int
gsl_linalg_solve_symm_tridiag(
const gsl_vector * diag,
const gsl_vector * offdiag,
const gsl_vector * rhs,
gsl_vector * solution)
{
if(diag->size != rhs->size)
{
GSL_ERROR ("size of diag must match rhs", GSL_EBADLEN);
}
else if (offdiag->size != rhs->size-1)
{
GSL_ERROR ("size of offdiag must match rhs-1", GSL_EBADLEN);
}
else if (solution->size != rhs->size)
{
GSL_ERROR ("size of solution must match rhs", GSL_EBADLEN);
}
else
{
return solve_tridiag(diag->data, diag->stride,
offdiag->data, offdiag->stride,
rhs->data, rhs->stride,
solution->data, solution->stride,
diag->size);
}
}
void cubic_spline(int ni, float *xi, float *yi, int no, float *xo, float *yo) {
int i, j;
float *h = malloc(sizeof(float)*(ni-1)); /* input data point spacings */
float *d = malloc(sizeof(float)*(ni-1)); /* input data slopes */
float *s = malloc(sizeof(float)*(ni)); /* second order derivative */
float *a0 = malloc(sizeof(float)*ni);
float *a1 = malloc(sizeof(float)*ni);
float *a2 = malloc(sizeof(float)*ni);
float *b = malloc(sizeof(float)*ni);
if (ni == 2) {
/* use linear interpolation when there are only two input points */
for (i = 0; i < no-1; ++i) {
if (xo[i] < xi[0] || xo[i] > xi[1]) {
printf("[Error]: cubic_spline: Use linear interpolation, "
"but output point is not inside the input segment!\n");
exit(-1);
}
float c = (xi[1]-xo[i])/(xi[1]-xi[0]);
yo[i] = c*yi[0]+(1.0-c)*yi[1];
}
return;
}
for (i = 0; i < ni-1; ++i) {
h[i] = xi[i+1]-xi[i];
if (h[i] == 0.0) {
printf("[Error]: cubic_spline: Encounter zero interval!\n");
for (j = 0; j < ni; ++j) {
printf("xi[%d] = %f\n", j, xi[j]);
}
exit(-1);
}
d[i] = (yi[i+1]-yi[i])/h[i];
}
/* ---------------------------------------------------------------------- */
/* calculate second order derivatives */
/* set coefficients in internal region */
for (i = 1; i < ni-1; ++i) {
a0[i] = h[i-1];
a1[i] = 2*(h[i-1]+h[i]);
a2[i] = h[i];
b[i] = 6*(d[i]-d[i-1]);
}
/* set coefficients in boundary according to not-a-knot condition */
a0[0] = h[1];
a1[0] = -(h[0]+h[1]);
a2[0] = h[0];
b[0] = 0.0;
a0[ni-1] = h[ni-2];
a1[ni-1] = -(h[ni-3]+h[ni-2]);
a2[ni-1] = h[ni-3];
b[ni-1] = 0.0;
/* solve the linear equation of second order derivative */
solve_tridiag(ni, a0, a1, a2, b, s);
free(a0); free(a1); free(a2); free(b);
/* ---------------------------------------------------------------------- */
/* interpolate */
for (i = 0; i < no; ++i) {
for (j = 0; j < ni-1; ++j) {
if (xo[i] >= xi[j] && xo[i] <= xi[j+1]) {
break;
}
}
if (j == ni-1) {
printf("[Error]: cubic_spline: Interplating point %f "
"is not in any data segment!\n", xo[i]);
exit(-1);
}
float c0 = pow(xi[j+1]-xo[i], 3)/(6.0*h[j]);
float c1 = pow(xo[i]-xi[j], 3)/(6.0*h[j]);
float c2 = (yi[j+1]-yi[j])/h[j]-(s[j+1]-s[j])*h[j]/6.0;
float c3 = yi[j+1]-c2*xi[j+1]-pow(xi[j+1]-xi[j], 3)/(6.0*h[j])*s[j+1];
yo[i] = c0*s[j]+c1*s[j+1]+c2*xo[i]+c3;
}
free(h); free(d); free(s);
}