 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dget07()

 subroutine dget07 ( character TRANS, integer N, integer NRHS, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldxact, * ) XACT, integer LDXACT, double precision, dimension( * ) FERR, logical CHKFERR, double precision, dimension( * ) BERR, double precision, dimension( * ) RESLTS )

DGET07

Purpose:
``` DGET07 tests the error bounds from iterative refinement for the
computed solution to a system of equations op(A)*X = B, where A is a
general n by n matrix and op(A) = A or A**T, depending on TRANS.

RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )

A large value is returned if this ratio is not less than one.

RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( (n+1)*EPS + (*) ), where
(*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 Specifies the form of the system of equations. = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose = Transpose)``` [in] N ``` N is INTEGER The number of rows of the matrices X and XACT. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of columns of the matrices X and XACT. NRHS >= 0.``` [in] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) The original n by n matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] B ``` B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [in] X ``` X is DOUBLE PRECISION array, dimension (LDX,NRHS) The computed solution vectors. Each vector is stored as a column of the matrix X.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).``` [in] XACT ``` XACT is DOUBLE PRECISION array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.``` [in] LDXACT ``` LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).``` [in] FERR ``` FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.``` [in] CHKFERR ``` CHKFERR is LOGICAL Set to .TRUE. to check FERR, .FALSE. not to check FERR. When the test system is ill-conditioned, the "true" solution in XACT may be incorrect.``` [in] BERR ``` BERR is DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).``` [out] RESLTS ``` RESLTS is DOUBLE PRECISION array, dimension (2) The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( (n+1)*EPS + (*) )```

Definition at line 163 of file dget07.f.

165*
166* -- LAPACK test routine --
167* -- LAPACK is a software package provided by Univ. of Tennessee, --
168* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
169*
170* .. Scalar Arguments ..
171 CHARACTER TRANS
172 LOGICAL CHKFERR
173 INTEGER LDA, LDB, LDX, LDXACT, N, NRHS
174* ..
175* .. Array Arguments ..
176 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), BERR( * ), FERR( * ),
177 \$ RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
178* ..
179*
180* =====================================================================
181*
182* .. Parameters ..
183 DOUBLE PRECISION ZERO, ONE
184 parameter( zero = 0.0d+0, one = 1.0d+0 )
185* ..
186* .. Local Scalars ..
187 LOGICAL NOTRAN
188 INTEGER I, IMAX, J, K
189 DOUBLE PRECISION AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM
190* ..
191* .. External Functions ..
192 LOGICAL LSAME
193 INTEGER IDAMAX
194 DOUBLE PRECISION DLAMCH
195 EXTERNAL lsame, idamax, dlamch
196* ..
197* .. Intrinsic Functions ..
198 INTRINSIC abs, max, min
199* ..
200* .. Executable Statements ..
201*
202* Quick exit if N = 0 or NRHS = 0.
203*
204 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
205 reslts( 1 ) = zero
206 reslts( 2 ) = zero
207 RETURN
208 END IF
209*
210 eps = dlamch( 'Epsilon' )
211 unfl = dlamch( 'Safe minimum' )
212 ovfl = one / unfl
213 notran = lsame( trans, 'N' )
214*
215* Test 1: Compute the maximum of
216* norm(X - XACT) / ( norm(X) * FERR )
217* over all the vectors X and XACT using the infinity-norm.
218*
219 errbnd = zero
220 IF( chkferr ) THEN
221 DO 30 j = 1, nrhs
222 imax = idamax( n, x( 1, j ), 1 )
223 xnorm = max( abs( x( imax, j ) ), unfl )
224 diff = zero
225 DO 10 i = 1, n
226 diff = max( diff, abs( x( i, j )-xact( i, j ) ) )
227 10 CONTINUE
228*
229 IF( xnorm.GT.one ) THEN
230 GO TO 20
231 ELSE IF( diff.LE.ovfl*xnorm ) THEN
232 GO TO 20
233 ELSE
234 errbnd = one / eps
235 GO TO 30
236 END IF
237*
238 20 CONTINUE
239 IF( diff / xnorm.LE.ferr( j ) ) THEN
240 errbnd = max( errbnd, ( diff / xnorm ) / ferr( j ) )
241 ELSE
242 errbnd = one / eps
243 END IF
244 30 CONTINUE
245 END IF
246 reslts( 1 ) = errbnd
247*
248* Test 2: Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where
249* (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
250*
251 DO 70 k = 1, nrhs
252 DO 60 i = 1, n
253 tmp = abs( b( i, k ) )
254 IF( notran ) THEN
255 DO 40 j = 1, n
256 tmp = tmp + abs( a( i, j ) )*abs( x( j, k ) )
257 40 CONTINUE
258 ELSE
259 DO 50 j = 1, n
260 tmp = tmp + abs( a( j, i ) )*abs( x( j, k ) )
261 50 CONTINUE
262 END IF
263 IF( i.EQ.1 ) THEN
264 axbi = tmp
265 ELSE
266 axbi = min( axbi, tmp )
267 END IF
268 60 CONTINUE
269 tmp = berr( k ) / ( ( n+1 )*eps+( n+1 )*unfl /
270 \$ max( axbi, ( n+1 )*unfl ) )
271 IF( k.EQ.1 ) THEN
272 reslts( 2 ) = tmp
273 ELSE
274 reslts( 2 ) = max( reslts( 2 ), tmp )
275 END IF
276 70 CONTINUE
277*
278 RETURN
279*
280* End of DGET07
281*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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