 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dqlt02()

 subroutine dqlt02 ( 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 )

DQLT02

Purpose:
``` DQLT02 tests DORGQL, which generates an m-by-n matrix Q with
orthonornmal columns that is defined as the product of k elementary
reflectors.

Given the QL factorization of an m-by-n matrix A, DQLT02 generates
the orthogonal matrix Q defined by the factorization of the last k
columns of A; it compares L(m-n+1:m,n-k+1:n) with
Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns 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. M >= N >= 0.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.``` [in] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A which was factorized by DQLT01.``` [in] AF ``` AF is DOUBLE PRECISION array, dimension (LDA,N) Details of the QL factorization of A, as returned by DGEQLF. See DGEQLF for further details.``` [out] Q ` Q is DOUBLE PRECISION array, dimension (LDA,N)` [out] L ` L is DOUBLE PRECISION array, dimension (LDA,N)` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= M.``` [in] TAU ``` TAU is DOUBLE PRECISION array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QL 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 - Q'*A ) / ( M * norm(A) * EPS ) RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )```

Definition at line 134 of file dqlt02.f.

136 *
137 * -- LAPACK test routine --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 *
141 * .. Scalar Arguments ..
142  INTEGER K, LDA, LWORK, M, N
143 * ..
144 * .. Array Arguments ..
145  DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), L( LDA, * ),
146  \$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
147  \$ WORK( LWORK )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  DOUBLE PRECISION ZERO, ONE
154  parameter( zero = 0.0d+0, one = 1.0d+0 )
155  DOUBLE PRECISION ROGUE
156  parameter( rogue = -1.0d+10 )
157 * ..
158 * .. Local Scalars ..
159  INTEGER INFO
160  DOUBLE PRECISION ANORM, EPS, RESID
161 * ..
162 * .. External Functions ..
163  DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
164  EXTERNAL dlamch, dlange, dlansy
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL dgemm, dlacpy, dlaset, dorgql, dsyrk
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC dble, max
171 * ..
172 * .. Scalars in Common ..
173  CHARACTER*32 SRNAMT
174 * ..
175 * .. Common blocks ..
176  COMMON / srnamc / srnamt
177 * ..
178 * .. Executable Statements ..
179 *
180 * Quick return if possible
181 *
182  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
183  result( 1 ) = zero
184  result( 2 ) = zero
185  RETURN
186  END IF
187 *
188  eps = dlamch( 'Epsilon' )
189 *
190 * Copy the last k columns of the factorization to the array Q
191 *
192  CALL dlaset( 'Full', m, n, rogue, rogue, q, lda )
193  IF( k.LT.m )
194  \$ CALL dlacpy( 'Full', m-k, k, af( 1, n-k+1 ), lda,
195  \$ q( 1, n-k+1 ), lda )
196  IF( k.GT.1 )
197  \$ CALL dlacpy( 'Upper', k-1, k-1, af( m-k+1, n-k+2 ), lda,
198  \$ q( m-k+1, n-k+2 ), lda )
199 *
200 * Generate the last n columns of the matrix Q
201 *
202  srnamt = 'DORGQL'
203  CALL dorgql( m, n, k, q, lda, tau( n-k+1 ), work, lwork, info )
204 *
205 * Copy L(m-n+1:m,n-k+1:n)
206 *
207  CALL dlaset( 'Full', n, k, zero, zero, l( m-n+1, n-k+1 ), lda )
208  CALL dlacpy( 'Lower', k, k, af( m-k+1, n-k+1 ), lda,
209  \$ l( m-k+1, n-k+1 ), lda )
210 *
211 * Compute L(m-n+1:m,n-k+1:n) - Q(1:m,m-n+1:m)' * A(1:m,n-k+1:n)
212 *
213  CALL dgemm( 'Transpose', 'No transpose', n, k, m, -one, q, lda,
214  \$ a( 1, n-k+1 ), lda, one, l( m-n+1, n-k+1 ), lda )
215 *
216 * Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
217 *
218  anorm = dlange( '1', m, k, a( 1, n-k+1 ), lda, rwork )
219  resid = dlange( '1', n, k, l( m-n+1, n-k+1 ), lda, rwork )
220  IF( anorm.GT.zero ) THEN
221  result( 1 ) = ( ( resid / dble( max( 1, m ) ) ) / anorm ) / eps
222  ELSE
223  result( 1 ) = zero
224  END IF
225 *
226 * Compute I - Q'*Q
227 *
228  CALL dlaset( 'Full', n, n, zero, one, l, lda )
229  CALL dsyrk( 'Upper', 'Transpose', n, m, -one, q, lda, one, l,
230  \$ lda )
231 *
232 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
233 *
234  resid = dlansy( '1', 'Upper', n, l, lda, rwork )
235 *
236  result( 2 ) = ( resid / dble( max( 1, m ) ) ) / eps
237 *
238  RETURN
239 *
240 * End of DQLT02
241 *
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 dorgql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGQL
Definition: dorgql.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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