LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ cget54()

subroutine cget54 ( integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( lds, * )  S,
integer  LDS,
complex, dimension( ldt, * )  T,
integer  LDT,
complex, dimension( ldu, * )  U,
integer  LDU,
complex, dimension( ldv, * )  V,
integer  LDV,
complex, dimension( * )  WORK,
real  RESULT 
)

CGET54

Purpose:
 CGET54 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, SGET54 does nothing.
          It must be at least zero.
[in]A
          A is COMPLEX 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 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 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 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 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 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 array, dimension (3*N**2)
[out]RESULT
          RESULT is REAL
          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.

Definition at line 154 of file cget54.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 REAL RESULT
164* ..
165* .. Array Arguments ..
166 COMPLEX A( LDA, * ), B( LDB, * ), S( LDS, * ),
167 $ T( LDT, * ), U( LDU, * ), V( LDV, * ),
168 $ WORK( * )
169* ..
170*
171* =====================================================================
172*
173* .. Parameters ..
174 REAL ZERO, ONE
175 parameter( zero = 0.0e+0, one = 1.0e+0 )
176 COMPLEX CZERO, CONE
177 parameter( czero = ( 0.0e+0, 0.0e+0 ),
178 $ cone = ( 1.0e+0, 0.0e+0 ) )
179* ..
180* .. Local Scalars ..
181 REAL ABNORM, ULP, UNFL, WNORM
182* ..
183* .. Local Arrays ..
184 REAL DUM( 1 )
185* ..
186* .. External Functions ..
187 REAL CLANGE, SLAMCH
188 EXTERNAL clange, slamch
189* ..
190* .. External Subroutines ..
191 EXTERNAL cgemm, clacpy
192* ..
193* .. Intrinsic Functions ..
194 INTRINSIC max, min, real
195* ..
196* .. Executable Statements ..
197*
198 result = zero
199 IF( n.LE.0 )
200 $ RETURN
201*
202* Constants
203*
204 unfl = slamch( 'Safe minimum' )
205 ulp = slamch( 'Epsilon' )*slamch( 'Base' )
206*
207* compute the norm of (A,B)
208*
209 CALL clacpy( 'Full', n, n, a, lda, work, n )
210 CALL clacpy( 'Full', n, n, b, ldb, work( n*n+1 ), n )
211 abnorm = max( clange( '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 clacpy( ' ', n, n, a, lda, work, n )
216 CALL cgemm( 'N', 'N', n, n, n, cone, u, ldu, s, lds, czero,
217 $ work( n*n+1 ), n )
218*
219 CALL cgemm( '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 clacpy( ' ', n, n, b, ldb, work( n*n+1 ), n )
225 CALL cgemm( 'N', 'N', n, n, n, cone, u, ldu, t, ldt, czero,
226 $ work( 2*n*n+1 ), n )
227*
228 CALL cgemm( '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 = clange( '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, real( 2*n ) ) / ( 2*n*ulp )
242 END IF
243 END IF
244*
245 RETURN
246*
247* End of CGET54
248*
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
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
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
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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