LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zqrt01p()

subroutine zqrt01p ( 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 
)

ZQRT01P

Purpose:
 ZQRT01P tests ZGEQRFP, which computes the QR factorization of an m-by-n
 matrix A, and partially tests ZUNGQR which forms the m-by-m
 orthogonal matrix Q.

 ZQRT01P 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*16 array, dimension (LDA,N)
          The m-by-n matrix A.
[out]AF
          AF is COMPLEX*16 array, dimension (LDA,N)
          Details of the QR factorization of A, as returned by ZGEQRFP.
          See ZGEQRFP for further details.
[out]Q
          Q is COMPLEX*16 array, dimension (LDA,M)
          The m-by-m 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 R.
          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 ZGEQRFP.
[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 (M)
[out]RESULT
          RESULT is DOUBLE PRECISION 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.

Definition at line 124 of file zqrt01p.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, zgeqrfp, zherk, zlacpy, zlaset, zungqr
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 = 'ZGEQRFP'
180  CALL zgeqrfp( m, n, af, lda, tau, work, lwork, info )
181 *
182 * Copy details of Q
183 *
184  CALL zlaset( 'Full', m, m, rogue, rogue, q, lda )
185  CALL zlacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
186 *
187 * Generate the m-by-m matrix Q
188 *
189  srnamt = 'ZUNGQR'
190  CALL zungqr( m, m, minmn, q, lda, tau, work, lwork, info )
191 *
192 * Copy R
193 *
194  CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), r,
195  $ lda )
196  CALL zlacpy( 'Upper', m, n, af, lda, r, lda )
197 *
198 * Compute R - Q'*A
199 *
200  CALL zgemm( 'Conjugate transpose', 'No transpose', m, n, m,
201  $ dcmplx( -one ), q, lda, a, lda, dcmplx( one ), r,
202  $ lda )
203 *
204 * Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
205 *
206  anorm = zlange( '1', m, n, a, lda, rwork )
207  resid = zlange( '1', m, n, r, lda, rwork )
208  IF( anorm.GT.zero ) THEN
209  result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
210  ELSE
211  result( 1 ) = zero
212  END IF
213 *
214 * Compute I - Q'*Q
215 *
216  CALL zlaset( 'Full', m, m, dcmplx( zero ), dcmplx( one ), r, lda )
217  CALL zherk( 'Upper', 'Conjugate transpose', m, m, -one, q, lda,
218  $ one, r, lda )
219 *
220 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
221 *
222  resid = zlansy( '1', 'Upper', m, r, lda, rwork )
223 *
224  result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
225 *
226  RETURN
227 *
228 * End of ZQRT01P
229 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:173
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
subroutine zgeqrfp(M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGEQRFP
Definition: zgeqrfp.f:149
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
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 zungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQR
Definition: zungqr.f:128
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
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