[Math] Matrices

a = {
	len = function( self )
		return self.length
	end,
	wid = function( self )
		return self.width
	end,
	insert = function( self, x, y, value )
		if not self[ x ] then
			error( "x value out of bounds", 2 )
		end
		if not self[ x ][ y ] then
			error( "y value out of bounds", 2 )
		end
		self[ x ][ y ] = value
	end,
	getValue = function( self, x, y )
		return self[ x ] and self[ x ][ y ] or nil
	end,
}

mt = {
	__type = "array",
	__index = a,
	__add = function( lhs, rhs )
		if type( rhs ) ~= "table" then
			error( "attempt to add array and " .. type( rns ), 2 )
		elseif getmetatable( rhs ).__type ~= "array" then
			error( "attempt to add array and table", 2 )
		elseif lhs:len() ~= rhs:len() or lhs:wid() ~= rhs:wid() then
			error( "arrays' dimensions are not equal", 2 )
		end
		local array = create( lhs:len(), lhs:wid() )
		for x, tbl in ipairs( lhs ) do
			for y, value in ipairs( rhs ) do
				array:insert( x, y, rhs:getValue( x, y ) + lhs:getValue( x, y ) )
			end
		end
		return array
	end,
	__sub = function( lhs, rhs )
		if type( rhs ) ~= "table" and type( rhs ) ~= "number" then
			error( "attempt to subtract array and " .. type( rhs ), 2 )
		elseif getmetatable( rhs ).__type ~= "array" then
			error( "attempt to subtract array and table", 2 )
		elseif lhs:len() ~= rhs:len() or lhs:wid() ~= rhs:wid() then
			error( "arrays’ dimensions are not equal", 2 )
		end
		local array = create( lhs:len(), lhs:wid() )
		for x, tbl in ipairs( lhs ) do
			for y, value in ipairs( rhs ) do
				array:insert( x, y, rhs:getValue( x, y ) - lhs:getValue( x, y ) )
			end
		end
		return array
	end,
	__mul = function( lhs, rhs )
		if type( rhs ) ~= "table" and type( rhs ) ~= "number" then
			error( "attempt to multiply array and " .. type( rns ), 2 )
		elseif type( rhs ) == "table" and lhs:len() ~= rhs:wid() then
			error( 'attempt to multiply ' .. lhs:len() .. ", " .. lys:wid() .. " array with " .. rhs:len() .. ", " .. rhs:wid() .. " array", 2 )
		elseif type( rhs ) == "number" then
			local array = create( lhs:len(), lhs:wid() )
			for x = 1, lhs:len() do
				for y = 1, lhs:wid() do
					array:insert( x, y, lhs:getValue( x, y ) * rhs )
				end
			end
			return array
		elseif getmetatable( rhs ).__type ~= "array" then
			error( "attempt to multiply array and table", 2 )
		end
		local array = create( lhs:len(), rhs:wid() )
		for pos = 1, lhs:len() do
			for column = 1, rhs:len() do
				local value = 0
				for x = 1, lhs:wid() do
					value = value + lhs:getValue( pos, x ) * rhs:getValue( column, x )
				end
				array:insert( pos, column, value )
			end
		end
		return array
	end,
	__div = function( lhs, rhs )
		if type( rhs ) ~= "table" and type( rhs ) ~= "number" then
			error( "attempt to divide array and " .. type( rhs ), 2 )
		elseif type( rhs ) == "table" and getmetatable( rhs ).__type ~= "array" then
			error( "attempt to divide array and table", 2 )
		elseif type( rhs ) == "number" then
			local array = create( lhs:len(), lhs:wid() )
			for x = 1, lhs:len() do
				for y = 1, lhs:wid() do
					array:insert( x, y, lhs:getValue( x, y ) / rhs )
				end
			end
			return array
		end
		--#what to do here...
	end,
}

function create( length, width )
	if length and width then
		local array = { length = length, width = width }
		for x = 1, length do
			array[ x ] = {}
			for y = 1, width do
				array[ x ][ y ] = 0
			end
		end
		setmetatable( array, mt )
		return array
	end
	length.length = #length
	length.width = #length[ 1 ]
	setmetatable( length, mt )
	return length
end