/usr/lib/python2.7/dist-packages/mpmath/tests/test_rootfinding.py is in python-mpmath 0.19-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 | from mpmath import *
from mpmath.calculus.optimization import Secant, Muller, Bisection, Illinois, \
Pegasus, Anderson, Ridder, ANewton, Newton, MNewton, MDNewton
def test_findroot():
# old tests, assuming secant
mp.dps = 15
assert findroot(lambda x: 4*x-3, mpf(5)).ae(0.75)
assert findroot(sin, mpf(3)).ae(pi)
assert findroot(sin, (mpf(3), mpf(3.14))).ae(pi)
assert findroot(lambda x: x*x+1, mpc(2+2j)).ae(1j)
# test all solvers with 1 starting point
f = lambda x: cos(x)
for solver in [Newton, Secant, MNewton, Muller, ANewton]:
x = findroot(f, 2., solver=solver)
assert abs(f(x)) < eps
# test all solvers with interval of 2 points
for solver in [Secant, Muller, Bisection, Illinois, Pegasus, Anderson,
Ridder]:
x = findroot(f, (1., 2.), solver=solver)
assert abs(f(x)) < eps
# test types
f = lambda x: (x - 2)**2
#assert isinstance(findroot(f, 1, force_type=mpf, tol=1e-10), mpf)
#assert isinstance(findroot(f, 1., force_type=None, tol=1e-10), float)
#assert isinstance(findroot(f, 1, force_type=complex, tol=1e-10), complex)
assert isinstance(fp.findroot(f, 1, tol=1e-10), float)
assert isinstance(fp.findroot(f, 1+0j, tol=1e-10), complex)
def test_bisection():
# issue 273
assert findroot(lambda x: x**2-1,(0,2),solver='bisect') == 1
def test_mnewton():
f = lambda x: polyval([1,3,3,1],x)
x = findroot(f, -0.9, solver='mnewton')
assert abs(f(x)) < eps
def test_anewton():
f = lambda x: (x - 2)**100
x = findroot(f, 1., solver=ANewton)
assert abs(f(x)) < eps
def test_muller():
f = lambda x: (2 + x)**3 + 2
x = findroot(f, 1., solver=Muller)
assert abs(f(x)) < eps
def test_multiplicity():
for i in range(1, 5):
assert multiplicity(lambda x: (x - 1)**i, 1) == i
assert multiplicity(lambda x: x**2, 1) == 0
def test_multidimensional():
def f(*x):
return [3*x[0]**2-2*x[1]**2-1, x[0]**2-2*x[0]+x[1]**2+2*x[1]-8]
assert mnorm(jacobian(f, (1,-2)) - matrix([[6,8],[0,-2]]),1) < 1.e-7
for x, error in MDNewton(mp, f, (1,-2), verbose=0,
norm=lambda x: norm(x, inf)):
pass
assert norm(f(*x), 2) < 1e-14
# The Chinese mathematician Zhu Shijie was the very first to solve this
# nonlinear system 700 years ago
f1 = lambda x, y: -x + 2*y
f2 = lambda x, y: (x**2 + x*(y**2 - 2) - 4*y) / (x + 4)
f3 = lambda x, y: sqrt(x**2 + y**2)
def f(x, y):
f1x = f1(x, y)
return (f2(x, y) - f1x, f3(x, y) - f1x)
x = findroot(f, (10, 10))
assert [int(round(i)) for i in x] == [3, 4]
def test_trivial():
assert findroot(lambda x: 0, 1) == 1
assert findroot(lambda x: x, 0) == 0
#assert findroot(lambda x, y: x + y, (1, -1)) == (1, -1)
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