CCResult check_conformance(const Program& program, const Observer& observer, MemorySetup msetup) {
try {
auto fp = fixed_point(program, observer, msetup);
return CCResult(std::move(fp));
} catch (std::runtime_error& e) {
return CCResult(e.what());
}
}
void kde(double *data, int length, int n ,double dataMIN, double dataMAX, double **out_density, double **out_x, double *bw)
{
XML_IN;
/*
* function [bandwidth,density,xmesh,cdf]=kde(data,n,dataMIN,dataMAX)
* Reference:
* Kernel density estimation via diffusion
* Z. I. Botev, J. F. Grotowski, and D. P. Kroese (2010)
* Annals of Statistics, Volume 38, Number 5, pages 2916-2957.
*/
/* if n is not supplied switch to the default
n = pow( 2 , 14 );
*/
n = pow( 2 , ceil(log2(n)) ); // round up n to the next power of 2;
double tol=1e-6;
if ( (fabs(dataMIN+1)<tol) && (fabs(dataMAX+1)<tol) )
{
printf("using automatic extrema determination\n");
//define the default interval [MIN,MAX]
double maximum,minimum;
find_max_min_array_doubles(data,length,&maximum,&minimum);
double Range=maximum-minimum;
dataMIN=minimum-Range/10.0; dataMAX=maximum+Range/10.0;
printf("min: %g max: %g\n",dataMIN,dataMAX);
}
/*set up the grid over which the density estimate is computed;*/
double R=dataMAX-dataMIN;
double dx=R/(n-1);
double* xmesh=(double*)malloc(n*sizeof(*xmesh));
for (int i=0; i<n; i++ ) xmesh[i] = dataMIN+i*dx;
double N = length; //double N=length(unique(data)); //qsort(data, length, sizeof(double), compare_doubles);
N=256; //FIXME: we have emulate the unique matlab function.
/*bin the data uniformly using the grid defined above;*/
double initial_data[n];
histc(data, length, xmesh, n , initial_data);
double sum_initial_data = 0;
for(int i=0;i<n;i++){
initial_data[i]=initial_data[i]/N;
sum_initial_data+=initial_data[i];
}
for(int i=0;i<n;i++)
initial_data[i]=initial_data[i]/sum_initial_data;
double a[n];
kde_dct_fftw(initial_data,n,a); // discrete cosine transform of initial data
/*now compute the optimal bandwidth^2 using the referenced method*/
double It[n-1];
for (int i=0;i<n-1;i++)
It[i]=pow(i+1,2.0);
double a2[n-1];
for(int i=0;i<n-1;i++)
a2[i] = pow(a[i+1]/2.0,2.0);
double t_star=0;
/*use fzero to solve the equation t=zeta*gamma^[5](t)*/
/* try
t_star=fzero(@(t)fixed_point(t,N,I,a2),[0,.1])
catch
t_star=.28*N^(-2/5);
end
*/
//test fixed point values
double t=0;
double tt;
tt=fixed_point(0.01,N,It,a2,n);
printf("tt: %g\n",tt);
tt=fixed_point(0.0,N,It,a2,n);
printf("tt: %g\n",tt);
tt=fixed_point(0.1,N,It,a2,n);
printf("tt: %g\n",tt);
int status=fzero(&t_star,N,It,a2,n);
printf("t_star: %g\n",t_star);
//t_star=.28*pow(N,-2.0/5.0);
//printf("t_star: %g\n",t_star);
/*smooth the discrete cosine transform of initial data using t_star*/
double a_t[n];
for(int i=0;i<n;i++)
a_t[i]=a[i]*exp(-pow(i*M_PI,2.0)*t_star/2.0);
double *density=(double* )malloc(n*sizeof(*density));
kde_idct_fftw(a_t,n,density);
for(int i=0;i<n;i++)
density[i]/=R*n*2;
double bandwidth=sqrt(t_star)*R;
printf("bandwidth: %g\n",bandwidth);
if (verbose>=2 || verbose<=3)
{
int range[2]={0,128};
print_vec(xmesh,"xmesh",0,n);
print_vec(data,"data",0,length);
print_vec(initial_data,"initial_data",0,n);
print_vec(a,"a",0,n);
print_vec(a_t,"a_t",0,n);
print_vec(a2,"a_2",0,n-1);
print_vec(density,"density",0,n);
}
if (verbose>=3)
{
array_write_ascii(xmesh,n,"xmesh.txt");
array_write_ascii(initial_data, n, "initial_data.txt");
array_write_ascii(data, length, "data.txt");
array_write_ascii(density, n, "density.txt");
array_write_ascii(a_t, n, "a_t.txt");
array_write_ascii(a2, n-1, "a_2.txt");
}
//prepare output
*bw=bandwidth;
if(!(*out_density))
*out_density=density;
if(!(*out_x))
*out_x=xmesh;
XML_OUT;
}
fixed_point fixed_point::operator -() const{
return fixed_point(-mQ);
}
