LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dqrt01p()

 subroutine dqrt01p ( integer M, integer N, double precision, dimension( lda, * ) A, double precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) Q, double precision, dimension( lda, * ) R, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * ) RWORK, double precision, dimension( * ) RESULT )

DQRT01P

Purpose:
``` DQRT01P tests DGEQRFP, which computes the QR factorization of an m-by-n
matrix A, and partially tests DORGQR which forms the m-by-m
orthogonal matrix Q.

DQRT01P 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 DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A.``` [out] AF ``` AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of A, as returned by DGEQRFP. See DGEQRFP for further details.``` [out] Q ``` Q is DOUBLE PRECISION array, dimension (LDA,M) The m-by-m orthogonal matrix Q.``` [out] R ` R is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by DGEQRFP.``` [out] WORK ` WORK is DOUBLE PRECISION 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 )```
Date
December 2016

Definition at line 128 of file dqrt01p.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  DOUBLE PRECISION a( lda, * ), af( lda, * ), q( lda, * ),
139  \$ r( lda, * ), result( * ), rwork( * ), tau( * ),
140  \$ work( lwork )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  DOUBLE PRECISION zero, one
147  parameter( zero = 0.0d+0, one = 1.0d+0 )
148  DOUBLE PRECISION rogue
149  parameter( rogue = -1.0d+10 )
150 * ..
151 * .. Local Scalars ..
152  INTEGER info, minmn
153  DOUBLE PRECISION anorm, eps, resid
154 * ..
155 * .. External Functions ..
156  DOUBLE PRECISION dlamch, dlange, dlansy
157  EXTERNAL dlamch, dlange, dlansy
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL dgemm, dgeqrfp, dlacpy, dlaset, dorgqr, dsyrk
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC dble, max, min
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 = dlamch( 'Epsilon' )
175 *
176 * Copy the matrix A to the array AF.
177 *
178  CALL dlacpy( 'Full', m, n, a, lda, af, lda )
179 *
180 * Factorize the matrix A in the array AF.
181 *
182  srnamt = 'DGEQRFP'
183  CALL dgeqrfp( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL dlaset( 'Full', m, m, rogue, rogue, q, lda )
188  CALL dlacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
189 *
190 * Generate the m-by-m matrix Q
191 *
192  srnamt = 'DORGQR'
193  CALL dorgqr( m, m, minmn, q, lda, tau, work, lwork, info )
194 *
195 * Copy R
196 *
197  CALL dlaset( 'Full', m, n, zero, zero, r, lda )
198  CALL dlacpy( 'Upper', m, n, af, lda, r, lda )
199 *
200 * Compute R - Q'*A
201 *
202  CALL dgemm( 'Transpose', 'No transpose', m, n, m, -one, q, lda, a,
203  \$ lda, one, r, lda )
204 *
205 * Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
206 *
207  anorm = dlange( '1', m, n, a, lda, rwork )
208  resid = dlange( '1', m, n, r, lda, rwork )
209  IF( anorm.GT.zero ) THEN
210  result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
211  ELSE
212  result( 1 ) = zero
213  END IF
214 *
215 * Compute I - Q'*Q
216 *
217  CALL dlaset( 'Full', m, m, zero, one, r, lda )
218  CALL dsyrk( 'Upper', 'Transpose', m, m, -one, q, lda, one, r,
219  \$ lda )
220 *
221 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
222 *
223  resid = dlansy( '1', 'Upper', m, r, lda, rwork )
224 *
225  result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
226 *
227  RETURN
228 *
229 * End of DQRT01P
230 *
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:105
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
double precision function dlansy(NORM, UPLO, N, A, LDA, WORK)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.
Definition: dlansy.f:124
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: dlaset.f:112
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:171
subroutine dorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGQR
Definition: dorgqr.f:130
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:116
subroutine dgeqrfp(M, N, A, LDA, TAU, WORK, LWORK, INFO)
DGEQRFP
Definition: dgeqrfp.f:141
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