Class Matrix

A matrix is just like a mathematical matrix where it is similar to essentially a 2d array of of the given type Template parameters are the type, how many rows, and how many columns

Constructors

Name	Description
this	Constructs a matrix from a two-dimensional array of elements
this	Constructs a matrix that is identically one value
this	Constructs a matrix as an identity matrix
this	Copy constructor for a matrix; creates a copy of the given matrix

Fields

Name	Type	Description
elements	T[columns][rows]	The elements of the matrix; stored as an array of rows (i.e. row vectors)

Properties

Name	Type	Description
determinant[get]	T	Recursively finds the determinant of the matrix if the matrix is square Task is done in O(n!) for an nxn matrix, so determinants of matrices of at most size 3x3 are already defined to be more efficient Not very efficient for large matrices
inverse[get]	Matrix!(T,rows,columns)	Returns the inverse of a square matrix, which should give the identity if they are multiplied.
reducedRowEchelon[get]	Matrix!(T,rows,columns)	Returns the matrix in row-echelon form In reduced row-echelon form, the diagonal elements are equal to one and all elements below and above the diagonal are zero This method uses the Gauss-Jordan algorithm, which has arithmetic complexity O(n^3) Be wary of truncation for integer matrices
rowEchelon[get]	Matrix!(T,rows,columns)	Returns the matrix in row-echelon form In row-echelon form, the diagonal elements are equal to one and all elements below the diagonal are zero This method uses the Gauss-Jordan algorithm, which has arithmetic complexity O(n^3) Be wary of truncation for integer matrices
transpose[get]	Matrix!(T,columns,rows)	The transpose operation returns the matrix 'flipped' about its diagonal - That is, rows and columns are switched

Methods

Name	Description
getColumn	Returns the nth column of the matrix
getRow	Returns the nth row of the matrix
getSlice	Returns a rectangular slice of the matrix with the upper left corner at the specified location and a specified size Usable to get rows and columns; just set the height or width to 1
opAssign	Allows assigning the matrix to a static two-dimensional array to set all components of the matrix
opAssign	Allows assigning the matrix to a single value to set all elements of the matrix to such a value
opBinary	Multiplication of a matrix by a vector This is essentially a matrix multiplication, but is handled separately for convenience If Vector is made to extend Matrix in the future, this will become obsolete
opBinary	Pairwise operations on matrices
opBinary	Pairwise operations on matrices with a constant
setColumn	Sets the nth column of the matrix
setRow	Sets the nth row of the matrix
toString	Returns the matrix as a string

TODO

frustums, transformations, speed everything up with parallelism