LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ zget54()

subroutine zget54 ( integer  N,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( ldb, * )  B,
integer  LDB,
complex*16, dimension( lds, * )  S,
integer  LDS,
complex*16, dimension( ldt, * )  T,
integer  LDT,
complex*16, dimension( ldu, * )  U,
integer  LDU,
complex*16, dimension( ldv, * )  V,
integer  LDV,
complex*16, dimension( * )  WORK,
double precision  RESULT 
)

ZGET54

Purpose:
 ZGET54 checks a generalized decomposition of the form

          A = U*S*V'  and B = U*T* V'

 where ' means conjugate transpose and U and V are unitary.

 Specifically,

   RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp )
Parameters
[in]N
          N is INTEGER
          The size of the matrix.  If it is zero, DGET54 does nothing.
          It must be at least zero.
[in]A
          A is COMPLEX*16 array, dimension (LDA, N)
          The original (unfactored) matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of A.  It must be at least 1
          and at least N.
[in]B
          B is COMPLEX*16 array, dimension (LDB, N)
          The original (unfactored) matrix B.
[in]LDB
          LDB is INTEGER
          The leading dimension of B.  It must be at least 1
          and at least N.
[in]S
          S is COMPLEX*16 array, dimension (LDS, N)
          The factored matrix S.
[in]LDS
          LDS is INTEGER
          The leading dimension of S.  It must be at least 1
          and at least N.
[in]T
          T is COMPLEX*16 array, dimension (LDT, N)
          The factored matrix T.
[in]LDT
          LDT is INTEGER
          The leading dimension of T.  It must be at least 1
          and at least N.
[in]U
          U is COMPLEX*16 array, dimension (LDU, N)
          The orthogonal matrix on the left-hand side in the
          decomposition.
[in]LDU
          LDU is INTEGER
          The leading dimension of U.  LDU must be at least N and
          at least 1.
[in]V
          V is COMPLEX*16 array, dimension (LDV, N)
          The orthogonal matrix on the left-hand side in the
          decomposition.
[in]LDV
          LDV is INTEGER
          The leading dimension of V.  LDV must be at least N and
          at least 1.
[out]WORK
          WORK is COMPLEX*16 array, dimension (3*N**2)
[out]RESULT
          RESULT is DOUBLE PRECISION
          The value RESULT, It is currently limited to 1/ulp, to
          avoid overflow. Errors are flagged by RESULT=10/ulp.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 158 of file zget54.f.

158 *
159 * -- LAPACK test routine (version 3.7.0) --
160 * -- LAPACK is a software package provided by Univ. of Tennessee, --
161 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
162 * December 2016
163 *
164 * .. Scalar Arguments ..
165  INTEGER lda, ldb, lds, ldt, ldu, ldv, n
166  DOUBLE PRECISION result
167 * ..
168 * .. Array Arguments ..
169  COMPLEX*16 a( lda, * ), b( ldb, * ), s( lds, * ),
170  $ t( ldt, * ), u( ldu, * ), v( ldv, * ),
171  $ work( * )
172 * ..
173 *
174 * =====================================================================
175 *
176 * .. Parameters ..
177  DOUBLE PRECISION zero, one
178  parameter( zero = 0.0d+0, one = 1.0d+0 )
179  COMPLEX*16 czero, cone
180  parameter( czero = ( 0.0d+0, 0.0d+0 ),
181  $ cone = ( 1.0d+0, 0.0d+0 ) )
182 * ..
183 * .. Local Scalars ..
184  DOUBLE PRECISION abnorm, ulp, unfl, wnorm
185 * ..
186 * .. Local Arrays ..
187  DOUBLE PRECISION dum( 1 )
188 * ..
189 * .. External Functions ..
190  DOUBLE PRECISION dlamch, zlange
191  EXTERNAL dlamch, zlange
192 * ..
193 * .. External Subroutines ..
194  EXTERNAL zgemm, zlacpy
195 * ..
196 * .. Intrinsic Functions ..
197  INTRINSIC dble, max, min
198 * ..
199 * .. Executable Statements ..
200 *
201  result = zero
202  IF( n.LE.0 )
203  $ RETURN
204 *
205 * Constants
206 *
207  unfl = dlamch( 'Safe minimum' )
208  ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
209 *
210 * compute the norm of (A,B)
211 *
212  CALL zlacpy( 'Full', n, n, a, lda, work, n )
213  CALL zlacpy( 'Full', n, n, b, ldb, work( n*n+1 ), n )
214  abnorm = max( zlange( '1', n, 2*n, work, n, dum ), unfl )
215 *
216 * Compute W1 = A - U*S*V', and put in the array WORK(1:N*N)
217 *
218  CALL zlacpy( ' ', n, n, a, lda, work, n )
219  CALL zgemm( 'N', 'N', n, n, n, cone, u, ldu, s, lds, czero,
220  $ work( n*n+1 ), n )
221 *
222  CALL zgemm( 'N', 'C', n, n, n, -cone, work( n*n+1 ), n, v, ldv,
223  $ cone, work, n )
224 *
225 * Compute W2 = B - U*T*V', and put in the workarray W(N*N+1:2*N*N)
226 *
227  CALL zlacpy( ' ', n, n, b, ldb, work( n*n+1 ), n )
228  CALL zgemm( 'N', 'N', n, n, n, cone, u, ldu, t, ldt, czero,
229  $ work( 2*n*n+1 ), n )
230 *
231  CALL zgemm( 'N', 'C', n, n, n, -cone, work( 2*n*n+1 ), n, v, ldv,
232  $ cone, work( n*n+1 ), n )
233 *
234 * Compute norm(W)/ ( ulp*norm((A,B)) )
235 *
236  wnorm = zlange( '1', n, 2*n, work, n, dum )
237 *
238  IF( abnorm.GT.wnorm ) THEN
239  result = ( wnorm / abnorm ) / ( 2*n*ulp )
240  ELSE
241  IF( abnorm.LT.one ) THEN
242  result = ( min( wnorm, 2*n*abnorm ) / abnorm ) / ( 2*n*ulp )
243  ELSE
244  result = min( wnorm / abnorm, dble( 2*n ) ) / ( 2*n*ulp )
245  END IF
246  END IF
247 *
248  RETURN
249 *
250 * End of ZGET54
251 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:117
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