5.2.2.21 Fitting with Piecewise Functions

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 User-Defined Fitting Functions-2.png 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:

xc: 1
a: 1
b: -1
t1: 0.1

Click Fit button to generate the results:

xc: 0.24
a: 36.76585
b: -24.62876
t1: 0.04961

Note that this function is sensitive to xc and t1, different initial values could generate different results.