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# ezcontour

Contour plotter

## Syntax

ezcontour(f)
ezcontour(f,domain)
ezcontour(...,n)

## Description

ezcontour(f) plots the contour lines of f(x,y), where f is a symbolic expression that represents a mathematical function of two variables, such as x and y.

The function f is plotted over the default domain –2π < x < 2π, –2π < y < 2π. MATLAB® software chooses the computational grid according to the amount of variation that occurs; if the function f is not defined (singular) for points on the grid, then these points are not plotted.

ezcontour(f,domain) plots f(x,y) over the specified domain. domain can be either a 4-by-1 vector [xmin, xmax, ymin, ymax] or a 2-by-1 vector [min, max] (where, min < x < max, min < y < max).

If f is a function of the variables u and v (rather than x and y), then the domain endpoints umin, umax, vmin, and vmax are sorted alphabetically. Thus, ezcontour(u^2 - v^3,[0,1],[3,6]) plots the contour lines for u2 - v3 over 0 < u < 1, 3 < v < 6.

ezcontour(...,n) plots f over the default domain using an n-by-n grid. The default value for n is 60.

ezcontour automatically adds a title and axis labels.

## Examples

### Plot the Contour Lines of a Symbolic Expression

The following mathematical expression defines a function of two variables, x and y.

$f\left(x,y\right)=3{\left(1-x\right)}^{2}{e}^{-{x}^{2}-{\left(y+1\right)}^{2}}-10\left(\frac{x}{5}-{x}^{3}-{y}^{5}\right){e}^{-{x}^{2}-{y}^{2}}-\frac{1}{3}{e}^{-{\left(x+1\right)}^{2}-{y}^{2}}.$

ezcontour requires a sym argument that expresses this function using MATLAB syntax to represent exponents, natural logs, etc. This function is represented by the symbolic expression

```syms x y
f = 3*(1-x)^2*exp(-(x^2)-(y+1)^2)...
- 10*(x/5 - x^3 - y^5)*exp(-x^2-y^2)...
- 1/3*exp(-(x+1)^2 - y^2);```

For convenience, this expression is written on three lines.

Pass the sym f to ezcontour along with a domain ranging from -3 to 3 and specify a computational grid of 49-by-49.

```ezcontour(f,[-3,3],49)
```

In this particular case, the title is too long to fit at the top of the graph so MATLAB abbreviates the string.