LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
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 )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011

Definition at line 128 of file cqrt01.f.

128 *
129 * -- LAPACK test routine (version 3.4.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * November 2011
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, cgeqrf, cherk, clacpy, claset, cungqr
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 = 'CGEQRF'
183  CALL cgeqrf( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL claset( 'Full', m, m, rogue, rogue, q, lda )
188  CALL clacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
189 *
190 * Generate the m-by-m matrix Q
191 *
192  srnamt = 'CUNGQR'
193  CALL cungqr( m, m, minmn, q, lda, tau, work, lwork, info )
194 *
195 * Copy R
196 *
197  CALL claset( 'Full', m, n, cmplx( zero ), cmplx( zero ), r, lda )
198  CALL clacpy( 'Upper', m, n, af, lda, r, lda )
199 *
200 * Compute R - Q'*A
201 *
202  CALL cgemm( 'Conjugate transpose', 'No transpose', m, n, m,
203  $ cmplx( -one ), q, lda, a, lda, cmplx( one ), r, lda )
204 *
205 * Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
206 *
207  anorm = clange( '1', m, n, a, lda, rwork )
208  resid = clange( '1', m, n, r, lda, rwork )
209  IF( anorm.GT.zero ) THEN
210  result( 1 ) = ( ( resid / REAL( MAX( 1, M ) ) ) / anorm ) / eps
211  ELSE
212  result( 1 ) = zero
213  END IF
214 *
215 * Compute I - Q'*Q
216 *
217  CALL claset( 'Full', m, m, cmplx( zero ), cmplx( one ), r, lda )
218  CALL cherk( 'Upper', 'Conjugate transpose', m, m, -one, q, lda,
219  $ one, r, lda )
220 *
221 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
222 *
223  resid = clansy( '1', 'Upper', m, r, lda, rwork )
224 *
225  result( 2 ) = ( resid / REAL( MAX( 1, M ) ) ) / eps
226 *
227  RETURN
228 *
229 * End of CQRT01
230 *
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 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 cgeqrf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGEQRF
Definition: cgeqrf.f:138
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 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 slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine cungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGQR
Definition: cungqr.f:130
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189

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