LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine sqlt02 ( integer M, integer N, integer K, real, dimension( lda, * ) A, real, dimension( lda, * ) AF, real, dimension( lda, * ) Q, real, dimension( lda, * ) L, integer LDA, real, dimension( * ) TAU, real, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT )

SQLT02

Purpose:
``` SQLT02 tests SORGQL, 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, SQLT02 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 REAL array, dimension (LDA,N) The m-by-n matrix A which was factorized by SQLT01.``` [in] AF ``` AF is REAL array, dimension (LDA,N) Details of the QL factorization of A, as returned by SGEQLF. See SGEQLF for further details.``` [out] Q ` Q is REAL array, dimension (LDA,N)` [out] L ` L is REAL 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 REAL array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QL factorization in AF.``` [out] WORK ` WORK is REAL array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK.``` [out] RWORK ` RWORK is REAL array, dimension (M)` [out] RESULT ``` RESULT is REAL array, dimension (2) The test ratios: RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS ) RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )```
Date
November 2011

Definition at line 138 of file sqlt02.f.

138 *
139 * -- LAPACK test routine (version 3.4.0) --
140 * -- LAPACK is a software package provided by Univ. of Tennessee, --
141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142 * November 2011
143 *
144 * .. Scalar Arguments ..
145  INTEGER k, lda, lwork, m, n
146 * ..
147 * .. Array Arguments ..
148  REAL a( lda, * ), af( lda, * ), l( lda, * ),
149  \$ q( lda, * ), result( * ), rwork( * ), tau( * ),
150  \$ work( lwork )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  REAL zero, one
157  parameter ( zero = 0.0e+0, one = 1.0e+0 )
158  REAL rogue
159  parameter ( rogue = -1.0e+10 )
160 * ..
161 * .. Local Scalars ..
162  INTEGER info
163  REAL anorm, eps, resid
164 * ..
165 * .. External Functions ..
166  REAL slamch, slange, slansy
167  EXTERNAL slamch, slange, slansy
168 * ..
169 * .. External Subroutines ..
170  EXTERNAL sgemm, slacpy, slaset, sorgql, ssyrk
171 * ..
172 * .. Intrinsic Functions ..
173  INTRINSIC max, real
174 * ..
175 * .. Scalars in Common ..
176  CHARACTER*32 srnamt
177 * ..
178 * .. Common blocks ..
179  COMMON / srnamc / srnamt
180 * ..
181 * .. Executable Statements ..
182 *
183 * Quick return if possible
184 *
185  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
186  result( 1 ) = zero
187  result( 2 ) = zero
188  RETURN
189  END IF
190 *
191  eps = slamch( 'Epsilon' )
192 *
193 * Copy the last k columns of the factorization to the array Q
194 *
195  CALL slaset( 'Full', m, n, rogue, rogue, q, lda )
196  IF( k.LT.m )
197  \$ CALL slacpy( 'Full', m-k, k, af( 1, n-k+1 ), lda,
198  \$ q( 1, n-k+1 ), lda )
199  IF( k.GT.1 )
200  \$ CALL slacpy( 'Upper', k-1, k-1, af( m-k+1, n-k+2 ), lda,
201  \$ q( m-k+1, n-k+2 ), lda )
202 *
203 * Generate the last n columns of the matrix Q
204 *
205  srnamt = 'SORGQL'
206  CALL sorgql( m, n, k, q, lda, tau( n-k+1 ), work, lwork, info )
207 *
208 * Copy L(m-n+1:m,n-k+1:n)
209 *
210  CALL slaset( 'Full', n, k, zero, zero, l( m-n+1, n-k+1 ), lda )
211  CALL slacpy( 'Lower', k, k, af( m-k+1, n-k+1 ), lda,
212  \$ l( m-k+1, n-k+1 ), lda )
213 *
214 * Compute L(m-n+1:m,n-k+1:n) - Q(1:m,m-n+1:m)' * A(1:m,n-k+1:n)
215 *
216  CALL sgemm( 'Transpose', 'No transpose', n, k, m, -one, q, lda,
217  \$ a( 1, n-k+1 ), lda, one, l( m-n+1, n-k+1 ), lda )
218 *
219 * Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
220 *
221  anorm = slange( '1', m, k, a( 1, n-k+1 ), lda, rwork )
222  resid = slange( '1', n, k, l( m-n+1, n-k+1 ), lda, rwork )
223  IF( anorm.GT.zero ) THEN
224  result( 1 ) = ( ( resid / REAL( MAX( 1, M ) ) ) / anorm ) / eps
225  ELSE
226  result( 1 ) = zero
227  END IF
228 *
229 * Compute I - Q'*Q
230 *
231  CALL slaset( 'Full', n, n, zero, one, l, lda )
232  CALL ssyrk( 'Upper', 'Transpose', n, m, -one, q, lda, one, l,
233  \$ lda )
234 *
235 * Compute norm( I - Q'*Q ) / ( M * EPS ) .
236 *
237  resid = slansy( '1', 'Upper', n, l, lda, rwork )
238 *
239  result( 2 ) = ( resid / REAL( MAX( 1, M ) ) ) / eps
240 *
241  RETURN
242 *
243 * End of SQLT02
244 *
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:171
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:105
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: slaset.f:112
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:116
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine sorgql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQL
Definition: sorgql.f:130
real function slansy(NORM, UPLO, N, A, LDA, WORK)
SLANSY 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: slansy.f:124

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