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The MATLAB Array

The MATLAB® language works with a single object type: the MATLAB array. All MATLAB variables (including scalars, vectors, matrices, character arrays, cell arrays, structures, and objects) are stored as MATLAB arrays. In C/C++, the MATLAB array is declared to be of type mxArray. The mxArray structure contains the following information about the array:

  • Its type

  • Its dimensions

  • The data associated with this array

  • If numeric, whether the variable is real or complex

  • If sparse, its indices and nonzero maximum elements

  • If a structure or object, the number of fields and field names

To access the mxArray structure, use the API functions in the Matrix Library. These functions allow you to create, read, and query information about the MATLAB data in your MEX files. Matrix Library functions use the mwSize type to avoid portability issues and allow MEX source files to be compiled correctly on all systems.

Lifecycle of mxArray

Like MATLAB functions, a MEX-file gateway routine passes MATLAB variables by reference. However, these arguments are C pointers. A pointer to a variable is the address (location in memory) of the variable. MATLAB functions handle data storage for you automatically. When passing data to a MEX-file, you use pointers, which follow specific rules for accessing and manipulating variables. For information about working with pointers, refer to a programming reference, such as The C Programming Language by Kernighan, B. W., and D. M. Ritchie.

    Note:   Since variables use memory, you need to understand how your MEX-file creates an mxArray and your responsibility for releasing (freeing) the memory. This is important to prevent memory leaks. The lifecycle of an mxArray—and the rules for managing memory—depends on whether it is an input argument, output argument, or local variable. The function you call to deallocate an mxArray depends on the function you used to create it. For more information, look up the function in Create or Delete Array in the C/C++ Matrix Library.

Input Argument prhs

An mxArray passed to a MEX-file through the prhs input parameter exists outside the scope of the MEX-file. Do not free memory for any mxArray in the prhs parameter. Additionally, prhs variables are read-only; do not modify them in your MEX-file.

Output Argument plhs

If you create an mxArray (allocate memory and create data) for an output argument, the memory and data exist beyond the scope of the MEX-file. Do not free memory on an mxArray returned in the plhs output parameter.

Local Variable

You allocate memory whenever you use an mxCreate* function to create an mxArray or when you call the mxCalloc and associated functions. After observing the rules for handling input and output arguments, the MEX-file should destroy temporary arrays and free dynamically allocated memory. To deallocate memory, use either mxDestroyArray or mxFree. For information about which function to use, see MX Matrix Library.

Data Storage

MATLAB stores data in a column-major (columnwise) numbering scheme, which is how Fortran stores matrices. MATLAB uses this convention because it was originally written in Fortran. MATLAB internally stores data elements from the first column first, then data elements from the second column second, and so on, through the last column.

For example, given the matrix:

a = ['house'; 'floor'; 'porch']
a =

its dimensions are:

ans =
     3     5

and its data is stored as:

If a matrix is N-dimensional, MATLAB represents the data in N-major order. For example, consider a three-dimensional array having dimensions 4-by-2-by-3. Although you can visualize the data as:

MATLAB internally represents the data for this three-dimensional array in the following order:

















































The mxCalcSingleSubscript function creates the offset from the first element of an array to the desired element, using N-dimensional subscripting.


Complex Double-Precision Matrices

The most common data type in MATLAB is the complex double-precision, nonsparse matrix. These matrices are of type double and have dimensions m-by-n, where m is the number of rows and n is the number of columns. The data is stored as two vectors of double-precision numbers—one contains the real data and one contains the imaginary data. The pointers to this data are referred to as pr (pointer to real data) and pi (pointer to imaginary data), respectively. A noncomplex matrix is one whose pi is NULL.

Other Numeric Matrices

MATLAB supports single-precision floating-point and 8-, 16-, and 32-bit integers, both signed and unsigned. The data is stored in two vectors in the same manner as double-precision matrices.

Logical Matrices

The logical data type represents a logical true or false state using the numbers 1 and 0, respectively. Certain MATLAB functions and operators return logical 1 or logical 0 to indicate whether a certain condition was found to be true or not. For example, the statement (5 * 10) > 40 returns a logical 1 value.

MATLAB Strings

MATLAB strings are of type char and are stored the same way as unsigned 16-bit integers except there is no imaginary data component. Unlike C, MATLAB strings are not null terminated.

Cell Arrays

Cell arrays are a collection of MATLAB arrays where each mxArray is referred to as a cell. Cell arrays allow MATLAB arrays of different types to be stored together. Cell arrays are stored in a similar manner to numeric matrices, except the data portion contains a single vector of pointers to mxArrays. Members of this vector are called cells. Each cell can be of any supported data type, even another cell array.


A 1-by-1 structure is stored in the same manner as a 1-by-n cell array where n is the number of fields in the structure. Members of the data vector are called fields. Each field is associated with a name stored in the mxArray.


Objects are stored and accessed the same way as structures. In MATLAB, objects are named structures with registered methods. Outside MATLAB, an object is a structure that contains storage for an additional class name that identifies the name of the object.

Multidimensional Arrays

MATLAB arrays of any type can be multidimensional. A vector of integers is stored where each element is the size of the corresponding dimension. The storage of the data is the same as matrices.

Empty Arrays

MATLAB arrays of any type can be empty. An empty mxArray is one with at least one dimension equal to zero. For example, a double-precision mxArray of type double, where m and n equal 0 and pr is NULL, is an empty array.

Sparse Matrices

Sparse matrices have a different storage convention from full matrices in MATLAB. The parameters pr and pi are still arrays of double-precision numbers or logical values, but these arrays contain only nonzero data elements. pi contains data only if the sparse matrix is complex.

There are three additional parameters: nzmax, ir, and jc. Use the mwSize and mwIndex types when declaring variables for these parameters.

  • nzmax is an integer that contains the length of ir, pr, and pi, if it exists. It is the maximum number of nonzero elements in the sparse matrix.

  • ir points to an integer array of length nzmax containing the row indices of the corresponding elements in pr and pi.

  • jc points to an integer array of length n+1, where n is the number of columns in the sparse matrix. Note that in C, the first element of an mxArray has an index of 0. The jc array contains column index information. If the jth column of the sparse matrix has any nonzero elements, jc[j] is the index into ir, pr, and pi of the first nonzero element in the jth column. Index jc[j+1] - 1 contains the last nonzero element in that column. For the jth column of the sparse matrix, jc[j] is the total number of nonzero elements in all preceding columns. The last element of the jc array, jc[n], is equal to nnz, the number of nonzero elements in the entire sparse matrix. If nnz is less than nzmax, more nonzero entries can be inserted into the array without allocating more storage.

Using Data Types

You can write source MEX files, MAT-file applications, and engine applications in C/C++ that accept any class or data type supported by MATLAB (see Data Types). In Fortran, only the creation of double-precision n-by-m arrays and strings are supported. You use binary C/C++ and Fortran MEX files like MATLAB functions.

    Caution   MATLAB does not check the validity of MATLAB data structures created in C/C++ or Fortran using one of the Matrix Library create functions (for example, mxCreateStructArray). Using invalid syntax to create a MATLAB data structure can result in unexpected behavior in your C/C++ or Fortran program.

Declaring Data Structures

To handle MATLAB arrays, use type mxArray. The following statement declares an mxArray named myData:

mxArray *myData;

To define the values of myData, use one of the mxCreate* functions. Some useful array creation routines are mxCreateNumericArray, mxCreateCellArray, and mxCreateCharArray. For example, the following statement allocates an m-by-1 floating-point mxArray initialized to 0:

myData = mxCreateDoubleMatrix(m, 1, mxREAL);

C/C++ programmers should note that data in a MATLAB array is in column-major order. (For an illustration, see Data Storage.) Use the MATLAB mxGet* array access routines to read data from an mxArray.

Manipulating Data

The mxGet* array access routines get references to the data in an mxArray. Use these routines to modify data in your MEX file. Each function provides access to specific information in the mxArray. Some useful functions are mxGetData, mxGetPr, mxGetM, and mxGetString. Many of these functions have corresponding mxSet* routines to allow you to modify values in the array.

The following statements read the input prhs[0] into a C-style string buf.

char *buf;
int buflen;
int status;
buflen = mxGetN(prhs[0])*sizeof(mxChar)+1;
buf = mxMalloc(buflen);
status = mxGetString(prhs[0], buf, buflen);

The explore Example

There is an example source MEX file included with MATLAB, called explore.c, that identifies the data type of an input variable. The source code for this example is in matlabroot/extern/examples/mex, where matlabroot represents the top-level folder where MATLAB is installed on your system.

    Note:   In platform-independent discussions that refer to folder paths, this documentation uses the UNIX® convention. For example, a general reference to the mex folder is matlabroot/extern/examples/mex.

To build the example MEX file, first copy the file to a writable folder on your path.


Use the mex command to build the MEX file.

mex explore.c


x = 2;
Name: prhs[0]
Dimensions: 1x1 
Class Name: double
	(1,1) = 2

explore accepts any data type. Try using explore with these examples:

explore([1 2 3 4 5])
explore 1 2 3 4 5
explore({1 2 3 4 5})
explore(int8([1 2 3 4 5]))
explore {1 2 3 4 5}
explore(struct('name', 'Joe Jones', 'ext', 7332))
explore(1, 2, 3, 4, 5)

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