from sympy.mpmath import mnorm
from sympy.solvers import nsolve
from sympy.utilities.lambdify import lambdify
from sympy import Symbol, Matrix, sqrt, Eq

def test_nsolve():
    # onedimensional
    from sympy import Symbol, sin, pi
    x = Symbol('x')
    assert nsolve(sin(x), 2) - pi.evalf() < 1e-16
    assert nsolve(Eq(2*x, 2), x, -10) == nsolve(2*x - 2, -10)
    # 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((f1,  f2,  f3), (x,  y,  z), x0)
        assert mnorm(F(*root),1) <= 1.e-8
        return root
    assert map(round,  getroot((1,  1,  1))) == [2.0,  1.0,  0.0]