def test_equality(self):
real = 1
imaginary = 2
for precision in [10**-2, 10**-5, 10**-10]:
input_number = ComplexNumber(real, imaginary, precision=precision)
for imaginary_offset in [0, 1, -1]:
for real_offset in [0, 1, -1]:
if imaginary_offset == 0 and real_offset == 0:
continue
expected_in = ComplexNumber(
real + (0.9 * precision * real_offset),
imaginary + (0.9 * precision * imaginary_offset),
precision=precision)
expected_out = ComplexNumber(
real + (1.1 * precision * real_offset),
imaginary + (1.1 * precision * imaginary_offset),
precision=precision)
self.assertEqual(input_number, expected_in)
self.assertNotEqual(input_number, expected_out)
def test_divide_purely_real_numbers(self):
input_number = ComplexNumber(1.0, 0.0)
expected = ComplexNumber(0.5, 0.0)
divider = ComplexNumber(2.0, 0.0)
self.assertEqual(expected.real, input_number.div(divider).real)
self.assertEqual(expected.imaginary,
input_number.div(divider).imaginary)
def test_divide_numbers_with_real_and_imaginary_part(self):
input_number = ComplexNumber(1, 2)
expected = ComplexNumber(0.44, 0.08)
divider = ComplexNumber(3, 4)
self.assertEqual(input_number.div(divider).real, expected.real)
self.assertEqual(
input_number.div(divider).imaginary, expected.imaginary)
def test_divide_purely_imaginary_numbers(self):
input_number = ComplexNumber(0, 1)
expected = ComplexNumber(0.5, 0)
divider = ComplexNumber(0, 2)
self.assertEqual(input_number.div(divider).real, expected.real)
self.assertEqual(
input_number.div(divider).imaginary, expected.imaginary)
def test_absolute_value_of_a_positive_purely_real_number(self):
self.assertEqual(abs(ComplexNumber(5, 0)), 5)
def test_divide_purely_imaginary_numbers(self):
self.assertAlmostEqual(
ComplexNumber(0, 1) / ComplexNumber(0, 2), ComplexNumber(0.5, 0))
def test_multiply_numbers_with_real_and_imaginary_part(self):
self.assertEqual(
ComplexNumber(1, 2) * ComplexNumber(3, 4), ComplexNumber(-5, 10))
def test_multiply_purely_real_numbers(self):
self.assertEqual(
ComplexNumber(1, 0) * ComplexNumber(2, 0), ComplexNumber(2, 0))
def test_subtract_purely_imaginary_numbers(self):
self.assertEqual(
ComplexNumber(0, 1) - ComplexNumber(0, 2), ComplexNumber(0, -1))
def test_add_numbers_with_real_and_imaginary_part(self):
self.assertEqual(
ComplexNumber(1, 2) + ComplexNumber(3, 4), ComplexNumber(4, 6))
def test_exponential_of_a_purely_real_number(self):
self.assertAlmostEqual(
ComplexNumber(1, 0).exp(), ComplexNumber(math.e, 0))
def test_exponential_of_0(self):
self.assertAlmostEqual(ComplexNumber(0, 0).exp(), ComplexNumber(1, 0))
def test_euler_s_identity_formula(self):
self.assertAlmostEqual(
ComplexNumber(0, math.pi).exp(), ComplexNumber(-1, 0))
def test_conjugate_a_number_with_real_and_imaginary_part(self):
self.assertEqual(ComplexNumber(1, 1).conjugate(), ComplexNumber(1, -1))
def test_exponential_of_0(self):
input_number = ComplexNumber(0, 0)
expected = ComplexNumber(1, 0)
self.assertEqual(input_number.exp().real, expected.real)
self.assertEqual(input_number.exp().imaginary, expected.imaginary)
def test_conjugate_a_number_with_real_and_imaginary_part(self):
input_number = ComplexNumber(1, 1)
expected = ComplexNumber(1, -1)
self.assertEqual(input_number.conjugate().real, expected.real)
self.assertEqual(input_number.conjugate().imaginary,
expected.imaginary)
def test_exponential_of_a_purely_real_number(self):
input_number = ComplexNumber(1, 0)
expected = ComplexNumber(math.e, 0)
actual = input_number.exp()
self.assertAlmostEqual(actual.real, expected.real)
self.assertAlmostEqual(actual.imaginary, expected.imaginary)
def test_real_part_of_a_purely_real_number(self):
self.assertEqual(ComplexNumber(1, 0).real, 1)
def test_add_purely_imaginary_numbers(self):
self.assertEqual(
ComplexNumber(0, 1) + ComplexNumber(0, 2), ComplexNumber(0, 3))
def test_exponential_of_a_number_with_real_and_imaginary_part(self):
self.assertAlmostEqual(
ComplexNumber(math.log(2), math.pi).exp(), ComplexNumber(-2, 0))
def test_subtract_purely_real_numbers(self):
self.assertEqual(
ComplexNumber(1, 0) - ComplexNumber(2, 0), ComplexNumber(-1, 0))
def test_equality_of_complex_numbers(self):
self.assertEqual(ComplexNumber(1, 2), ComplexNumber(1, 2))
def test_subtract_numbers_with_real_and_imaginary_part(self):
self.assertEqual(
ComplexNumber(1, 2) - ComplexNumber(3, 4), ComplexNumber(-2, -2))
def test_inequality_of_real_part(self):
self.assertNotEqual(ComplexNumber(1, 2), ComplexNumber(2, 2))
def test_multiply_purely_imaginary_numbers(self):
self.assertEqual(
ComplexNumber(0, 1) * ComplexNumber(0, 2), ComplexNumber(-2, 0))
def test_inequality_of_imaginary_part(self):
self.assertNotEqual(ComplexNumber(1, 2), ComplexNumber(1, 1))
def test_divide_purely_real_numbers(self):
self.assertAlmostEqual(
ComplexNumber(1, 0) / ComplexNumber(2, 0), ComplexNumber(0.5, 0))
def test_imaginary_part_of_a_purely_real_number(self):
self.assertEqual(ComplexNumber(1, 0).imaginary, 0)
def test_divide_numbers_with_real_and_imaginary_part(self):
self.assertAlmostEqual(
ComplexNumber(1, 2) / ComplexNumber(3, 4),
ComplexNumber(0.44, 0.08))
def test_imaginary_part_of_a_purely_imaginary_number(self):
self.assertEqual(ComplexNumber(0, 1).imaginary, 1)
def test_conjugate_a_purely_imaginary_number(self):
input_number = ComplexNumber(0, 5)
expected = ComplexNumber(0, -5)
self.assertEqual(input_number.conjugate().real, expected.real)
self.assertEqual(input_number.conjugate().imaginary,
expected.imaginary)
def test_imaginary_part_of_a_number_with_real_and_imaginary_part(self):
self.assertEqual(ComplexNumber(1, 2).imaginary, 2)
def test_eulers_identity_formula(self):
input_number = ComplexNumber(0, math.pi)
expected = ComplexNumber(-1, 0)
actual = input_number.exp()
self.assertAlmostEqual(actual.real, expected.real)
self.assertAlmostEqual(actual.imaginary, expected.imaginary)
def test_imaginary_unit(self):
self.assertEqual(
ComplexNumber(0, 1) * ComplexNumber(0, 1), ComplexNumber(-1, 0))
def test_exponential_of_a_number_with_real_and_imaginary_part(self):
input_number = ComplexNumber(math.log(2), math.pi)
expected = ComplexNumber(-2, 0)
actual = input_number.exp()
self.assertAlmostEqual(actual.real, expected.real)
self.assertAlmostEqual(actual.imaginary, expected.imaginary)
def test_add_purely_real_numbers(self):
self.assertEqual(
ComplexNumber(1, 0) + ComplexNumber(2, 0), ComplexNumber(3, 0))
