140 lines
4.6 KiB
Python
140 lines
4.6 KiB
Python
from sympy.core.function import nfloat
|
|
from sympy.core.numbers import (Float, I, Rational, pi)
|
|
from sympy.core.relational import Eq
|
|
from sympy.core.symbol import (Symbol, symbols)
|
|
from sympy.functions.elementary.miscellaneous import sqrt
|
|
from sympy.functions.elementary.piecewise import Piecewise
|
|
from sympy.functions.elementary.trigonometric import sin
|
|
from sympy.integrals.integrals import Integral
|
|
from sympy.matrices.dense import Matrix
|
|
from mpmath import mnorm, mpf
|
|
from sympy.solvers import nsolve
|
|
from sympy.utilities.lambdify import lambdify
|
|
from sympy.testing.pytest import raises, XFAIL
|
|
from sympy.utilities.decorator import conserve_mpmath_dps
|
|
|
|
@XFAIL
|
|
def test_nsolve_fail():
|
|
x = symbols('x')
|
|
# Sometimes it is better to use the numerator (issue 4829)
|
|
# but sometimes it is not (issue 11768) so leave this to
|
|
# the discretion of the user
|
|
ans = nsolve(x**2/(1 - x)/(1 - 2*x)**2 - 100, x, 0)
|
|
assert ans > 0.46 and ans < 0.47
|
|
|
|
|
|
def test_nsolve_denominator():
|
|
x = symbols('x')
|
|
# Test that nsolve uses the full expression (numerator and denominator).
|
|
ans = nsolve((x**2 + 3*x + 2)/(x + 2), -2.1)
|
|
# The root -2 was divided out, so make sure we don't find it.
|
|
assert ans == -1.0
|
|
|
|
def test_nsolve():
|
|
# onedimensional
|
|
x = Symbol('x')
|
|
assert nsolve(sin(x), 2) - pi.evalf() < 1e-15
|
|
assert nsolve(Eq(2*x, 2), x, -10) == nsolve(2*x - 2, -10)
|
|
# Testing checks on number of inputs
|
|
raises(TypeError, lambda: nsolve(Eq(2*x, 2)))
|
|
raises(TypeError, lambda: nsolve(Eq(2*x, 2), x, 1, 2))
|
|
# multidimensional
|
|
x1 = Symbol('x1')
|
|
x2 = Symbol('x2')
|
|
f1 = 3 * x1**2 - 2 * x2**2 - 1
|
|
f2 = x1**2 - 2 * x1 + x2**2 + 2 * x2 - 8
|
|
f = Matrix((f1, f2)).T
|
|
F = lambdify((x1, x2), f.T, modules='mpmath')
|
|
for x0 in [(-1, 1), (1, -2), (4, 4), (-4, -4)]:
|
|
x = nsolve(f, (x1, x2), x0, tol=1.e-8)
|
|
assert mnorm(F(*x), 1) <= 1.e-10
|
|
# The Chinese mathematician Zhu Shijie was the very first to solve this
|
|
# nonlinear system 700 years ago (z was added to make it 3-dimensional)
|
|
x = Symbol('x')
|
|
y = Symbol('y')
|
|
z = Symbol('z')
|
|
f1 = -x + 2*y
|
|
f2 = (x**2 + x*(y**2 - 2) - 4*y) / (x + 4)
|
|
f3 = sqrt(x**2 + y**2)*z
|
|
f = Matrix((f1, f2, f3)).T
|
|
F = lambdify((x, y, z), f.T, modules='mpmath')
|
|
|
|
def getroot(x0):
|
|
root = nsolve(f, (x, y, z), x0)
|
|
assert mnorm(F(*root), 1) <= 1.e-8
|
|
return root
|
|
assert list(map(round, getroot((1, 1, 1)))) == [2, 1, 0]
|
|
assert nsolve([Eq(
|
|
f1, 0), Eq(f2, 0), Eq(f3, 0)], [x, y, z], (1, 1, 1)) # just see that it works
|
|
a = Symbol('a')
|
|
assert abs(nsolve(1/(0.001 + a)**3 - 6/(0.9 - a)**3, a, 0.3) -
|
|
mpf('0.31883011387318591')) < 1e-15
|
|
|
|
|
|
def test_issue_6408():
|
|
x = Symbol('x')
|
|
assert nsolve(Piecewise((x, x < 1), (x**2, True)), x, 2) == 0.0
|
|
|
|
|
|
def test_issue_6408_integral():
|
|
x, y = symbols('x y')
|
|
assert nsolve(Integral(x*y, (x, 0, 5)), y, 2) == 0.0
|
|
|
|
|
|
@conserve_mpmath_dps
|
|
def test_increased_dps():
|
|
# Issue 8564
|
|
import mpmath
|
|
mpmath.mp.dps = 128
|
|
x = Symbol('x')
|
|
e1 = x**2 - pi
|
|
q = nsolve(e1, x, 3.0)
|
|
|
|
assert abs(sqrt(pi).evalf(128) - q) < 1e-128
|
|
|
|
def test_nsolve_precision():
|
|
x, y = symbols('x y')
|
|
sol = nsolve(x**2 - pi, x, 3, prec=128)
|
|
assert abs(sqrt(pi).evalf(128) - sol) < 1e-128
|
|
assert isinstance(sol, Float)
|
|
|
|
sols = nsolve((y**2 - x, x**2 - pi), (x, y), (3, 3), prec=128)
|
|
assert isinstance(sols, Matrix)
|
|
assert sols.shape == (2, 1)
|
|
assert abs(sqrt(pi).evalf(128) - sols[0]) < 1e-128
|
|
assert abs(sqrt(sqrt(pi)).evalf(128) - sols[1]) < 1e-128
|
|
assert all(isinstance(i, Float) for i in sols)
|
|
|
|
def test_nsolve_complex():
|
|
x, y = symbols('x y')
|
|
|
|
assert nsolve(x**2 + 2, 1j) == sqrt(2.)*I
|
|
assert nsolve(x**2 + 2, I) == sqrt(2.)*I
|
|
|
|
assert nsolve([x**2 + 2, y**2 + 2], [x, y], [I, I]) == Matrix([sqrt(2.)*I, sqrt(2.)*I])
|
|
assert nsolve([x**2 + 2, y**2 + 2], [x, y], [I, I]) == Matrix([sqrt(2.)*I, sqrt(2.)*I])
|
|
|
|
def test_nsolve_dict_kwarg():
|
|
x, y = symbols('x y')
|
|
# one variable
|
|
assert nsolve(x**2 - 2, 1, dict = True) == \
|
|
[{x: sqrt(2.)}]
|
|
# one variable with complex solution
|
|
assert nsolve(x**2 + 2, I, dict = True) == \
|
|
[{x: sqrt(2.)*I}]
|
|
# two variables
|
|
assert nsolve([x**2 + y**2 - 5, x**2 - y**2 + 1], [x, y], [1, 1], dict = True) == \
|
|
[{x: sqrt(2.), y: sqrt(3.)}]
|
|
|
|
def test_nsolve_rational():
|
|
x = symbols('x')
|
|
assert nsolve(x - Rational(1, 3), 0, prec=100) == Rational(1, 3).evalf(100)
|
|
|
|
|
|
def test_issue_14950():
|
|
x = Matrix(symbols('t s'))
|
|
x0 = Matrix([17, 23])
|
|
eqn = x + x0
|
|
assert nsolve(eqn, x, x0) == nfloat(-x0)
|
|
assert nsolve(eqn.T, x.T, x0.T) == nfloat(-x0)
|