matrix.lua

--/ Matrix class for Lua \--


Matrix = {}
Matrix.__index = Matrix


-- \
-- | Constructor
-- /


-- Returns a (n,p) order matrix.
function Matrix:new(n, p)
  if n < 0 or p < 0 then
    return nil
  end
  if n == 0 or p == 0 then
    n, p = 0, 0
  end

  local t = {n=n, p=p}
  setmetatable(t, self)
  for i=1, n do
    t[i] = {}
    for j=1, p do
      t[i][j] = 0
    end
  end

  return t
end


-- \
-- | Methods
-- /


-- Prints a matrix to the shell.
function Matrix:print()
  if self.n == 0 or self.p == 0 then
    print("||")
    return
  end

  for i=1, self.n do
    io.write("|")
    for j=1, self.p do
      io.write(self[i][j])
      if j ~= self.p then
        io.write(" ")
      end
    end
    io.write("|\n")
  end
end


-- Fills a matrix with values from 'list'.
function Matrix:fill(list)
  if self.n * self.p ~= #list then
    return
  end

  for i=1, self.n do
    for j=1, self.p do
      self[i][j] = list[(i-1)*self.p + j]
    end
  end
end


-- Fills a matrix' row 'i' with values from 'list'.
function Matrix:fillRow(list, i)
  if i < 1 or i > self.n then
    return
  end
  if self.p ~= #list then
    return
  end

  self[i] = list
end


-- Fills a matrix' column 'j' with values from 'list'.
function Matrix:fillColumn(list, j)
  if j < 1 or j > self.p then
    return
  end
  if self.n ~= #list then
    return
  end

  for i=1, self.n do
    self[i][j] = list[i]
  end
end


-- Checks if a matrix has the same dimensions of 'm'.
function Matrix:isEquivalent(m)
  return self.n == m.n and self.p == m.p
end


-- Checks if a matrix is symetric.
function Matrix:isSymetric()
  return self == self:transpose()
end


-- Checks if a matrix is anti-symetric.
function Matrix:isAntiSymetric()
  return self == -self:transpose()
end


-- Checks if a matrix is upper triangular.
function Matrix:isUpperTriangular()
  for i=1, self.n do
    for j=1, i-1 do
      if self[i][j] ~= 0 then
        return false
      end
    end
  end

  return true
end


-- Checks if a matrix is lower triangular.
function Matrix:isLowerTriangular()
  for i=1, self.n do
    for j=i+1, self.p do
      if self[i][j] ~= 0 then
        return false
      end
    end
  end

  return true
end


-- Checks if a matrix is the inverse of 'm'
function Matrix:isInverse(m)
  if self:isEquivalent(m) == false or self.n ~= self.p then
    return false
  end

  local t = self * m;

  if t:isUpperTriangular() == false then
    return false
  end
  if t:isLowerTriangular() == false then
    return false
  end

  for i=1, t.n do
    if (t[i][i] ~= 1) then
      return false
    end
  end

  return true
end


-- Returns a 'n'-th order square matrix.
function Matrix:square(n)
  return Matrix:new(n, n)
end


-- Returns a 'n'-th order diagonal matrix, using values from 'list'.
function Matrix:diagonal(list)
  local t = Matrix:square(#list)

  for i=1, #list do
    t[i][i] = list[i]
  end

  return t
end


-- Returns a 'n'-th order identity matrix.
function Matrix:identity(n)
  local t = Matrix:square(n)

  for i=1, n do
    t[i][i] = 1
  end

  return t
end


-- Returns the transposed of a matrix.
function Matrix:transpose()
  local t = Matrix:new(self.p, self.n)

  for i=1, self.n do
    t:fillColumn(self[i],i)
  end

  return t
end


-- \
-- | Operators overcharge
-- /


-- Checks if 'a' equals 'b'
function Matrix.equals(a, b)
  if a:isEquivalent(b) == false then
    return false
  end

  for i=1, a.n do
    for j=1, a.p do
      if a[i][j] ~= b[i][j] then
        return false
      end
    end
  end

  return true
end


-- Returns the matrix sum of 'a' and 'b'
function Matrix.sum(a, b)
  if a:isEquivalent(b) == false then
    return nil
  end

  local t = Matrix:new(a.n, a.p)
  for i=1, a.n do
    for j=1, a.p do
      t[i][j] = a[i][j] + b[i][j]
    end
  end

  return t
end


-- Returns the matrix difference of 'a' and 'b'
function Matrix.difference(a, b)
  if a:isEquivalent(b) == false then
    return nil
  end

  local t = Matrix:new(a.n, a.p)
  for i=1, a.n do
    for j=1, a.p do
      t[i][j] = a[i][j] - b[i][j]
    end
  end

  return t
end


-- Returns the negative of a matrix
function Matrix.negative(m)
  return Matrix:new(m.n, m.p) - m
end


-- Returns the product of a matrix and a real 'r'
function Matrix.rproduct(m, r)
  local t = Matrix:new(m.n, m.p)

  for i=1, t.n do
    for j=1, t.p do
      t[i][j] = m[i][j] * r
    end
  end

  return t
end


-- Returns the matrix product of 'a' and 'b'
function Matrix.product(a, b)
  if getmetatable(a) ~= Matrix then
    return Matrix.rproduct(b, a)
  end
  if getmetatable(b) ~= Matrix then
    return Matrix.rproduct(a, b)
  end
  if a.p ~= b.n then
    return nil
  end

  local t = Matrix:new(a.n, b.p)
  for i=1, a.n do
    for j=1, b.p do
      t[i][j] = 0
      for k=1, a.p do
        t[i][j] = t[i][j] + a[i][k] * b[k][j]
      end
    end
  end

  return t
end


Matrix.__add = Matrix.sum
Matrix.__sub = Matrix.difference
Matrix.__mul = Matrix.product
Matrix.__pow = nil
Matrix.__unm = Matrix.negative
Matrix.__concat = nil
Matrix.__eq = Matrix.equals
Matrix.__lt = nil
Matrix.__le = nil

-- EOF