 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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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