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<?php
/*
* Modified : 19/dec/2009
* Pier-André Bouchard St-Amant pabsta [at] econ.queensu.ca
* Changes : 
*	- Introduction of the PLU decomposition of square matrices (through lu() for users, and PLU internally)
*	- Significant improvement in stability and speed for inversion and the computation of the determinant.
*
*
* Modified : 22/Nov/2009
* Pier-André Bouchard St-Amant pabsta [at] econ.queensu.ca<br>
* Kingston - Canada
* Changes : 
*	- Internal convention : zeros are no longer stored in memory. All functions were changed to reflect this. This is transparent to users.
* 	- Performance improvements for large sparse matrices (based on above), mostly for multiplication and inversion.
*	- Four new functions : utrig, ltrig, diag and smooth : 
*		upper triangular matrix, lower triangular matrix, diagonal matrix and smooth small number to zero (see documentation).
*	- Correction of numerous bugs.
*
* Modified : 10/Nov/2009
* Pier-André Bouchard St-Amant pabsta [at] econ.queensu.ca
* Kingston - Canada
*  - Changes : 
*		1) (Almost) all function specs so that inputs are matrix objects.
*		2) Deletion of five functions (including some "statistical" ones) and two global variables
*		3) Introduction of nine new "basic" functions
*			- get_data, get_value, set_value, get_columns, get_rows, set_columns, set_rows, delete_columns, delete_rows
*			- print_matrix (mostly for debugging purpose, as it prints a <table>)
*		4) Introduction of eleven new mathematical functions : 
*			- point to point product and division.
*			- eye (identity matrix), ones (matrix of ones), zeros (matrix of zeros) and random matrix "quasi-constructors"
*			- max, min of a column
*			- point to point greater than, greater or equal than, smaller than, smaller or equal, equal
*		5) Correction of numerous bugs.
*		6) Translation of spanish to english, identation and uniformisation of the function names
*
*  - Comments :
*		a) All mathematical functions are written to ressemble paper algebra : 
*				- AxB ==> $A->times($B);
*				- A-B ==> $A->minus($B);
*				- A^(-1) ==> $A->inv();
*				- A' ==> $A->prime();
*				- det(A) ==> $A->det($A);
*				- etc.
*			This restricts nested calls, but augment readability.
*		b) The algorithm for matrix inversion is based on PLU decomposition. The algorithm performs relatively well numerically, but it requires an order of 2*n^2 x sizeof(doubles) of memory space.
*		c) Error messages are echoed to the standard output (likely to be your webpage)
*
* A class for operations on matrices
* Creation date: 30/sept/2005
* Diego Carrera - Kleber BaÒo
* Guayaquil - Ecuador (Spanish version)
*/
?>
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