 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dqrt01()

 subroutine dqrt01 ( 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 )

DQRT01

Purpose:
``` DQRT01 tests DGEQRF, 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.

DQRT01 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 DGEQRF. See DGEQRF 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 DGEQRF.``` [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 )```

Definition at line 124 of file dqrt01.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 A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
136 \$ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
137 \$ WORK( LWORK )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 DOUBLE PRECISION ZERO, ONE
144 parameter( zero = 0.0d+0, one = 1.0d+0 )
145 DOUBLE PRECISION ROGUE
146 parameter( rogue = -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, DLANGE, DLANSY
154 EXTERNAL dlamch, dlange, dlansy
155* ..
156* .. External Subroutines ..
157 EXTERNAL dgemm, dgeqrf, dlacpy, dlaset, dorgqr, dsyrk
158* ..
159* .. Intrinsic Functions ..
160 INTRINSIC dble, 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 dlacpy( 'Full', m, n, a, lda, af, lda )
176*
177* Factorize the matrix A in the array AF.
178*
179 srnamt = 'DGEQRF'
180 CALL dgeqrf( m, n, af, lda, tau, work, lwork, info )
181*
182* Copy details of Q
183*
184 CALL dlaset( 'Full', m, m, rogue, rogue, q, lda )
185 CALL dlacpy( 'Lower', m-1, n, af( 2, 1 ), lda, q( 2, 1 ), lda )
186*
187* Generate the m-by-m matrix Q
188*
189 srnamt = 'DORGQR'
190 CALL dorgqr( m, m, minmn, q, lda, tau, work, lwork, info )
191*
192* Copy R
193*
194 CALL dlaset( 'Full', m, n, zero, zero, r, lda )
195 CALL dlacpy( 'Upper', m, n, af, lda, r, lda )
196*
197* Compute R - Q'*A
198*
199 CALL dgemm( 'Transpose', 'No transpose', m, n, m, -one, q, lda, a,
200 \$ lda, one, r, lda )
201*
202* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
203*
204 anorm = dlange( '1', m, n, a, lda, rwork )
205 resid = dlange( '1', m, n, r, lda, rwork )
206 IF( anorm.GT.zero ) THEN
207 result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
208 ELSE
209 result( 1 ) = zero
210 END IF
211*
212* Compute I - Q'*Q
213*
214 CALL dlaset( 'Full', m, m, zero, one, r, lda )
215 CALL dsyrk( 'Upper', 'Transpose', m, m, -one, q, lda, one, r,
216 \$ lda )
217*
218* Compute norm( I - Q'*Q ) / ( M * EPS ) .
219*
220 resid = dlansy( '1', 'Upper', m, r, lda, rwork )
221*
222 result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
223*
224 RETURN
225*
226* End of DQRT01
227*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
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:110
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:169
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
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:114
subroutine dgeqrf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
DGEQRF
Definition: dgeqrf.f:146
subroutine dorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGQR
Definition: dorgqr.f:128
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,...
Definition: dlansy.f:122
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