LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine srqt01 ( integer M, integer N, 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 )

SRQT01

Purpose:
``` SRQT01 tests SGERQF, which computes the RQ factorization of an m-by-n
matrix A, and partially tests SORGRQ which forms the n-by-n
orthogonal matrix Q.

SRQT01 compares R with A*Q', and checks that Q is orthogonal.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix A. N >= 0.``` [in] A ``` A is REAL array, dimension (LDA,N) The m-by-n matrix A.``` [out] 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) The n-by-n orthogonal matrix Q.``` [out] R ` R is REAL array, dimension (LDA,max(M,N))` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= max(M,N).``` [out] TAU ``` TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by SGERQF.``` [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 (max(M,N))` [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 )```
Date
November 2011

Definition at line 128 of file srqt01.f.

128 *
129 * -- LAPACK test routine (version 3.4.0) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * November 2011
133 *
134 * .. Scalar Arguments ..
135  INTEGER lda, lwork, m, n
136 * ..
137 * .. Array Arguments ..
138  REAL a( lda, * ), af( lda, * ), q( lda, * ),
139  \$ r( lda, * ), result( * ), rwork( * ), tau( * ),
140  \$ work( lwork )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  REAL zero, one
147  parameter ( zero = 0.0e+0, one = 1.0e+0 )
148  REAL rogue
149  parameter ( rogue = -1.0e+10 )
150 * ..
151 * .. Local Scalars ..
152  INTEGER info, minmn
153  REAL anorm, eps, resid
154 * ..
155 * .. External Functions ..
156  REAL slamch, slange, slansy
157  EXTERNAL slamch, slange, slansy
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL sgemm, sgerqf, slacpy, slaset, sorgrq, ssyrk
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC max, min, real
164 * ..
165 * .. Scalars in Common ..
166  CHARACTER*32 srnamt
167 * ..
168 * .. Common blocks ..
169  COMMON / srnamc / srnamt
170 * ..
171 * .. Executable Statements ..
172 *
173  minmn = min( m, n )
174  eps = slamch( 'Epsilon' )
175 *
176 * Copy the matrix A to the array AF.
177 *
178  CALL slacpy( 'Full', m, n, a, lda, af, lda )
179 *
180 * Factorize the matrix A in the array AF.
181 *
182  srnamt = 'SGERQF'
183  CALL sgerqf( m, n, af, lda, tau, work, lwork, info )
184 *
185 * Copy details of Q
186 *
187  CALL slaset( 'Full', n, n, rogue, rogue, q, lda )
188  IF( m.LE.n ) THEN
189  IF( m.GT.0 .AND. m.LT.n )
190  \$ CALL slacpy( 'Full', m, n-m, af, lda, q( n-m+1, 1 ), lda )
191  IF( m.GT.1 )
192  \$ CALL slacpy( 'Lower', m-1, m-1, af( 2, n-m+1 ), lda,
193  \$ q( n-m+2, n-m+1 ), lda )
194  ELSE
195  IF( n.GT.1 )
196  \$ CALL slacpy( 'Lower', n-1, n-1, af( m-n+2, 1 ), lda,
197  \$ q( 2, 1 ), lda )
198  END IF
199 *
200 * Generate the n-by-n matrix Q
201 *
202  srnamt = 'SORGRQ'
203  CALL sorgrq( n, n, minmn, q, lda, tau, work, lwork, info )
204 *
205 * Copy R
206 *
207  CALL slaset( 'Full', m, n, zero, zero, r, lda )
208  IF( m.LE.n ) THEN
209  IF( m.GT.0 )
210  \$ CALL slacpy( 'Upper', m, m, af( 1, n-m+1 ), lda,
211  \$ r( 1, n-m+1 ), lda )
212  ELSE
213  IF( m.GT.n .AND. n.GT.0 )
214  \$ CALL slacpy( 'Full', m-n, n, af, lda, r, lda )
215  IF( n.GT.0 )
216  \$ CALL slacpy( 'Upper', n, n, af( m-n+1, 1 ), lda,
217  \$ r( m-n+1, 1 ), lda )
218  END IF
219 *
220 * Compute R - A*Q'
221 *
222  CALL sgemm( 'No transpose', 'Transpose', m, n, n, -one, a, lda, q,
223  \$ lda, one, r, lda )
224 *
225 * Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
226 *
227  anorm = slange( '1', m, n, a, lda, rwork )
228  resid = slange( '1', m, n, r, lda, rwork )
229  IF( anorm.GT.zero ) THEN
230  result( 1 ) = ( ( resid / REAL( MAX( 1, N ) ) ) / anorm ) / eps
231  ELSE
232  result( 1 ) = zero
233  END IF
234 *
235 * Compute I - Q*Q'
236 *
237  CALL slaset( 'Full', n, n, zero, one, r, lda )
238  CALL ssyrk( 'Upper', 'No transpose', n, n, -one, q, lda, one, r,
239  \$ lda )
240 *
241 * Compute norm( I - Q*Q' ) / ( N * EPS ) .
242 *
243  resid = slansy( '1', 'Upper', n, r, lda, rwork )
244 *
245  result( 2 ) = ( resid / REAL( MAX( 1, N ) ) ) / eps
246 *
247  RETURN
248 *
249 * End of SRQT01
250 *
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
subroutine sgerqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGERQF
Definition: sgerqf.f:140
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine sorgrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGRQ
Definition: sorgrq.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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