 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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.```
Date
December 2016

Definition at line 158 of file dget54.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  DOUBLE PRECISION 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 * ..
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, dlange
188  EXTERNAL dlamch, dlange
189 * ..
190 * .. External Subroutines ..
191  EXTERNAL dgemm, dlacpy
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 dlacpy( 'Full', n, n, a, lda, work, n )
210  CALL dlacpy( 'Full', n, n, b, ldb, work( n*n+1 ), n )
211  abnorm = max( dlange( '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 dlacpy( ' ', n, n, a, lda, work, n )
216  CALL dgemm( 'N', 'N', n, n, n, one, u, ldu, s, lds, zero,
217  \$ work( n*n+1 ), n )
218 *
219  CALL dgemm( 'N', 'C', n, n, n, -one, work( n*n+1 ), n, v, ldv,
220  \$ one, 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 dlacpy( ' ', n, n, b, ldb, work( n*n+1 ), n )
225  CALL dgemm( 'N', 'N', n, n, n, one, u, ldu, t, ldt, zero,
226  \$ work( 2*n*n+1 ), n )
227 *
228  CALL dgemm( 'N', 'C', n, n, n, -one, work( 2*n*n+1 ), n, v, ldv,
229  \$ one, work( n*n+1 ), n )
230 *
231 * Compute norm(W)/ ( ulp*norm((A,B)) )
232 *
233  wnorm = dlange( '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 DGET54
248 *
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:105
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
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:116
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