/usr/share/doc/libsuperlu-dev/tests/sp_zget07.c is in libsuperlu3-dev 3.0+20070106-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 | /*
* -- SuperLU routine (version 3.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* October 15, 2003
*
*/
#include <math.h>
#include "slu_zdefs.h"
int sp_zget07(trans_t trans, int n, int nrhs, SuperMatrix *A, doublecomplex *b,
int ldb, doublecomplex *x, int ldx, doublecomplex *xact,
int ldxact, double *ferr, double *berr, double *reslts)
{
/*
Purpose
=======
SP_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 )
Arguments
=========
TRANS (input) trans_t
Specifies the form of the system of equations.
= NOTRANS: A *x = b
= TRANS : A'*x = b, where A' is the transpose of A
= CONJ : A'*x = b, where A' is the transpose of A
N (input) INT
The number of rows of the matrices X and XACT. N >= 0.
NRHS (input) INT
The number of columns of the matrices X and XACT. NRHS >= 0.
A (input) SuperMatrix *, dimension (A->nrow, A->ncol)
The original n by n matrix A.
B (input) DOUBLE COMPLEX PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB (input) INT
The leading dimension of the array B. LDB >= max(1,N).
X (input) DOUBLE COMPLEX PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X.
LDX (input) INT
The leading dimension of the array X. LDX >= max(1,N).
XACT (input) DOUBLE COMPLEX PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT.
LDXACT (input) INT
The leading dimension of the array XACT. LDXACT >= max(1,N).
FERR (input) DOUBLE COMPLEX 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.
BERR (input) DOUBLE COMPLEX 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).
RESLTS (output) 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 + (*) )
=====================================================================
*/
/* Table of constant values */
int c__1 = 1;
/* System generated locals */
double d__1, d__2;
double d__3, d__4;
/* Local variables */
double diff, axbi;
int imax, irow, n__1;
int i, j, k;
double unfl, ovfl;
double xnorm;
double errbnd;
int notran;
double eps, tmp;
double *rwork;
doublecomplex *Aval;
NCformat *Astore;
/* Function prototypes */
extern int lsame_(char *, char *);
extern int izamax_(int *, doublecomplex *, int *);
extern double dlamch_(char *);
/* Quick exit if N = 0 or NRHS = 0. */
if ( n <= 0 || nrhs <= 0 ) {
reslts[0] = 0.;
reslts[1] = 0.;
return 0;
}
eps = dlamch_("Epsilon");
unfl = dlamch_("Safe minimum");
ovfl = 1. / unfl;
notran = (trans == NOTRANS);
rwork = (double *) SUPERLU_MALLOC(n*sizeof(double));
if ( !rwork ) ABORT("SUPERLU_MALLOC fails for rwork");
Astore = A->Store;
Aval = (doublecomplex *) Astore->nzval;
/* Test 1: Compute the maximum of
norm(X - XACT) / ( norm(X) * FERR )
over all the vectors X and XACT using the infinity-norm. */
errbnd = 0.;
for (j = 0; j < nrhs; ++j) {
n__1 = n;
imax = izamax_(&n__1, &x[j*ldx], &c__1);
d__1 = (d__2 = x[imax-1 + j*ldx].r, fabs(d__2)) +
(d__3 = x[imax-1 + j*ldx].i, fabs(d__3));
xnorm = SUPERLU_MAX(d__1,unfl);
diff = 0.;
for (i = 0; i < n; ++i) {
d__1 = (d__2 = x[i+j*ldx].r - xact[i+j*ldxact].r, fabs(d__2)) +
(d__3 = x[i+j*ldx].i - xact[i+j*ldxact].i, fabs(d__3));
diff = SUPERLU_MAX(diff, d__1);
}
if (xnorm > 1.) {
goto L20;
} else if (diff <= ovfl * xnorm) {
goto L20;
} else {
errbnd = 1. / eps;
goto L30;
}
L20:
#if 0
if (diff / xnorm <= ferr[j]) {
d__1 = diff / xnorm / ferr[j];
errbnd = SUPERLU_MAX(errbnd,d__1);
} else {
errbnd = 1. / eps;
}
#endif
d__1 = diff / xnorm / ferr[j];
errbnd = SUPERLU_MAX(errbnd,d__1);
/*printf("Ferr: %f\n", errbnd);*/
L30:
;
}
reslts[0] = errbnd;
/* Test 2: Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where
(*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) + abs(b))_i ) */
for (k = 0; k < nrhs; ++k) {
for (i = 0; i < n; ++i)
rwork[i] = (d__1 = b[i + k*ldb].r, fabs(d__1)) +
(d__2 = b[i + k*ldb].i, fabs(d__2));
if ( notran ) {
for (j = 0; j < n; ++j) {
tmp = (d__1 = x[j + k*ldx].r, fabs(d__1)) +
(d__2 = x[j + k*ldx].i, fabs(d__2));
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
d__1 = (d__2 = Aval[i].r, fabs(d__2)) +
(d__3 = Aval[i].i, fabs(d__3));
rwork[Astore->rowind[i]] += d__1 * tmp;
}
}
} else {
for (j = 0; j < n; ++j) {
tmp = 0.;
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
irow = Astore->rowind[i];
d__1 = (d__2 = x[irow + k*ldx].r, fabs(d__2)) +
(d__3 = x[irow + k*ldx].i, fabs(d__3));
d__2 = (d__3 = Aval[i].r, fabs(d__3)) +
(d__4 = Aval[i].i, fabs(d__4));
tmp += d__2 * d__1;
}
rwork[j] += tmp;
}
}
axbi = rwork[0];
for (i = 1; i < n; ++i) axbi = SUPERLU_MIN(axbi, rwork[i]);
/* Computing MAX */
d__1 = axbi, d__2 = (n + 1) * unfl;
tmp = berr[k] / ((n + 1) * eps + (n + 1) * unfl / SUPERLU_MAX(d__1,d__2));
if (k == 0) {
reslts[1] = tmp;
} else {
reslts[1] = SUPERLU_MAX(reslts[1],tmp);
}
}
SUPERLU_FREE(rwork);
return 0;
} /* sp_zget07 */
|