programmers-introduction-to-mathematics/newtons_method/newton_test.py at master · pim-book/programmers-introduction-to-mathematics · GitHub

Name: programmers-introduction-to-mathematics/newtons_method/newton_test.py at master · pim-book/programmers-introduction-to-mathematics · GitHub
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fromitertoolsimporttakewhile
fromassertpyimportassert_that

fromnewtonimportnewton_sequence

EPSILON=1e-4


deftest_newtons_sequence_converge():
deff(x):
returnx**5-x-1

deff_derivative(x):
return5*x**4-1

starting_x=1

approximation= [
 (x, f(x))
forxinlist(newton_sequence(f, f_derivative, starting_x))
 ]

assert_that(approximation[-1][0]).is_close_to(1.1673, EPSILON)
assert_that(approximation[-1][1]).is_close_to(0, EPSILON)


deftest_newtons_sequence_fails_to_converge():
deff(x):
returnx**5-x-1

deff_derivative(x):
return5*x**4-1

starting_x=0
approximation= [
 (x, f(x)) for (i, x) intakewhile(
lambdaz: z[0] <10000,
enumerate(newton_sequence(f, f_derivative, starting_x))
 )
 ]

for (x, y) inapproximation:
assert_that(abs(x-1.1673)).is_greater_than(EPSILON)
assert_that(abs(y)).is_greater_than(EPSILON)


deftest_newtons_sequence_converges_large_root():
deff(x):
return (x-100)**5- (x-100) -1

deff_derivative(x):
return5* (x-100)**4-1

starting_x=103

approximation= [
 (x, f(x))
forxinlist(newton_sequence(f, f_derivative, starting_x))
 ]

assert_that(approximation[-1][0]).is_close_to(101.1673, EPSILON)
assert_that(approximation[-1][1]).is_close_to(0, EPSILON)