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#### 15.1.1.1 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 (fn, limits, tol)
Function File: fplot (fn, limits, n)
Function File: fplot (…, fmt)

Plot a function fn, within the defined limits. fn an be either a string, a function handle or an inline function. The limits of the plot are given by limits of the form `[xlo, xhi]` or ```[xlo, xhi, ylo, yhi]```. tol is the default tolerance to use for the plot, and if tol is an integer it is assumed that it defines the number points to use in the plot. The fmt argument is passed to the plot command.

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

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

Plots in two-dimensions the curve defined by 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 f has two variables then `f(x,y) = 0` is calculated over the meshed domain ```-2*pi < x | y < 2*pi``` with 60 by 60 in the mesh. For example

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

If two functions are passed as strings, inline functions or function handles, 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 value of x, y and t. If it is a four element vector, then the minimum and maximum values of x and t are determined by the first two elements and the minimum and maximum of y by the second pair of elements.

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

The optional return value h provides a list of handles to the the line objects plotted.

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

Plots 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 domain `-2*pi < x < 2*pi` and ```-2*pi < y < 2*pi``` with 60 points in each dimension.

If dom is a two element vector, it represents the minimum and maximum value of both x and y. If dom is a four element vector, then the minimum and maximum value of x and y are specify separately.

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

The optional return value h provides a list of handles to the the parts of the vector field (body, arrow and marker).

 ```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 (h, …)
Function File: h = ezcontourf (…)

Plots 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 domain `-2*pi < x < 2*pi` and `-2*pi < y < 2*pi` with 60 points in each dimension.

If dom is a two element vector, it represents the minimum and maximum value of both x and y. If dom is a four element vector, then the minimum and maximum value of x and y are specify separately.

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

The optional return value h provides a list of handles to the the parts of the vector field (body, arrow and marker).

 ```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 (h, …)
Function File: h = ezpolar (…)

Plots in polar plot defined by a function. The function f is either a string, inline function or function handle with one arguments defining the function. By default the plot is over the domain ```0 < x < 2*pi``` with 60 points.

If dom is a two element vector, it represents the minimum and maximum value of both t. n is a scalar defining the number of points to use.

The optional return value h provides a list of handles to the the parts of the vector field (body, arrow and marker).

 ```ezpolar (@(t) 1 + sin (t)); ```

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