As all of you know, MATLAB is a powerful engineering language. Because of some limitation, some tasks take very long time to proceed. Also MATLAB is an interpreter not a compiler. For this reason, executing a MATLAB program (m file) is time consuming. For solving this problem, Mathworks provides us C Math Library or in common language, MATLAB API. A developer can employ these APIs to solve engineering problems very fast and easy. This article is about how can use these APIs.

## Introduction

## MATrix LABoratory

MATLAB is abbreviation of Matrix Laboratory. This means every computation was performed in matrix form. In other hand every data type wrapped in matrix form and every functions take these matrix as input argument.

For example you want to multiply to polynomial as follow:

A = (3x^{2} + 5x + 7) (4x^{5} + 3x^{3} - x^{2} + 1)

You can use two matrices for coefficients of any polynomials:

[3 5 7] for (3x^{2} + 5x + 7) and [4 0 3 -1 0 1] for (4x^{5} + 3x^{3} - x^{2} + 1), using ** conv** function, we can obtain coefficients of result: conv([3 5 7], [4 0 3 -1 0 1]):

A = [12 20 37 12 16 -4 5 7]

means: A= 12x^{7} + 20x^{6} + 37x^{5} + 12x^{4} + 16x^{3} - 4x^{2} + 5x + 7

## C Math Library

The functions fall into two groups: the mathematical functions and the utility functions. We use mathematical functions for computing and utility functions for constructing an array or matrix or printing content of a matrix. Every matrices represented by `mxArray`

a data type introduced by MATLAB for constructing a matrix. As I said before, every data must be wrapped in a matrix form in other hand: `mxArray`

One C prototype supports all the possible ways to call a particular MATLAB C Math Library function. You can reconstruct the C prototype by examining the MATLAB syntax for a function. In the following procedure, the MATLAB function *svd()* and the corresponding library function *mlfSvd()* are used to illustrate the process.

**MATLAB Syntax**

s = svd (X)

[U, S, V] = svd (X)

[U, S, V] = svd (X, 0)

The C prototype for *mlfSvd()* is constructed step-by-step. Until the last step, the prototype is incomplete.

### Adding the Output Arguments

1- Find the statement that includes the largest number of output arguments.

Choose:

[U, S, V] = svd (X, 0)

2- Subtract out the first output argument, U, to be the return value from the function. The data type for the return value is *mxArray**.

*mxArray* mlfSvd(*

3- Add the remaining number of MATLAB output arguments, S and V, as the first, second, etc., arguments to the C function. The data type for a C output argument is *mxArray***.

*mxArray* mlfSvd(mxArray **S, mxArray **V*

### Adding the Input Arguments

1- Find the syntax that includes the largest number of input arguments.

Choose:

[U, S, V] = svd (X, 0)

2- Add that number of input arguments, X and Zero, to the prototype, one after another following the output arguments. The data type for an input argument is *mxArray**.

*mxArray* mlfSvd (mxArray** S, mxArray** V, mxArray* X, mxArray* Zero);*

The prototype is complete.

**How to Translate a MATLAB Call into a C Call**

This procedure demonstrates how to translate the MATLAB *svd()* calls into MATLAB C Math Library calls to *mlfSvd()*. The procedure applies to library functions in general.

Note that within a call to a MATLAB C Math Library function, an output argument is preceded by &, an input argument is not.

MATLAB Syntax:

s = svd (X)

[U, S, V] = svd (X)

[U, S, V] = svd (X, 0)

The MATLAB arguments to *svd()* fall into these categories:

U (or s) is a required output argument.

S and V are optional output arguments.

X is a required input argument.

Zero is an optional input argument.

1- Declare input, output, and return variables as *mxArray** variables, and assign values to the input variables.

2- Make the first output argument the return value from the function.

s =

U =

U =

3- Pass any additional required or optional output arguments as the first arguments to the function. Pass a NULL argument wherever an optional output argument does not apply to the particular call.

s = mlfSvd (NULL, NULL,

U = mlfSvd(&S, &V,

U = mlfSvd(&S, &V,

4- Pass any required or optional input arguments that apply to the C function, following the output arguments. Pass a NULL argument wherever an optional input argument does not apply to the particular call.

s = mlfSvd (NULL, NULL, X, NULL);

U = mlfSvd (&S, &V, X, NULL);

U = mlfSvd (&S, &V, X, Zero);

## Mathematical Functions

Every mathematical functions are begin with *mlf *prefix. mlf is an abbreviation for MATLAB Function. Below is a list of useful mathematical functions:

mlfPlus, mlfMinus | mlfMtimes, mlfMpower | mlfAcos, mlfAsin | mlfConv |

mlfConj | mlfDec2bin, mlfDec2hex | mlfDisp | mlfFft, mlfFft2 |

mlfLinspace | mlfMax, mlfMin | mlfRoots | mlfRot90 |

For example, *Conv* statement in MATLAB will become *mlfConv* in C.

## Utility Functions

We use utility functions for some tasks like printing content of a matrix or saving/loading data to/from a file. Every utility functions are begin with *mx* prefix. Below is a list of some utility functions:

mxCalloc, mxFree | mxCreateDoubleMatrix | mxCreateNumericArray | mxCreateString |

mxGetPi, mxGetPr | mxMalloc, mxRealloc | mxGetData, mxSetData | mxDestroyArray |

## Using C Math Library

To add support of MATLAB C Math Library follow these instructions:

1- Add following line at the end of stdafx.h

<P>#include <span class="code-keyword"><matlab.h></P></span>

matlab.h is interface of MATLAB APIs. Add directory of MATLAB interface files (*.h) to Visual Studio (Tools -> Options -> Directories). For example: x:\matlab\extern\include where x is drive letter of matlab path.

2- Add desired libraries to your project (In this example, libmat.lib, libmx.lib, libmatlbmx.lib and libmatlb.lib)

3- Compile your project!

## Sample Program

<P>#include <span class="code-string">"stdafx.h"</P> </span> <P> int main(int argc, char* argv[]) { double dblArray[]={1, 2, 3, 4, 5, 6, 7, 8, 9}; mxArray *A, *B; A=mxCreateDoubleMatrix(3, 3, mxREAL);</P><P></P><P> //copy array to matrix A</P><P> memcpy(mxGetPr(A), dblArray, 9 * sizeof(double));</P><P> </P><P> A=mlfMTimes(A, A); //A=A.^2;</P><P> mlfPrintMatrix(A); //Creating Magic Matrix</P><P> B=mlfMagic(mlfScalar(3)); //Magic matrix of order 3 mlfPrintMatrix(B); mxDestroyArray(A); mxDestroyArray(B); return 0; } </P>

## Requirements

1- MATLAB v5.0 or higher

2- MATLAB C Math Library Toolbox

3- Knowledge of MATLAB programming!

## References

1- MATLAB C Math Library (Mathworks)

2- C Math Library Reference (Mathworks)

Enjoy!