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]
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]
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)
# Testing checks on number of inputs
raises(TypeError, "nsolve(Eq(2*x,2))")
raises(TypeError, "nsolve(Eq(2*x,2),x,1,2)")
# Issue 1730
assert nsolve(x**2 / (1 - x) / (1 - 2 * x)**2 - 100, x, 0) # doesn't fail
# 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]
assert nsolve([Eq(f1), Eq(f2), Eq(f3)], [x, y, z],
(1, 1, 1)) # just see that it works
a = Symbol('a')
assert nsolve(1 / (0.001 + a)**3 - 6 / (0.9 - a)**3, a,
0.3).ae(mpf('0.31883011387318591'))
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))
# issue 4829
assert nsolve(x**2/(1 - x)/(1 - 2*x)**2 - 100, x, 0) # doesn't fail
# 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)))) == [2.0, 1.0, 0.0]
assert nsolve([Eq(
f1), Eq(f2), Eq(f3)], [x, y, z], (1, 1, 1)) # just see that it works
a = Symbol('a')
assert nsolve(1/(0.001 + a)**3 - 6/(0.9 - a)**3, a, 0.3).ae(
mpf('0.31883011387318591'))
def getroot(x0):
root = nsolve(f, (x, y, z), x0)
assert mnorm(F(*root), 1) <= 1.e-8
return root
def getroot(x0):
root = nsolve(f, (x, y, z), x0)
assert mnorm(F(*root), 1) <= 1.e-8
return root
def getroot(x0):
root = nsolve((f1, f2, f3), (x, y, z), x0)
assert mnorm(F(*root), 1) <= 1.0e-8
return root