 LAPACK  3.10.0 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 )```

Definition at line 124 of file crqt01.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, * ), Q( LDA, * ),
137  \$ R( 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 cgemm, cgerqf, cherk, clacpy, claset, cungrq
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 = 'CGERQF'
180  CALL cgerqf( 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( m.LE.n ) THEN
186  IF( m.GT.0 .AND. m.LT.n )
187  \$ CALL clacpy( 'Full', m, n-m, af, lda, q( n-m+1, 1 ), lda )
188  IF( m.GT.1 )
189  \$ CALL clacpy( '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 clacpy( '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 = 'CUNGRQ'
200  CALL cungrq( n, n, minmn, q, lda, tau, work, lwork, info )
201 *
202 * Copy R
203 *
204  CALL claset( 'Full', m, n, cmplx( zero ), cmplx( zero ), r, lda )
205  IF( m.LE.n ) THEN
206  IF( m.GT.0 )
207  \$ CALL clacpy( 'Upper', m, m, af( 1, n-m+1 ), lda,
208  \$ r( 1, n-m+1 ), lda )
209  ELSE
210  IF( m.GT.n .AND. n.GT.0 )
211  \$ CALL clacpy( 'Full', m-n, n, af, lda, r, lda )
212  IF( n.GT.0 )
213  \$ CALL clacpy( 'Upper', n, n, af( m-n+1, 1 ), lda,
214  \$ r( m-n+1, 1 ), lda )
215  END IF
216 *
217 * Compute R - A*Q'
218 *
219  CALL cgemm( 'No transpose', 'Conjugate transpose', m, n, n,
220  \$ cmplx( -one ), a, lda, q, lda, cmplx( one ), r, lda )
221 *
222 * Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
223 *
224  anorm = clange( '1', m, n, a, lda, rwork )
225  resid = clange( '1', m, n, r, lda, rwork )
226  IF( anorm.GT.zero ) THEN
227  result( 1 ) = ( ( resid / real( max( 1, n ) ) ) / anorm ) / eps
228  ELSE
229  result( 1 ) = zero
230  END IF
231 *
232 * Compute I - Q*Q'
233 *
234  CALL claset( 'Full', n, n, cmplx( zero ), cmplx( one ), r, lda )
235  CALL cherk( 'Upper', 'No transpose', n, n, -one, q, lda, one, r,
236  \$ lda )
237 *
238 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
239 *
240  resid = clansy( '1', 'Upper', n, r, lda, rwork )
241 *
242  result( 2 ) = ( resid / real( max( 1, n ) ) ) / eps
243 *
244  RETURN
245 *
246 * End of CRQT01
247 *
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 cgerqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGERQF
Definition: cgerqf.f:138
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 cungrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGRQ
Definition: cungrq.f:128
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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