forum.alglib.net

ALGLIB forum
It is currently Thu Mar 28, 2024 8:57 am

All times are UTC


Forum rules


1. This forum can be used for discussion of both ALGLIB-related and general numerical analysis questions
2. This forum is English-only - postings in other languages will be removed.



Post new topic Reply to topic  [ 5 posts ] 
Author Message
 Post subject: spline1dintegrate function
PostPosted: Wed Jan 25, 2017 2:22 am 
Offline

Joined: Tue Jan 17, 2017 11:16 pm
Posts: 10
Dear Support,

I have an array of X nodes = [0, 1/12, 3/12, 1/2, 1, 2, 5, 10,15, 20] and a spline built successfully.

I try to use the spline1dintegrate(spline,X) function to integrate the function. I have produced the results for the integration. However, I am uncertain that if the spline1dintegrate(spline,X) function integrates from the starting node in the array to next node or from each pair of the consecutive nodes?
e.g. [0, 1/12], [0, 3/12], [0,1/2]..... or [0,1/12], [1/12,3/12] or [3/12, 1/2]

Please help ! Many thanks.
Van
[#include <iostream>

#include <cstdio>
#include <cstdlib>
#include <vector>
#include <interpolation.h>
#include "interpolation.cpp"
#include "ap.cpp"
#include "alglibinternal.cpp"
#include "alglibmisc.cpp"
#include "linalg.cpp"
#include "solvers.cpp"
#include "optimization.cpp"
#include "specialfunctions.cpp"
#include "integration.cpp"

#include <vector>

using namespace std;

double B(double a,double T);
double B(double a,double T)
{
return (1/a*(1-exp(-a*T)));
}
double A(double a, double b, double var, double T);
double A(double a, double b, double var, double T)
{
return -(var/(4*a))*pow(B(a,T),2)+(b-(var/(2*pow(a,2))))*(B(a,T)-T);
}
double p(double T, double a, double b, double var, double r0);
double p(double T, double a, double b, double var, double r0)
{
return exp(A(a,b,var,T)-r0*B(a,T));
}

double D1G(int n, double a, double b, double c, double T);
double D1G(int n, double a, double b, double c, double T)
{

if(n == 0){
return (1/a)*((1/a*(1-exp(-a*T)))-T);
}
else {
return (1/a)*(pow(T,n)*B(a,T)+n*D1G(n-1,a,b,c,T)-pow(T,n+1)/(n+1));
}
}

double D2G(int n, double a, double b, double c, double T);
double D2G(int n, double a, double b, double c, double T)
{
if(n == 0){
return -(1/(2*a))*pow(B(a,T),2)- (1/pow(a,2))*(B(a,T)-T);

}
else {
//-(1/(2*a))*(T^n*B(T,a,b,sigma2)^2-n*D2G(n-1,a,b,sigma2))-(1/a^2)*(T^n*B(T,a,b,sigma2)+n*D1G(n-1,a,b,sigma2)-T^(n+1)/(n+1));
return -(1/(2*a))*(pow(T,n)*pow(B(a,T),2)-n*D2G(n-1, a, b, c, T))- (1/pow(a,2))*(pow(T,n)*B(a,T)+n*D1G(n-1, a, b, c, T)-pow(T,n+1)/(n+1));
}
}



int main()
{
double a= 3.5, b = 0.03, var = 0.3, r0 = 0.03, q2;
//int i;
//float X[9], Y[9];
std::vector<double> X(9), Y(9);
X[0]=0;
X[1]=1.0/12;
X[2]=0.25;
X[3]=0.5;
X[4]=1;
X[5]=2;
X[6]=5;
X[7]=10;
X[8]=15;
X[9]=20;

/*for (i=0;i<10;i++){
cout << "x:" << X[i]<< ", f(x):";
Y[i] = X[i]*log(p(X[i],a,b,var,r0));
cout << Y[i] << endl;
}*/
cout << "\n"<< endl;
for (int n = 0; n<3; n++){
Y[0] = pow(X[0],n)*log(p(X[0],a,b,var,r0));
Y[1] = pow(X[1],n)*log(p(X[1],a,b,var,r0));
Y[2] = pow(X[2],n)*log(p(X[2],a,b,var,r0));
Y[3] = pow(X[3],n)*log(p(X[3],a,b,var,r0));
Y[4] = pow(X[4],n)*log(p(X[4],a,b,var,r0));
Y[5] = pow(X[5],n)*log(p(X[5],a,b,var,r0));
Y[6] = pow(X[6],n)*log(p(X[6],a,b,var,r0));
Y[7] = pow(X[7],n)*log(p(X[7],a,b,var,r0));
Y[8] = pow(X[8],n)*log(p(X[8],a,b,var,r0));
Y[9] = pow(X[9],n)*log(p(X[9],a,b,var,r0));
}


alglib::real_1d_array AX, AY; // alglib building vector X and Y
AX.setcontent(X.size(), &(X[0]));
AY.setcontent(Y.size(), &(Y[0]));

alglib::spline1dinterpolant spline; //alglib defining a spline
alglib::spline1dbuildlinear(AX, AY,spline); //alglib building the linear spline
for (int i = 0; i <10;i++){
q2 = spline1dintegrate(spline,X[i]);
cout <<q2 << endl;
}
//cout <<q2 << endl; //alglib integrating at value X = 20
//int k =2;
//double T = 20.0;
//(T^(n+1)/(n+1))*A(T,a,b,sigma2)-(sigma2/(2*(n+1)))*D2G(n+1,a,b,sigma2) ...
// -(a*b/(n+1))*D1G(n+1,a,b,sigma2)+r0*D1G(n,a,b,sigma2)-q(n);

//cout <<(pow(T,k+1)/(k+1))*A(a,b,var,T)-(var/(2*(k+1)))*D2G(k+1,a,b, var,T)-(a*b/(k+1))*D1G(k+1,a,b, var,T)+r0*D1G(k,a,b, var,T)<< endl;
return EXIT_SUCCESS;
}]


Top
 Profile  
 
 Post subject: Re: spline1dintegrate function
PostPosted: Fri Jan 27, 2017 3:21 pm 
Offline
Site Admin

Joined: Fri May 07, 2010 7:06 am
Posts: 903
Hi! It calculates integral with fixed lower bound equal to min(x[]). In your case it calculates integral(S(x)dx,0,t) for t=1/12, 3/12 and so on.


Top
 Profile  
 
 Post subject: Re: spline1dintegrate function
PostPosted: Mon Jan 30, 2017 3:29 am 
Offline

Joined: Tue Jan 17, 2017 11:16 pm
Posts: 10
Dear Sergey,

Thank you so much.

Cheers,
Van


Top
 Profile  
 
 Post subject: Re: spline1dintegrate function
PostPosted: Mon Jan 30, 2017 3:37 am 
Offline

Joined: Tue Jan 17, 2017 11:16 pm
Posts: 10
Dear Sergey,

I also have another query in regards to the spline1dbuildlinear(AX, AY,spline) function.

As I understand that the function currently only accepts array of physical values, if I have X nodes = [0, 1/12, 3/12, 1/2, 1, 2, 5, 10,15, 20] and Y[i] = X[i]*log(p(X[i],a,b,var,r0)), how do I store the values of Y[i] as array to apply to the spline1dbuildlinear(AX, AY,spline) function ?

Your help is much appreciated. Many thanks.

Cheers,
Van


Top
 Profile  
 
 Post subject: Re: spline1dintegrate function
PostPosted: Mon Jan 30, 2017 10:11 am 
Offline
Site Admin

Joined: Fri May 07, 2010 7:06 am
Posts: 903
See separate topic on this question :)


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 5 posts ] 

All times are UTC


Who is online

Users browsing this forum: No registered users and 52 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group