 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ cqrt01()

 subroutine cqrt01 ( 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 )

CQRT01

Purpose:
``` CQRT01 tests CGEQRF, which computes the QR factorization of an m-by-n
matrix A, and partially tests CUNGQR which forms the m-by-m
orthogonal matrix Q.

CQRT01 compares R with Q'*A, 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 QR factorization of A, as returned by CGEQRF. See CGEQRF for further details.``` [out] Q ``` Q is COMPLEX array, dimension (LDA,M) The m-by-m 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 R. LDA >= max(M,N).``` [out] TAU ``` TAU is COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by CGEQRF.``` [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 (M)` [out] RESULT ``` RESULT is REAL array, dimension (2) The test ratios: RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS ) RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )```

Definition at line 124 of file cqrt01.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, cgeqrf, cherk, clacpy, claset, cungqr
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 = 'CGEQRF'
180  CALL cgeqrf( m, n, af, lda, tau, work, lwork, info )
181 *
182 * Copy details of Q
183 *
184  CALL claset( 'Full', m, m, rogue, rogue, q, lda )
185  CALL clacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
186 *
187 * Generate the m-by-m matrix Q
188 *
189  srnamt = 'CUNGQR'
190  CALL cungqr( m, m, minmn, q, lda, tau, work, lwork, info )
191 *
192 * Copy R
193 *
194  CALL claset( 'Full', m, n, cmplx( zero ), cmplx( zero ), r, lda )
195  CALL clacpy( 'Upper', m, n, af, lda, r, lda )
196 *
197 * Compute R - Q'*A
198 *
199  CALL cgemm( 'Conjugate transpose', 'No transpose', m, n, m,
200  \$ cmplx( -one ), q, lda, a, lda, cmplx( one ), r, lda )
201 *
202 * Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
203 *
204  anorm = clange( '1', m, n, a, lda, rwork )
205  resid = clange( '1', m, n, r, lda, rwork )
206  IF( anorm.GT.zero ) THEN
207  result( 1 ) = ( ( resid / real( max( 1, m ) ) ) / anorm ) / eps
208  ELSE
209  result( 1 ) = zero
210  END IF
211 *
212 * Compute I - Q'*Q
213 *
214  CALL claset( 'Full', m, m, cmplx( zero ), cmplx( one ), r, lda )
215  CALL cherk( 'Upper', 'Conjugate transpose', m, m, -one, q, lda,
216  \$ one, r, lda )
217 *
218 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
219 *
220  resid = clansy( '1', 'Upper', m, r, lda, rwork )
221 *
222  result( 2 ) = ( resid / real( max( 1, m ) ) ) / eps
223 *
224  RETURN
225 *
226 * End of CQRT01
227 *
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 cgeqrf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGEQRF
Definition: cgeqrf.f:146
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 cungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGQR
Definition: cungqr.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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