A 2-Dimensional Matrix Container

This component is a 2-dimensional rectangular matrix. It is a template class which is parameterised by the type stored at each element of the matrix in the style of the STL containers.

The matrix is rather different from most of the 1-dimensional structures in the STL in that it has no iterators. However, in the future I may intruduce the concept of row, column and element iterators if they seem suficiently useful and well-defined.

The matrix also has to introduce the concept of a 'fill' value. Basically the matrix forms a rectangle of rows and columns of elements. It is not necessary to specify all of the element values. Where elements are missing, there is still space allocated so this space is filled with the fill value. So, for example, you can enlarge the matrix and specify what fill value to use for the extra elements added by the expansion.

Each operation that creates elements takes a fill value as a parameter, with a default value which is the value produced by the default constructor of the contained class. For example, the default value for the smart_ptr is a null pointer.

The matrix template takes only one template parameter, the type to store in the matrix:

template<typename T> class matrix

The matrix has a single constructor which takes as its arguments the size in rows and columns. It also takes a fill value to pre-fill the matrix with. For example, in a numeric matrix you might choose to fill with 0.

matrix::matrix(unsigned rows = 0, unsigned cols = 0, const T& fill = T());

All parameters to the constructor take default values. The default matrix is 0 rows by 0 columns. The default fill value is that given by the contained type's default constructor. For example, the default value of a string is the empty string.

Here's how to declare a 10x10 matrix of strings with the default value of ".":

matrix<string> string100(10, 10, ".");

The resize function has the same parameters as the constructor and allows the matrix to be resized to a different number of rows and columns. As with the constructor, there is a fill value which is used to initialise any new elements created by the resize operation.

void matrix::resize(unsigned rows, unsigned cols, const T& fill = T());

When resizing larger, newly created elements are filled with the fill value. When resizing smaller, elements outside the rectangle of the new size are discarded but elements within the rectangle are kept. The resize operation works by copying all kept elements into a new matrix of the correct size and discarding the old one, so with large matrices or matrices containing large data structures it could prove expensive. In this case, it is recommended that smart pointers are used as the matrix elements.

A matrix is a number of elements organised as rows and columns, the convention being that the row comes first, the column second, so for example the index 2,3 refers to row 2, column 3. Both rows and columns are indexed using C++ conventions in that they start at 0 and count upwards. Indices are of type unsigned to be compatible with the STL vector. There are two ways of accessing an element: using a function and using an operator. The function first:

const T& matrix::item(unsigned row, unsigned col) const; T& matrix::item(unsigned row, unsigned col);

The first form is picked by the compiler whenever accessing a const matrix - for example the right-hand side of an assignment. The second form ispicked by the compiler for a non-const matrix - such as the left-hand side of an assignment, meaning that you can assign to the element returned to update the element in the matrix:

strings100.item(2,3) = strings100.item(3,2);

The operator form uses operator() as an index operator. I would have liked to use operator[] but the standard only allows that to have one argument. Unfortunately the use of operator() makes matrix accesses look like function calls:

strings100(2,3) = strings100(3,2);

Accessing an element outside of the range of the matrix throws an exception. You don't want to do this, so interrogate the matrix first to see how many rows and columns it has:

unsigned matrix::rows(void) const; unsigned matrix::columns(void) const;

For example, to uppercase every element of the string matrix:

for (unsigned r = 0; r < string100.rows(); r++) for (unsigned c = 0; c < string100.columns(); c++) string100(r,c) = uppercase(string100(r,c));

There's a set of methods that allow you to fill the whole matrix, or a single row, column or diagonal with a value. The full set are:

void matrix::fill(const T& item = T()); void matrix::fill_column(unsigned col, const T& item = T()); void matrix::fill_row(unsigned row, const T& item = T()); void matrix::fill_leading_diagonal(const T& item = T()); void matrix::fill_trailing_diagonal(const T& item = T()); void matrix::make_identity(const T& one, const T& zero = T());

Method fill simply fills the whole matrix with the same value. If no value is specified, the default value created by the contained type's default constructor is used.

The fill_column method just fills a single column with a value. Again, the value is optional and defaults to the type's default constructor. The fill_row method does the same for a whole row.

The fill_leading_diagonal applies the same value to each element on the leading diagonal of the matrix, namely elements (0,0), (1,1) etc. It doesn't touch the other elements in the matrix. Similarly, fill_trailing diagonal does the same for the matrix's trailing diagonal. In the case of the 10x10 matrix this would be elements (9,0), (8,1) etc.

The make_identity method fills the leading diagonal with the one value and the other elements in the matrix with the zero value. The zero value is optional and defaults to the type's default constructor.

The matrix only has one transform at the moment:

void matrix::transpose(void);

This operation swaps the rows and columns of the matrix. It does so by creating a new matrix and copying elements from the old to the new, discarding the old matrix. Once again, this is expensive if the element is a large type.