def test():
I2 = m.Matrix([[1, 0], [0, 1]])
I2_neg = m.Matrix([[-1, 0], [0, -1]])
zero = m.Matrix([[0, 0], [0, 0]])
m1 = m.Matrix([[1, 2, 3], [4, 5, 6]])
m2 = m.Matrix([[7, -2], [-3, -5], [4, 1]])
m1_x_m2 = m.Matrix([[13, -9], [37, -27]])
m2_x_m1 = m.Matrix([[-1, 4, 9], [-23, -31, -39], [8, 13, 18]])
m1_m2_inv = m.Matrix([[1.5, -0.5], [2.0555556, -0.722222222]])
top_ones = m.Matrix([[1, 1], [0, 0]])
left_ones = m.Matrix([[1, 0], [1, 0]])
assert equal(-I2, I2_neg)
assert equal(I2 + I2_neg, zero)
assert equal(m1 * m2, m1_x_m2)
assert equal(m2 * m1, m2_x_m1)
assert equal(m1_x_m2.inverse(), m1_m2_inv)
assert equal(I2.inverse(), I2)
assert equal(top_ones.T(), left_ones)
assert equal(left_ones.T(), top_ones)
assert equal(top_ones - left_ones.T(), m.zeroes(2, 2))
assert (4 * m.identity(5)).trace() == 20
print("Congratulations! All tests pass. Your Matrix class is working"
"as expected.")
def test():
I2 = m.Matrix([[1, 0], [0, 1]])
I2_neg = m.Matrix([[-1, 0], [0, -1]])
zero = m.Matrix([[0, 0], [0, 0]])
m1 = m.Matrix([[1, 2, 3], [4, 5, 6]])
m2 = m.Matrix([[7, -2], [-3, -5], [4, 1]])
m1_x_m2 = m.Matrix([[13, -9], [37, -27]])
m2_x_m1 = m.Matrix([[-1, 4, 9], [-23, -31, -39], [8, 13, 18]])
m1_m2_inv = m.Matrix([[1.5, -0.5], [2.0555556, -0.722222222]])
top_ones = m.Matrix([
[1, 1],
[0, 0],
])
left_ones = m.Matrix([[1, 0], [1, 0]])
assert equal(-I2, I2_neg), "Error in your __neg__ function"
assert equal(I2 + I2_neg, zero), "Error in your __add__ function"
assert equal(m1 * m2, m1_x_m2), "Error in your __mul__ function"
assert equal(m2 * m1, m2_x_m1), "Error in your __mul__ function"
assert equal(
m1_x_m2.inverse(),
m1_m2_inv), """Error in your inverse function for the 1 x 1 case"""
assert equal(I2.inverse(),
I2), """Error in your inverse function for the 2 x 2 case"""
assert equal(top_ones.T(),
left_ones), "Error in your T function (transpose)"
assert equal(left_ones.T(),
top_ones), "Error in your T function (transpose)"
assert equal(top_ones - left_ones.T(),
m.zeroes(2, 2)), "Error in your __sub__ function"
assert (4 * m.identity(5))[0][0] == 4, "Error in your __rmul__ function"
assert (4 * m.identity(5)).trace() == 20, "Error in your trace function"
print(
"Congratulations! All tests pass. Your Matrix class is working as expected."
)
# some functionality already exists... here's a demo
m1 = Matrix([[1, 2], [3, 4]])
m2 = Matrix([[2, 5], [6, 1]])
print("m1 is")
print(m1)
print("m2 is")
print(m2)
print("we've also provided you with a function called zeros")
print("here's what happens when you call zeros(4,2)")
print(zeroes(4, 2))
print("we've also provided you with a function called identity")
print("here's identity(3)")
print(identity(3))
print("but not everything works yet!")
print("for example, matrix addition...")
print("run the cell below to see what happens when we try...")
# In[3]:
m1 = Matrix([[1, 2], [3, 4]])
m2 = Matrix([[2, 5], [6, 1]])
def test():
I2 = m.Matrix([[1, 0], [0, 1]])
I2_neg = m.Matrix([[-1, 0], [0, -1]])
zero = m.Matrix([[0, 0], [0, 0]])
m1 = m.Matrix([[1, 2, 3], [4, 5, 6]])
m1_transposed = m.Matrix([[1, 4], [2, 5], [3, 6]])
m2 = m.Matrix([[7, -2], [-3, -5], [4, 1]])
m3 = m.Matrix([[8]])
m3_inv = m.Matrix([[0.125]])
m1_x_m2 = m.Matrix([[13, -9], [37, -27]])
m2_x_m1 = m.Matrix([[-1, 4, 9], [-23, -31, -39], [8, 13, 18]])
m1_m2_inv = m.Matrix([[1.5, -0.5], [2.0555556, -0.722222222]])
top_ones = m.Matrix([
[1, 1],
[0, 0],
])
left_ones = m.Matrix([[1, 0], [1, 0]])
## test determinant functionality
invertable1 = m.Matrix([[100]])
invertable2 = m.Matrix([[4, 5], [7, 1]])
not_invertable1 = m.Matrix([[0]])
not_invertable2 = m.Matrix([[4, 2], [14, 7]])
## test determinant
# invertable matrices
assert invertable1.determinant() == 100
assert invertable2.determinant() == -31
# non-invertable matrices
#not_invertable1.determinant()
#not_invertable2.determinant()
## base testing
assert equal(-I2, I2_neg), "Error in your __neg__ function"
assert equal(I2 + I2_neg, zero), "Error in your __add__ function"
assert equal(m1.T(), m1_transposed), "Error in your T function (transpose)"
assert equal(m1 * m2, m1_x_m2), "Error in your __mul__ function"
assert equal(m2 * m1, m2_x_m1), "Error in your __mul__ function"
assert equal(
m3.inverse(),
m3_inv), """Error in your inverse function for the 1 x 1 case"""
assert equal(
m1_x_m2.inverse(), m1_m2_inv
), """Error in your inverse function for the first 2 x 2 case"""
assert equal(
I2.inverse(),
I2), """Error in your inverse function for the second 2 x 2 case"""
assert equal(top_ones.T(),
left_ones), "Error in your T function (transpose)"
assert equal(left_ones.T(),
top_ones), "Error in your T function (transpose)"
assert equal(top_ones - left_ones.T(),
m.zeroes(2, 2)), "Error in your __sub__ function"
assert (4 * m.identity(5))[0][0] == 4, "Error in your __rmul__ function"
assert (4 * m.identity(5)).trace() == 20, "Error in your trace function"
assert type(-I2) == type(
I2_neg
), "Error: Your __neg__ function does not return a Matrix does not return a Matrix"
assert type(I2 + I2_neg) == type(
zero), "Error: Your __add__ function does not return a Matrix"
assert type(m1 * m2) == type(
m1_x_m2), "Error: Your __mul__ function does not return a Matrix"
assert type(m2 * m1) == type(
m2_x_m1), "Error: Your __mul__ function does not return a Matrix"
assert type(m3.inverse()) == type(
m3_inv
), """Error: Your inverse function for the 1 x 1 case does not return a Matrix"""
assert type(I2.inverse()) == type(
I2
), """Error: Your inverse function for the 2 x 2 case does not return a Matrix"""
assert type(top_ones.T()) == type(
left_ones
), "Error: Your T function (transpose) does not return a Matrix"
assert type(left_ones.T()) == type(
top_ones
), "Error: Your T function (transpose) does not return a Matrix"
assert type(top_ones - left_ones.T()) == type(m.zeroes(
2, 2)), "Error: Your __sub__ function does not return a Matrix"
print(
"Congratulations! All tests pass. Your Matrix class is working as expected."
)
