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.

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

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

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