4.2.2.21 Fitting with Piecewise Functions

1 Summary
2 What you will learn
3 Example and Steps
- 3.1 Define the Function
- 3.2 Fit the Curve

Summary

We will show you how to define piecewise fitting function in this tutorial.

Minimum Origin Version Required: Origin 8.0 SR6

What you will learn

This tutorial will show you how to:

Define piecewise (conditional) fitting functions.

Example and Steps

We can start this tutorial by importing the sample \Samples\Curve Fitting\Exponential Decay.dat data file. Highlight column D and plot a Scatter Graph. You can fit this curve using built-in functions under Growth/Sigmoidal category, however, in this tutorial, we will separate the curve into two parts by a piecewise function.

Tutorial Fitting with Piecewise Functions 001.png

So the equation will be:

$y = \begin{cases} a+bx+e^{-\frac{x-x_c}{t1}}, & \mbox{if } x<x_c \\ a+bx, & \mbox{if } x \ge x_c \end{cases}$

Define the Function

Press F9 to open the Fitting Function Organizer and define a function like:

Function Name:	piecewise
Function Type:	User-Defined
Independent Variables:	x
Dependent Variables:	y
Parameter Names:	xc, a, b, t1
Function Form:	Origin C
Function:

Click the button on the right of the Function edit box and define the fitting function in Code Builder using:

void _nlsfpiecewise(
// Fit Parameter(s):
double xc, double a, double b, double t1,
// Independent Variable(s):
double x,
// Dependent Variable(s):
double& y)
{
	// Beginning of editable part
	// Divide the curve by if condition.
	if(x<xc) {
		y = a+b*x+exp(-(x-xc)/t1);
	} else {
		y = a+b*x;
	}
	// End of editable part
}

Fit the Curve

Press Ctrl + Y to bring up NLFit dialog with the graph window active. Select the piecewise function we defined and initialize the parameter values: