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test_lambdify.py
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test_lambdify.py
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from sympy.utilities.pytest import XFAIL
from sympy import symbols, lambdify, sqrt, sin, cos, pi, atan, Rational, Real, Matrix
from sympy import mpmath
import math, sympy
# high precision output of sin(0.2*pi) is used to detect if precision is lost unwanted
mpmath.mp.dps = 50
sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
x,y,z = symbols('xyz')
#================== Test different arguments ==============
def test_no_args():
f = lambdify([], 1)
try:
f(-1)
raise Exception()
except TypeError:
pass
assert f() == 1
def test_single_arg():
f = lambdify(x, 2*x)
assert f(1) == 2
def test_list_args():
f = lambdify([x,y], x+y)
assert f(1,2) == 3
def test_str_args():
f = lambdify('x,y,z', 'z,y,x')
assert f(3,2,1) == (1,2,3)
assert f(1.0,2.0,3.0) == (3.0,2.0,1.0)
# make sure correct number of args required
try:
f(0)
raise Exception()
except TypeError:
pass
def test_own_namespace():
myfunc = lambda x:1
f = lambdify(x, sin(x), {"sin":myfunc})
assert f(0.1) == 1
assert f(100) == 1
def test_own_module():
f = lambdify(x, sin(x), math)
assert f(0)==0.0
f = lambdify(x, sympy.ceiling(x), math)
try:
f(4.5)
raise Exception
except NameError:
pass
def test_bad_args():
try:
# no vargs given
f = lambdify(1)
raise Exception()
except TypeError:
pass
try:
# same with vector exprs
f = lambdify([1,2])
raise Exception()
except TypeError:
pass
#================== Test different modules ================
def test_sympy_lambda():
f = lambdify(x, sin(x), "sympy")
assert f(x) is sin(x)
prec = 1e-15
assert -prec < f(Rational(1,5)).evalf() - Real(str(sin02)) < prec
try:
# arctan is in numpy module and should not be available
f = lambdify(x, arctan(x), "sympy")
raise Exception
except NameError:
pass
def test_math_lambda():
f = lambdify(x, sin(x), "math")
prec = 1e-15
assert -prec < f(0.2) - sin02 < prec
try:
f(x) # if this succeeds, it can't be a python math function
raise Exception
except ValueError:
pass
def test_mpmath_lambda():
f = lambdify(x, sin(x), "mpmath")
prec = 1e-49 # mpmath precision is around 50 decimal places
assert -prec < f(mpmath.mpf("0.2")) - sin02 < prec
try:
f(x) # if this succeeds, it can't be a mpmath function
raise Exception
except TypeError:
pass
@XFAIL
def test_number_precision():
f = lambdify(x, sin02, "mpmath")
prec = 1e-49 # mpmath precision is around 50 decimal places
assert -prec < f(0) - sin02 < prec
#================== Test Translations =====================
# We can only check if all translated functions are valid. It has to be checked
# by hand if they are complete.
def test_math_transl():
from sympy.utilities.lambdify import MATH_TRANSLATIONS
for sym, mat in MATH_TRANSLATIONS.iteritems():
assert sym in sympy.functions.__dict__
assert mat in math.__dict__
def test_mpmath_transl():
from sympy.utilities.lambdify import MPMATH_TRANSLATIONS
for sym, mat in MPMATH_TRANSLATIONS.iteritems():
assert sym in sympy.functions.__dict__
assert mat in mpmath.__dict__
#================== Test some functions ===================
def test_exponentiation():
f = lambdify(x, x**2)
assert f(-1) == 1
assert f(0) == 0
assert f(1) == 1
assert f(-2) == 4
assert f(2) == 4
assert f(2.5) == 6.25
def test_sqrt():
f = lambdify(x, sqrt(x))
assert f(0) == 0.0
assert f(1) == 1.0
assert f(4) == 2.0
assert abs(f(2) - 1.414) < 0.001
assert f(6.25) == 2.5
try:
f(-1)
raise Exception()
except ValueError: pass
def test_trig():
f = lambdify([x], [cos(x),sin(x)])
d = f(pi)
prec = 1e-11
assert -prec < d[0]+1 < prec
assert -prec < d[1] < prec
d = f(3.14159)
prec = 1e-5
assert -prec < d[0]+1 < prec
assert -prec < d[1] < prec
#================== Test vectors ==========================
def test_vector_simple():
f = lambdify((x,y,z), (z,y,x))
assert f(3,2,1) == (1,2,3)
assert f(1.0,2.0,3.0) == (3.0,2.0,1.0)
# make sure correct number of args required
try:
f(0)
raise Exception()
except TypeError: pass
def test_vector_discontinuous():
f = lambdify(x, (-1/x, 1/x))
try:
f(0)
raise Exception()
except ZeroDivisionError: pass
assert f(1) == (-1.0, 1.0)
assert f(2) == (-0.5, 0.5)
assert f(-2) == (0.5, -0.5)
def test_trig_symbolic():
f = lambdify([x], [cos(x),sin(x)])
d = f(pi)
assert abs(d[0]+1) < 0.0001
assert abs(d[1]-0) < 0.0001
def test_trig_float():
f = lambdify([x], [cos(x),sin(x)])
d = f(3.14159)
assert abs(d[0]+1) < 0.0001
assert abs(d[1]-0) < 0.0001
def test_docs():
f = lambdify(x, x**2)
assert f(2) == 4
f = lambdify([x,y,z], [z,y,x])
assert f(1, 2, 3) == [3, 2, 1]
f = lambdify(x, sqrt(x))
assert f(4) == 2.0
f = lambdify((x,y), sin(x*y)**2)
assert f(0, 5) == 0
def test_math():
f = lambdify((x, y), sin(x), modules="math")
assert f(0, 5) == 0
def test_sin():
f = lambdify(x, sin(x)**2)
assert isinstance(f(2), float)
f = lambdify(x, sin(x)**2, modules="math")
assert isinstance(f(2), float)
def test_matrix():
A = Matrix([[x, x*y], [sin(z)+4, x**z]])
sol = Matrix([[1, 2], [sin(3)+4, 1]])
f = lambdify((x,y,z), A, modules="sympy")
assert f(1,2,3) == sol
f = lambdify((x,y,z), (A, [A]), modules="sympy")
assert f(1,2,3) == (sol,[sol])