def test_continued_fraction_golden_ratio(self):
golden_ratio = (1 + math.sqrt(5)) / 2
expected = [1] * 40
result = list(contfrac.continued_fraction(golden_ratio, maxlen=2))
self.assertListEqual(expected[:2], result)
result = list(contfrac.continued_fraction(golden_ratio, maxlen=20))
self.assertListEqual(expected[:20], result)
result = list(contfrac.continued_fraction(golden_ratio, maxlen=31))
self.assertListEqual(expected[:31], result)
def test_rounding_errors(self):
golden_ratio = (1 + math.sqrt(5)) / 2
as_ratio = golden_ratio.as_integer_ratio()
result = list(contfrac.continued_fraction(golden_ratio, maxlen=50))
self.assertNotEqual([1] * 50, result)
evaluated_value = contfrac.evaluate(result)
self.assertEqual(golden_ratio, evaluated_value)
result = list(contfrac.continued_fraction(as_ratio, maxlen=50))
self.assertNotEqual([1] * 50, result)
evaluated_value = contfrac.evaluate(result)
self.assertEqual(as_ratio, evaluated_value.as_integer_ratio())
def get_alpha_1_2(alpha):
coefficients = list(contfrac.continued_fraction(alpha))
alpha_1 = contfrac_to_fraction(coefficients[:-1])
coefficients[-1] -= 1
alpha_2 = contfrac_to_fraction(coefficients)
return alpha_1, alpha_2
def test_example_irrational(self):
import contfrac
import math
coefficients = list(contfrac.continued_fraction(math.e, maxlen=10))
print(coefficients)
convergent = contfrac.convergent(math.e, 3)
print(convergent, convergent[0] / convergent[1], math.e)
convergent = contfrac.convergent(math.e, 7)
print(convergent, convergent[0] / convergent[1], math.e)
def test_continued_fraction_illegal_maxlen(self):
self.assertRaises(ValueError,
contfrac.continued_fraction,
2.2,
maxlen=-1)
self.assertRaises(ValueError,
contfrac.continued_fraction,
2.2,
maxlen=0)
list(contfrac.continued_fraction(2.2, maxlen=1))
def test_example_high_accuracy(self):
import contfrac
value = (415, 93)
coefficients = list(contfrac.continued_fraction(value))
print(coefficients)
expression = contfrac.arithmetical_expr(coefficients)
print('Value: {:} = {:s}'.format(value, expression))
eval_value = contfrac.evaluate(coefficients)
print(eval_value, value[0] / value[1])
convergents = list(contfrac.convergents(value))
print(convergents)
def test_example_usage_as_in_readme(self):
import contfrac
value = 415 / 93
coefficients = list(contfrac.continued_fraction(value))
print(coefficients)
expression = contfrac.arithmetical_expr(coefficients)
print('Value: {:f} = {:s}'.format(value, expression))
eval_value = contfrac.evaluate(coefficients)
print(eval_value, value)
convergents = list(contfrac.convergents(value))
print(convergents)
def test_continued_fraction_legal_values(self):
test_values = {
# Integers
0: [0],
1: [1],
123: [123],
-1: [-1],
-123: [-123],
# Tuples: (nominator, denominator)
(649, 200): [3, 4, 12, 4],
(415, 93): [4, 2, 6, 7],
(-649, 200): [-4, 1, 3, 12, 4],
(415, -93): [-5, 1, 1, 6, 7],
# Fractions
fractions.Fraction(649, 200): [3, 4, 12, 4],
fractions.Fraction(415, 93): [4, 2, 6, 7],
fractions.Fraction(-649, 200): [-4, 1, 3, 12, 4],
fractions.Fraction(415, -93): [-5, 1, 1, 6, 7],
# Floats
649 / 200: [3, 4, 12, 4],
-649 / 200: [-3, -4, -12, -4],
415 / 93: [4, 2, 6, 7],
0.84375: [0, 1, 5, 2, 2],
}
for input_value, expected_output in test_values.items():
with self.subTest(contfrac_of=input_value):
result = list(contfrac.continued_fraction(input_value))
self.assertListEqual(expected_output, result)
with self.subTest(evaluating_contfrac_of=input_value):
if isinstance(input_value, tuple):
input_value = input_value[0] / input_value[1]
elif isinstance(input_value, fractions.Fraction):
input_value = float(input_value)
evaluated = contfrac.evaluate(result)
self.assertAlmostEqual(input_value, evaluated, delta=1e-8)
print("\tMean eq. year without adjustment = {} days, {} hours, {} minutes, {} seconds\n".format(dd,hh,mm,ss))
approx = (days + adjust) / float(years)
print("\tAdjusted days =", days + adjust)
print("\tbasetup =", basetup)
print("\tendtup =", endtup)
print("\tDecimal mean eq. year =", approx)
frac = (days + adjust) / float(years)
dd, hh, mm, ss = frac2dhms(frac)
print(("Mean eq. year = {} days, "
"{} hours, "
"{} minutes, "
"{} seconds").format(dd,hh,mm,ss))
contfrac.main(frac)
fmt = ("\tx ~= p / q = {p:10} / {q:10} = {d:03} "
"{h:02}:{m:02}:{s:07.4f} "
", p days modulo 7 = {r:1}")
print("\nContinued fraction approximations in DHMS form:")
for a, p, q in contfrac.continued_fraction(frac):
d, h, m, s = frac2dhms(p / float(q))
r = p % 7
print(fmt.format(p=p, q=q, d=d, h=h, m=m, s=s, r=r))
print(
"\tMean eq. year without adjustment = {} days, {} hours, {} minutes, {} seconds\n"
.format(dd, hh, mm, ss))
approx = (days + adjust) / float(years)
print("\tAdjusted days =", days + adjust)
print("\tbasetup =", basetup)
print("\tendtup =", endtup)
print("\tDecimal mean eq. year =", approx)
frac = (days + adjust) / float(years)
dd, hh, mm, ss = frac2dhms(frac)
print(("Mean eq. year = {} days, "
"{} hours, "
"{} minutes, "
"{} seconds").format(dd, hh, mm, ss))
contfrac.main(frac)
fmt = ("\tx ~= p / q = {p:10} / {q:10} = {d:03} "
"{h:02}:{m:02}:{s:07.4f} "
", p days modulo 7 = {r:1}")
print("\nContinued fraction approximations in DHMS form:")
for a, p, q in contfrac.continued_fraction(frac):
d, h, m, s = frac2dhms(p / float(q))
r = p % 7
print(fmt.format(p=p, q=q, d=d, h=h, m=m, s=s, r=r))
def test_continued_fraction_is_generators(self):
result = contfrac.continued_fraction(1)
self.assertIsInstance(result, typing.Generator)
