 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dget54()

 subroutine dget54 ( integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( lds, * ) S, integer LDS, double precision, dimension( ldt, * ) T, integer LDT, double precision, dimension( ldu, * ) U, integer LDU, double precision, dimension( ldv, * ) V, integer LDV, double precision, dimension( * ) WORK, double precision RESULT )

DGET54

Purpose:
``` DGET54 checks a generalized decomposition of the form

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

where ' means transpose and U and V are orthogonal.

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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 dget54.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 DOUBLE PRECISION 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* ..
177* .. Local Scalars ..
178 DOUBLE PRECISION ABNORM, ULP, UNFL, WNORM
179* ..
180* .. Local Arrays ..
181 DOUBLE PRECISION DUM( 1 )
182* ..
183* .. External Functions ..
184 DOUBLE PRECISION DLAMCH, DLANGE
185 EXTERNAL dlamch, dlange
186* ..
187* .. External Subroutines ..
188 EXTERNAL dgemm, dlacpy
189* ..
190* .. Intrinsic Functions ..
191 INTRINSIC dble, max, min
192* ..
193* .. Executable Statements ..
194*
195 result = zero
196 IF( n.LE.0 )
197 \$ RETURN
198*
199* Constants
200*
201 unfl = dlamch( 'Safe minimum' )
202 ulp = dlamch( 'Epsilon' )*dlamch( 'Base' )
203*
204* compute the norm of (A,B)
205*
206 CALL dlacpy( 'Full', n, n, a, lda, work, n )
207 CALL dlacpy( 'Full', n, n, b, ldb, work( n*n+1 ), n )
208 abnorm = max( dlange( '1', n, 2*n, work, n, dum ), unfl )
209*
210* Compute W1 = A - U*S*V', and put in the array WORK(1:N*N)
211*
212 CALL dlacpy( ' ', n, n, a, lda, work, n )
213 CALL dgemm( 'N', 'N', n, n, n, one, u, ldu, s, lds, zero,
214 \$ work( n*n+1 ), n )
215*
216 CALL dgemm( 'N', 'C', n, n, n, -one, work( n*n+1 ), n, v, ldv,
217 \$ one, work, n )
218*
219* Compute W2 = B - U*T*V', and put in the workarray W(N*N+1:2*N*N)
220*
221 CALL dlacpy( ' ', n, n, b, ldb, work( n*n+1 ), n )
222 CALL dgemm( 'N', 'N', n, n, n, one, u, ldu, t, ldt, zero,
223 \$ work( 2*n*n+1 ), n )
224*
225 CALL dgemm( 'N', 'C', n, n, n, -one, work( 2*n*n+1 ), n, v, ldv,
226 \$ one, work( n*n+1 ), n )
227*
228* Compute norm(W)/ ( ulp*norm((A,B)) )
229*
230 wnorm = dlange( '1', n, 2*n, work, n, dum )
231*
232 IF( abnorm.GT.wnorm ) THEN
233 result = ( wnorm / abnorm ) / ( 2*n*ulp )
234 ELSE
235 IF( abnorm.LT.one ) THEN
236 result = ( min( wnorm, 2*n*abnorm ) / abnorm ) / ( 2*n*ulp )
237 ELSE
238 result = min( wnorm / abnorm, dble( 2*n ) ) / ( 2*n*ulp )
239 END IF
240 END IF
241*
242 RETURN
243*
244* End of DGET54
245*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:114
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