public class qspline{
double[] x,y,b,c;
int n => x.Length;
public qspline(double[] x,double[] y){
	this.x=(double[])x.Clone();
	this.y=(double[])y.Clone();
	b=new double[n-1];
	c=new double[n-1];
	var p=new double[n-1];
	var h=new double[n-1];
	for(int i=0;i<n-1;i++){
		h[i]=x[i+1]-x[i];
		p[i]=(y[i+1]-y[i])/h[i];
		}
	c[0]=0;                                     //recursion up:
	for(int i=0;i<n-2;i++)
		c[i+1]=(p[i+1]-p[i]-c[i]*h[i])/h[i+1];
	c[n-2]/=2;                                 //recursion down:
	for(int i=n-3;i>=0;i--)
		c[i]=(p[i+1]-p[i]-c[i+1]*h[i+1])/h[i];
	for(int i=0;i<n-1;i++)
		b[i]=p[i]-c[i]*h[i];
	}
int binsearch(double z){                     //binary search:
	if(z<x[0] || z>x[n-1]) throw new System.ArgumentException();
	int i=0, j=n-1;
	while(j-i>1){
		int m=(i+j)/2;
		if(z>x[m]) i=m;
		else j=m;
		}
	return i;
	}

public double eval(double z){ //evaluates s(z)
	int i=binsearch(z);
	double h=z-x[i];
	return y[i]+h*(b[i]+h*c[i]);
	}

public double deriv(double z){//evaluates s'(z)
	int i=binsearch(z);
	double h=z-x[i];
	return b[i]+2*h*c[i];
	}

public double integ(double z){//evaluates inegral of s(z) from x_0 to z
	int i=binsearch(z);
	double sum=0,h;
	for(int k=0;k<i;k++){
		h=x[k+1]-x[k];
		sum+=h*(y[k]+h*(b[k]/2+h*c[k]/3));
		}
	h=z-x[i];
	return sum+h*(y[i]+h*(b[i]/2+h*c[i]/3));
	}

}//qspline