1.151 FAQ-779 How to create a 2D nested function plot?

Nest-Func-Mat

Last Update: 8/24/2015

In Origin, we can plot 2D nested functions as below by using matrix objects.

$f(\mathbf{x},\mathbf{y})=\sigma(u(\mathbf{x},\mathbf{y}),\mathbf{x},\mathbf{y})$

Example

In this tutorial we will a 2D function $f(\mathbf{x},\mathbf{y})$ and make a contour plot from it.

$\left\{\begin{matrix} f(\mathbf{x},\mathbf{y})=\sqrt{u}+x+y\\ u(\mathbf{x},\mathbf{y})=x^2+y^2 \end{matrix}\right.$

while $\mathbf{x}=\mathbf{y}=[0,0.1,0.2,0.3...,10]$

Steps:

Click the New Matrix button to create a new matrix.
To set the dimensions, select Matrix: Set Dimension/Labels from Origin menu menu, and set values as the image below, then click OK to apply:
Then we are going to set values for the active matrix object to make it be
- Select Matrix: Set Values from Origin menu. You can set values for Mat(1) in the opened dialog
```
x^2+y^2
```
Now add an extra matrix object to act as , which will call Mat(1) in calculation.
- Click the D button, in the upper-left corner of matrix and choose Add from the context menu
- Click the D button, again and choose 2 to active the 2nd matrix object.
- While the 2nd matrix object is active, set values for Mat(2) using formula below:
```
sqrt(Mat(1))+x+y
```
Finally, we can plot a contour graph from the Mat(2), which will be similar to this one: