LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ crqt01()

 subroutine crqt01 ( integer M, integer N, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) R, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT )

CRQT01

Purpose:
``` CRQT01 tests CGERQF, which computes the RQ factorization of an m-by-n
matrix A, and partially tests CUNGRQ which forms the n-by-n
orthogonal matrix Q.

CRQT01 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 array, dimension (LDA,N) The m-by-n matrix A.``` [out] AF ``` AF is COMPLEX array, dimension (LDA,N) Details of the RQ factorization of A, as returned by CGERQF. See CGERQF for further details.``` [out] Q ``` Q is COMPLEX array, dimension (LDA,N) The n-by-n orthogonal matrix Q.``` [out] R ` R 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 CGERQF.``` [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( R - A*Q' ) / ( N * norm(A) * EPS ) RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )```
Date
December 2016

Definition at line 128 of file crqt01.f.

128 *
129 * -- LAPACK test routine (version 3.7.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * December 2016
133 *
134 * .. Scalar Arguments ..
135  INTEGER lda, lwork, m, n
136 * ..
137 * .. Array Arguments ..
138  REAL result( * ), rwork( * )
139  COMPLEX a( lda, * ), af( lda, * ), q( lda, * ),
140  \$ r( lda, * ), tau( * ), work( lwork )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  REAL zero, one
147  parameter( zero = 0.0e+0, one = 1.0e+0 )
148  COMPLEX rogue
149  parameter( rogue = ( -1.0e+10, -1.0e+10 ) )
150 * ..
151 * .. Local Scalars ..
152  INTEGER info, minmn
153  REAL anorm, eps, resid
154 * ..
155 * .. External Functions ..
156  REAL clange, clansy, slamch
157  EXTERNAL clange, clansy, slamch
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL cgemm, cgerqf, cherk, clacpy, claset, cungrq
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC cmplx, max, min, real
164 * ..
165 * .. Scalars in Common ..
166  CHARACTER*32 srnamt
167 * ..
168 * .. Common blocks ..
169  COMMON / srnamc / srnamt
170 * ..
171 * .. Executable Statements ..
172 *
173  minmn = min( m, n )
174  eps = slamch( 'Epsilon' )
175 *
176 * Copy the matrix A to the array AF.
177 *
178  CALL clacpy( 'Full', m, n, a, lda, af, lda )
179 *
180 * Factorize the matrix A in the array AF.
181 *
182  srnamt = 'CGERQF'
183  CALL cgerqf( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL claset( 'Full', n, n, rogue, rogue, q, lda )
188  IF( m.LE.n ) THEN
189  IF( m.GT.0 .AND. m.LT.n )
190  \$ CALL clacpy( 'Full', m, n-m, af, lda, q( n-m+1, 1 ), lda )
191  IF( m.GT.1 )
192  \$ CALL clacpy( 'Lower', m-1, m-1, af( 2, n-m+1 ), lda,
193  \$ q( n-m+2, n-m+1 ), lda )
194  ELSE
195  IF( n.GT.1 )
196  \$ CALL clacpy( 'Lower', n-1, n-1, af( m-n+2, 1 ), lda,
197  \$ q( 2, 1 ), lda )
198  END IF
199 *
200 * Generate the n-by-n matrix Q
201 *
202  srnamt = 'CUNGRQ'
203  CALL cungrq( n, n, minmn, q, lda, tau, work, lwork, info )
204 *
205 * Copy R
206 *
207  CALL claset( 'Full', m, n, cmplx( zero ), cmplx( zero ), r, lda )
208  IF( m.LE.n ) THEN
209  IF( m.GT.0 )
210  \$ CALL clacpy( 'Upper', m, m, af( 1, n-m+1 ), lda,
211  \$ r( 1, n-m+1 ), lda )
212  ELSE
213  IF( m.GT.n .AND. n.GT.0 )
214  \$ CALL clacpy( 'Full', m-n, n, af, lda, r, lda )
215  IF( n.GT.0 )
216  \$ CALL clacpy( 'Upper', n, n, af( m-n+1, 1 ), lda,
217  \$ r( m-n+1, 1 ), lda )
218  END IF
219 *
220 * Compute R - A*Q'
221 *
222  CALL cgemm( 'No transpose', 'Conjugate transpose', m, n, n,
223  \$ cmplx( -one ), a, lda, q, lda, cmplx( one ), r, lda )
224 *
225 * Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
226 *
227  anorm = clange( '1', m, n, a, lda, rwork )
228  resid = clange( '1', m, n, r, lda, rwork )
229  IF( anorm.GT.zero ) THEN
230  result( 1 ) = ( ( resid / REAL( MAX( 1, N ) ) ) / anorm ) / eps
231  ELSE
232  result( 1 ) = zero
233  END IF
234 *
235 * Compute I - Q*Q'
236 *
237  CALL claset( 'Full', n, n, cmplx( zero ), cmplx( one ), r, lda )
238  CALL cherk( 'Upper', 'No transpose', n, n, -one, q, lda, one, r,
239  \$ lda )
240 *
241 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
242 *
243  resid = clansy( '1', 'Upper', n, r, lda, rwork )
244 *
245  result( 2 ) = ( resid / REAL( MAX( 1, N ) ) ) / eps
246 *
247  RETURN
248 *
249 * End of CRQT01
250 *
subroutine cungrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGRQ
Definition: cungrq.f:130
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:108
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:175
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:117
subroutine cgerqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGERQF
Definition: cgerqf.f:140
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:105
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, or the element of largest absolute value of a complex symmetric matrix.
Definition: clansy.f:125
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
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