LAPACK  3.8.0
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 )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 178 of file cgqrts.f.

178 *
179 * -- LAPACK test routine (version 3.7.0) --
180 * -- LAPACK is a software package provided by Univ. of Tennessee, --
181 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
182 * December 2016
183 *
184 * .. Scalar Arguments ..
185  INTEGER lda, ldb, lwork, m, p, n
186 * ..
187 * .. Array Arguments ..
188  REAL rwork( * ), result( 4 )
189  COMPLEX a( lda, * ), af( lda, * ), r( lda, * ),
190  $ q( lda, * ), b( ldb, * ), bf( ldb, * ),
191  $ t( ldb, * ), z( ldb, * ), bwk( ldb, * ),
192  $ taua( * ), taub( * ), work( lwork )
193 * ..
194 *
195 * =====================================================================
196 *
197 * .. Parameters ..
198  REAL zero, one
199  parameter( zero = 0.0e+0, one = 1.0e+0 )
200  COMPLEX czero, cone
201  parameter( czero = ( 0.0e+0, 0.0e+0 ),
202  $ cone = ( 1.0e+0, 0.0e+0 ) )
203  COMPLEX crogue
204  parameter( crogue = ( -1.0e+10, 0.0e+0 ) )
205 * ..
206 * .. Local Scalars ..
207  INTEGER info
208  REAL anorm, bnorm, ulp, unfl, resid
209 * ..
210 * .. External Functions ..
211  REAL slamch, clange, clanhe
212  EXTERNAL slamch, clange, clanhe
213 * ..
214 * .. External Subroutines ..
215  EXTERNAL cgemm, clacpy, claset, cungqr,
216  $ cungrq, cherk
217 * ..
218 * .. Intrinsic Functions ..
219  INTRINSIC max, min, real
220 * ..
221 * .. Executable Statements ..
222 *
223  ulp = slamch( 'Precision' )
224  unfl = slamch( 'Safe minimum' )
225 *
226 * Copy the matrix A to the array AF.
227 *
228  CALL clacpy( 'Full', n, m, a, lda, af, lda )
229  CALL clacpy( 'Full', n, p, b, ldb, bf, ldb )
230 *
231  anorm = max( clange( '1', n, m, a, lda, rwork ), unfl )
232  bnorm = max( clange( '1', n, p, b, ldb, rwork ), unfl )
233 *
234 * Factorize the matrices A and B in the arrays AF and BF.
235 *
236  CALL cggqrf( n, m, p, af, lda, taua, bf, ldb, taub, work,
237  $ lwork, info )
238 *
239 * Generate the N-by-N matrix Q
240 *
241  CALL claset( 'Full', n, n, crogue, crogue, q, lda )
242  CALL clacpy( 'Lower', n-1, m, af( 2,1 ), lda, q( 2,1 ), lda )
243  CALL cungqr( n, n, min( n, m ), q, lda, taua, work, lwork, info )
244 *
245 * Generate the P-by-P matrix Z
246 *
247  CALL claset( 'Full', p, p, crogue, crogue, z, ldb )
248  IF( n.LE.p ) THEN
249  IF( n.GT.0 .AND. n.LT.p )
250  $ CALL clacpy( 'Full', n, p-n, bf, ldb, z( p-n+1, 1 ), ldb )
251  IF( n.GT.1 )
252  $ CALL clacpy( 'Lower', n-1, n-1, bf( 2, p-n+1 ), ldb,
253  $ z( p-n+2, p-n+1 ), ldb )
254  ELSE
255  IF( p.GT.1)
256  $ CALL clacpy( 'Lower', p-1, p-1, bf( n-p+2, 1 ), ldb,
257  $ z( 2, 1 ), ldb )
258  END IF
259  CALL cungrq( p, p, min( n, p ), z, ldb, taub, work, lwork, info )
260 *
261 * Copy R
262 *
263  CALL claset( 'Full', n, m, czero, czero, r, lda )
264  CALL clacpy( 'Upper', n, m, af, lda, r, lda )
265 *
266 * Copy T
267 *
268  CALL claset( 'Full', n, p, czero, czero, t, ldb )
269  IF( n.LE.p ) THEN
270  CALL clacpy( 'Upper', n, n, bf( 1, p-n+1 ), ldb, t( 1, p-n+1 ),
271  $ ldb )
272  ELSE
273  CALL clacpy( 'Full', n-p, p, bf, ldb, t, ldb )
274  CALL clacpy( 'Upper', p, p, bf( n-p+1, 1 ), ldb, t( n-p+1, 1 ),
275  $ ldb )
276  END IF
277 *
278 * Compute R - Q'*A
279 *
280  CALL cgemm( 'Conjugate transpose', 'No transpose', n, m, n, -cone,
281  $ q, lda, a, lda, cone, r, lda )
282 *
283 * Compute norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP ) .
284 *
285  resid = clange( '1', n, m, r, lda, rwork )
286  IF( anorm.GT.zero ) THEN
287  result( 1 ) = ( ( resid / REAL( MAX(1,M,N) ) ) / anorm ) / ulp
288  ELSE
289  result( 1 ) = zero
290  END IF
291 *
292 * Compute T*Z - Q'*B
293 *
294  CALL cgemm( 'No Transpose', 'No transpose', n, p, p, cone, t, ldb,
295  $ z, ldb, czero, bwk, ldb )
296  CALL cgemm( 'Conjugate transpose', 'No transpose', n, p, n, -cone,
297  $ q, lda, b, ldb, cone, bwk, ldb )
298 *
299 * Compute norm( T*Z - Q'*B ) / ( MAX(P,N)*norm(A)*ULP ) .
300 *
301  resid = clange( '1', n, p, bwk, ldb, rwork )
302  IF( bnorm.GT.zero ) THEN
303  result( 2 ) = ( ( resid / REAL( MAX(1,P,N ) ) )/bnorm ) / ulp
304  ELSE
305  result( 2 ) = zero
306  END IF
307 *
308 * Compute I - Q'*Q
309 *
310  CALL claset( 'Full', n, n, czero, cone, r, lda )
311  CALL cherk( 'Upper', 'Conjugate transpose', n, n, -one, q, lda,
312  $ one, r, lda )
313 *
314 * Compute norm( I - Q'*Q ) / ( N * ULP ) .
315 *
316  resid = clanhe( '1', 'Upper', n, r, lda, rwork )
317  result( 3 ) = ( resid / REAL( MAX( 1, N ) ) ) / ulp
318 *
319 * Compute I - Z'*Z
320 *
321  CALL claset( 'Full', p, p, czero, cone, t, ldb )
322  CALL cherk( 'Upper', 'Conjugate transpose', p, p, -one, z, ldb,
323  $ one, t, ldb )
324 *
325 * Compute norm( I - Z'*Z ) / ( P*ULP ) .
326 *
327  resid = clanhe( '1', 'Upper', p, t, ldb, rwork )
328  result( 4 ) = ( resid / REAL( MAX( 1, P ) ) ) / ulp
329 *
330  RETURN
331 *
332 * End of CGQRTS
333 *
subroutine cungrq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGRQ
Definition: cungrq.f:130
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:108
subroutine cungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGQR
Definition: cungqr.f:130
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:175
subroutine cggqrf(N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK, INFO)
CGGQRF
Definition: cggqrf.f:217
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:117
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:105
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, or the element of largest absolute value of a complex Hermitian matrix.
Definition: clanhe.f:126
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
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