 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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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