 LAPACK  3.10.1 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 )```

Definition at line 133 of file dlqt02.f.

135 *
136 * -- LAPACK test routine --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 *
140 * .. Scalar Arguments ..
141  INTEGER K, LDA, LWORK, M, N
142 * ..
143 * .. Array Arguments ..
144  DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), L( LDA, * ),
145  \$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
146  \$ WORK( LWORK )
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Parameters ..
152  DOUBLE PRECISION ZERO, ONE
153  parameter( zero = 0.0d+0, one = 1.0d+0 )
154  DOUBLE PRECISION ROGUE
155  parameter( rogue = -1.0d+10 )
156 * ..
157 * .. Local Scalars ..
158  INTEGER INFO
159  DOUBLE PRECISION ANORM, EPS, RESID
160 * ..
161 * .. External Functions ..
162  DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
163  EXTERNAL dlamch, dlange, dlansy
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL dgemm, dlacpy, dlaset, dorglq, dsyrk
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC dble, max
170 * ..
171 * .. Scalars in Common ..
172  CHARACTER*32 SRNAMT
173 * ..
174 * .. Common blocks ..
175  COMMON / srnamc / srnamt
176 * ..
177 * .. Executable Statements ..
178 *
179  eps = dlamch( 'Epsilon' )
180 *
181 * Copy the first k rows of the factorization to the array Q
182 *
183  CALL dlaset( 'Full', m, n, rogue, rogue, q, lda )
184  CALL dlacpy( 'Upper', k, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
185 *
186 * Generate the first n columns of the matrix Q
187 *
188  srnamt = 'DORGLQ'
189  CALL dorglq( m, n, k, q, lda, tau, work, lwork, info )
190 *
191 * Copy L(1:k,1:m)
192 *
193  CALL dlaset( 'Full', k, m, zero, zero, l, lda )
194  CALL dlacpy( 'Lower', k, m, af, lda, l, lda )
195 *
196 * Compute L(1:k,1:m) - A(1:k,1:n) * Q(1:m,1:n)'
197 *
198  CALL dgemm( 'No transpose', 'Transpose', k, m, n, -one, a, lda, q,
199  \$ lda, one, l, lda )
200 *
201 * Compute norm( L - A*Q' ) / ( N * norm(A) * EPS ) .
202 *
203  anorm = dlange( '1', k, n, a, lda, rwork )
204  resid = dlange( '1', k, m, l, lda, rwork )
205  IF( anorm.GT.zero ) THEN
206  result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
207  ELSE
208  result( 1 ) = zero
209  END IF
210 *
211 * Compute I - Q*Q'
212 *
213  CALL dlaset( 'Full', m, m, zero, one, l, lda )
214  CALL dsyrk( 'Upper', 'No transpose', m, n, -one, q, lda, one, l,
215  \$ lda )
216 *
217 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
218 *
219  resid = dlansy( '1', 'Upper', m, l, lda, rwork )
220 *
221  result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
222 *
223  RETURN
224 *
225 * End of DLQT02
226 *
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 dorglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGLQ
Definition: dorglq.f:127
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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