def test_matrix_multiplication(self):
m = Matrix(rows=[[1, 2], [3, 4]])
# Left and right multiplication with identity
self.assertEqual(Matrix.identity(2) * m, m)
self.assertEqual(m * Matrix.identity(2), m)
# Left and right multiplication with zero
self.assertEqual(Matrix.zero(2) * m, Matrix.zero(2))
self.assertEqual(m * Matrix.zero(2), Matrix.zero(2))
# Scaling by multiplication with scaled identity
self.assertEqual((5 * Matrix.identity(2)) * m, 5 * m)
self.assertEqual(m * (5 * Matrix.identity(2)), 5 * m)
# Multiplications
m1 = Matrix(rows=[[1, 2], [3, 4]])
m2 = Matrix(rows=[[5, 6], [7, 8]])
m3 = Matrix(rows=[[19, 22], [43, 50]])
flip = Matrix(rows=[[1, 0], [0, -1]])
turn = Matrix(rows=[[0, -1], [1, 0]])
self.assertEqual(flip * m1,
Matrix(rows=[[1, 2], [-3, -4]])) # Invert y
self.assertEqual(m1 * flip, Matrix(rows=[[1, -2], [3, -4]]))
self.assertEqual(
turn * m1, Matrix(rows=[[-3, -4], [1, 2]])) # Rotate by 90 degrees
self.assertEqual(m1 * m2, m3) # Arbitrary
# 2x3 * 3x2
self.assertEqual(
Matrix(rows=[[10, 11, 12], [13, 14, 15]]) *
Matrix(rows=[[16, 17], [18, 19], [20, 21]]),
Matrix(rows=[[598, 631], [760, 802]]))
# 3x2 * 2x3
self.assertEqual(
Matrix(rows=[[10, 11], [12, 13], [14, 15]]) *
Matrix(rows=[[16, 17, 18], [19, 20, 21]]),
Matrix(rows=[[369, 390, 411], [439, 464, 489], [509, 538, 567]]))
# 3x3
self.assertEqual(
Matrix(rows=[[10, 11, 12], [13, 14, 15], [16, 17, 18]]) *
Matrix(rows=[[19, 20, 21], [22, 23, 24], [25, 26, 27]]),
Matrix(
rows=[[732, 765, 798], [930, 972, 1014], [1128, 1179, 1230]]))
# Dimensions mismatch
with self.assertRaises(ValueError):
Matrix.identity(3) * m
with self.assertRaises(ValueError):
m * Matrix.identity(3)
with self.assertRaises(ValueError):
(Matrix(rows=[[16, 17, 18], [19, 20, 21]]) *
Matrix(rows=[[10, 11], [12, 13]]))
def test_matrix_multiplication(self):
# Identity * Vector
self.assertEqual(
Matrix.identity(3) * Vector(1, 3, 10), Vector(1, 3, 10))
with self.assertRaises(ValueError):
Matrix.identity(4) * Vector(1, 2, 3)
# Zero * Vector
self.assertEqual(Matrix.zero(3) * Vector(1, 2, 3), Vector(0, 0, 0))
# (Square) Matrix * Vector
m = Matrix(rows=[[1, 1, 1], [0, 1, 1], [0, 0, 1]])
self.assertEqual(m * Vector(0, 0, 0), Vector(0, 0, 0))
self.assertEqual(m * Vector(1, 2, 3), Vector(6, 5, 3))
with self.assertRaises(ValueError):
m * Vector(1, 2, 3, 4)
# (Non-square) Matrix * Vector
m = Matrix(rows=[[1, 1, 1], [0, 2, 2], [0, 3, 0], [0, 0, 4]])
self.assertEqual(m * Vector(0, 0, 0), Vector(0, 0, 0, 0))
self.assertEqual(m * Vector(1, 2, 3), Vector(6, 10, 6, 12))
with self.assertRaises(ValueError):
m * Vector(1, 2, 3, 4)
# Scaling by multiplication with scaled identity
self.assertEqual((5 * Matrix.identity(3)) * Vector(1, 2, 3),
Vector(5, 10, 15))
# Vector * Matrix is invalid
with self.assertRaises(TypeError):
Vector(1, 2, 3) * Matrix.identity(3)
def test_zero(self):
self.assertEqual(Matrix.zero(0).row_values, [])
self.assertEqual(Matrix.zero(1).row_values, [[0]])
self.assertEqual(Matrix.zero(2).row_values, [[0, 0], [0, 0]])
self.assertEqual(
Matrix.zero(3).row_values, [[0, 0, 0], [0, 0, 0], [0, 0, 0]])