# include <stdio.h>
# include <stdlib.h>
# include <math.h>

double function(double x)
{
	x = sin(x);
	return x;
}

double U(double x)
{
	double pi=4*atan(1.);
	x = -sin(x)+(x/pi);
	return x;
}

int main (void)
{
	int i,j, n = 1000;
	double x = 0.,pi=4*atan(1.), h;
	h=pi/n;

	double * v;
	double *chis;
	double * koef;

	FILE *A;
	A = fopen("out.txt","w");

	v = (double *)malloc((n+1)*sizeof(double));
	chis = (double *)malloc(n*sizeof(double));
	koef = (double *)malloc(n*n*sizeof(double));
	for(i=0;i<(n*n);i++)
	{
		koef[i]=0;
	}

	chis[0]=U(x);
	chis[n-1]=U(pi);
	for(i=1;i<=(n-1);i++)
	{
		koef[i]=0.;
	}
	koef[0]=1;
	for(i=0;i<(n-1);i++)
	{
		koef[n*n + i -1 ]=0;
	}
	koef[n*n -1]=1;
	x=h;

	for (i=1;i<(n-1);i++)
	{
		koef[i*n + i -1] = 1;
		koef[i*n + i] = -2;
		koef[i*n + i + 1] =1;
		chis[i] = function(x)*h*h;
		x += h;

	}

	chis[1]=(chis[1] - chis[0]*koef[n])/(-2);
	koef[n]=0;
	koef[n+1] = koef[n+1]*(-0.5);
	koef[n+2] = koef[n+2]*(-0.5);
	for(i=2;i<(n-1);i++)
	{
		chis[i]=chis[i]-chis[i-1];
		koef[i*n+i-1]-=koef[(i-1)*n+i-1];
		koef[i*n+i]-=koef[(i-1)*n+i];
		koef[i*n+i+1]-=koef[(i-1)*n+i+1];
		chis[i]=chis[i]/koef[i*n+i];
		koef[i*n+i+1]=koef[i*n+i+1]/(koef[i*n+i]);
		koef[i*n+i]=1;

	}

	v[n]=chis[n];
	v[0]=chis[0];

	v[n-1]=chis[n-1]-koef[n*n-1-n]*v[n];
	for(i=n-2;i>=1;i--)
	{
		v[i]=chis[i]-(v[i+1]*koef[i*n+i+1]);
	}


	x=0.;
	for(i=0;i<=n;i++)
	{
		fprintf(A,"%lf %lf %lf\n",x,v[i],U(x));
		x=x+h;
	}
	return 0;
}