#### A.1.2 Matrices and Arrays in Oct-Files

Octave supports a number of different array and matrix classes, the majority of which are based on the Array class. The exception is the sparse matrix types discussed separately below. There are three basic matrix types

`Matrix`
  A double precision matrix class defined in dMatrix.h,
`ComplexMatrix`
  A complex matrix class defined in CMatrix.h, and
`BoolMatrix`
  A boolean matrix class defined in boolMatrix.h.

These are the basic two-dimensional matrix types of octave. In additional there are a number of multi-dimensional array types, these being

`NDArray`
  A double precision array class defined in `dNDArray.h`
`ComplexNDarray`
  A complex array class defined in `CNDArray.h`
`boolNDArray`
  A boolean array class defined in `boolNDArray.h`
`int8NDArray`
`int16NDArray`
`int32NDArray`
`int64NDArray`
  8, 16, 32 and 64-bit signed array classes defined in `int8NDArray.h`, `int16NDArray.h`, etc.
`uint8NDArray`
`uint16NDArray`
`uint32NDArray`
`uint64NDArray`
  8, 16, 32 and 64-bit unsigned array classes defined in `uint8NDArray.h`, `uint16NDArray.h`, etc.

There are several basic means of constructing matrices of multi-dimensional arrays. Considering the `Matrix` type as an example

- We can create an empty matrix or array with the empty constructor. For example

                Matrix a;

  This can be used on all matrix and array types

- Define the dimensions of the matrix or array with a dim_vector. For example

                dim_vector dv (2);
                dv(0) = 2; dv(1) = 2;
                Matrix a (dv);

  This can be used on all matrix and array types

- Define the number of rows and columns in the matrix. For example:

                Matrix a (2, 2)

  However, this constructor can only be used with the matrix types.

These types all share a number of basic methods and operators, a selection of which include

— Method: T& operator () (octave_idx_type)
— Method: T& elem (octave_idx_type)

> The `()` operator or `elem` method allow the values of the matrix or array to be read or set. These can take a single argument, which is of type `octave_idx_type`, that is the index into the matrix or array. Additionally, the matrix type allows two argument versions of the `()` operator and elem method, giving the row and column index of the value to obtain or set.

Note that these functions do significant error checking and so in some circumstances the user might prefer to access the data of the array or matrix directly through the fortran_vec method discussed below.

— Method: octave_idx_type nelem (void) const

> The total number of elements in the matrix or array.

— Method: size_t byte_size (void) const

> The number of bytes used to store the matrix or array.

— Method: dim_vector dims (void) const

> The dimensions of the matrix or array in value of type dim_vector.

— Method: void resize (const dim_vector&)

> A method taking either an argument of type `dim_vector`, or in the case of a matrix two arguments of type `octave_idx_type` defining the number of rows and columns in the matrix.

— Method: T* fortran_vec (void)

> This method returns a pointer to the underlying data of the matrix or a array so that it can be manipulated directly, either within Octave or by an external library.

Operators such an `+`, `-`, or `*` can be used on the majority of the above types. In addition there are a number of methods that are of interest only for matrices such as `transpose`, `hermitian`, `solve`, etc.

The typical way to extract a matrix or array from the input arguments of `DEFUN_DLD` function is as follows

         #include <octave/oct.h>

         DEFUN_DLD (addtwomatrices, args, , "Add A to B")
         {
           int nargin = args.length ();
           if (nargin != 2)
             print_usage ();
           else
             {
               NDArray A = args(0).array_value ();
               NDArray B = args(1).array_value ();
               if (! error_state)
                 return octave_value (A + B);
             }
           return octave_value_list ();
         }

To avoid segmentation faults causing Octave to abort, this function explicitly checks that there are sufficient arguments available before accessing these arguments. It then obtains two multi-dimensional arrays of type `NDArray` and adds these together. Note that the array_value method is called without using the `is_matrix_type` type, and instead the error_state is checked before returning `A + B`. The reason to prefer this is that the arguments might be a type that is not an `NDArray`, but it would make sense to convert it to one. The `array_value` method allows this conversion to be performed transparently if possible, and sets `error_state` if it is not.

`A + B`, operating on two `NDArray`'s returns an `NDArray`, which is cast to an `octave_value` on the return from the function. An example of the use of this demonstration function is

         addtwomatrices (ones (2, 2), ones (2, 2))
               ⇒  2  2
                   2  2

A list of the basic `Matrix` and `Array` types, the methods to extract these from an `octave_value` and the associated header is listed below.

`RowVector` | `row_vector_value` | `dRowVector.h`
`ComplexRowVector` | `complex_row_vector_value` | `CRowVector.h`
`ColumnVector` | `column_vector_value` | `dColVector.h`
`ComplexColumnVector` | `complex_column_vector_value` | `CColVector.h`
`Matrix` | `matrix_value` | `dMatrix.h`
`ComplexMatrix` | `complex_matrix_value` | `CMatrix.h`
`boolMatrix` | `bool_matrix_value` | `boolMatrix.h`
`charMatrix` | `char_matrix_value` | `chMatrix.h`
`NDArray` | `array_value` | `dNDArray.h`
`ComplexNDArray` | `complex_array_value` | `CNDArray.h`
`boolNDArray` | `bool_array_value` | `boolNDArray.h`
`charNDArray` | `char_array_value` | `charNDArray.h`
`int8NDArray` | `int8_array_value` | `int8NDArray.h`
`int16NDArray` | `int16_array_value` | `int16NDArray.h`
`int32NDArray` | `int32_array_value` | `int32NDArray.h`
`int64NDArray` | `int64_array_value` | `int64NDArray.h`
`uint8NDArray` | `uint8_array_value` | `uint8NDArray.h`
`uint16NDArray` | `uint16_array_value` | `uint16NDArray.h`
`uint32NDArray` | `uint32_array_value` | `uint32NDArray.h`
`uint64NDArray` | `uint64_array_value` | `uint64NDArray.h`