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#### 15.2.1.2 Two-dimensional Function Plotting

Octave can plot a function from a function handle, inline function, or string defining the function without the user needing to explicitly create the data to be plotted. The function `fplot` also generates two-dimensional plots with linear axes using a function name and limits for the range of the x-coordinate instead of the x and y data. For example,

```fplot (@sin, [-10, 10], 201);
```

produces a plot that is equivalent to the one above, but also includes a legend displaying the name of the plotted function.

Function File: fplot (fn, limits)
Function File: fplot (…, tol)
Function File: fplot (…, n)
Function File: fplot (…, fmt)
Function File: [x, y] = fplot (…)

Plot a function fn within the range defined by limits.

fn is a function handle, inline function, or string containing the name of the function to evaluate.

The limits of the plot are of the form `[xlo, xhi]` or `[xlo, xhi, ylo, yhi]`.

The next three arguments are all optional and any number of them may be given in any order.

tol is the relative tolerance to use for the plot and defaults to 2e-3 (.2%).

n is the minimum number of points to use. When n is specified, the maximum stepsize will be `xhi - xlo / n`. More than n points may still be used in order to meet the relative tolerance requirement.

The fmt argument specifies the linestyle to be used by the plot command.

If the first argument hax is an axes handle, then plot into this axis, rather than the current axes returned by `gca`.

With no output arguments the results are immediately plotted. With two output arguments the 2-D plot data is returned. The data can subsequently be plotted manually with `plot (x, y)`.

Example:

```fplot (@cos, [0, 2*pi])
fplot ("[cos(x), sin(x)]", [0, 2*pi])
```

Programming Notes:

`fplot` works best with continuous functions. Functions with discontinuities are unlikely to plot well. This restriction may be removed in the future.

`fplot` requires that the function accept and return a vector argument. Consider this when writing user-defined functions and use `.*`, `./`, etc. See the function `vectorize` for potentially converting inline or anonymous functions to vectorized versions.

Other functions that can create two-dimensional plots directly from a function include `ezplot`, `ezcontour`, `ezcontourf` and `ezpolar`.

Function File: ezplot (f)
Function File: ezplot (f2v)
Function File: ezplot (fx, fy)
Function File: ezplot (…, dom)
Function File: ezplot (…, n)
Function File: ezplot (hax, …)
Function File: h = ezplot (…)

Plot the 2-D curve defined by the function f.

The function f may be a string, inline function, or function handle and can have either one or two variables. If f has one variable, then the function is plotted over the domain `-2*pi < x < 2*pi` with 500 points.

If f2v is a function of two variables then the implicit function `f(x,y) = 0` is calculated over the meshed domain `-2*pi <= x | y <= 2*pi` with 60 points in each dimension.

For example:

```ezplot (@(x, y) x.^2 - y.^2 - 1)
```

If two functions are passed as inputs then the parametric function

```x = fx (t)
y = fy (t)
```

is plotted over the domain `-2*pi <= t <= 2*pi` with 500 points.

If dom is a two element vector, it represents the minimum and maximum values of both x and y, or t for a parametric plot. If dom is a four element vector, then the minimum and maximum values are `[xmin xmax ymin ymax]`.

n is a scalar defining the number of points to use in plotting the function.

If the first argument hax is an axes handle, then plot into this axis, rather than the current axes returned by `gca`.

The optional return value h is a vector of graphics handles to the created line objects.

Function File: ezcontour (f)
Function File: ezcontour (…, dom)
Function File: ezcontour (…, n)
Function File: ezcontour (hax, …)
Function File: h = ezcontour (…)

Plot the contour lines of a function.

f is a string, inline function, or function handle with two arguments defining the function. By default the plot is over the meshed domain `-2*pi <= x | y <= 2*pi` with 60 points in each dimension.

If dom is a two element vector, it represents the minimum and maximum values of both x and y. If dom is a four element vector, then the minimum and maximum values are `[xmin xmax ymin ymax]`.

n is a scalar defining the number of points to use in each dimension.

If the first argument hax is an axes handle, then plot into this axis, rather than the current axes returned by `gca`.

The optional return value h is a graphics handle to the created plot.

Example:

```f = @(x,y) sqrt (abs (x .* y)) ./ (1 + x.^2 + y.^2);
ezcontour (f, [-3, 3]);
```

Function File: ezcontourf (f)
Function File: ezcontourf (…, dom)
Function File: ezcontourf (…, n)
Function File: ezcontourf (hax, …)
Function File: h = ezcontourf (…)

Plot the filled contour lines of a function.

f is a string, inline function, or function handle with two arguments defining the function. By default the plot is over the meshed domain `-2*pi <= x | y <= 2*pi` with 60 points in each dimension.

If dom is a two element vector, it represents the minimum and maximum values of both x and y. If dom is a four element vector, then the minimum and maximum values are `[xmin xmax ymin ymax]`.

n is a scalar defining the number of points to use in each dimension.

If the first argument hax is an axes handle, then plot into this axis, rather than the current axes returned by `gca`.

The optional return value h is a graphics handle to the created plot.

Example:

```f = @(x,y) sqrt (abs (x .* y)) ./ (1 + x.^2 + y.^2);
ezcontourf (f, [-3, 3]);
```

Function File: ezpolar (f)
Function File: ezpolar (…, dom)
Function File: ezpolar (…, n)
Function File: ezpolar (hax, …)
Function File: h = ezpolar (…)

Plot a 2-D function in polar coordinates.

The function f is a string, inline function, or function handle with a single argument. The expected form of the function is `rho = f(theta)`. By default the plot is over the domain `0 <= theta <= 2*pi` with 500 points.

If dom is a two element vector, it represents the minimum and maximum values of theta.

n is a scalar defining the number of points to use in plotting the function.

If the first argument hax is an axes handle, then plot into this axis, rather than the current axes returned by `gca`.

The optional return value h is a graphics handle to the created plot.

Example:

```ezpolar (@(t) sin (5/4 * t), [0, 8*pi]);
```