 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine sgqrts ( integer N, integer M, integer P, real, dimension( lda, * ) A, real, dimension( lda, * ) AF, real, dimension( lda, * ) Q, real, dimension( lda, * ) R, integer LDA, real, dimension( * ) TAUA, real, dimension( ldb, * ) B, real, dimension( ldb, * ) BF, real, dimension( ldb, * ) Z, real, dimension( ldb, * ) T, real, dimension( ldb, * ) BWK, integer LDB, real, dimension( * ) TAUB, real, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( 4 ) RESULT )

SGQRTS

Purpose:
``` SGQRTS tests SGGQRF, which computes the GQR factorization of an
N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z.```
Parameters
 [in] N ``` N is INTEGER The number of rows of the matrices A and B. N >= 0.``` [in] M ``` M is INTEGER The number of columns of the matrix A. M >= 0.``` [in] P ``` P is INTEGER The number of columns of the matrix B. P >= 0.``` [in] A ``` A is REAL array, dimension (LDA,M) The N-by-M matrix A.``` [out] AF ``` AF is REAL array, dimension (LDA,N) Details of the GQR factorization of A and B, as returned by SGGQRF, see SGGQRF for further details.``` [out] Q ``` Q is REAL array, dimension (LDA,N) The M-by-M 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, R and Q. LDA >= max(M,N).``` [out] TAUA ``` TAUA is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by SGGQRF.``` [in] B ``` B is REAL array, dimension (LDB,P) On entry, the N-by-P matrix A.``` [out] BF ``` BF is REAL array, dimension (LDB,N) Details of the GQR factorization of A and B, as returned by SGGQRF, see SGGQRF for further details.``` [out] Z ``` Z is REAL array, dimension (LDB,P) The P-by-P orthogonal matrix Z.``` [out] T ` T is REAL array, dimension (LDB,max(P,N))` [out] BWK ` BWK is REAL array, dimension (LDB,N)` [in] LDB ``` LDB is INTEGER The leading dimension of the arrays B, BF, Z and T. LDB >= max(P,N).``` [out] TAUB ``` TAUB is REAL array, dimension (min(P,N)) The scalar factors of the elementary reflectors, as returned by SGGRQF.``` [out] WORK ` WORK is REAL array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK, LWORK >= max(N,M,P)**2.``` [out] RWORK ` RWORK is REAL array, dimension (max(N,M,P))` [out] RESULT ``` RESULT is REAL array, dimension (4) The test ratios: RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP) RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP) RESULT(3) = norm( I - Q'*Q ) / ( M*ULP ) RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )```
Date
November 2011

Definition at line 178 of file sgqrts.f.

178 *
179 * -- LAPACK test routine (version 3.4.0) --
180 * -- LAPACK is a software package provided by Univ. of Tennessee, --
181 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
182 * November 2011
183 *
184 * .. Scalar Arguments ..
185  INTEGER lda, ldb, lwork, m, p, n
186 * ..
187 * .. Array Arguments ..
188  REAL a( lda, * ), af( lda, * ), r( lda, * ),
189  \$ q( lda, * ), b( ldb, * ), bf( ldb, * ),
190  \$ t( ldb, * ), z( ldb, * ), bwk( ldb, * ),
191  \$ taua( * ), taub( * ), result( 4 ),
192  \$ rwork( * ), work( lwork )
193 * ..
194 *
195 * =====================================================================
196 *
197 * .. Parameters ..
198  REAL zero, one
199  parameter ( zero = 0.0e+0, one = 1.0e+0 )
200  REAL rogue
201  parameter ( rogue = -1.0e+10 )
202 * ..
203 * .. Local Scalars ..
204  INTEGER info
205  REAL anorm, bnorm, ulp, unfl, resid
206 * ..
207 * .. External Functions ..
208  REAL slamch, slange, slansy
209  EXTERNAL slamch, slange, slansy
210 * ..
211 * .. External Subroutines ..
212  EXTERNAL sgemm, slacpy, slaset, sorgqr,
213  \$ sorgrq, ssyrk
214 * ..
215 * .. Intrinsic Functions ..
216  INTRINSIC max, min, real
217 * ..
218 * .. Executable Statements ..
219 *
220  ulp = slamch( 'Precision' )
221  unfl = slamch( 'Safe minimum' )
222 *
223 * Copy the matrix A to the array AF.
224 *
225  CALL slacpy( 'Full', n, m, a, lda, af, lda )
226  CALL slacpy( 'Full', n, p, b, ldb, bf, ldb )
227 *
228  anorm = max( slange( '1', n, m, a, lda, rwork ), unfl )
229  bnorm = max( slange( '1', n, p, b, ldb, rwork ), unfl )
230 *
231 * Factorize the matrices A and B in the arrays AF and BF.
232 *
233  CALL sggqrf( n, m, p, af, lda, taua, bf, ldb, taub, work,
234  \$ lwork, info )
235 *
236 * Generate the N-by-N matrix Q
237 *
238  CALL slaset( 'Full', n, n, rogue, rogue, q, lda )
239  CALL slacpy( 'Lower', n-1, m, af( 2,1 ), lda, q( 2,1 ), lda )
240  CALL sorgqr( n, n, min( n, m ), q, lda, taua, work, lwork, info )
241 *
242 * Generate the P-by-P matrix Z
243 *
244  CALL slaset( 'Full', p, p, rogue, rogue, z, ldb )
245  IF( n.LE.p ) THEN
246  IF( n.GT.0 .AND. n.LT.p )
247  \$ CALL slacpy( 'Full', n, p-n, bf, ldb, z( p-n+1, 1 ), ldb )
248  IF( n.GT.1 )
249  \$ CALL slacpy( 'Lower', n-1, n-1, bf( 2, p-n+1 ), ldb,
250  \$ z( p-n+2, p-n+1 ), ldb )
251  ELSE
252  IF( p.GT.1)
253  \$ CALL slacpy( 'Lower', p-1, p-1, bf( n-p+2, 1 ), ldb,
254  \$ z( 2, 1 ), ldb )
255  END IF
256  CALL sorgrq( p, p, min( n, p ), z, ldb, taub, work, lwork, info )
257 *
258 * Copy R
259 *
260  CALL slaset( 'Full', n, m, zero, zero, r, lda )
261  CALL slacpy( 'Upper', n, m, af, lda, r, lda )
262 *
263 * Copy T
264 *
265  CALL slaset( 'Full', n, p, zero, zero, t, ldb )
266  IF( n.LE.p ) THEN
267  CALL slacpy( 'Upper', n, n, bf( 1, p-n+1 ), ldb, t( 1, p-n+1 ),
268  \$ ldb )
269  ELSE
270  CALL slacpy( 'Full', n-p, p, bf, ldb, t, ldb )
271  CALL slacpy( 'Upper', p, p, bf( n-p+1, 1 ), ldb, t( n-p+1, 1 ),
272  \$ ldb )
273  END IF
274 *
275 * Compute R - Q'*A
276 *
277  CALL sgemm( 'Transpose', 'No transpose', n, m, n, -one, q, lda, a,
278  \$ lda, one, r, lda )
279 *
280 * Compute norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP ) .
281 *
282  resid = slange( '1', n, m, r, lda, rwork )
283  IF( anorm.GT.zero ) THEN
284  result( 1 ) = ( ( resid / REAL( MAX(1,M,N) ) ) / anorm ) / ulp
285  ELSE
286  result( 1 ) = zero
287  END IF
288 *
289 * Compute T*Z - Q'*B
290 *
291  CALL sgemm( 'No Transpose', 'No transpose', n, p, p, one, t, ldb,
292  \$ z, ldb, zero, bwk, ldb )
293  CALL sgemm( 'Transpose', 'No transpose', n, p, n, -one, q, lda,
294  \$ b, ldb, one, bwk, ldb )
295 *
296 * Compute norm( T*Z - Q'*B ) / ( MAX(P,N)*norm(A)*ULP ) .
297 *
298  resid = slange( '1', n, p, bwk, ldb, rwork )
299  IF( bnorm.GT.zero ) THEN
300  result( 2 ) = ( ( resid / REAL( MAX(1,P,N ) ) )/bnorm ) / ulp
301  ELSE
302  result( 2 ) = zero
303  END IF
304 *
305 * Compute I - Q'*Q
306 *
307  CALL slaset( 'Full', n, n, zero, one, r, lda )
308  CALL ssyrk( 'Upper', 'Transpose', n, n, -one, q, lda, one, r,
309  \$ lda )
310 *
311 * Compute norm( I - Q'*Q ) / ( N * ULP ) .
312 *
313  resid = slansy( '1', 'Upper', n, r, lda, rwork )
314  result( 3 ) = ( resid / REAL( MAX( 1, N ) ) ) / ulp
315 *
316 * Compute I - Z'*Z
317 *
318  CALL slaset( 'Full', p, p, zero, one, t, ldb )
319  CALL ssyrk( 'Upper', 'Transpose', p, p, -one, z, ldb, one, t,
320  \$ ldb )
321 *
322 * Compute norm( I - Z'*Z ) / ( P*ULP ) .
323 *
324  resid = slansy( '1', 'Upper', p, t, ldb, rwork )
325  result( 4 ) = ( resid / REAL( MAX( 1, P ) ) ) / ulp
326 *
327  RETURN
328 *
329 * End of SGQRTS
330 *
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 sggqrf(N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO)
SGGQRF
Definition: sggqrf.f:217
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine sorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQR
Definition: sorgqr.f:130
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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