double integ(VEC &X,VEC &Y,int n){ // composite nth order Newton-Cotes integral
int iter = (X.len()-1)/n;
//printf("iter : %d\n",iter);
double space = X[X.len()] - X[0];
double h = space/(X.len()-1);
double sum = 0.0;
VEC w(n+1);
if(n == 1)
w[0] = w[1] = 0.5;
else if (n == 2)
w[0] = w[2] = 1./3. , w[1] = 4./3.;
else if (n == 3)
w[0] = w[3] = 3./8. , w[1] = w[2] = 9./8.;
else if (n == 4)
w[0] = w[4] = 14./45. , w[1] = w[3] = 64./45. , w[2] = 24./45.;
else if (n == 5)
w[0] = w[5] = 95./288. , w[1] = w[4] = 375./288. , w[2] = w[3] = 250./288.;
else if (n == 6)
w[0] = w[6] = 41./140. , w[1] = w[5] = 216./140. , w[2] = w[4] = 27./140. , w[3] = 272./140.;
/*for(int i = 0; i<=n;i++)
printf("w%d = %f\n",i,w[i]);
printf("space = %f\n h = %f\n",space,h);*/
for(int i = 0; i< iter; i++){
for(int j = 0; j<= n; j++){
sum += (w[j] * Y[ n*i + j ]);
//printf("%d\n",n*i+j);
}
}
return sum * h;
}
double l1norm(VEC x){
double sum = 0.0;
for (int i = 0; i < x.len(); i++){
sum += std::abs(x[i]);
}
return sum;
}
double l2norm(VEC x){
double sum = 0.0;
for(int i = 0; i< x.len(); i++){
sum += (x[i]*x[i]);
}
return sqrt(sum);
}
double Lagrange(double x,VEC &XDATA,VEC &YDATA){
int n = XDATA.len();
double NS[n];
int i,j,k;
for (i=0; i<n; i++) NS[i]=YDATA[i];
for (k=1; k<n; k++) {
for (j=0; j<n-k; j++) {
NS[j]=((x-XDATA[j])*NS[j+1]-(x-XDATA[k+j])*NS[j])
/(XDATA[j+k]-XDATA[j]);
}
}
return NS[0];
}
double linfnorm(VEC x){
double max=0.0;
for (int i = 0 ;i< x.len();i++)
max = std::max(std::abs(x[i]),max);
return max;
}
