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import pytest
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, tol=1e-10), mpf)
assert isinstance(iv.findroot(f, 1., tol=1e-10), iv.mpf)
assert isinstance(fp.findroot(f, 1, tol=1e-10), float)
assert isinstance(fp.findroot(f, 1+0j, tol=1e-10), complex)
# issue 401
with pytest.raises(ValueError):
with workprec(2):
findroot(lambda x: x**2 - 4456178*x + 60372201703370,
mpc(real='5.278e+13', imag='-5.278e+13'))
# issue 192
with pytest.raises(ValueError):
findroot(lambda x: -1, 0)
# issue 387
with pytest.raises(ValueError):
findroot(lambda p: (1 - p)**30 - 1, 0.9)
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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