Simple 3x3 matrix inverse code (C++)

Question

What\'s the easiest way to compute a 3x3 matrix inverse?

I\'m just looking for a short code snippet that\'ll do the trick for non-singular matrices, possibly using C

Answer 1

I went ahead and wrote it in python since I think it's a lot more readable than in c++ for a problem like this. The function order is in order of operations for solving this by hand via this video. Just import this and call "print_invert" on your matrix.

def print_invert (matrix):
  i_matrix = invert_matrix (matrix)
  for line in i_matrix:
    print (line)
  return

def invert_matrix (matrix):
  determinant = str (determinant_of_3x3 (matrix))
  cofactor = make_cofactor (matrix)
  trans_matrix = transpose_cofactor (cofactor)

  trans_matrix[:] = [[str (element) +'/'+ determinant for element in row] for row in trans_matrix]

  return trans_matrix

def determinant_of_3x3 (matrix):
  multiplication = 1
  neg_multiplication = 1
  total = 0
  for start_column in range (3):
    for row in range (3):
      multiplication *= matrix[row][(start_column+row)%3]
      neg_multiplication *= matrix[row][(start_column-row)%3]
    total += multiplication - neg_multiplication
    multiplication = neg_multiplication = 1
  if total == 0:
    total = 1
  return total

def make_cofactor (matrix):
  cofactor = [[0,0,0],[0,0,0],[0,0,0]]
  matrix_2x2 = [[0,0],[0,0]]
  # For each element in matrix...
  for row in range (3):
    for column in range (3):

      # ...make the 2x2 matrix in this inner loop
      matrix_2x2 = make_2x2_from_spot_in_3x3 (row, column, matrix)
      cofactor[row][column] = determinant_of_2x2 (matrix_2x2)

  return flip_signs (cofactor)

def make_2x2_from_spot_in_3x3 (row, column, matrix):
  c_count = 0
  r_count = 0
  matrix_2x2 = [[0,0],[0,0]]
  # ...make the 2x2 matrix in this inner loop
  for inner_row in range (3):
    for inner_column in range (3):
      if row is not inner_row and inner_column is not column:
        matrix_2x2[r_count % 2][c_count % 2] = matrix[inner_row][inner_column]
        c_count += 1
    if row is not inner_row:
      r_count += 1
  return matrix_2x2

def determinant_of_2x2 (matrix):
  total = matrix[0][0] * matrix [1][1]
  return total - (matrix [1][0] * matrix [0][1])

def flip_signs (cofactor):
  sign_pos = True 
  # For each element in matrix...
  for row in range (3):
    for column in range (3):
      if sign_pos:
        sign_pos = False
      else:
        cofactor[row][column] *= -1
        sign_pos = True
  return cofactor

def transpose_cofactor (cofactor):
  new_cofactor = [[0,0,0],[0,0,0],[0,0,0]]
  for row in range (3):
    for column in range (3):
      new_cofactor[column][row] = cofactor[row][column]
  return new_cofactor