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Generate MATLAB Functions from Symbolic Expressions

You can use matlabFunction to generate a MATLAB® function handle that calculates numerical values as if you were substituting numbers for variables in a symbolic expression. Also, matlabFunction can create a file that accepts numeric arguments and evaluates the symbolic expression applied to the arguments. The generated file is available for use in any MATLAB calculation, whether or not the computer running the file has a license for Symbolic Math Toolbox™ functions.

Generating a Function Handle

matlabFunction can generate a function handle from any symbolic expression. For example:

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

You can use this function handle to calculate numerically:

ans =

You can pass the usual MATLAB double-precision numbers or matrices to the function handle. For example:

cc = [.5,3]; 
dd = [-.5,.5];
ht(cc, dd)
ans =
    0.6089    0.9954


Some symbolic expressions cannot be represented using MATLAB functions. matlabFunction cannot convert these symbolic expressions, but issues a warning. Since these expressions might result in undefined function calls, always check conversion results and verify the results by executing the resulting function.

Control the Order of Variables

matlabFunction generates input variables in alphabetical order from a symbolic expression. That is why the function handle in Generating a Function Handle has x before y:

ht = @(x,y)tanh((x.^2 + y.^2).^(1./2))

You can specify the order of input variables in the function handle using the vars option. You specify the order by passing a cell array of character vectors or symbolic arrays, or a vector of symbolic variables. For example:

syms x y z
r = sqrt(x^2 + 3*y^2 + 5*z^2);
ht1 = matlabFunction(tanh(r), 'vars', [y x z])
ht1 = 
  function_handle with value:
ht2 = matlabFunction(tanh(r), 'vars', {'x', 'y', 'z'})
ht2 = 
  function_handle with value:
ht3 = matlabFunction(tanh(r), 'vars', {'x', [y z]})
ht3 = 
  function_handle with value:

Generate a File

You can generate a file from a symbolic expression, in addition to a function handle. Specify the file name using the file option. Pass a character vector containing the file name or the path to the file. If you do not specify the path to the file, matlabFunction creates this file in the current folder.

This example generates a file that calculates the value of the symbolic matrix F for double-precision inputs t, x, and y:

syms x y t
z = (x^3 - tan(y))/(x^3 + tan(y));
w = z/(1 + t^2);
F = [w,(1 + t^2)*x/y; (1 + t^2)*x/y,3*z - 1];

The file testMatrix.m contains the following code:

function F = testMatrix(t,x,y)

t2 = x.^2;
t3 = tan(y);
t4 = t2.*x;
t5 = t.^2;
t6 = t5 + 1;
t7 = 1./y;
t8 = t6.*t7.*x;
t9 = t3 + t4;
t10 = 1./t9;
F = [-(t10.*(t3 - t4))./t6,t8; t8,- t10.*(3.*t3 - 3.*t2.*x) - 1];

matlabFunction generates many intermediate variables. This is called optimized code. MATLAB generates intermediate variables as a lowercase letter t followed by an automatically generated number, for example t32. Intermediate variables can make the resulting code more efficient by reusing intermediate expressions (such as t4, t6, t8, t9, and t10 in the calculation of F). Using intermediate variables can make the code easier to read by keeping expressions short.

If you don't want the default alphabetical order of input variables, use the vars option to control the order. Continuing the example,

matlabFunction(F,'file','testMatrix.m','vars',[x y t])

generates a file equivalent to the previous one, with a different order of inputs:

function F = testMatrix(x,y,t)

Name Output Variables

By default, the names of the output variables coincide with the names you use calling matlabFunction. For example, if you call matlabFunction with the variable F

syms x y t
z = (x^3 - tan(y))/(x^3 + tan(y));
w = z/(1 + t^2);
F = [w, (1 + t^2)*x/y; (1 + t^2)*x/y,3*z - 1];
matlabFunction(F,'file','testMatrix.m','vars',[x y t])

the generated name of an output variable is also F:

function F = testMatrix(x,y,t)

If you call matlabFunction using an expression instead of individual variables

syms x y t
z = (x^3 - tan(y))/(x^3 + tan(y));
w = z/(1 + t^2);
F = [w,(1 + t^2)*x/y; (1 + t^2)*x/y,3*z - 1];
matlabFunction(w + z + F,'file','testMatrix.m',...
'vars',[x y t])
the default names of output variables consist of the word out followed by the number, for example:
function out1 = testMatrix(x,y,t)
To customize the names of output variables, use the output option:

syms x y z
r = x^2 + y^2 + z^2;
q = x^2 - y^2 - z^2;
f = matlabFunction(r, q, 'file', 'new_function',...
'outputs', {'name1','name2'})

The generated function returns name1 and name2 as results:

function [name1,name2] = new_function(x,y,z)