test_math.py

import unittest

from algorithms.math.approx_cdf import cdf
from algorithms.math.extended_gcd import extended_gcd
from algorithms.math.lcm import lcm
from algorithms.math.primality_test import is_prime
from algorithms.math.sieve_atkin import atkin
from algorithms.math.sieve_eratosthenes import eratosthenes
from algorithms.math.std_normal_pdf import pdf


class TestApproxCdf(unittest.TestCase):

    def test_cdf(self):
        # Calculate cumulative distribution function for x=1
        a = cdf(1)
        self.assertAlmostEqual(a, 0.841344746068543)

        # Calculate cumulative distribution function x=0
        a = cdf(0)
        self.assertAlmostEqual(a, 0.5)

        # Calculate cumulative distribution function for x=(-1)
        a = cdf(-1)
        self.assertAlmostEqual(a, 0.15865525393145702)


class TestExtendedGCD(unittest.TestCase):

    def test_extended_gcd(self):
        # Find extended_gcd of 35 and 77
        (a, b) = extended_gcd(35, 77)
        print(a, b)
        self.assertIs(35 * a + 77 * b, 7)

        # Find extended_gcd of 15 and 19
        (a, b) = extended_gcd(15, 19)
        self.assertIs(15 * a + 19 * b, 1)

        # Find extended_gcd of 18 and 9
        (a, b) = extended_gcd(18, 9)
        self.assertIs(18 * a + 9 * b, 9)

        # Find extended_gcd of 99 and 81
        (a, b) = extended_gcd(99, 81)
        self.assertIs(99 * a + 81 * b, 9)

        # Find extended_gcd of 50 and 15
        (a, b) = extended_gcd(50, 15)
        self.assertIs(50 * a + 15 * b, 5)


class TestLCM(unittest.TestCase):
    def test_lcm(self):
        # Find lcm of (16, 20) and (20, 16)
        r, r2 = lcm(16, 20), lcm(20, 16)
        self.assertEqual(r, 80)

        # Checks that lcm function is commutative
        self.assertEqual(r, r2)


class TestPrimalityTest(unittest.TestCase):
    def test_is_prime(self):
        self.assertIs(is_prime(3), True)
        self.assertIs(is_prime(15), False)
        self.assertIs(is_prime(20), False)
        self.assertIs(is_prime(37), True)
        self.assertIs(is_prime(63), False)
        self.assertIs(is_prime(87), False)
        self.assertIs(is_prime(103), True)


class TestSieveOfAtkin(unittest.TestCase):

    def test_atkin(self):
        rv1 = atkin(10)
        rv2 = atkin(100)
        rv3 = atkin(1000)
        rv4 = atkin(-10)
        self.assertEqual(rv1, [2, 3, 5, 7])
        self.assertEqual(
            rv2,
            [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
             61, 67, 71, 73, 79, 83, 89, 97]
        )
        self.assertEqual(
            rv3,
            [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
             61, 67, 71, 73, 79, 83, 89, 97,  101, 103, 107, 109, 113, 127,
             131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193,
             197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269,
             271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
             353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431,
             433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
             509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599,
             601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673,
             677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761,
             769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857,
             859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947,
             953, 967, 971, 977, 983, 991, 997]
        )
        self.assertEqual(rv4, [])


class TestSieveOfEratosthenes(unittest.TestCase):

    def test_eratosthenes(self):
        rv1 = eratosthenes(-10)
        rv2 = eratosthenes(10)
        rv3 = eratosthenes(100, 5)
        rv4 = eratosthenes(100, -10)
        self.assertEqual(rv1, [])
        self.assertEqual(rv2, [2, 3, 5, 7])
        self.assertEqual(
            rv3,
            [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
             67, 71, 73, 79, 83, 89, 97]
        )
        self.assertEqual(
            rv4,
            [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
             61, 67, 71, 73, 79, 83, 89, 97]
        )


class TestStdNormPDF(unittest.TestCase):

    def test_pdf(self):
        # Calculate standard normal pdf for x=1
        a = pdf(1)
        self.assertAlmostEqual(a, 0.24197072451914337)

        # Calculate standard normal pdf for x=(-1)
        a = pdf(-1)
        self.assertAlmostEqual(a, 0.24197072451914337)

        # Calculate standard normal pdf for x=13, mean=10, std_dev=1
        a = pdf(x=13, mean=10, std_dev=1)
        self.assertAlmostEqual(a, 0.004431848411938008)