double
d2fi(int n, double x) {
if (n == 0)
return 0;
if (n == 1)
return 0;
return 4 * dfi(n - 1, x) + 2 * x * d2fi(n - 1, x) - d2fi(n - 2, x);
}
void
make_spl(points_t * pts, spline_t * spl) {
matrix_t *eqs = NULL;
double *x = pts->x;
double *y = pts->y;
double a = x[0];
double b = x[pts->n - 1];
int i, j, k;
int nb = pts->n - 3 > 10 ? 10 : pts->n - 3;
char *nbEnv = getenv("APPROX_BASE_SIZE");
if (nbEnv != NULL && atoi(nbEnv) > 0)
nb = atoi(nbEnv);
eqs = make_matrix(nb, nb + 1);
for (j = 0; j < nb; j++) {
for (i = 0; i < nb; i++)
for (k = 0; k < pts->n; k++)
add_to_entry_matrix(eqs, j, i, fi(i, x[k]) * fi(j, x[k]));
for (k = 0; k < pts->n; k++)
add_to_entry_matrix(eqs, j, nb, y[k] * fi(j, x[k]));
}
if (piv_ge_solver(eqs)) {
spl->n = 0;
return;
}
if (alloc_spl(spl, nb) == 0) {
for (i = 0; i < spl->n; i++) {
double xx = spl->x[i] = a + i * (b - a) / (spl->n - 1);
xx += 10.0 * DBL_EPSILON; //by nie ulokować punktu w poprz. przedziale
spl->f[i] = 0;
spl->f1[i] = 0;
spl->f2[i] = 0;
spl->f3[i] = 0;
for (k = 0; k < nb; k++) {
double ck = get_entry_matrix(eqs, k, nb);
spl->f[i] += ck * fi (k, xx);
spl->f1[i] += ck * dfi (k, xx);
spl->f2[i] += ck * d2fi(k, xx);
spl->f3[i] += ck * d3fi(k, xx);
}
}
}
}
void
make_spl(points_t * pts, spline_t * spl)
{
matrix_t *eqs= NULL;
double *x = pts->x;
double *y = pts->y;
double a = x[0];
double b = x[pts->n - 1];
int i, j, k;
int nb = pts->n - 3 > 10 ? 10 : pts->n - 3;
char *nbEnv= getenv( "APPROX_BASE_SIZE" );
if( nbEnv != NULL && atoi( nbEnv ) > 0 )
nb = atoi( nbEnv );
eqs = make_matrix(nb, nb + 1);
#ifdef DEBUG
#define TESTBASE 500
{
FILE *tst = fopen("debug_base_plot.txt", "w");
double dx = (b - a) / (TESTBASE - 1);
for( j= 0; j < nb; j++ )
xfi( a, b, nb, j, tst );
for (i = 0; i < TESTBASE; i++) {
fprintf(tst, "%g", a + i * dx);
for (j = 0; j < nb; j++) {
fprintf(tst, " %g", fi (a, b, nb, j, a + i * dx));
fprintf(tst, " %g", dfi (a, b, nb, j, a + i * dx));
fprintf(tst, " %g", d2fi(a, b, nb, j, a + i * dx));
fprintf(tst, " %g", d3fi(a, b, nb, j, a + i * dx));
}
fprintf(tst, "\n");
}
fclose(tst);
}
#endif
for (j = 0; j < nb; j++) {
for (i = 0; i < nb; i++)
for (k = 0; k < pts->n; k++)
add_to_entry_matrix(eqs, j, i, fi(a, b, nb, i, x[k]) * fi(a, b, nb, j, x[k]));
for (k = 0; k < pts->n; k++)
add_to_entry_matrix(eqs, j, nb, y[k] * fi(a, b, nb, j, x[k]));
}
#ifdef DEBUG
write_matrix(eqs, stdout);
#endif
if (piv_ge_solver(eqs)) {
spl->n = 0;
return;
}
#ifdef DEBUG
write_matrix(eqs, stdout);
#endif
if (alloc_spl(spl, nb) == 0) {
for (i = 0; i < spl->n; i++) {
double xx = spl->x[i] = a + i*(b-a)/(spl->n-1);
xx+= 10.0*DBL_EPSILON; // zabezpieczenie przed ulokowaniem punktu w poprzednim przedziale
spl->f[i] = 0;
spl->f1[i] = 0;
spl->f2[i] = 0;
spl->f3[i] = 0;
for (k = 0; k < nb; k++) {
double ck = get_entry_matrix(eqs, k, nb);
spl->f[i] += ck * fi (a, b, nb, k, xx);
spl->f1[i] += ck * dfi (a, b, nb, k, xx);
spl->f2[i] += ck * d2fi(a, b, nb, k, xx);
spl->f3[i] += ck * d3fi(a, b, nb, k, xx);
}
}
}
#ifdef DEBUG
{
FILE *tst = fopen("debug_spline_plot.txt", "w");
double dx = (b - a) / (TESTBASE - 1);
for (i = 0; i < TESTBASE; i++) {
double yi= 0;
double dyi= 0;
double d2yi= 0;
double d3yi= 0;
double xi= a + i * dx;
for( k= 0; k < nb; k++ ) {
yi += get_entry_matrix(eqs, k, nb) * fi(a, b, nb, k, xi);
dyi += get_entry_matrix(eqs, k, nb) * dfi(a, b, nb, k, xi);
d2yi += get_entry_matrix(eqs, k, nb) * d2fi(a, b, nb, k, xi);
d3yi += get_entry_matrix(eqs, k, nb) * d3fi(a, b, nb, k, xi);
}
fprintf(tst, "%g %g %g %g %g\n", xi, yi, dyi, d2yi, d3yi );
}
fclose(tst);
}
#endif
}
