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# distplot

Plot Markov chain redistributions

## Syntax

``distplot(mc,X)``
``distplot(mc,X,Name,Value)``
``distplot(ax,___)``
``h = distplot(___)``

## Description

example

````distplot(mc,X)` creates a heatmap from the data `X` showing the evolution of a distribution of states in the discrete-time Markov chain `mc`.```

example

````distplot(mc,X,Name,Value)` uses additional options specified by one or more name-value pair arguments. For example, specify the type of plot or the frame rate for animated plots.```
``` `distplot(ax,___)` plots on the axes specified by `ax` instead of the current axes (`gca`) using any of the input arguments in the previous syntaxes. The option `ax` can precede any of the input argument combinations in the previous syntaxes.```
``` `h = distplot(___)` returns a handle to the distribution plot. Use `h` to modify properties of the plot after you create it.```

## Examples

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Create a four-state Markov chain from a randomly generated transition matrix containing eight infeasible transitions.

```rng('default'); % For reproducibility mc = mcmix(4,'Zeros',8);```

`mc` is a `dtmc` object.

Plot a digraph of the Markov chain.

```figure; graphplot(mc);```

State `4` is an absorbing state.

Compute the state redistributions at each step for 10 discrete time steps. Assume an initial uniform distribution over the states.

`X = redistribute(mc,10)`
```X = 11×4 0.2500 0.2500 0.2500 0.2500 0.0869 0.2577 0.3088 0.3467 0.1073 0.2990 0.1536 0.4402 0.0533 0.2133 0.1844 0.5489 0.0641 0.2010 0.1092 0.6257 0.0379 0.1473 0.1162 0.6985 0.0404 0.1316 0.0765 0.7515 0.0266 0.0997 0.0746 0.7991 0.0259 0.0864 0.0526 0.8351 0.0183 0.0670 0.0484 0.8663 ⋮ ```

`X` is an 11-by-4 matrix. Rows correspond to time steps, and columns correspond to states.

Visualize the state redistribution.

```figure; distplot(mc,X)```

After 10 transitions, the distribution appears to settle with a majority of the probability mass in state `4`.

Consider this theoretical, right-stochastic transition matrix of a stochastic process.

`$P=\left[\begin{array}{ccccccc}0& 0& 1/2& 1/4& 1/4& 0& 0\\ 0& 0& 1/3& 0& 2/3& 0& 0\\ 0& 0& 0& 0& 0& 1/3& 2/3\\ 0& 0& 0& 0& 0& 1/2& 1/2\\ 0& 0& 0& 0& 0& 3/4& 1/4\\ 1/2& 1/2& 0& 0& 0& 0& 0\\ 1/4& 3/4& 0& 0& 0& 0& 0\end{array}\right].$`

Create the Markov chain that is characterized by the transition matrix P.

```P = [ 0 0 1/2 1/4 1/4 0 0 ; 0 0 1/3 0 2/3 0 0 ; 0 0 0 0 0 1/3 2/3; 0 0 0 0 0 1/2 1/2; 0 0 0 0 0 3/4 1/4; 1/2 1/2 0 0 0 0 0 ; 1/4 3/4 0 0 0 0 0 ]; mc = dtmc(P);```

Compute the state redistributions at each step for 20 discrete time steps.

`X = redistribute(mc,20);`

Animate the redistributions in a histogram. Specify a half-second frame rate.

```figure; distplot(mc,X,'Type','histogram','FrameRate',0.5);```

## Input Arguments

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Discrete-time Markov chain with `NumStates` states and transition matrix `P`, specified as a `dtmc` object.

Evolution of state probabilities, specified as a ```(1 + numSteps)```-by-`NumStates` nonnegative numeric matrix returned by `redistribute`. The first row is the initial state distribution. Subsequent rows are the redistributions at each step. `distplot` normalizes the rows by their respective sums before plotting.

Data Types: `double`

Axes on which to plot, specified as an `Axes` object.

By default, `distplot` plots to the current axes (`gca`).

### Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

Example: `'Type','graph','FrameRate',3` creates an animated plot of the redistributions using a frame rate of 3 seconds.

Plot type, specified as the comma-separated pair consisting of `'Type'` and a value in this table.

ValueDescription
`'evolution'`

Evolution of the initial distribution. The plot is a ```(1 + NumSteps)```-by-`NumStates` heatmap. Row i displays the redistribution at step i.

`'histogram'`

Animated histogram of the redistributions. The vertical axis displays probability mass, and the horizontal axis displays states. The `'FrameRate'` name-value pair argument controls the animation progress.

`'graph'`

Animated graph of the redistributions. `distplot` colors the nodes by their probability mass at each step. The `'FrameRate'` name-value pair argument controls the animation progress.

Example: `'Type','graph'`

Data Types: `string` | `char`

Length of discrete time steps, in seconds, for animated plots, specified as the comma-separated pair consisting of `'FrameRate'` and a positive scalar.

The default is a pause at each time step. The animation proceeds when you press the space bar.

Example: `'FrameRate',3`

Data Types: `double`

## Output Arguments

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Handle to the distribution plot, returned as a graphics object. `h` contains a unique plot identifier, which you can use to query or modify properties of the plot.