#include <origin.h>

// Add your special include files here.
// For example, if you want to fit with functions from the NAG library, 
// add the header file for the NAG functions here.
#include <OC_nag.h>



// Add code here for other Origin C functions that you want to define in this file,
// and access in your fitting function.

struct user
{
	double l, E0, q, mu, fitX;  // fitX the independent variable of fitting function
 
};
static double NAG_CALL f_callback(double x, Nag_User *comm)  // x is the independent variable of the integrand
{
 
	struct user *sp = (struct user *)(comm->p);
 
        double ll, E0E0, qq, mumu, fitX; // temp variable to accept the parameters in the Nag_User communication struct
        ll = sp->l;
        E0E0 = sp->E0;
        qq   = sp->q;
        mumu = sp->mu;
        
        fitX = sp->fitX;
        
       
	
		 return x*exp(mumu*x - (2*E0E0/(qq*fitX*ll))*asin(x/(2*E0E0*E0E0/(qq*fitX)))) ;
				
       
}

       
		
// You can access C functions defined in other files, if those files are loaded and compiled 
// in your workspace, and the functions have been prototyped in a header file that you have
// included above. 

// You can access NLSF object methods and properties directly in your function code.

// You should follow C-language syntax in defining your function. 
// For instance, if your parameter name is P1, you cannot use p1 in your function code. 
// When using fractions, remember that integer division such as 1/2 is equal to 0, and not 0.5
// Use 0.5 or 1/2.0 to get the correct value.

// For more information and examples, please refer to the "User-Defined Fitting Function" 
// section of the Origin Help file.


//----------------------------------------------------------
// 
void _nlsfalphavslowB(
// Fit Parameter(s):
double r0, double l,
// Independent Variable(s):
double B,
// Dependent Variable(s):
double& y)
{
	const double E0=10;
	const double q=3;
	const double mu=0.01579;
	// Beginning of editable part
	// Beginning of editable part
	double epsabs = 0.00001, epsrel = 0.0000001, result, abserr;
	Integer max_num_subint = 500;  
	        // you may use epsabs and epsrel and this quantity to enhance your desired precision 
	        // when not enough precision encountered
	
	Nag_QuadProgress qp;
	static NagError fail;
	
	// the parameters parameterize the integrand can be input to the call_back function
	        // through the Nag_User communication struct 
	        Nag_User comm;	
	struct user s;
	s.l = l;
	s.E0 = E0;
	s.q = q;
	s.mu = mu;
	s.fitX = B;
	        comm.p = (Pointer)&s;
	
	if (B==0)
	{
		
	(l*(l + ((-r0 +l*(-1 + mu*r0))*exp((mu - 1/l)*r0))/((-1 +l*mu)^2)));
	
	}
	else{
	d01sjc(f_callback, 0, r0, epsabs, epsrel, max_num_subint, &result, &abserr, &qp, &comm, &fail);
	}
	
	        // you may want to exam the error by printing out error message, just uncomment the following lines
	// if (fail.code != NE_NOERROR)
	        // printf("%s\n", fail.message);
	
	
	// For the error other than the following three errors which are due to bad input parameters 
	// or allocation failure  NE_INT_ARG_LT  NE_BAD_PARAM   NE_ALLOC_FAIL
	// You will need to free the memory allocation before calling the integration routine again to 
	        // avoid memory leakage
	if (fail.code != NE_INT_ARG_LT && fail.code != NE_BAD_PARAM && fail.code != NE_ALLOC_FAIL)
	{
		NAG_FREE(qp.sub_int_beg_pts);
		NAG_FREE(qp.sub_int_end_pts);
		NAG_FREE(qp.sub_int_result);
		NAG_FREE(qp.sub_int_error);
	}
	
	
	y = result/(l*(l + ((-r0 +l*(-1 + mu*r0))*exp((mu - 1/l)*r0))/((-1 +l*mu)^2))); 
	     
	// End of editable part
}

newbook;
col(a)={-5:0.5:5};
col(b)=sin(col(a))/col(a);
col(c)=IntegrateXY(col(a), col(b));
col(c)[C]$ = "Area";

quote:

---

Originally posted by riclambo@hotmail.com

Hi Yuki,
Your reply did provide some help. As you said, when x= 0, sin[x]/x will be a missing value. If I try to integrate it according to your code, the integral will also have a missing value.
However, I can input the value x=0, sin[x]/x if I use this code:

newbook;
col(a)={-5:0.5:5};
col(b)=sin(col(a))/col(a);
cell(11, 2) = 1;
col(c)=IntegrateXY(col(a), col(b));
col(c)[C]$ = "Area";

Please try it to see the difference. It will give me a continous function and a continuous integral. This is what I'm trying to do with my integral. I'm trying to find out how to make the program realise that when rho=0, alpha =1.
I submitted this question to tech@originlab.com, but I have not recieved a reply yet.
Probably what I need to do is a piecewise fit. Something like:
https://www.originlab.com/doc/Tutorials/Fitting-Piecewise-Linear


RL

---

                                          &&&&&&&&&
                                        &&&
                                       &&
                                      &  _____ ___________
                                     II__|[] | |   I I   |
                                    |        |_|_  I I  _|
                                   < OO----OOO   OO---OO
**********************************************************

quote:

---

Originally posted by riclambo@hotmail.com

Got it,Castiel. However, I was just using sin(x)/x to illustrate my main point, which is how to fit with a function that has a removable singularity. The function that I am genuinely interested in is the one that appears in my first post.

RL

---

	if (B==0)
	{
		
	(l*(l + ((-r0 +l*(-1 + mu*r0))*exp((mu - 1/l)*r0))/((-1 +l*mu)^2)));
	
	}

                                          &&&&&&&&&
                                        &&&
                                       &&
                                      &  _____ ___________
                                     II__|[] | |   I I   |
                                    |        |_|_  I I  _|
                                   < OO----OOO   OO---OO
**********************************************************

if (B==0)
	{
		
	(l*(l + ((-r0 +l*(-1 + mu*r0))*exp((mu - 1/l)*r0))/((-1 +l*mu)^2)));
	
	}
else{
	d01sjc(f_callback, 0, r0, epsabs, epsrel, max_num_subint, &result, &abserr, &qp, &comm, &fail);
	}

y = result/(l*(l + ((-r0 +l*(-1 + mu*r0))*exp((mu - 1/l)*r0))/((-1 +l*mu)^2))); 
	     
	// End of editable part

quote:

---

Originally posted by riclambo@hotmail.com

I really appreciate your taking a look, Castiel, since this is a struggle for a weak programmer like myself. As you say, the following lines seem to be the problem:

if (B==0)
	{
		
	(l*(l + ((-r0 +l*(-1 + mu*r0))*exp((mu - 1/l)*r0))/((-1 +l*mu)^2)));
	
	}
else{
	d01sjc(f_callback, 0, r0, epsabs, epsrel, max_num_subint, &result, &abserr, &qp, &comm, &fail);
	}

However, what I'm trying to do is make "y=1" when B=0. If you look down to near the end of the code, I've written:

y = result/(l*(l + ((-r0 +l*(-1 + mu*r0))*exp((mu - 1/l)*r0))/((-1 +l*mu)^2))); 
	     
	// End of editable part

In other words, I'd hoped numerator and denominator would cancel to give y=1 at B=0. This was the idea, however, I'm not quite able to execute it.



RL

---

if (B==0)
    {	
        (l*(l + ((-r0 +l*(-1 + mu*r0))*exp((mu - 1/l)*r0))/((-1 +l*mu)^2)));
    }

                                          &&&&&&&&&
                                        &&&
                                       &&
                                      &  _____ ___________
                                     II__|[] | |   I I   |
                                    |        |_|_  I I  _|
                                   < OO----OOO   OO---OO
**********************************************************

#include <origin.h>


#include <origin.h>

// Add your special include files here.
// For example, if you want to fit with functions from the NAG library, 
// add the header file for the NAG functions here.
#include <OC_nag.h>



// Add code here for other Origin C functions that you want to define in this file,
// and access in your fitting function.

struct user
{
	double l, E0, q, mu, fitX;  // fitX the independent variable of fitting function
 
};
static double NAG_CALL f_callback(double x, Nag_User *comm)  // x is the independent variable of the integrand
{
 
	struct user *sp = (struct user *)(comm->p);
 
        double ll, E0E0, qq, mumu, fitX; // temp variable to accept the parameters in the Nag_User communication struct
        ll = sp->l;
        E0E0 = sp->E0;
        qq   = sp->q;
        mumu = sp->mu;
        
        fitX = sp->fitX;
        
       
	
		 return x*exp(mumu*x - (2*E0E0/(qq*fitX*ll))*asin(x/(2*E0E0/(qq*fitX)))) ;
				
       
}

		
// You can access C functions defined in other files, if those files are loaded and compiled 
// in your workspace, and the functions have been prototyped in a header file that you have
// included above. 

// You can access NLSF object methods and properties directly in your function code.

// You should follow C-language syntax in defining your function. 
// For instance, if your parameter name is P1, you cannot use p1 in your function code. 
// When using fractions, remember that integer division such as 1/2 is equal to 0, and not 0.5
// Use 0.5 or 1/2.0 to get the correct value.

// For more information and examples, please refer to the "User-Defined Fitting Function" 
// section of the Origin Help file.

//----------------------------------------------------------
// 
void _nlsfalphavslowB_test(
// Fit Parameter(s):
double r0, double l,
// Independent Variable(s):
double B,
// Dependent Variable(s):
double& y)
{
	const double E0=10;
	const double q=3;
	const double mu=0.01579;
	// Beginning of editable part
	// Beginning of editable part
	double epsabs = 0.00001, epsrel = 0.0000001, result, abserr, result1;
	Integer max_num_subint = 1000;  
	        // you may use epsabs and epsrel and this quantity to enhance your desired precision 
	        // when not enough precision encountered
	
	Nag_QuadProgress qp;
	static NagError fail;
	
	// the parameters parameterize the integrand can be input to the call_back function
	        // through the Nag_User communication struct 
	        Nag_User comm;	
	struct user s;
	s.l = l;
	s.E0 = E0;
	s.q = q;
	s.mu = mu;
	s.fitX = B;
	        comm.p = (Pointer)&s;
	
	d01sjc(f_callback, 0, r0, epsabs, epsrel, max_num_subint, &result, &abserr, &qp, &comm, &fail);
	d01sjc(f_callback1, 0, r0, epsabs, epsrel, max_num_subint, &result1, &abserr, &qp, &comm, &fail);
	        // you may want to exam the error by printing out error message, just uncomment the following lines
	// if (fail.code != NE_NOERROR)
	        // printf("%s\n", fail.message);
	
	
	// For the error other than the following three errors which are due to bad input parameters 
	// or allocation failure  NE_INT_ARG_LT  NE_BAD_PARAM   NE_ALLOC_FAIL
	// You will need to free the memory allocation before calling the integration routine again to 
	        // avoid memory leakage
	if (fail.code != NE_INT_ARG_LT && fail.code != NE_BAD_PARAM && fail.code != NE_ALLOC_FAIL)
	{
		NAG_FREE(qp.sub_int_beg_pts);
		NAG_FREE(qp.sub_int_end_pts);
		NAG_FREE(qp.sub_int_result);
		NAG_FREE(qp.sub_int_error);
	}
	
	if(B==0) {
		y = 1;
	} else {
		y = result/(l*(l + ((-r0 +l*(-1 + mu*r0))*exp((mu - 1/l)*r0)))/((-1 
	+l*mu)^2));
	}
	
	  
	// End of editable part
}