 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ cgqrts()

 subroutine cgqrts ( integer N, integer M, integer P, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) R, integer LDA, complex, dimension( * ) TAUA, complex, dimension( ldb, * ) B, complex, dimension( ldb, * ) BF, complex, dimension( ldb, * ) Z, complex, dimension( ldb, * ) T, complex, dimension( ldb, * ) BWK, integer LDB, complex, dimension( * ) TAUB, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( 4 ) RESULT )

CGQRTS

Purpose:
CGQRTS tests CGGQRF, 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 COMPLEX array, dimension (LDA,M) The N-by-M matrix A. [out] AF AF is COMPLEX array, dimension (LDA,N) Details of the GQR factorization of A and B, as returned by CGGQRF, see CGGQRF for further details. [out] Q Q is COMPLEX array, dimension (LDA,N) The M-by-M unitary matrix Q. [out] R R is COMPLEX 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 COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by CGGQRF. [in] B B is COMPLEX array, dimension (LDB,P) On entry, the N-by-P matrix A. [out] BF BF is COMPLEX array, dimension (LDB,N) Details of the GQR factorization of A and B, as returned by CGGQRF, see CGGQRF for further details. [out] Z Z is COMPLEX array, dimension (LDB,P) The P-by-P unitary matrix Z. [out] T T is COMPLEX array, dimension (LDB,max(P,N)) [out] BWK BWK is COMPLEX 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 COMPLEX array, dimension (min(P,N)) The scalar factors of the elementary reflectors, as returned by SGGRQF. [out] WORK WORK is COMPLEX 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 )

Definition at line 174 of file cgqrts.f.

176 *
177 * -- LAPACK test routine --
178 * -- LAPACK is a software package provided by Univ. of Tennessee, --
179 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
180 *
181 * .. Scalar Arguments ..
182  INTEGER LDA, LDB, LWORK, M, P, N
183 * ..
184 * .. Array Arguments ..
185  REAL RWORK( * ), RESULT( 4 )
186  COMPLEX A( LDA, * ), AF( LDA, * ), R( LDA, * ),
187  \$ Q( LDA, * ), B( LDB, * ), BF( LDB, * ),
188  \$ T( LDB, * ), Z( LDB, * ), BWK( LDB, * ),
189  \$ TAUA( * ), TAUB( * ), WORK( LWORK )
190 * ..
191 *
192 * =====================================================================
193 *
194 * .. Parameters ..
195  REAL ZERO, ONE
196  parameter( zero = 0.0e+0, one = 1.0e+0 )
197  COMPLEX CZERO, CONE
198  parameter( czero = ( 0.0e+0, 0.0e+0 ),
199  \$ cone = ( 1.0e+0, 0.0e+0 ) )
200  COMPLEX CROGUE
201  parameter( crogue = ( -1.0e+10, 0.0e+0 ) )
202 * ..
203 * .. Local Scalars ..
204  INTEGER INFO
205  REAL ANORM, BNORM, ULP, UNFL, RESID
206 * ..
207 * .. External Functions ..
208  REAL SLAMCH, CLANGE, CLANHE
209  EXTERNAL slamch, clange, clanhe
210 * ..
211 * .. External Subroutines ..
212  EXTERNAL cgemm, clacpy, claset, cungqr,
213  \$ cungrq, cherk
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 clacpy( 'Full', n, m, a, lda, af, lda )
226  CALL clacpy( 'Full', n, p, b, ldb, bf, ldb )
227 *
228  anorm = max( clange( '1', n, m, a, lda, rwork ), unfl )
229  bnorm = max( clange( '1', n, p, b, ldb, rwork ), unfl )
230 *
231 * Factorize the matrices A and B in the arrays AF and BF.
232 *
233  CALL cggqrf( 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 claset( 'Full', n, n, crogue, crogue, q, lda )
239  CALL clacpy( 'Lower', n-1, m, af( 2,1 ), lda, q( 2,1 ), lda )
240  CALL cungqr( n, n, min( n, m ), q, lda, taua, work, lwork, info )
241 *
242 * Generate the P-by-P matrix Z
243 *
244  CALL claset( 'Full', p, p, crogue, crogue, z, ldb )
245  IF( n.LE.p ) THEN
246  IF( n.GT.0 .AND. n.LT.p )
247  \$ CALL clacpy( 'Full', n, p-n, bf, ldb, z( p-n+1, 1 ), ldb )
248  IF( n.GT.1 )
249  \$ CALL clacpy( '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 clacpy( 'Lower', p-1, p-1, bf( n-p+2, 1 ), ldb,
254  \$ z( 2, 1 ), ldb )
255  END IF
256  CALL cungrq( p, p, min( n, p ), z, ldb, taub, work, lwork, info )
257 *
258 * Copy R
259 *
260  CALL claset( 'Full', n, m, czero, czero, r, lda )
261  CALL clacpy( 'Upper', n, m, af, lda, r, lda )
262 *
263 * Copy T
264 *
265  CALL claset( 'Full', n, p, czero, czero, t, ldb )
266  IF( n.LE.p ) THEN
267  CALL clacpy( 'Upper', n, n, bf( 1, p-n+1 ), ldb, t( 1, p-n+1 ),
268  \$ ldb )
269  ELSE
270  CALL clacpy( 'Full', n-p, p, bf, ldb, t, ldb )
271  CALL clacpy( '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 cgemm( 'Conjugate transpose', 'No transpose', n, m, n, -cone,
278  \$ q, lda, a, lda, cone, r, lda )
279 *
280 * Compute norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP ) .
281 *
282  resid = clange( '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 cgemm( 'No Transpose', 'No transpose', n, p, p, cone, t, ldb,
292  \$ z, ldb, czero, bwk, ldb )
293  CALL cgemm( 'Conjugate transpose', 'No transpose', n, p, n, -cone,
294  \$ q, lda, b, ldb, cone, bwk, ldb )
295 *
296 * Compute norm( T*Z - Q'*B ) / ( MAX(P,N)*norm(A)*ULP ) .
297 *
298  resid = clange( '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 claset( 'Full', n, n, czero, cone, r, lda )
308  CALL cherk( 'Upper', 'Conjugate transpose', n, n, -one, q, lda,
309  \$ one, r, lda )
310 *
311 * Compute norm( I - Q'*Q ) / ( N * ULP ) .
312 *
313  resid = clanhe( '1', 'Upper', n, r, lda, rwork )
314  result( 3 ) = ( resid / real( max( 1, n ) ) ) / ulp
315 *
316 * Compute I - Z'*Z
317 *
318  CALL claset( 'Full', p, p, czero, cone, t, ldb )
319  CALL cherk( 'Upper', 'Conjugate transpose', p, p, -one, z, ldb,
320  \$ one, t, ldb )
321 *
322 * Compute norm( I - Z'*Z ) / ( P*ULP ) .
323 *
324  resid = clanhe( '1', 'Upper', p, t, ldb, rwork )
325  result( 4 ) = ( resid / real( max( 1, p ) ) ) / ulp
326 *
327  RETURN
328 *
329 * End of CGQRTS
330 *
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:173
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
real function clanhe(NORM, UPLO, N, A, LDA, WORK)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clanhe.f:124
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
subroutine cungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGQR
Definition: cungqr.f:128
subroutine cggqrf(N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO)
CGGQRF
Definition: cggqrf.f:215
subroutine cungrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGRQ
Definition: cungrq.f:128
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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