LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ srqt02()

subroutine srqt02 ( integer  m,
integer  n,
integer  k,
real, dimension( lda, * )  a,
real, dimension( lda, * )  af,
real, dimension( lda, * )  q,
real, dimension( lda, * )  r,
integer  lda,
real, dimension( * )  tau,
real, dimension( lwork )  work,
integer  lwork,
real, dimension( * )  rwork,
real, dimension( * )  result 
)

SRQT02

Purpose:
 SRQT02 tests SORGRQ, which generates an m-by-n matrix Q with
 orthonormal rows that is defined as the product of k elementary
 reflectors.

 Given the RQ factorization of an m-by-n matrix A, SRQT02 generates
 the orthogonal matrix Q defined by the factorization of the last k
 rows of A; it compares R(m-k+1:m,n-m+1:n) with
 A(m-k+1:m,1:n)*Q(n-m+1:n,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 REAL array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by SRQT01.
[in]AF
          AF is REAL array, dimension (LDA,N)
          Details of the RQ factorization of A, as returned by SGERQF.
          See SGERQF for further details.
[out]Q
          Q is REAL array, dimension (LDA,N)
[out]R
          R is REAL 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 REAL array, dimension (M)
          The scalar factors of the elementary reflectors corresponding
          to the RQ 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( R - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 134 of file srqt02.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 REAL A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
146 $ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
147 $ WORK( LWORK )
148* ..
149*
150* =====================================================================
151*
152* .. Parameters ..
153 REAL ZERO, ONE
154 parameter( zero = 0.0e+0, one = 1.0e+0 )
155 REAL ROGUE
156 parameter( rogue = -1.0e+10 )
157* ..
158* .. Local Scalars ..
159 INTEGER INFO
160 REAL ANORM, EPS, RESID
161* ..
162* .. External Functions ..
163 REAL SLAMCH, SLANGE, SLANSY
164 EXTERNAL slamch, slange, slansy
165* ..
166* .. External Subroutines ..
167 EXTERNAL sgemm, slacpy, slaset, sorgrq, ssyrk
168* ..
169* .. Intrinsic Functions ..
170 INTRINSIC max, real
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 = slamch( 'Epsilon' )
189*
190* Copy the last k rows of the factorization to the array Q
191*
192 CALL slaset( 'Full', m, n, rogue, rogue, q, lda )
193 IF( k.LT.n )
194 $ CALL slacpy( 'Full', k, n-k, af( m-k+1, 1 ), lda,
195 $ q( m-k+1, 1 ), lda )
196 IF( k.GT.1 )
197 $ CALL slacpy( 'Lower', k-1, k-1, af( m-k+2, n-k+1 ), lda,
198 $ q( m-k+2, n-k+1 ), lda )
199*
200* Generate the last n rows of the matrix Q
201*
202 srnamt = 'SORGRQ'
203 CALL sorgrq( m, n, k, q, lda, tau( m-k+1 ), work, lwork, info )
204*
205* Copy R(m-k+1:m,n-m+1:n)
206*
207 CALL slaset( 'Full', k, m, zero, zero, r( m-k+1, n-m+1 ), lda )
208 CALL slacpy( 'Upper', k, k, af( m-k+1, n-k+1 ), lda,
209 $ r( m-k+1, n-k+1 ), lda )
210*
211* Compute R(m-k+1:m,n-m+1:n) - A(m-k+1:m,1:n) * Q(n-m+1:n,1:n)'
212*
213 CALL sgemm( 'No transpose', 'Transpose', k, m, n, -one,
214 $ a( m-k+1, 1 ), lda, q, lda, one, r( m-k+1, n-m+1 ),
215 $ lda )
216*
217* Compute norm( R - A*Q' ) / ( N * norm(A) * EPS ) .
218*
219 anorm = slange( '1', k, n, a( m-k+1, 1 ), lda, rwork )
220 resid = slange( '1', k, m, r( m-k+1, n-m+1 ), lda, rwork )
221 IF( anorm.GT.zero ) THEN
222 result( 1 ) = ( ( resid / real( max( 1, n ) ) ) / anorm ) / eps
223 ELSE
224 result( 1 ) = zero
225 END IF
226*
227* Compute I - Q*Q'
228*
229 CALL slaset( 'Full', m, m, zero, one, r, lda )
230 CALL ssyrk( 'Upper', 'No transpose', m, n, -one, q, lda, one, r,
231 $ lda )
232*
233* Compute norm( I - Q*Q' ) / ( N * EPS ) .
234*
235 resid = slansy( '1', 'Upper', m, r, lda, rwork )
236*
237 result( 2 ) = ( resid / real( max( 1, n ) ) ) / eps
238*
239 RETURN
240*
241* End of SRQT02
242*
subroutine sgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
SGEMM
Definition sgemm.f:188
subroutine ssyrk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
SSYRK
Definition ssyrk.f:169
subroutine slacpy(uplo, m, n, a, lda, b, ldb)
SLACPY copies all or part of one two-dimensional array to another.
Definition slacpy.f:103
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
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:114
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,...
Definition slansy.f:122
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:110
subroutine sorgrq(m, n, k, a, lda, tau, work, lwork, info)
SORGRQ
Definition sorgrq.f:128
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