3.142 FAQ-858 How to build up a summation fitting function or a double integral fitting funtion?

Last Update: 10/12/2017

You can create your user-defined summation or double integral fitting function by LabTalk scripts or Origin C codes, in Tools: Fitting Function Organizer.

summation fitting function

You can define the fitting function with an embedded For loop in the function definition box. Take the following function as an example.

$y=\sum_{i=1}^{10}a \cdot x^2$

Suppose you define the fitting function in the Function box as follow:

y = sum(x, a, n); //n is a constant, and n=10

Then define the user-defined LabTalk functions sum in the LabTalk Functions Definition and Initializations box as follow:

function double sum(double x, double a, int n)
{
    double bb = 0;
    for(ii =1; ii<=n; ii++)
    {
    	bb = a * x * x + bb;
    }
    return bb;
}

double integral fitting function

You can define an Origin C fitting function in which NAG functions are called to perform the integration. Take the following function as an example.

$y=\int_{amp}^x \int_{amp}^x (z_{1}+z_{2})dz_{1}dz_{2}$

Click the button next to the Function edit box to open the Code Builder.
Scroll up to go to line
```
//add the header file for the NAG functions here.
```
and add the header file for the NAG functions below this line:
```
#include <OC_nag.h>
```

Define your fitting model.

static double NAG_CALL f(int n, double z[], Nag_User *comm)
{
	int *use_comm = (int *)comm->p;
	double dUserSuppliedFunction;
	dUserSuppliedFunction = z[0] + z[n-1];
	return dUserSuppliedFunction;
}

Edit your fitting function.

void _nlsfnag_double_integral_fitting(
// Fit Parameter(s):
double amp,
// Independent Variable(s):
double x,
// Dependent Variable(s):
double& y)
{
	// Beginning of editable part
        static int use_comm;
	int ndim = 2;  // the integral dimension
	int maxpts = 1000*2;  // maximum number of function evaluation 
	double a[2], b[2];
	
	static NagError fail;
	double finval;
	int minpts;
	double acc, eps;
	Nag_User comm;
	comm.p = (Pointer)&use_comm; // For communication with user-supplied functions
	
	for (int k=0; k < ndim; ++k)  // integration interval
	{
	  a[k] = amp;
	  b[k] = x;
	}
	eps = 0.0001; // set the precision
	minpts = 0;
		
	d01wcc(ndim, f, a, b, &minpts, maxpts, eps, &finval, &acc, &comm, &fail);
	
	y = finval;
	// End of editable part
}

Click Compile button to compile.

We provide several tutorials of user-defined integral functions. Refer to the corresponding topic for detailed steps if needed:

Keywords: integrate, integral, fitting, Origin C, LabTalk, NAG, summation, double integral