Interpolation error with gsl_interp_linear - c++

Question

I need to interpolate a modified Bessel function and I use for that the function gsl_spline_eval(). I get a 'gsl: interp.c:145: ERROR: interpolation error' with the following code:
#define MAXPOINTS 10000
int main()
{
double nu;
gsl_function F;
F.function = &sync;
F.params =0;
size_t size;
double table[2][MAXPOINTS];
size = read_table(table[0],table[1]);
gsl_interp_accel *acc = gsl_interp_accel_alloc ();
gsl_spline *spline = gsl_spline_alloc (gsl_interp_linear, 5401);
gsl_spline_init(spline,table[0],table[1],size);
cout <<" nu: "<< nu<< " GSL_FN_EVAL(&F,nu): "<<nu*GSL_FN_EVAL(&F,nu)<<endl;
return 0;
}
Where sync() returns the integral of the function sync_kern() using the gsl function gsl_integration_qag(). The function read_table() is defined as follow:
size_t read_table(double *xa, double *ya)
{
size_t datapoints;
datapoints = 5401;
double x[] = {
1.388794e-11,
1.395756e-11,
... };
double y[] = {
5.166810e-04,
5.175428e-04,
...
};
int i = 0;
while(i<datapoints){
xa[i]=log(x[i]);
ya[i]=log(y[i]);
i++;
}
return datapoints;
}
The function sync_kern() is the following:
double sync_kern(double gamma, void *params)
{
struct func_params *part= (struct func_params *)params;
double result;
double P,x, nuc, nu_0;
double nu = *(double *)params;
gamma = exp(gamma);
nu_0 = (3*E_COULOMB*B*sqrt(2/3.0))/(4.0*M_PI*M*C);
nuc = nu_0*sq(gamma);
x = nu/nuc;
gsl_interp_accel *acc = gsl_interp_accel_alloc ();
gsl_spline *spline = gsl_spline_alloc (gsl_interp_linear, 5401);
/* double table[2][MAXPOINTS];
size = read_table(table[0],table[1]);
gsl_interp_accel *acc = gsl_interp_accel_alloc ();
gsl_spline *spline = gsl_spline_alloc (gsl_interp_interp, 5401);
gsl_spline_init(spline,table[0],table[1],size); */
P = gsl_spline_eval(spline,log(x),acc);
result = exp(P)*f(gamma)*gamma;
return(result);
}
When I include the lines
/* double table[2][MAXPOINTS];
size = read_table(table[0],table[1]);
gsl_interp_accel *acc = gsl_interp_accel_alloc ();
gsl_spline *spline = gsl_spline_alloc (gsl_interp_interp, 5401);
gsl_spline_init(spline,table[0],table[1],size); */
in the function sync_kern() and not in main() then it works: I get the right value of GSL_FN_EVAL(&F,nu) but it takes of course too much time...
I hope my message wasn't too long...I am not a great expert of c++ and I've look all the aspects of the problem and I still don't understand where it comes from...Does someone have any idea?
Please don't hesitate do ask me if you need any further informations.
Thanks a lot for your help!
Maybe I should precise that I got my code from my supervisor's code. Which is slightly different:
int main(int argc,char *argv[])
{
FILE *fp;
struct func_params params;
size_t size;
int i;
/* initializing parameters */
initialize(argc, argv, &params);
/* Interpolation of Synchrotronfunction F(x) */
double table[2][MAXPOINTS];
size = read_table(table[0],table[1]); /*Tabelle fuer Interpolation einlesen aus create_table.c*/
params.acc = gsl_interp_accel_alloc();
params.spline = gsl_spline_alloc(gsl_interp_linear, size);
gsl_spline_init(params.spline,table[0],table[1],size);
...
return (0);
}
double
sync_kern(double gamma, void *params)
{
struct func_params *part= (struct func_params *)params;
double result;
double P,nu_c,x;
gamma = exp(gamma);
nu_c = part->nu_0*sq(gamma);
x = part->nu_s/nu_c;
P = gsl_spline_eval(part->spline,log(x),part->acc); /*Aus Interpolation: Pointer auf spline */
result = exp(P)*f(gamma)*gamma;
return(result);
}
Where spline and acc are defined in a file.h:
struct func_params
{
gsl_spline *spline;
gsl_interp_accel *acc;
...
}
void initialize(int argc, char *argv[], void *params)
{
struct func_params *part= (struct func_params *)params;
/* Default values for parameters: */
part->gmin=1.0e7/M_E_EV;
part->gamma=1.0e10/M_E_EV;
part->gmax=2.0e18/M_E_EV; /*Integrationgrenzen fuer gamma festlegen*/
part->nu=1e-9/H_EV;
...
}
I defined spline and acc in my function sync_kern() and him in a structure. Does someone has an idea where the error can come from?

Answer 1

The function read_table() gives the arrays 'x[]' and 'y[]' used for
the interpolation
double table[2][MAXPOINTS];
size = read_table(table[0],table[1]);
You define an array of doubles, but don't initialize it. It contains random values. So likely it runs with absurd results.
You pass two values to read_table(). If you want the function to change them, the definition of this function should be
size_t read_table(double& val1, double& val2);
Review your code. There are some vars without declaration (nu_0, nuc, acc)
EDIT
After you edited the question, I see how read_table() is defined. It uses two pointers. You have an only array, two dimensions, fixed size. Because of this fixed size, it's OK to pass the array by using two pointers, table[0] and table[1].
double table[2][N] is same as double** table. So passing table[1] is passing a pointer to an array[N].
The gsl error is due to this code at gsl:interp.c
https://github.com/ampl/gsl/blob/master/interpolation/interp.c
if (x < interp->xmin || x > interp->xmax)
{
GSL_ERROR_VAL("interpolation error", GSL_EDOM, GSL_NAN);
}
It seems you are trying an interpolation out of limits (called "extrapolation")