plot::Listplot – finite lists of 2D points

plot::Listplot holds a list of -values, which are visualized as 2D points with equidistant -values. Alternatively, a list of 2D points with given - and -coordinates can be specified.

→ Examples

Calls:

plot::Listplot([y1, y2, ...], <x = $`x_{min}`$ .. $`x_{max}`$ >, <a = amin .. amax>, Options)

plot::Listplot(A1, <x = $`x_{min}`$ .. $`x_{max}`$ >, <a = amin .. amax>, Options)

plot::Listplot([[x1, y1], [x2, y2], ...], <a = amin .. amax>, Options)

plot::Listplot(A2, <a = amin .. amax>, Options)

Parameters:

y1, y2, ...:	vertical coordinates: numerical values or expressions of the animation parameter a. y1, y2, ... is equivalent to the attribute Data.
x:	name of the horizontal coordinate: an identifier or an indexed identifier. It is used as the title of the coordinate axis in direction. x is equivalent to the attribute XName.
$`x_{min}`$ .. $`x_{max}`$ :	the range of the horizontal coordinate: xmin, xmax must be numerical real value or expressions of the animation parameter a. $`x_{min}`$ .. $`x_{max}`$ is equivalent to the attributes XRange, XMin, XMax.
A1:	a 1-dimensional array of domain type DOM_ARRAY or a matrix of category Cat::Matrix (e.g., of type matrix or densematrix) with 1 row or 1 column. The entries must be numerical real values or arithmetical expressions of the animation parameter a. The entries in A1 are regarded as data values etc.. A1 is equivalent to the attribute Data.
x1, x2, ...:	horizontal coordinates: numerical values or expressions of the animation parameter a.
A2:	a 2-dimensional array of domain type DOM_ARRAY or a matrix of category Cat::Matrix (e.g., of type matrix or densematrix) with at least two rows and two columns. The entries must be numerical real values or arithmetical expressions of the animation parameter a. The -th row is regarded as the data point . If more than 2 columns are provided, only the data in the first two columns are considered; all additional columns are ignored. A2 is equivalent to the attribute Data.

Details:

plot::Listplot serves for visualizing discrete data values . If no range $x = `x_{min}`..`x_{max}`$ is specified, the data are plotted as the points , etc. with equidistant -values x1 = 1, x2 = 2 etc. If a range $x = `x_{min}`..`x_{max}`$ is specified, equidistant -values between $`x_{min}`$ and $`x_{max}`$ are used.
If the data are specified as a list of coordinate pairs , plot::Listplot generates plot points with these coordinates.
With the attribute LinesVisible = TRUE, each pair of consecutive data points is connected by a curve.

With InterpolationStyle = Linear (default), the points are connected by straight line segments.

With InterpolationStyle = Cubic, a cubic spline curve is used to connect the points. The spline curve between two data points is rendered as a collection of straight line segments, where is specified by the attribute Submesh = m.

Use LinesVisible = FALSE, if only the data points without connecting lines are to be rendered.

Example 1

We plot 5 discrete data values as points with equidistant -values :

plot(plot::Listplot([1, 0, 1, 0, 1]))

MuPAD graphics

We plot two data samples and place them side by side by specifing suitable ranges for the horizontal variable:

plot(plot::Listplot([1, 0, 2, 1], x = 0..1, Color = RGB::Red),
plot::Listplot([0, 1, 0, 2], x = 1..2, Color = RGB::Blue))

MuPAD graphics

We specify -coordinates for the data points:

plot(plot::Listplot([[0.1, 1], [0.15, 0], [0.2, 1],
[0.3, 0], [0.5, 1]]))

MuPAD graphics

Example 2

We demonstrate the difference between linear and cubic spline interpolation:

plot(plot::Listplot([10, 0, 20, 0, 30], Color = RGB::Red,
                     InterpolationStyle = Linear),
     plot::Listplot([10, 0, 20, 0, 30], Color = RGB::Blue,
                    InterpolationStyle = Cubic))

MuPAD graphics

We smoothen the cubic spline curve by increasing the Submesh value:

plot(plot::Listplot([10, 0, 20, 0, 30], Color = RGB::Red,
                     InterpolationStyle = Linear),
     plot::Listplot([10, 0, 20, 0, 30], Color = RGB::Blue,
                    InterpolationStyle = Cubic, Submesh = 12))

MuPAD graphics

Example 3

A random variable describing the number of successes in Bernoulli trials with success probability is binomially distributed with expectation value and variance . For large values of , the binomial distribution is approximated by a corresponding normal distribution.

We use plot::Listplot to visualize the discrete probability values of the binomial distribution. The normal distribution is visualized via plot::Function2d:

n := 10: p:= 0.4:
plot(plot::Listplot([stats::binomialPF(n, p)(i) $ i = 0..n],
                     x = 0..n, Color = RGB::Red),
     plot::Function2d(stats::normalPDF(n*p, n*p*(1 - p))(x),
                      x = 0..n, Color = RGB::Blue)):

MuPAD graphics

delete n, p:

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