## Accelerate MATLAB Algorithm by Generating MEX Function

You can use MATLAB^{®}
Coder™ to generate a MEX function from your MATLAB code. A MEX function is a MATLAB executable. It is generated code that can be called from inside
MATLAB. While working inside the MATLAB environment, use MEX functions to accelerate the computationally intensive
portions of your MATLAB code. Generate a MEX function from your MATLAB code by using the MATLAB
Coder app or by using `codegen`

at the MATLAB command line.

In this tutorial, you use the MATLAB
Coder
`codegen`

command to generate a MEX
function for a MATLAB function. You first generate a MEX function that can accept only inputs
that have fixed, preassigned size. You then generate another MEX function that can
accept inputs of many different sizes.

### Tutorial Files: Euclidean Distance

Open this example to obtain the files for this tutorial.

### Description of Tutorial Files

This tutorial uses the `euclidean_data.mat`

,
`euclidean.m`

, `test.m`

,
`test_2d.m`

, `build_mex_fixed.m`

, and
`build_mex_variable.m`

files.

The MATLAB data file

`euclidean_data.mat`

contains two pieces of data: a single point in three-dimensional Euclidean space and a set of several other points in three-dimensional Euclidean space. More specifically:`x`

is a`3`

-by-`1`

column vector that represents a point in three-dimensional Euclidean space.`cb`

is a`3`

-by-`216`

array. Each column in`cb`

represents a point in three-dimensional Euclidean space.

The MATLAB file

`euclidean.m`

contains the function`euclidean`

that implements the*core algorithm*in this example. The function takes`x`

and`cb`

as inputs. It calculates the Euclidean distance between`x`

and each point in`cb`

and returns these quantities:The column vector

`y_min`

, which is equal to the column in`cb`

that represents the point closest to`x`

.The column vector

`y_max`

, which is equal to the column in`cb`

that represents the point farthest from`x`

.The 2-dimensional vector

`idx`

that contains the column indices of the vectors`y_min`

and`y_max`

in`cb`

.The 2-dimensional vector

`distance`

that contains the calculated smallest and largest distances to`x`

.

function [y_min,y_max,idx,distance] = euclidean(x,cb) % Initialize minimum distance as distance to first element of cb % Initialize maximum distance as distance to first element of cb idx(1)=1; idx(2)=1; distance(1)=norm(x-cb(:,1)); distance(2)=norm(x-cb(:,1)); % Find the vector in cb with minimum distance to x % Find the vector in cb with maximum distance to x for index=2:size(cb,2) d=norm(x-cb(:,index)); if d < distance(1) distance(1)=d; idx(1)=index; end if d > distance(2) distance(2)=d; idx(2)=index; end end % Output the minimum and maximum distance vectors y_min=cb(:,idx(1)); y_max=cb(:,idx(2)); end

The MATLAB script

`test.m`

loads the data file`euclidean_data.mat`

into the workspace. It calls the function`euclidean`

to calculate`y_min`

,`y_max`

,`idx`

, and`distance`

. The script then displays the calculated quantities at the command line.Loading

`euclidean_data.mat`

is the preprocessing step that is executed before calling the core algorithm. Displaying the results is the post-processing step.% Load test data load euclidean_data.mat % Determine closest and farthest points and corresponding distances [y_min,y_max,idx,distance] = euclidean(x,cb); % Display output for the closest point disp('Coordinates of the closest point are: '); disp(num2str(y_min')); disp(['Index of the closest point is ', num2str(idx(1))]); disp(['Distance to the closest point is ', num2str(distance(1))]); disp(newline); % Display output for the farthest point disp('Coordinates of the farthest point are: '); disp(num2str(y_max')); disp(['Index of the farthest point is ', num2str(idx(2))]); disp(['Distance to the farthest point is ', num2str(distance(2))]);

The MATLAB script

`test_2d.m`

is a modification of`test.m`

for points in two-dimensional Euclidean space. The contents of`test_2d.m`

are shown later in the tutorial, when you use it to test the MEX function for variable-size inputs.The build scripts

`build_mex_fixed.m`

and`build_mex_variable.m`

contain commands for generating MEX functions from your MATLAB code that accept fixed-size and variable-size inputs, respectively. The contents of these scripts are shown later in the tutorial, when you generate the C code.

**Tip**

You can generate code from MATLAB functions by using MATLAB Coder. Code generation from MATLAB scripts is not supported.

Use test scripts to separate the pre- and post-processing steps from the function that implements the core algorithm. This practice enables you to easily reuse your algorithm. You generate code for the MATLAB function implementing the core algorithm. You do not generate code for the test script.

### Generate MEX Function for the MATLAB Function

#### Run the Original MATLAB Code

Run the test script `test.m`

in MATLAB. The output displays `y`

, `idx`

,
and `distance`

.

Coordinates of the closest point are: 0.8 0.8 0.4 Index of the closest point is 171 Distance to the closest point is 0.080374 Coordinates of the farthest point are: 0 0 1 Index of the farthest point is 6 Distance to the farthest point is 1.2923

#### Make the MATLAB Code Suitable for Code Generation

To make your MATLAB code suitable for code generation, you use the Code Analyzer and the Code Generation Readiness Tool. The Code Analyzer in the MATLAB Editor continuously checks your code as you enter it. It reports issues and recommends modifications to maximize performance and maintainability. The Code Generation Readiness Tool screens the MATLAB code for features and functions that are not supported for code generation.

Certain MATLAB built-in functions and toolbox functions, classes, and System
objects that are supported for C/C++ code generation have specific code
generation limitations. These limitations and related usage notes are listed in
the **Extended Capabilities** sections of their corresponding
reference pages. For more information, see Functions and Objects Supported for C/C++ Code Generation.

Open

`euclidean.m`

in the MATLAB Editor. The Code Analyzer message indicator in the top right corner of the MATLAB Editor is green. The analyzer did not detect errors, warnings, or opportunities for improvement in the code.After the function declaration, add the

`%#codegen`

directive:Thefunction [y,idx,distance] = euclidean(x,cb) %#codegen

`%#codegen`

directive prompts the Code Analyzer to identify warnings and errors specific to code generation.The Code Analyzer message indicator becomes red, indicating that it has detected code generation issues.

To view the warning messages, move your cursor to the underlined code fragments. The warnings indicate that code generation requires the variables

`idx`

and`distance`

to be fully defined before subscripting them. This warning appears because the code generator must determine the sizes of these variables at their first appearance in the code. To fix this issue, use the`ones`

function to simultaneously allocate and initialize these arrays.% Initialize minimum distance as distance to first element of cb % Initialize maximum distance as distance to first element of cb idx = ones(1,2); distance = ones(1,2)*norm(x-cb(:,1));

The Code Analyzer message indicator becomes green again, indicating that it does not detect any more code generation issues.

For more information about using the Code Analyzer, see Check Code for Errors and Warnings Using the Code Analyzer.

Save the file.

To run the Code Generation Readiness Tool, call the

`coder.screener`

function from the MATLAB command line:`coder.screener('euclidean')`

The tool does not detect any code generation issues for

`euclidean`

. For more information, see Code Generation Readiness Tool.**Note**The Code Analyzer and the Code Generation Readiness Tool might not detect all code generation issues. After eliminating the errors or warnings that these tools detect, generate code by using MATLAB Coder to determine if your MATLAB code has other compliance issues.

You are now ready to compile your code by using the `codegen`

command. Here,
*compilation* refers to the generation of C/C++ code
from your MATLAB code.

**Note**

Compilation of MATLAB code refers to the generation of C/C++ code from the MATLAB code. In other contexts, the term compilation could refer to the action of a C/C++ compiler.

#### Defining Input Types

Because C uses static typing, the code generator must determine the class,
size, and complexity of all variables in the
MATLAB files at code generation time, also known as *compile
time*. Therefore, when you generate code for the files, you must
specify the properties of all input arguments
to the entry-point functions. An *entry-point function* is
a top-level MATLAB function from which you generate code.

When you generate code by using the `codegen`

command, use
the `-args`

option to specify sample input parameters to the
entry-point functions. The code generator uses this information to determine the
properties of the input arguments.

In the next step, you use the `codegen`

command to generate
a MEX file from your entry-point function `euclidean`

.

#### Generate and Validate the MEX Function

The build script `build_mex_fixed.m`

contains the commands
that you use to generate and validate a MEX function for
`euclidean.m`

. To validate the MEX function, you run the
test script `test`

with calls to the MATLAB function `euclidean`

replaced with calls to the
generated MEX
function.

% Load the test data load euclidean_data.mat % Generate code for euclidean.m with codegen. Use the test data as example input. % Validate MEX by using test.m. codegen -report euclidean.m -args {x, cb} -test test

By default,

`codegen`

generates a MEX function named`euclidean_mex`

in the current folder.The

`-report`

option instructs`codegen`

to generate a code generation report that you can use to debug code generation issues and verify that your MATLAB code is suitable for code generation.The

`-args`

option specifies sample input parameters to the entry-point function`euclidean`

. The code generator uses this information to determine the class, size, and complexity of the input arguments.You use the

`-test`

option to run the test file`test.m`

. This option replaces the calls to`euclidean`

in the test file with calls to`euclidean_mex`

.

For more information on the code generation options, see `codegen`

.

Run the build script

`build_mex_fixed.m`

.The code generator produces a MEX function

`euclidean_mex`

in the current working folder.The output is:

This output matches the output that was generated by the original MATLAB function and verifies the MEX function.`Code generation successful:`

*View report.*Running test file: 'test' with MEX function 'euclidean_mex'. Coordinates of the closest point are: 0.8 0.8 0.4 Index of the closest point is 171 Distance to the closest point is 0.080374 Coordinates of the farthest point are: 0 0 1 Index of the farthest point is 6 Distance to the farthest point is 1.2923To view the code generation report in the Report Viewer, click

**View report**.If the code generator detects errors or warnings during code generation, the report describes the issues and provides links to the problematic MATLAB code. See Code Generation Reports.

**Tip**

Use a build script to generate code at the command line. A build script automates a series of MATLAB commands that you perform repeatedly at the command line, saving you time and eliminating input errors.

### Generate MEX Function for Variable-Size Inputs

The MEX function that you generated for `euclidean.m`

can accept
only inputs that have the same size as the sample inputs that you specified during
code generation. However, the input arrays to the corresponding MATLAB function can be of any size. In
this part of the tutorial, you generate a MEX function from
`euclidean.m`

that accepts variable-size inputs.

Suppose that you want the dimensions of `x`

and
`cb`

in the generated MEX function to have these properties:

The first dimension of both

`x`

and`cb`

can vary in size up to`3`

.The second dimension of

`x`

is fixed and has the value`1`

.The second dimension of

`cb`

can vary in size up to`216`

.

To specify these input properties, you use the `coder.typeof`

function. `coder.typeof(A,B,1)`

specifies a variable-size input with the same class and complexity as
`A`

and upper bounds given by the corresponding element of the
size vector `B`

. Use the build script
`build_mex_variable.m`

that uses
`coder.typeof`

to specify the properties of variable-size
inputs in the generated MEX
function.

% Load the test data load euclidean_data.mat % Use coder.typeof to specify variable-size inputs eg_x=coder.typeof(x,[3 1],1); eg_cb=coder.typeof(cb,[3 216],1); % Generate code for euclidean.m using coder.typeof to specify % upper bounds for the example inputs codegen -report euclidean.m -args {eg_x,eg_cb}

You can verify that the new MEX function `euclidean_mex`

accepts
inputs of dimensions different from those of `x`

and
`cb`

. The test script `test_2d.m`

creates the
input arrays `x2d`

and `cb2d`

that are
two-dimensional versions of `x`

and `cb`

,
respectively. It then calls the MATLAB function `euclidean`

by using these input
parameters.

% Load the test data load euclidean_data.mat % Create 2-D versions of x and cb x2d=x(1:2,:); cb2d=cb(1:2,1:6:216); % Determine closest and farthest points and corresponding distances [y_min,y_max,idx,distance] = euclidean(x2d,cb2d); % Display output for the closest point disp('Coordinates of the closest point are: '); disp(num2str(y_min')); disp(['Index of the closest point is ', num2str(idx(1))]); disp(['Distance to the closest point is ', num2str(distance(1))]); disp(newline); % Display output for the farthest point disp('Coordinates of the farthest point are: '); disp(num2str(y_max')); disp(['Index of the farthest point is ', num2str(idx(2))]); disp(['Distance to the farthest point is ', num2str(distance(2))]);

Running `test_2d.m`

produces the output:

Coordinates of the closest point are: 0.8 0.8 Index of the closest point is 29 Distance to the closest point is 0.078672 Coordinates of the farthest point are: 0 0 Index of the farthest point is 1 Distance to the farthest point is 1.1357

To run the test script `test_2d.m`

with the calls to
`euclidean`

replaced with calls to
`euclidean_mex`

, use `coder.runTest`

.

coder.runTest('test_2d','euclidean')

`x`

and
`cb`

.### Next Steps

Goal | More Information |
---|---|

Learn about code generation support for MATLAB built-in functions and toolbox functions, classes, and System objects | |

Generate C++ MEX code | |

Create and edit input types interactively | |

Optimize the execution speed or memory usage of generated code | |

Learn about the code generation report | |

See execution times and code coverage for generated MEX functions in MATLAB Profiler |