LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zrqt01()

 subroutine zrqt01 ( integer m, integer n, complex*16, dimension( lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension( lda, * ) q, complex*16, dimension( lda, * ) r, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result )

ZRQT01

Purpose:
``` ZRQT01 tests ZGERQF, which computes the RQ factorization of an m-by-n
matrix A, and partially tests ZUNGRQ which forms the n-by-n
orthogonal matrix Q.

ZRQT01 compares R 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 RQ factorization of A, as returned by ZGERQF. See ZGERQF for further details.``` [out] Q ``` Q is COMPLEX*16 array, dimension (LDA,N) The n-by-n orthogonal matrix Q.``` [out] R ` R 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 ZGERQF.``` [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( R - A*Q' ) / ( N * norm(A) * EPS ) RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )```

Definition at line 124 of file zrqt01.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, * ), Q( LDA, * ),
137 \$ R( 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 zgemm, zgerqf, zherk, zlacpy, zlaset, zungrq
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 = 'ZGERQF'
180 CALL zgerqf( 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( m.LE.n ) THEN
186 IF( m.GT.0 .AND. m.LT.n )
187 \$ CALL zlacpy( 'Full', m, n-m, af, lda, q( n-m+1, 1 ), lda )
188 IF( m.GT.1 )
189 \$ CALL zlacpy( 'Lower', m-1, m-1, af( 2, n-m+1 ), lda,
190 \$ q( n-m+2, n-m+1 ), lda )
191 ELSE
192 IF( n.GT.1 )
193 \$ CALL zlacpy( 'Lower', n-1, n-1, af( m-n+2, 1 ), lda,
194 \$ q( 2, 1 ), lda )
195 END IF
196*
197* Generate the n-by-n matrix Q
198*
199 srnamt = 'ZUNGRQ'
200 CALL zungrq( n, n, minmn, q, lda, tau, work, lwork, info )
201*
202* Copy R
203*
204 CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), r,
205 \$ lda )
206 IF( m.LE.n ) THEN
207 IF( m.GT.0 )
208 \$ CALL zlacpy( 'Upper', m, m, af( 1, n-m+1 ), lda,
209 \$ r( 1, n-m+1 ), lda )
210 ELSE
211 IF( m.GT.n .AND. n.GT.0 )
212 \$ CALL zlacpy( 'Full', m-n, n, af, lda, r, lda )
213 IF( n.GT.0 )
214 \$ CALL zlacpy( 'Upper', n, n, af( m-n+1, 1 ), lda,
215 \$ r( m-n+1, 1 ), lda )
216 END IF
217*
218* Compute R - A*Q'
219*
220 CALL zgemm( 'No transpose', 'Conjugate transpose', m, n, n,
221 \$ dcmplx( -one ), a, lda, q, lda, dcmplx( one ), r,
222 \$ lda )
223*
224* Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
225*
226 anorm = zlange( '1', m, n, a, lda, rwork )
227 resid = zlange( '1', m, n, r, lda, rwork )
228 IF( anorm.GT.zero ) THEN
229 result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
230 ELSE
231 result( 1 ) = zero
232 END IF
233*
234* Compute I - Q*Q'
235*
236 CALL zlaset( 'Full', n, n, dcmplx( zero ), dcmplx( one ), r, lda )
237 CALL zherk( 'Upper', 'No transpose', n, n, -one, q, lda, one, r,
238 \$ lda )
239*
240* Compute norm( I - Q*Q' ) / ( N * EPS ) .
241*
242 resid = zlansy( '1', 'Upper', n, r, lda, rwork )
243*
244 result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
245*
246 RETURN
247*
248* End of ZRQT01
249*
subroutine zgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZGEMM
Definition zgemm.f:188
subroutine zgerqf(m, n, a, lda, tau, work, lwork, info)
ZGERQF
Definition zgerqf.f:139
subroutine zherk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
ZHERK
Definition zherk.f:173
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
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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
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
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 zungrq(m, n, k, a, lda, tau, work, lwork, info)
ZUNGRQ
Definition zungrq.f:128
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