plot::Matrixplot – surface plot of matrix data

plot::Matrixplot(A) visualizes the matrix as a 3D function graph by interpolating the matrix values as a function of the matrix indices.

→ Examples

Calls:

plot::Matrixplot(A, Options)

plot::Matrixplot(A, x = $`x_{min}`$ .. $`x_{max}`$ , y = $`y_{min}`$ .. $`y_{max}`$ , <a = amin .. amax>, Options)

plot::Matrixplot(row1, row2, ..., Options)

plot::Matrixplot(row1, row2, ..., x = $`x_{min}`$ .. $`x_{max}`$ , y = $`y_{min}`$ .. $`y_{max}`$ , <a = amin .. amax>, Options)

plot::Matrixplot([row1, row2, ...], Options)

plot::Matrixplot([row1, row2, ...], x = $`x_{min}`$ .. $`x_{max}`$ , y = $`y_{min}`$ .. $`y_{max}`$ , <a = amin .. amax>, Options)

plot::Matrixplot(s, <c1, c2, ...>, Options)

plot::Matrixplot(s, <c1, c2, ...>, x = $`x_{min}`$ .. $`x_{max}`$ , y = $`y_{min}`$ .. $`y_{max}`$ , <a = amin .. amax>, Options)

plot::Matrixplot(s, <[c1, c2, ...]>, Options)

plot::Matrixplot(s, <[c1, c2, ...]>, x = $`x_{min}`$ .. $`x_{max}`$ , y = $`y_{min}`$ .. $`y_{max}`$ , <a = amin .. amax>, Options)

Parameters:

A:	a matrix of category Cat::Matrix or an array containing real numerical values or expressions of the animation parameter a. A is equivalent to the attribute Data.
row1, row2, ...:	the matrix rows: each row must be a list of real numerical values or expressions of the animation parameter a. All rows must have the same length. row1, row2, ... is equivalent to the attribute Data.
s:	a data sample of domain type stats::sample. s is equivalent to the attribute Data.
c1, c2, ...:	column indices of s: positive integers. These indices, if given, indicate that only the specified columns should be used. The indexed columns must contain real numerical values or expressions of the animation parameter a, If no columns are specified, all columns of s are used.
x:	name of the first 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 first coordinate: $`x_{min}`$ , $`x_{max}`$ must be numerical real value or expressions of the animation parameter . $`x_{min}`$ .. $`x_{max}`$ is equivalent to the attributes XRange, XMin, XMax.
y:	name of the second coordinate: an identifier or an indexed identifier. It is used as the title of the coordinate axis in direction. y is equivalent to the attribute YName.
$`y_{min}`$ .. $`y_{max}`$ :	the range of the second coordinate: $`y_{min}`$ , $`y_{max}`$ must be numerical real value or expressions of the animation parameter . $`y_{min}`$ .. $`y_{max}`$ is equivalent to the attributes YRange, YMin, YMax.

Details:

Matrixplot interprets the indices of a matrix as and coordinates and the corresponding matrix entry as the corresponding coordinate. Thus, the matrix is regarded as a discretized function in variables. The function graph is displayed as a 3D surface using interpolation between the data points.
If no ranges $x = `x_{min}`..`x_{max}`$ , $y = `y_{min}`..`y_{max}`$ are specified, the matrix entry A[i, j] is diplayed as the 3D point , , = A[i, j] with integer positions , . If plot ranges are specified, the matrix indices are used to define an equidistant mesh in the plot range.
The attribute InterpolationStyle allows to define the surface via linear or cubic spline interpolation of the data points: Choose between InterpolationStyle = Linear or InterpolationStyle = Cubic. The default is linear interpolation. With cubic interpolation, the data surface may be smoothened by setting the numbers of plot points between the data points via the attribute Submesh = . The numbers mx, my must be (small) non-negative integers.
With InterpolationStyle = Linear, symbolic values and complex numbers are accepted and ignored, leading to gaps in the surface. With InterpolationStyle = Cubic, symbolic values or complex numbers lead to an error. Cf. example 4.
Per default, the data points are rendered on the surface. Use PointsVisible = FALSE to make them disappear.
Animations are triggered by specifying a range $a = `a_{min}`..`a_{max}`$ for a parameter a that is different from the variables x, y. Thus, in animations, both the ranges $x = `x_{min}`..`x_{max}`$ , $y = `y_{min}`..`y_{max}`$ as well as the animation range $a = `a_{min}`..`a_{max}`$ must be specified.

Example 1

This example demonstrates the general calling syntax. The data are passed in different ways using a list of rows, an array, and a matrix, respectively:

A := [[2, 1, 1],
      [3, 4, 3],
      [3, 5, 4],
      [2, 6, 5]]:
plot(plot::Matrixplot(A))

MuPAD graphics

With InterpolationStyle = Cubic, the matrix data are plotted as a cubic spline surface:

A := array(1..4, 1..3, A):
plot(plot::Matrixplot(A, InterpolationStyle = Cubic)):

MuPAD graphics

The spline surface can be smoothened by using the Submesh attribute to add further evaluation points:

A := matrix(A):
plot(plot::Matrixplot(A, Submesh = [6, 6],
InterpolationStyle = Cubic)):

MuPAD graphics

delete A:

Example 2

Various plot attributes can be specified:

plot(plot::Matrixplot(
   [[-0.5,   0.5, 0.7, 0.5, -1 ],
    [ 1.2, 1.3, 1.4, 1.4, 1 ],
    [ 1.4, 1.5, 1.6, 1.5, 1.2],
    [ 0.6, 0.8, 1,   1,    1 ],
    [-0.7, 0.5, 0.5, 0,   -1 ]],
    PointsVisible = FALSE,
    FillColor = RGB::Green,
    LineColor = RGB::Red))

MuPAD graphics

Example 3

Choosing appropriate coordinate ranges, we place two matrix plots side by side:

plot(plot::Matrixplot(matrix::random(5, 5, frandom),
                      x = 0..1, y = 0..1,
                      Color = RGB::Red),
     plot::Matrixplot(matrix::random(6, 6, frandom),
                      x = 2..3, y = 0..1,
                      Color = RGB::Green),
     Scaling = Constrained)

MuPAD graphics

Example 4

We plot a Hilbert matrix:

A := linalg::hilbert(10):
plot(plot::Matrixplot(A), CameraDirection = [3, 2, 1])

MuPAD graphics

Some of the entries are replaced by values that cannot be plotted. Consequently, the plot contains holes:

A[2, 2] := NIL:
A[4, 5] := infinity:
A[5, 5] := x:
plot(plot::Matrixplot(A), CameraDirection = [3, 2, 1])

MuPAD graphics

With InterpolationStyle = Cubic, an error is raised:

plot(plot::Matrixplot(A, InterpolationStyle = Cubic))

Error: Data contains nonreal numeric values. Use 'Style = Linear' to plot matrices containing such data. [plot::Matrixplot::doPlotStatic]

delete A:

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