# symfunmatrix

Create symbolic matrix function

Since R2022a

## Syntax

``f = symfunmatrix(formula,inputs)``
``f = symfunmatrix(formula,inputs,[nrow ncol])``

## Description

example

````f = symfunmatrix(formula,inputs)` creates the symbolic matrix function `f`. The symbolic expression `formula` is the body of the function `f` that can be converted to the `symmatrix` data type. The variables in `inputs` are the input arguments of the function `f`. If the input arguments of function `f` are multiple variables, `inputs` must be a cell array of symbolic scalar and matrix variables.If the input argument of function `f` is a single variable, you can specify `inputs` as a symbolic scalar variable or a symbolic matrix variable. ```
````f = symfunmatrix(formula,inputs,[nrow ncol])` also explicitly specifies the size of the evaluated symbolic matrix function `f(var1,var2,...)` as `nrow`-by-`ncol` for the `inputs = {var1,var2,...}`.If `formula` represents an unassigned abstract function, then `f(var1,var2,...)` has the size of `nrow`-by-`ncol`. For example:syms x 2 matrix; f = symfunmatrix('g(x)',{x},[3 4]); size(f(x))ans = 3 4If `formula` represents a symbolic expression or a function with definition, then the size of `f(var1,var2,...)` follows the size of `formula`. For example:syms X Y 2 matrix; f = symfunmatrix(X*Y - Y*X,{X,Y},[3 3]); size(f(X,Y))ans = 2 2```

## Examples

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Create two symbolic matrix variables with size `2`-by-`2`.

`syms X Y [2 2] matrix`

Create a symbolic matrix function that represents the matrix operation $\mathbit{XY}-\mathbit{YX}$ by using `symfunmatrix`.

`f = symfunmatrix(X*Y - Y*X,{X,Y})`
`f(X, Y) = $X Y-Y X$`

Evaluate the function for the matrix values $\mathbit{X}=\left[\begin{array}{cc}1& 2\\ 2& 2\end{array}\right]$ and $\mathbit{Y}=\left[\begin{array}{cc}-2& 1\\ 0& 4\end{array}\right]$. The evaluated function is a symbolic matrix variable of data type `symmatrix`.

`fEval = f([1 2; 2 2],[-2 1; 0 4])`
```fEval =  ```
`class(fEval)`
```ans = 'symmatrix' ```

Convert the evaluated function to the `sym` data type.

`fSym = symmatrix2sym(fEval)`
```fSym =  $\left(\begin{array}{cc}-2& 11\\ -12& 2\end{array}\right)$```

## Input Arguments

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Function body, specified as a symbolic expression that can be converted to the `symmatrix` data type or an abstract function.

Example: `X*Y.'`

Input argument or arguments of a function, specified as a cell array of symbolic scalar and matrix variables, a symbolic scalar variable, or a symbolic matrix variable.

Example: `{X,Y}`, ```symmatrix('t',[2 3])```

Data Types: `cell` | `sym` | `symmatrix`

Dimensions of the evaluated symbolic matrix function, specified as a vector of nonnegative integers. As a shortcut, you can create a square symbolic matrix function by specifying only one integer.

Example: `[2 3]`

## Output Arguments

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Symbolic matrix function, returned as a `symfunmatrix` object.

While the data type of the function `f` is `symfunmatrix`, the data type of the evaluated function, such as `f([-2 3],[1 0])`, is `symmatrix`.

## Limitations

• To show all the functions in Symbolic Math Toolbox™ that accept symbolic matrix functions as input, use the command `methods symfunmatrix`.

## Tips

• When evaluating a symbolic matrix function, you must substitute values that have the same size as the defined input arguments. For example, see Define and Evaluate Symbolic Matrix Functions. For comparison, this example returns an error:

```syms X [2 2] matrix syms f(X) [1 1] matrix keepargs f(ones(4)) ```

## Version History

Introduced in R2022a

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