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

Summation-DoubleIntegral-Func

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.

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.

1. Click the button next to the Function edit box to open the Code Builder.
2. 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>

3. 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;
   }

4. 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
   }

5. Click Compile button to compile.

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

• Using Origin C and NAG library functions
• Using LabTalk script
• Fitting with Two Integrals using LabTalk Function
• Fitting with Summation

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