LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dlqt02()

 subroutine dlqt02 ( integer M, integer N, integer K, double precision, dimension( lda, * ) A, double precision, dimension( lda, * ) AF, double precision, dimension( lda, * ) Q, double precision, dimension( lda, * ) L, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( lwork ) WORK, integer LWORK, double precision, dimension( * ) RWORK, double precision, dimension( * ) RESULT )

DLQT02

Purpose:
``` DLQT02 tests DORGLQ, which generates an m-by-n matrix Q with
orthonornmal rows that is defined as the product of k elementary
reflectors.

Given the LQ factorization of an m-by-n matrix A, DLQT02 generates
the orthogonal matrix Q defined by the factorization of the first k
rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
checks that the rows of Q are orthonormal.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix Q to be generated. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix Q to be generated. N >= M >= 0.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.``` [in] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A which was factorized by DLQT01.``` [in] AF ``` AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the LQ factorization of A, as returned by DGELQF. See DGELQF for further details.``` [out] Q ` Q is DOUBLE PRECISION array, dimension (LDA,N)` [out] L ` L is DOUBLE PRECISION array, dimension (LDA,M)` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= N.``` [in] TAU ``` TAU is DOUBLE PRECISION array, dimension (M) The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.``` [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( L - A*Q' ) / ( N * norm(A) * EPS ) RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )```
Date
December 2016

Definition at line 137 of file dlqt02.f.

137 *
138 * -- LAPACK test routine (version 3.7.0) --
139 * -- LAPACK is a software package provided by Univ. of Tennessee, --
140 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141 * December 2016
142 *
143 * .. Scalar Arguments ..
144  INTEGER k, lda, lwork, m, n
145 * ..
146 * .. Array Arguments ..
147  DOUBLE PRECISION a( lda, * ), af( lda, * ), l( lda, * ),
148  \$ q( lda, * ), result( * ), rwork( * ), tau( * ),
149  \$ work( lwork )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  DOUBLE PRECISION zero, one
156  parameter( zero = 0.0d+0, one = 1.0d+0 )
157  DOUBLE PRECISION rogue
158  parameter( rogue = -1.0d+10 )
159 * ..
160 * .. Local Scalars ..
161  INTEGER info
162  DOUBLE PRECISION anorm, eps, resid
163 * ..
164 * .. External Functions ..
165  DOUBLE PRECISION dlamch, dlange, dlansy
166  EXTERNAL dlamch, dlange, dlansy
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL dgemm, dlacpy, dlaset, dorglq, dsyrk
170 * ..
171 * .. Intrinsic Functions ..
172  INTRINSIC dble, max
173 * ..
174 * .. Scalars in Common ..
175  CHARACTER*32 srnamt
176 * ..
177 * .. Common blocks ..
178  COMMON / srnamc / srnamt
179 * ..
180 * .. Executable Statements ..
181 *
182  eps = dlamch( 'Epsilon' )
183 *
184 * Copy the first k rows of the factorization to the array Q
185 *
186  CALL dlaset( 'Full', m, n, rogue, rogue, q, lda )
187  CALL dlacpy( 'Upper', k, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
188 *
189 * Generate the first n columns of the matrix Q
190 *
191  srnamt = 'DORGLQ'
192  CALL dorglq( m, n, k, q, lda, tau, work, lwork, info )
193 *
194 * Copy L(1:k,1:m)
195 *
196  CALL dlaset( 'Full', k, m, zero, zero, l, lda )
197  CALL dlacpy( 'Lower', k, m, af, lda, l, lda )
198 *
199 * Compute L(1:k,1:m) - A(1:k,1:n) * Q(1:m,1:n)'
200 *
201  CALL dgemm( 'No transpose', 'Transpose', k, m, n, -one, a, lda, q,
202  \$ lda, one, l, lda )
203 *
204 * Compute norm( L - A*Q' ) / ( N * norm(A) * EPS ) .
205 *
206  anorm = dlange( '1', k, n, a, lda, rwork )
207  resid = dlange( '1', k, m, l, lda, rwork )
208  IF( anorm.GT.zero ) THEN
209  result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
210  ELSE
211  result( 1 ) = zero
212  END IF
213 *
214 * Compute I - Q*Q'
215 *
216  CALL dlaset( 'Full', m, m, zero, one, l, lda )
217  CALL dsyrk( 'Upper', 'No transpose', m, n, -one, q, lda, one, l,
218  \$ lda )
219 *
220 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
221 *
222  resid = dlansy( '1', 'Upper', m, l, lda, rwork )
223 *
224  result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
225 *
226  RETURN
227 *
228 * End of DLQT02
229 *
subroutine dorglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGLQ
Definition: dorglq.f:129
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
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
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 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
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:171
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