The MATLAB Array (MATLAB Application Program Interface)

The MATLAB language works with only a single object type: the MATLAB array. All MATLAB variables, including scalars, vectors, matrices, strings, cell arrays, structures, and objects are stored as MATLAB arrays. In C, the MATLAB array is declared to be of type mxArray. The mxArray structure contains, among other things:

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 fieldnames

Data Storage

All MATLAB data is stored columnwise. This is how Fortran stores matrices; MATLAB uses this convention because it was originally written in Fortran. For example, given the matrix:

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

a =
house
floor
porch

its dimensions are:

size(a)

ans =
3     5

and its data is stored as:

Data Types in MATLAB

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 real-only, double-precision matrix is one whose pi is NULL.

Numeric Matrices

MATLAB also supports other types of numeric matrices. These are 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.

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. Each character in the string is stored as 16-bit ASCII Unicode. Unlike C, MATLAB strings are not null terminated.

Sparse Matrices

Sparse matrices have a different storage convention in MATLAB. The parameters pr and pi are still arrays of double-precision numbers, but there are three additional parameters, nzmax, ir, and jc:

nzmax is an integer that contains the length of ir, pr, and, if it exists, pi. It is the maximum possible 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 that contains column index information. For j, in the range 0 j N-1, jc[j] is the index in ir and pr (and pi if it exists) of the first nonzero entry in the jth column and
jc[j+1] - 1 index of the last nonzero entry. As a result, jc[N] is also equal to nnz, the number of nonzero entries in the matrix. If nnz is less than nzmax, then more nonzero entries can be inserted in the array without allocating additional storage.

Cell Arrays

Cell arrays are a collection of MATLAB arrays where each mxArray is referred to as a cell. This allows 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.

Structures

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

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 classname 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.

Logical Arrays

Any noncomplex numeric or sparse array can be flagged as logical. The storage for a logical array is the same as the storage for a nonlogical array.

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.

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