void make_spl (points_t * pts, spline_t * spl){
int n = pts->n - 1;
matrix_t *eqs = make_matrix(n*3, n*3+1);
double *x = pts->x;
double *y = pts->y;
int i;
for(i= 0; i < n; i++){
double dx = x[i+1] - x[i];
int if1 = 3*i;
int if2 = if1+1;
int if3 = if2+1;
put_entry_matrix(eqs, if1, if1, dx);
put_entry_matrix(eqs, if1, if2, dx*dx/2);
put_entry_matrix(eqs, if1, if3, dx*dx*dx/6);
put_entry_matrix(eqs, if1, n*3, y[i+1]-y[i]);
put_entry_matrix(eqs, if2, if1, 1);
put_entry_matrix(eqs, if2, if2, dx);
put_entry_matrix(eqs, if2, if3, dx*dx/2);
if(if3+1 < n*3)
put_entry_matrix(eqs, if2, if3+1, -1);
else
put_entry_matrix(eqs, if2, if1, 0);
put_entry_matrix(eqs, if3, if2, 1);
put_entry_matrix(eqs, if3, if3, dx);
if(if3+2 < n*3)
put_entry_matrix(eqs, if3, if3+2, -1);
}
#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, pts->n) == 0){
spl->n = pts->n;
for(i = 0; i < n; i++) {
spl->x[i] = pts->x[i];
spl->f[i] = pts->y[i];
spl->f1[i] = get_entry_matrix(eqs, 3*i, 3*n);
spl->f2[i] = get_entry_matrix(eqs, 3*i+1, 3*n);
spl->f3[i] = get_entry_matrix(eqs, 3*i+2, 3*n);
}
spl->x[n] = pts->x[n];
spl->f[n] = pts->y[n];
spl->f1[n] = spl->f1[n-1];
spl->f2[n] = 0;
spl->f3[n] = 0;
}
}
void
make_spl(points_t * pts, spline_t * spl)
{
double *x = pts->x;
double *y = pts->y;
int i, j, m, n=pts->n;
double a0=0.0,a[n],b[n], p = x[0], q = x[n-1],dt;
m = (n-1)/2;
for(i=0; i<n ; i++)
{
a0+=y[i];
}
a0/=n;
for(i=0; i<m ; i++)
{
a[i]=0.0;
for(j=0; j<n ; j++)
{
a[i]+=y[j]*cos((2*M_PI*i*j)/n);
}
a[i]*=2;
a[i]/=n;
b[i]=0.0;
for(j=0; j<n ; j++)
{
b[i]+=y[j]*sin((2*M_PI*i*j)/n);
}
b[i]*=2;
b[i]/=n;
}
if (alloc_spl(spl, n) == 0)
{
for(i = 0 ; i < n ; i++)
{
double xx = spl->x[i] = p + i*(q-p)/(m-1);
spl->f[i] = 0;
spl->f1[i] = 0;
spl->f2[i] = 0;
spl->f3[i] = 0;
for (j = 0 ; j < m ; j++)
{
dt = 2.0*M_PI*j/n;
spl->f[i] += a[j]*cos(dt*xx) + b[j]*sin(dt*xx);
spl->f1[i] += (-1)*(dt*(a[j]*sin(dt*xx) - b[j]*cos(dt*xx)));
spl->f2[i] += (-1)*dt*dt*(a[j]*cos(dt*xx) + b[j]*sin(dt*xx));
spl->f3[i] += pow(dt,3)*(a[j]*sin(dt*xx) - b[j]*cos(dt*xx));
}
}
}
}
void make_spl (points_t * pts, spline_t * spl){
if (alloc_spl(spl, pts->n) == 0) {
spl->x = pts->x;
int i,j;
int n=pts->n;
int L;
int nb;
if(n % 2)
L=((n-1)/2);
else
L=(n/2);
char *nbEnv= getenv( "APPROX_BASE_SIZE" );
if( nbEnv != NULL && atoi( nbEnv ) > 0 && atoi(nbEnv)<(n/2))
nb = atoi( nbEnv );
else
nb=L-1;
for( i=0; i<n; i++)
spl->a[0]+=(1.0/L)*pts->y[i];
spl->b[0]=0;
for(j=1;j<=nb;j++){
spl->a[j]=0.0;
spl->b[j]=0.0;
for(i=0;i<n;i++){
spl->a[j]+=(1.0/L)*pts->y[i]*cos((M_PI*i*j)/L);
spl->b[j]+=(1.0/L)*pts->y[i]*sin((M_PI*i*j)/L);
}
}
for(j=0;j<n;j++){
spl->f[j]=spl->a[0]/2;
spl->f1[j]=0.0;
spl->f2[j]=0.0;
spl->f3[j]=0.0;
spl->f4[j]=0.0;
double tmp=spl->x[j];
for(i=1;i<=nb;i++){
spl->f[j]+=spl->a[i]*cos(i * (tmp)) + spl->b[i]*sin(i * (tmp));
spl->f1[j]+= -i * spl->a[i]*sin(i*(tmp)) + i *spl->b[i]*cos(i*(tmp));
spl->f2[j]+= -i * i *spl->a[i]*cos(i*(tmp)) - i * i * spl->b[i]*sin(i*(tmp));
spl->f3[j]+= i * i * i * spl->a[i]*sin(i*(tmp)) - i * i * i * spl->b[i]*cos(i*(tmp));
spl->f4[j]+= i * i * i * i * spl->a[i]*cos(i*(tmp)) + i * i * i * i * spl->b[i]*sin(i*(tmp));
}
}
}
}
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);
}
}
}
}
int
read_spl (FILE * inf, spline_t * spl)
{
int i;
if (fscanf (inf, "%d", &(spl->n)) != 1 || spl->n < 0)
return 1;
if (alloc_spl (spl, spl->n))
return 1;
for (i = 0; i < spl->n; i++)
if (fscanf
(inf, "%lf %lf %lf %lf %lf", spl->x + i, spl->f + i, spl->f1 + i,
spl->f2 + i, spl->f3 + i) != 5)
return 1;
return 0;
}
void make_spl(points_t * pts, spline_t * spl){
matrix_t *eqs= NULL;
double *x = pts->x;
double *y = pts->y;
int i, j, k;
int n = pts->n > 8 ? 8 : pts->n;
double a = x[0];
double b = x[pts->n - 1];
char *nEnv= getenv( "APPROX_BASE_SIZE" );
if( nEnv != NULL && atoi( nEnv ) > 0 )
n = atoi( nEnv );
eqs = make_matrix(n, n+1);
wypelnijMacierze(eqs, pts, n);
if (piv_ge_solver(eqs)) {
spl->n = 0;
return;
}
if (alloc_spl(spl, n) == 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 < n; k++) {
double ck = get_entry_matrix(eqs, k, n);
spl->f[i] += ck * hermite(xx, k);
spl->f1[i] += ck * hermiteD1(xx, k);
spl->f2[i] += ck * hermiteD2(xx, k);
spl->f3[i] += ck * hermiteD3(xx, k);
}
}
}
free(eqs);
free(x);
free(y);
}
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
}
