy( 'Upper', m, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
187*
188* Generate the n-by-n matrix Q
189*
190 srnamt = 'CUNGLQ'
191 CALL cunglq( n, n, minmn, q, lda, tau, work, lwork, info )
192*
193* Copy L
194*
195 CALL claset( 'Full', m, n, cmplx( zero ), cmplx( zero ), l, lda )
196 CALL clacpy( 'Lower', m, n, af, lda, l, lda )
197*
198* Compute L - A*Q'
199*
200 CALL cgemm( 'No transpose', 'Conjugate transpose', m, n, n,
201 \$ cmplx( -one ), a, lda, q, lda, cmplx( one ), l, lda )
202*
203* Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) .
204*
205 anorm = clange( '1', m, n, a, lda, rwork )
206 resid = clange( '1', m, n, l, lda, rwork )
207 IF( anorm.GT.zero ) THEN
208 result( 1 ) = ( ( resid / real( max( 1, n ) ) ) / anorm ) / eps
209 ELSE
210 result( 1 ) = zero
211 END IF
212*
213* Compute I - Q*Q'
214*
215 CALL claset( 'Full', n, n, cmplx( zero ), cmplx( one ), l, lda )
216 CALL cherk( 'Upper', 'No transpose', n, n, -one, q, lda, one, l,
217 \$ lda )
218*
219* Compute norm( I - Q*Q' ) / ( N * EPS ) .
220*
221 resid = clansy( '1', 'Upper', n, l, lda, rwork )
222*
223 result( 2 ) = ( resid / real( max( 1, n ) ) ) / eps
224*
225 RETURN
226*
227* End of CLQT01
228*
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:173
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
subroutine cgelqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGELQF
Definition: cgelqf.f:143
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
subroutine cunglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGLQ
Definition: cunglq.f:127
real function clansy(NORM, UPLO, N, A, LDA, WORK)
CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansy.f:123
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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