LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zget07()

 subroutine zget07 ( character TRANS, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldxact, * ) XACT, integer LDXACT, double precision, dimension( * ) FERR, logical CHKFERR, double precision, dimension( * ) BERR, double precision, dimension( * ) RESLTS )

ZGET07

Purpose:
ZGET07 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 164 of file zget07.f.

166*
167* -- LAPACK test routine --
168* -- LAPACK is a software package provided by Univ. of Tennessee, --
169* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
170*
171* .. Scalar Arguments ..
172 CHARACTER TRANS
173 LOGICAL CHKFERR
174 INTEGER LDA, LDB, LDX, LDXACT, N, NRHS
175* ..
176* .. Array Arguments ..
177 DOUBLE PRECISION BERR( * ), FERR( * ), RESLTS( * )
178 COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * ),
179 \$ XACT( LDXACT, * )
180* ..
181*
182* =====================================================================
183*
184* .. Parameters ..
185 DOUBLE PRECISION ZERO, ONE
186 parameter( zero = 0.0d+0, one = 1.0d+0 )
187* ..
188* .. Local Scalars ..
189 LOGICAL NOTRAN
190 INTEGER I, IMAX, J, K
191 DOUBLE PRECISION AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM
192 COMPLEX*16 ZDUM
193* ..
194* .. External Functions ..
195 LOGICAL LSAME
196 INTEGER IZAMAX
197 DOUBLE PRECISION DLAMCH
198 EXTERNAL lsame, izamax, dlamch
199* ..
200* .. Intrinsic Functions ..
201 INTRINSIC abs, dble, dimag, max, min
202* ..
203* .. Statement Functions ..
204 DOUBLE PRECISION CABS1
205* ..
206* .. Statement Function definitions ..
207 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
208* ..
209* .. Executable Statements ..
210*
211* Quick exit if N = 0 or NRHS = 0.
212*
213 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
214 reslts( 1 ) = zero
215 reslts( 2 ) = zero
216 RETURN
217 END IF
218*
219 eps = dlamch( 'Epsilon' )
220 unfl = dlamch( 'Safe minimum' )
221 ovfl = one / unfl
222 notran = lsame( trans, 'N' )
223*
224* Test 1: Compute the maximum of
225* norm(X - XACT) / ( norm(X) * FERR )
226* over all the vectors X and XACT using the infinity-norm.
227*
228 errbnd = zero
229 IF( chkferr ) THEN
230 DO 30 j = 1, nrhs
231 imax = izamax( n, x( 1, j ), 1 )
232 xnorm = max( cabs1( x( imax, j ) ), unfl )
233 diff = zero
234 DO 10 i = 1, n
235 diff = max( diff, cabs1( x( i, j )-xact( i, j ) ) )
236 10 CONTINUE
237*
238 IF( xnorm.GT.one ) THEN
239 GO TO 20
240 ELSE IF( diff.LE.ovfl*xnorm ) THEN
241 GO TO 20
242 ELSE
243 errbnd = one / eps
244 GO TO 30
245 END IF
246*
247 20 CONTINUE
248 IF( diff / xnorm.LE.ferr( j ) ) THEN
249 errbnd = max( errbnd, ( diff / xnorm ) / ferr( j ) )
250 ELSE
251 errbnd = one / eps
252 END IF
253 30 CONTINUE
254 END IF
255 reslts( 1 ) = errbnd
256*
257* Test 2: Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where
258* (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
259*
260 DO 70 k = 1, nrhs
261 DO 60 i = 1, n
262 tmp = cabs1( b( i, k ) )
263 IF( notran ) THEN
264 DO 40 j = 1, n
265 tmp = tmp + cabs1( a( i, j ) )*cabs1( x( j, k ) )
266 40 CONTINUE
267 ELSE
268 DO 50 j = 1, n
269 tmp = tmp + cabs1( a( j, i ) )*cabs1( x( j, k ) )
270 50 CONTINUE
271 END IF
272 IF( i.EQ.1 ) THEN
273 axbi = tmp
274 ELSE
275 axbi = min( axbi, tmp )
276 END IF
277 60 CONTINUE
278 tmp = berr( k ) / ( ( n+1 )*eps+( n+1 )*unfl /
279 \$ max( axbi, ( n+1 )*unfl ) )
280 IF( k.EQ.1 ) THEN
281 reslts( 2 ) = tmp
282 ELSE
283 reslts( 2 ) = max( reslts( 2 ), tmp )
284 END IF
285 70 CONTINUE
286*
287 RETURN
288*
289* End of ZGET07
290*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function izamax(N, ZX, INCX)
IZAMAX
Definition: izamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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