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:

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