# matlabFunction

Convert symbolic expression to function handle or file

## Description

example

g = matlabFunction(f) converts the symbolic expression or function f to a MATLAB® function with handle g. If there is an equivalent MATLAB function operating on double data type for the symbolic expression or function, then the converted function can be used without Symbolic Math Toolbox™.

example

g = matlabFunction(f1,...,fN) converts f1,...,fN to a MATLAB function with N outputs. The function handle is g. Each element of f1,...,fN can be a symbolic expression, function, or a vector of symbolic expressions or functions.

example

g = matlabFunction(___,Name,Value) uses additional options specified by one or more Name,Value pair arguments. You can specify Name,Value after the input arguments used in the previous syntaxes.

## Examples

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Convert the symbolic expression r to a MATLAB function with the handle ht. The converted function can be used without Symbolic Math Toolbox.

syms x y
r = sqrt(x^2 + y^2);
ht = matlabFunction(r)
ht =
function_handle with value:
@(x,y)sqrt(x.^2+y.^2)

Convert multiple symbolic expressions using comma-separated input.

ht = matlabFunction(r, r^2)
ht =
function_handle with value:
@(x,y)deal(sqrt(x.^2+y.^2),x.^2+y.^2)

Create a symbolic function and convert it to a MATLAB function with the handle ht.

syms x y
f(x,y) = x^3 + y^3;
ht = matlabFunction(f)
ht =
function_handle with value:
@(x,y)x.^3+y.^3

Write the generated MATLAB function to a file by specifying the File option. Existing files are overwritten. When writing to a file, matlabFunction optimizes the code using intermediate variables named t0, t1, …. Include comments in the file by using the Comments option.

Write the MATLAB function generated from f to the file myfile.

syms x
f = x^2 + log(x^2);
matlabFunction(f,'File','myfile');
function f = myfile(x)
%MYFILE
%    F = MYFILE(X)

%    This function was generated by the Symbolic Math Toolbox version 8.4.
%    01-Sep-2019 00:00:00

t2 = x.^2;
f = t2+log(t2);

Include the comment Version: 1.1 in the file.

function f = myfile(x)
...
%Version: 1.1
t2 = x.^2;
...

When you convert a symbolic expression to a MATLAB function and write the resulting function to a file, matlabFunction optimizes the code by default. This approach can help simplify and speed up further computations that use the file. However, generating the optimized code from some symbolic expressions and functions can be time-consuming. Use Optimize to disable code optimization.

Create a symbolic expression.

syms x
r = x^2*(x^2 + 1);

Convert r to a MATLAB function and write the function to the file myfile. By default, matlabFunction creates a file containing the optimized code.

f =  matlabFunction(r,'File','myfile');
function r = myfile(x)
%MYFILE
%    R = MYFILE(X)
t2 = x.^2;
r = t2.*(t2+1.0);

Disable the code optimization by setting the value of Optimize to false.

f =  matlabFunction(r,'File','myfile','Optimize',false);
function r = myfile(x)
%MYFILE
%    R = MYFILE(X)
r = x.^2.*(x.^2+1.0);

When you convert a symbolic matrix to a MATLAB function, matlabFunction represents it by a dense matrix by default. If most of the elements of the input symbolic matrix are zeros, the more efficient approach is to represent it by a sparse matrix.

Create a 3-by-3 symbolic diagonal matrix.

syms x
A = diag(x*ones(1,3))
A =
[ x, 0, 0]
[ 0, x, 0]
[ 0, 0, x]

Convert A to a MATLAB function representing a numeric matrix, and write the result to the file myfile1. By default, the generated MATLAB function creates the dense numeric matrix specifying each element of the matrix, including all zero elements.

f1 = matlabFunction(A,'File','myfile1');
function A = myfile1(x)
%MYFILE1
%    A = MYFILE1(X)
A = reshape([x,0.0,0.0,0.0,x,0.0,0.0,0.0,x],[3,3]);

Convert A to a MATLAB function by setting Sparse to true. Now, the generated MATLAB function creates the sparse numeric matrix specifying only nonzero elements and assuming that all other elements are zeros.

f2 = matlabFunction(A,'File','myfile2','Sparse',true);
function A = myfile2(x)
%MYFILE2
%    A = MYFILE2(X)
A = sparse([1,2,3],[1,2,3],[x,x,x],3,3);

When converting an expression to a MATLAB function, you can specify the order of the input arguments of the resulting function. You can also specify that some input arguments are vectors instead of single variables.

Create a symbolic expression.

syms x y z
r = x + y/2 + z/3;

Convert r to a MATLAB function and write this function to the file myfile. By default, matlabFunction uses alphabetical order of input arguments when converting symbolic expressions that contain only lowercase letters for the variable names.

matlabFunction(r,'File','myfile');
function r = myfile(x,y,z)
%MYFILE
%    R = MYFILE(X,Y,Z)
r = x+y./2.0+z./3.0;

Use the Vars argument to specify the order of input arguments for the generated MATLAB function.

matlabFunction(r,'File','myfile','Vars',[y z x]);
function r = myfile(y,z,x)
%MYFILE
%    R = MYFILE(Y,Z,X)
r = x+y./2.0+z./3.0;

Now, convert an expression r to a MATLAB function whose second input argument is a vector.

syms x y z t
r = (x + y/2 + z/3)*exp(-t);
matlabFunction(r,'File','myfile','Vars',{t,[x y z]});
function r = myfile(t,in2)
%MYFILE
%    R = MYFILE(T,IN2)
x = in2(:,1);
y = in2(:,2);
z = in2(:,3);
r = exp(-t).*(x+y./2.0+z./3.0);

When converting a symbolic expression to a MATLAB function, you can specify the names of the output variables. Note that matlabFunction without the File argument (or with a file path specified by an empty character vector) creates a function handle and ignores the Outputs flag.

Create symbolic expressions r and q.

syms x y z
r = x^2 + y^2 + z^2;
q = x^2 - y^2 - z^2;

Convert r and q to a MATLAB function and write the resulting function to a file myfile, which returns a vector of two elements, name1 and name2.

f = matlabFunction(r,q,'File','myfile',...
'Outputs',{'name1','name2'});
function [name1,name2] = myfile(x,y,z)
%MYFILE
%    [NAME1,NAME2] = MYFILE(X,Y,Z)
t2 = x.^2;
t3 = y.^2;
t4 = z.^2;
name1 = t2+t3+t4;
if nargout > 1
name2 = t2-t3-t4;
end

You can speed up the evaluation of a symbolic function at given coordinates by converting the symbolic function to an anonymous MATLAB function. Use matlabFunction to perform the conversion. Evaluation of a symbolic function returns symbolic numbers that are precise, while evaluation of a MATLAB function returns double-precision numbers.

Create a symbolic function f(x,y,z) that is a function of x, y, and z.

syms f(x,y,z)
f(x,y,z) = y*z*sin(x) + x*sin(z)*cos(y) - z^3;

Create 3-D grid coordinates at the specified intervals.

[xDouble,yDouble,zDouble] = meshgrid(1:20,1:50,1:20);

Evaluate the symbolic function at these coordinates. Measure the elapsed time using a pair of tic and toc calls.

tic
fResult = f(xDouble,yDouble,zDouble);
toc
Elapsed time is 2.709857 seconds.

Here, evaluation is slow, but it returns symbolic numbers that are precise. Show a sample of the results.

fResult(1:2,1:2,20)
ans =

$\left(\begin{array}{cc}20 \mathrm{sin}\left(1\right)+\mathrm{cos}\left(1\right) \mathrm{sin}\left(20\right)-8000& 20 \mathrm{sin}\left(2\right)+2 \mathrm{cos}\left(1\right) \mathrm{sin}\left(20\right)-8000\\ 40 \mathrm{sin}\left(1\right)+\mathrm{cos}\left(2\right) \mathrm{sin}\left(20\right)-8000& 40 \mathrm{sin}\left(2\right)+2 \mathrm{cos}\left(2\right) \mathrm{sin}\left(20\right)-8000\end{array}\right)$

To speed up the evaluation of the function, convert the symbolic function to a MATLAB function using matlabFunction. Evaluate the MATLAB function at the same coordinates.

f1 = matlabFunction(f);
tic
fResult = f1(xDouble,yDouble,zDouble);
toc
Elapsed time is 0.021283 seconds.

Here, evaluation is faster. The evaluated MATLAB function returns double-precision numbers. Show a sample of the results.

fResult(1:2,1:2,20)
ans = 2×2
103 ×

-7.9827   -7.9808
-7.9667   -7.9644

## Input Arguments

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Symbolic input to be converted to a MATLAB function, specified as a symbolic expression, function, vector, or matrix. When converting sparse symbolic vectors or matrices, use the name-value pair argument 'Sparse',true.

Symbolic input to be converted to MATLAB function with N outputs, specified as several symbolic expressions, functions, vectors, or matrices, separated by comma.

matlabFunction does not create a separate output argument for each element of a symbolic vector or matrix. For example, g = matlabFunction([x + 1, y + 1]) creates a MATLAB function with one output argument, while g = matlabFunction(x + 1, y + 1) creates a MATLAB function with two output arguments.

### Name-Value 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: matlabFunction(f,'File','myfile','Optimize',false)

Comments to include in the file header, specified as a character vector, cell array of character vectors, or string vector.

Path to the file containing the generated MATLAB function, specified as a character vector. The generated function accepts arguments of type double, and can be used without Symbolic Math Toolbox. If File is empty, matlabFunction generates an anonymous function. If File does not end in .m, the function appends .m.

When writing to a file, matlabFunction optimizes the code using intermediate variables named t0, t1, .... To disable code optimization, use the Optimize argument.

Flag preventing optimization of code written to a function file, specified as false or true.

When writing to a file, ccode optimizes the code using intermediate variables named t0, t1, ....

matlabFunction without the File argument (or with a file path specified by an empty character vector) creates a function handle. In this case, the code is not optimized. If you try to enforce code optimization by setting Optimize to true, then matlabFunction throws an error.

Flag that switches between sparse and dense matrix generation, specified as true or false. When you specify 'Sparse',true, the generated MATLAB function represents symbolic matrices by sparse numeric matrices. Use 'Sparse',true when you convert symbolic matrices containing many zero elements. Often, operations on sparse matrices are more efficient than the same operations on dense matrices.

Order of input variables or vectors in a generated MATLAB function, specified as a character vector, a vector of symbolic variables, or a one-dimensional cell array of character vectors, symbolic variables, or vectors of symbolic variables.

The number of specified input variables must equal or exceed the number of free variables in f. Do not use the same names for the input variables specified by Vars and the output variables specified by Outputs.

By default, when you convert symbolic expressions that contain only lowercase letters for the variable names, the order is alphabetical. When you convert symbolic functions, their input arguments appear in front of other variables, and all other variables are sorted alphabetically.

Names of output variables, specified as a one-dimensional cell array of character vectors.

If you do not specify the output variable names, then they coincide with the names you use when calling matlabFunction. If you call matlabFunction using an expression instead of individual variables, the default names of output variables consist of the word out followed by a number, for example, out3.

Do not use the same names for the input variables specified by Vars and the output variables specified by Outputs.

matlabFunction without the File argument (or with a file path specified by an empty character vector) creates a function handle. In this case, matlabFunction ignores the Outputs flag.

## Output Arguments

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Function handle that can serve as an input argument to numerical functions, returned as a MATLAB function handle.

## Limitations

• Some symbolic functions that have no corresponding MATLAB functions operating on double data type, such as simplify and solve, are kept as symbolic functions in the converted MATLAB function handle or file. The converted file that consists of these functions cannot be deployed using MATLAB Coder™ or MATLAB Compiler™. You need to create your own functions with double data type to replace these symbolic functions. If you are interested in a symbolic function that cannot be deployed, please contact MathWorks Technical Support.

## Tips

• When you use the File argument, use rehash to make the generated function available immediately. rehash updates the MATLAB list of known files for directories on the search path.

• If the File option is empty, then an anonymous function is returned.

• Use matlabFunction to convert one or more symbolic expressions to a MATLAB function and write the resulting function to an M-file. You can then use the generated M-file to create standalone applications and web apps using MATLAB Compiler. For example, see Deploy Generated MATLAB Functions from Symbolic Expressions with MATLAB Compiler.

• Use matlabFunction to convert one or more symbolic expressions to a MATLAB function and write the resulting function to an M-file. You can then use the generated M-file to create C or C++ code using MATLAB Coder app. For example, see Generate C Code from Symbolic Expressions Using the MATLAB Coder App.