Matrix

local 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,
    draw = function( self, a, b )
        term.setCursorPos( a, b )
        local maxNum = 0
        local maxDec = 0
        for x = 1, self:len() do
            for y = 1, self:wid() do
                local v = tostring( self:getValue( x, y ) )
                if #v > maxNum then
                    maxNum = #v
                end
            end
        end
        maxNum = maxNum + 1
        for x = 1, self:len() do
            for y = 1, self:wid() do
                local value = self:getValue( x, y )
                term.write( value .. string.rep( " ", maxNum ) )
            end
            local _, b = term.getCursorPos()
            term.setCursorPos( a, b + 1 )
        end
    end,
    transpose = function( self )
        local array = create( self:wid(), self:len() )
        for pos = 1, self:len() do
            for column = 1, array:len() do
                array:insert( column, pos, self:getValue( pos, column ) )
            end
        end
        return array
    end,
    trace = function( self )
        local v = 0
        for x = 1, self:len() do
            for y = 1, self:wid() do
                v = v + self:getValue( x, y )
            end
        end
        return v
    end,
}

local mt = {
    __metatable = { __type = "matrix" },
    __index = a,
    __add = function( lhs, rhs )
        if type( rhs ) ~= "table" then
            error( "attempt to add matrix and " .. type( rns ), 2 )
        elseif getmetatable( rhs ).__type ~= "matrix" then
            error( "attempt to add matrix and table", 2 )
        elseif lhs:len() ~= rhs:len() or lhs:wid() ~= rhs:wid() then
            error( "matrices' 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 matrix and " .. type( rhs ), 2 )
        elseif getmetatable( rhs ).__type ~= "matrix" then
            error( "attempt to subtract matrix and table", 2 )
        elseif lhs:len() ~= rhs:len() or lhs:wid() ~= rhs:wid() then
            error( "matrices' 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 matrix and " .. type( rns ), 2 )
        elseif type( rhs ) == "table" and lhs:len() ~= rhs:wid() then
            error( 'attempt to multiply ' .. lhs:len() .. "x" .. lys:wid() .. " matrix with " .. rhs:len() .. "x" .. rhs:wid() .. " matrix", 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 ~= "matrix" then
            error( "attempt to multiply matrix 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,
    __eq = function( o1, o2 )
        if o1:len() ~= o2:len() or o1:wid() ~= o2:wid() then
            return false
        end
        for x = 1, o1:len() do
            for y = 1, o1:wid() do
                if o1:getValue( x, y ) ~= o2:getValue( x, y ) then
                    return false
                end
            end
        end
        return true
    end,
    __lt = function( o1, o2 )
        return o1:trace() < o2:trace()
    end,
    __le = function( o1, o2 )
        return o1:trace() > o2:trace()
    end,
    __pow = function( lhs, rhs )
        if type( rhs ) ~= "number" then
            error( "attempt to perform arithmatic __pow on matrix and " .. type( rhs ), 2 )
        end
        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,
    __div = function( lhs, rhs )
        if type( rhs ) ~= "number" and type( rhs ) ~= "table" then
            error( "Attempt to divide matrix by " .. type( rhs ), 2 )
        elseif type( rhs ) == "table" and getmetatable( rhs ).__type == "matrix" then
            error( "Attempt to divide matrix by matrix", 2 )
        end
        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,
    __call = function()
        error( "attempt to call matrix", 2 )
    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