 LAPACK  3.10.0 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.

Definition at line 154 of file zget54.f.

156 *
157 * -- LAPACK test routine --
158 * -- LAPACK is a software package provided by Univ. of Tennessee, --
159 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
160 *
161 * .. Scalar Arguments ..
162  INTEGER LDA, LDB, LDS, LDT, LDU, LDV, N
163  DOUBLE PRECISION RESULT
164 * ..
165 * .. Array Arguments ..
166  COMPLEX*16 A( LDA, * ), B( LDB, * ), S( LDS, * ),
167  \$ T( LDT, * ), U( LDU, * ), V( LDV, * ),
168  \$ WORK( * )
169 * ..
170 *
171 * =====================================================================
172 *
173 * .. Parameters ..
174  DOUBLE PRECISION ZERO, ONE
175  parameter( zero = 0.0d+0, one = 1.0d+0 )
176  COMPLEX*16 CZERO, CONE
177  parameter( czero = ( 0.0d+0, 0.0d+0 ),
178  \$ cone = ( 1.0d+0, 0.0d+0 ) )
179 * ..
180 * .. Local Scalars ..
181  DOUBLE PRECISION ABNORM, ULP, UNFL, WNORM
182 * ..
183 * .. Local Arrays ..
184  DOUBLE PRECISION DUM( 1 )
185 * ..
186 * .. External Functions ..
187  DOUBLE PRECISION DLAMCH, ZLANGE
188  EXTERNAL dlamch, zlange
189 * ..
190 * .. External Subroutines ..
191  EXTERNAL zgemm, zlacpy
192 * ..
193 * .. Intrinsic Functions ..
194  INTRINSIC dble, max, min
195 * ..
196 * .. Executable Statements ..
197 *
198  result = zero
199  IF( n.LE.0 )
200  \$ RETURN
201 *
202 * Constants
203 *
204  unfl = dlamch( 'Safe minimum' )
205  ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
206 *
207 * compute the norm of (A,B)
208 *
209  CALL zlacpy( 'Full', n, n, a, lda, work, n )
210  CALL zlacpy( 'Full', n, n, b, ldb, work( n*n+1 ), n )
211  abnorm = max( zlange( '1', n, 2*n, work, n, dum ), unfl )
212 *
213 * Compute W1 = A - U*S*V', and put in the array WORK(1:N*N)
214 *
215  CALL zlacpy( ' ', n, n, a, lda, work, n )
216  CALL zgemm( 'N', 'N', n, n, n, cone, u, ldu, s, lds, czero,
217  \$ work( n*n+1 ), n )
218 *
219  CALL zgemm( 'N', 'C', n, n, n, -cone, work( n*n+1 ), n, v, ldv,
220  \$ cone, work, n )
221 *
222 * Compute W2 = B - U*T*V', and put in the workarray W(N*N+1:2*N*N)
223 *
224  CALL zlacpy( ' ', n, n, b, ldb, work( n*n+1 ), n )
225  CALL zgemm( 'N', 'N', n, n, n, cone, u, ldu, t, ldt, czero,
226  \$ work( 2*n*n+1 ), n )
227 *
228  CALL zgemm( 'N', 'C', n, n, n, -cone, work( 2*n*n+1 ), n, v, ldv,
229  \$ cone, work( n*n+1 ), n )
230 *
231 * Compute norm(W)/ ( ulp*norm((A,B)) )
232 *
233  wnorm = zlange( '1', n, 2*n, work, n, dum )
234 *
235  IF( abnorm.GT.wnorm ) THEN
236  result = ( wnorm / abnorm ) / ( 2*n*ulp )
237  ELSE
238  IF( abnorm.LT.one ) THEN
239  result = ( min( wnorm, 2*n*abnorm ) / abnorm ) / ( 2*n*ulp )
240  ELSE
241  result = min( wnorm / abnorm, dble( 2*n ) ) / ( 2*n*ulp )
242  END IF
243  END IF
244 *
245  RETURN
246 *
247 * End of ZGET54
248 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
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:115
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
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