You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
1863 lines
58 KiB
1863 lines
58 KiB
from itertools import product
|
|
import math
|
|
import inspect
|
|
|
|
|
|
|
|
import mpmath
|
|
from sympy.testing.pytest import raises, warns_deprecated_sympy
|
|
from sympy.concrete.summations import Sum
|
|
from sympy.core.function import (Function, Lambda, diff)
|
|
from sympy.core.numbers import (E, Float, I, Rational, oo, pi)
|
|
from sympy.core.relational import Eq
|
|
from sympy.core.singleton import S
|
|
from sympy.core.symbol import (Dummy, symbols)
|
|
from sympy.functions.combinatorial.factorials import (RisingFactorial, factorial)
|
|
from sympy.functions.combinatorial.numbers import bernoulli, harmonic
|
|
from sympy.functions.elementary.complexes import Abs
|
|
from sympy.functions.elementary.exponential import exp, log
|
|
from sympy.functions.elementary.hyperbolic import acosh
|
|
from sympy.functions.elementary.integers import floor
|
|
from sympy.functions.elementary.miscellaneous import (Max, Min, sqrt)
|
|
from sympy.functions.elementary.piecewise import Piecewise
|
|
from sympy.functions.elementary.trigonometric import (acos, cos, cot, sin,
|
|
sinc, tan)
|
|
from sympy.functions.special.bessel import (besseli, besselj, besselk, bessely)
|
|
from sympy.functions.special.beta_functions import (beta, betainc, betainc_regularized)
|
|
from sympy.functions.special.delta_functions import (Heaviside)
|
|
from sympy.functions.special.error_functions import (Ei, erf, erfc, fresnelc, fresnels, Si, Ci)
|
|
from sympy.functions.special.gamma_functions import (digamma, gamma, loggamma, polygamma)
|
|
from sympy.integrals.integrals import Integral
|
|
from sympy.logic.boolalg import (And, false, ITE, Not, Or, true)
|
|
from sympy.matrices.expressions.dotproduct import DotProduct
|
|
from sympy.tensor.array import derive_by_array, Array
|
|
from sympy.tensor.indexed import IndexedBase
|
|
from sympy.utilities.lambdify import lambdify
|
|
from sympy.core.expr import UnevaluatedExpr
|
|
from sympy.codegen.cfunctions import expm1, log1p, exp2, log2, log10, hypot
|
|
from sympy.codegen.numpy_nodes import logaddexp, logaddexp2
|
|
from sympy.codegen.scipy_nodes import cosm1, powm1
|
|
from sympy.functions.elementary.complexes import re, im, arg
|
|
from sympy.functions.special.polynomials import \
|
|
chebyshevt, chebyshevu, legendre, hermite, laguerre, gegenbauer, \
|
|
assoc_legendre, assoc_laguerre, jacobi
|
|
from sympy.matrices import Matrix, MatrixSymbol, SparseMatrix
|
|
from sympy.printing.lambdarepr import LambdaPrinter
|
|
from sympy.printing.numpy import NumPyPrinter
|
|
from sympy.utilities.lambdify import implemented_function, lambdastr
|
|
from sympy.testing.pytest import skip
|
|
from sympy.utilities.decorator import conserve_mpmath_dps
|
|
from sympy.utilities.exceptions import ignore_warnings
|
|
from sympy.external import import_module
|
|
from sympy.functions.special.gamma_functions import uppergamma, lowergamma
|
|
|
|
|
|
import sympy
|
|
|
|
|
|
MutableDenseMatrix = Matrix
|
|
|
|
numpy = import_module('numpy')
|
|
scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
|
|
numexpr = import_module('numexpr')
|
|
tensorflow = import_module('tensorflow')
|
|
cupy = import_module('cupy')
|
|
jax = import_module('jax')
|
|
numba = import_module('numba')
|
|
|
|
if tensorflow:
|
|
# Hide Tensorflow warnings
|
|
import os
|
|
os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'
|
|
|
|
w, x, y, z = symbols('w,x,y,z')
|
|
|
|
#================== Test different arguments =======================
|
|
|
|
|
|
def test_no_args():
|
|
f = lambdify([], 1)
|
|
raises(TypeError, lambda: f(-1))
|
|
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_nested_args():
|
|
f1 = lambdify([[w, x]], [w, x])
|
|
assert f1([91, 2]) == [91, 2]
|
|
raises(TypeError, lambda: f1(1, 2))
|
|
|
|
f2 = lambdify([(w, x), (y, z)], [w, x, y, z])
|
|
assert f2((18, 12), (73, 4)) == [18, 12, 73, 4]
|
|
raises(TypeError, lambda: f2(3, 4))
|
|
|
|
f3 = lambdify([w, [[[x]], y], z], [w, x, y, z])
|
|
assert f3(10, [[[52]], 31], 44) == [10, 52, 31, 44]
|
|
|
|
|
|
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
|
|
raises(TypeError, lambda: f(0))
|
|
|
|
|
|
def test_own_namespace_1():
|
|
myfunc = lambda x: 1
|
|
f = lambdify(x, sin(x), {"sin": myfunc})
|
|
assert f(0.1) == 1
|
|
assert f(100) == 1
|
|
|
|
|
|
def test_own_namespace_2():
|
|
def myfunc(x):
|
|
return 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
|
|
|
|
p, q, r = symbols("p q r", real=True)
|
|
ae = abs(exp(p+UnevaluatedExpr(q+r)))
|
|
f = lambdify([p, q, r], [ae, ae], modules=math)
|
|
results = f(1.0, 1e18, -1e18)
|
|
refvals = [math.exp(1.0)]*2
|
|
for res, ref in zip(results, refvals):
|
|
assert abs((res-ref)/ref) < 1e-15
|
|
|
|
|
|
def test_bad_args():
|
|
# no vargs given
|
|
raises(TypeError, lambda: lambdify(1))
|
|
# same with vector exprs
|
|
raises(TypeError, lambda: lambdify([1, 2]))
|
|
|
|
|
|
def test_atoms():
|
|
# Non-Symbol atoms should not be pulled out from the expression namespace
|
|
f = lambdify(x, pi + x, {"pi": 3.14})
|
|
assert f(0) == 3.14
|
|
f = lambdify(x, I + x, {"I": 1j})
|
|
assert f(1) == 1 + 1j
|
|
|
|
#================== Test different modules =========================
|
|
|
|
# high precision output of sin(0.2*pi) is used to detect if precision is lost unwanted
|
|
|
|
|
|
@conserve_mpmath_dps
|
|
def test_sympy_lambda():
|
|
mpmath.mp.dps = 50
|
|
sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
|
|
f = lambdify(x, sin(x), "sympy")
|
|
assert f(x) == sin(x)
|
|
prec = 1e-15
|
|
assert -prec < f(Rational(1, 5)).evalf() - Float(str(sin02)) < prec
|
|
# arctan is in numpy module and should not be available
|
|
# The arctan below gives NameError. What is this supposed to test?
|
|
# raises(NameError, lambda: lambdify(x, arctan(x), "sympy"))
|
|
|
|
|
|
@conserve_mpmath_dps
|
|
def test_math_lambda():
|
|
mpmath.mp.dps = 50
|
|
sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
|
|
f = lambdify(x, sin(x), "math")
|
|
prec = 1e-15
|
|
assert -prec < f(0.2) - sin02 < prec
|
|
raises(TypeError, lambda: f(x))
|
|
# if this succeeds, it can't be a Python math function
|
|
|
|
|
|
@conserve_mpmath_dps
|
|
def test_mpmath_lambda():
|
|
mpmath.mp.dps = 50
|
|
sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
|
|
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
|
|
raises(TypeError, lambda: f(x))
|
|
# if this succeeds, it can't be a mpmath function
|
|
|
|
ref2 = (mpmath.mpf("1e-30")
|
|
- mpmath.mpf("1e-45")/2
|
|
+ 5*mpmath.mpf("1e-60")/6
|
|
- 3*mpmath.mpf("1e-75")/4
|
|
+ 33*mpmath.mpf("1e-90")/40
|
|
)
|
|
f2a = lambdify((x, y), x**y - 1, "mpmath")
|
|
f2b = lambdify((x, y), powm1(x, y), "mpmath")
|
|
f2c = lambdify((x,), expm1(x*log1p(x)), "mpmath")
|
|
ans2a = f2a(mpmath.mpf("1")+mpmath.mpf("1e-15"), mpmath.mpf("1e-15"))
|
|
ans2b = f2b(mpmath.mpf("1")+mpmath.mpf("1e-15"), mpmath.mpf("1e-15"))
|
|
ans2c = f2c(mpmath.mpf("1e-15"))
|
|
assert abs(ans2a - ref2) < 1e-51
|
|
assert abs(ans2b - ref2) < 1e-67
|
|
assert abs(ans2c - ref2) < 1e-80
|
|
|
|
|
|
@conserve_mpmath_dps
|
|
def test_number_precision():
|
|
mpmath.mp.dps = 50
|
|
sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
|
|
f = lambdify(x, sin02, "mpmath")
|
|
prec = 1e-49 # mpmath precision is around 50 decimal places
|
|
assert -prec < f(0) - sin02 < prec
|
|
|
|
@conserve_mpmath_dps
|
|
def test_mpmath_precision():
|
|
mpmath.mp.dps = 100
|
|
assert str(lambdify((), pi.evalf(100), 'mpmath')()) == str(pi.evalf(100))
|
|
|
|
#================== 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.items():
|
|
assert sym in sympy.__dict__
|
|
assert mat in math.__dict__
|
|
|
|
|
|
def test_mpmath_transl():
|
|
from sympy.utilities.lambdify import MPMATH_TRANSLATIONS
|
|
for sym, mat in MPMATH_TRANSLATIONS.items():
|
|
assert sym in sympy.__dict__ or sym == 'Matrix'
|
|
assert mat in mpmath.__dict__
|
|
|
|
|
|
def test_numpy_transl():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
|
|
from sympy.utilities.lambdify import NUMPY_TRANSLATIONS
|
|
for sym, nump in NUMPY_TRANSLATIONS.items():
|
|
assert sym in sympy.__dict__
|
|
assert nump in numpy.__dict__
|
|
|
|
|
|
def test_scipy_transl():
|
|
if not scipy:
|
|
skip("scipy not installed.")
|
|
|
|
from sympy.utilities.lambdify import SCIPY_TRANSLATIONS
|
|
for sym, scip in SCIPY_TRANSLATIONS.items():
|
|
assert sym in sympy.__dict__
|
|
assert scip in scipy.__dict__ or scip in scipy.special.__dict__
|
|
|
|
|
|
def test_numpy_translation_abs():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
|
|
f = lambdify(x, Abs(x), "numpy")
|
|
assert f(-1) == 1
|
|
assert f(1) == 1
|
|
|
|
|
|
def test_numexpr_printer():
|
|
if not numexpr:
|
|
skip("numexpr not installed.")
|
|
|
|
# if translation/printing is done incorrectly then evaluating
|
|
# a lambdified numexpr expression will throw an exception
|
|
from sympy.printing.lambdarepr import NumExprPrinter
|
|
|
|
blacklist = ('where', 'complex', 'contains')
|
|
arg_tuple = (x, y, z) # some functions take more than one argument
|
|
for sym in NumExprPrinter._numexpr_functions.keys():
|
|
if sym in blacklist:
|
|
continue
|
|
ssym = S(sym)
|
|
if hasattr(ssym, '_nargs'):
|
|
nargs = ssym._nargs[0]
|
|
else:
|
|
nargs = 1
|
|
args = arg_tuple[:nargs]
|
|
f = lambdify(args, ssym(*args), modules='numexpr')
|
|
assert f(*(1, )*nargs) is not None
|
|
|
|
|
|
def test_issue_9334():
|
|
if not numexpr:
|
|
skip("numexpr not installed.")
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
expr = S('b*a - sqrt(a**2)')
|
|
a, b = sorted(expr.free_symbols, key=lambda s: s.name)
|
|
func_numexpr = lambdify((a,b), expr, modules=[numexpr], dummify=False)
|
|
foo, bar = numpy.random.random((2, 4))
|
|
func_numexpr(foo, bar)
|
|
|
|
|
|
def test_issue_12984():
|
|
if not numexpr:
|
|
skip("numexpr not installed.")
|
|
func_numexpr = lambdify((x,y,z), Piecewise((y, x >= 0), (z, x > -1)), numexpr)
|
|
with ignore_warnings(RuntimeWarning):
|
|
assert func_numexpr(1, 24, 42) == 24
|
|
assert str(func_numexpr(-1, 24, 42)) == 'nan'
|
|
|
|
|
|
def test_empty_modules():
|
|
x, y = symbols('x y')
|
|
expr = -(x % y)
|
|
|
|
no_modules = lambdify([x, y], expr)
|
|
empty_modules = lambdify([x, y], expr, modules=[])
|
|
assert no_modules(3, 7) == empty_modules(3, 7)
|
|
assert no_modules(3, 7) == -3
|
|
|
|
|
|
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
|
|
|
|
|
|
def test_trig():
|
|
f = lambdify([x], [cos(x), sin(x)], 'math')
|
|
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
|
|
|
|
|
|
def test_integral():
|
|
if numpy and not scipy:
|
|
skip("scipy not installed.")
|
|
f = Lambda(x, exp(-x**2))
|
|
l = lambdify(y, Integral(f(x), (x, y, oo)))
|
|
d = l(-oo)
|
|
assert 1.77245385 < d < 1.772453851
|
|
|
|
|
|
def test_double_integral():
|
|
if numpy and not scipy:
|
|
skip("scipy not installed.")
|
|
# example from http://mpmath.org/doc/current/calculus/integration.html
|
|
i = Integral(1/(1 - x**2*y**2), (x, 0, 1), (y, 0, z))
|
|
l = lambdify([z], i)
|
|
d = l(1)
|
|
assert 1.23370055 < d < 1.233700551
|
|
|
|
|
|
#================== 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
|
|
raises(TypeError, lambda: f(0))
|
|
|
|
|
|
def test_vector_discontinuous():
|
|
f = lambdify(x, (-1/x, 1/x))
|
|
raises(ZeroDivisionError, lambda: f(0))
|
|
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)], 'math')
|
|
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])
|
|
J = Matrix((x, x + y)).jacobian((x, y))
|
|
v = Matrix((x, y))
|
|
sol = Matrix([[1, 0], [1, 1]])
|
|
assert lambdify(v, J, modules='sympy')(1, 2) == sol
|
|
assert lambdify(v.T, J, modules='sympy')(1, 2) == sol
|
|
|
|
|
|
def test_numpy_matrix():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
A = Matrix([[x, x*y], [sin(z) + 4, x**z]])
|
|
sol_arr = numpy.array([[1, 2], [numpy.sin(3) + 4, 1]])
|
|
#Lambdify array first, to ensure return to array as default
|
|
f = lambdify((x, y, z), A, ['numpy'])
|
|
numpy.testing.assert_allclose(f(1, 2, 3), sol_arr)
|
|
#Check that the types are arrays and matrices
|
|
assert isinstance(f(1, 2, 3), numpy.ndarray)
|
|
|
|
# gh-15071
|
|
class dot(Function):
|
|
pass
|
|
x_dot_mtx = dot(x, Matrix([[2], [1], [0]]))
|
|
f_dot1 = lambdify(x, x_dot_mtx)
|
|
inp = numpy.zeros((17, 3))
|
|
assert numpy.all(f_dot1(inp) == 0)
|
|
|
|
strict_kw = {"allow_unknown_functions": False, "inline": True, "fully_qualified_modules": False}
|
|
p2 = NumPyPrinter(dict(user_functions={'dot': 'dot'}, **strict_kw))
|
|
f_dot2 = lambdify(x, x_dot_mtx, printer=p2)
|
|
assert numpy.all(f_dot2(inp) == 0)
|
|
|
|
p3 = NumPyPrinter(strict_kw)
|
|
# The line below should probably fail upon construction (before calling with "(inp)"):
|
|
raises(Exception, lambda: lambdify(x, x_dot_mtx, printer=p3)(inp))
|
|
|
|
|
|
def test_numpy_transpose():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
A = Matrix([[1, x], [0, 1]])
|
|
f = lambdify((x), A.T, modules="numpy")
|
|
numpy.testing.assert_array_equal(f(2), numpy.array([[1, 0], [2, 1]]))
|
|
|
|
|
|
def test_numpy_dotproduct():
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
A = Matrix([x, y, z])
|
|
f1 = lambdify([x, y, z], DotProduct(A, A), modules='numpy')
|
|
f2 = lambdify([x, y, z], DotProduct(A, A.T), modules='numpy')
|
|
f3 = lambdify([x, y, z], DotProduct(A.T, A), modules='numpy')
|
|
f4 = lambdify([x, y, z], DotProduct(A, A.T), modules='numpy')
|
|
|
|
assert f1(1, 2, 3) == \
|
|
f2(1, 2, 3) == \
|
|
f3(1, 2, 3) == \
|
|
f4(1, 2, 3) == \
|
|
numpy.array([14])
|
|
|
|
|
|
def test_numpy_inverse():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
A = Matrix([[1, x], [0, 1]])
|
|
f = lambdify((x), A**-1, modules="numpy")
|
|
numpy.testing.assert_array_equal(f(2), numpy.array([[1, -2], [0, 1]]))
|
|
|
|
|
|
def test_numpy_old_matrix():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
A = Matrix([[x, x*y], [sin(z) + 4, x**z]])
|
|
sol_arr = numpy.array([[1, 2], [numpy.sin(3) + 4, 1]])
|
|
f = lambdify((x, y, z), A, [{'ImmutableDenseMatrix': numpy.matrix}, 'numpy'])
|
|
with ignore_warnings(PendingDeprecationWarning):
|
|
numpy.testing.assert_allclose(f(1, 2, 3), sol_arr)
|
|
assert isinstance(f(1, 2, 3), numpy.matrix)
|
|
|
|
|
|
def test_scipy_sparse_matrix():
|
|
if not scipy:
|
|
skip("scipy not installed.")
|
|
A = SparseMatrix([[x, 0], [0, y]])
|
|
f = lambdify((x, y), A, modules="scipy")
|
|
B = f(1, 2)
|
|
assert isinstance(B, scipy.sparse.coo_matrix)
|
|
|
|
|
|
def test_python_div_zero_issue_11306():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
p = Piecewise((1 / x, y < -1), (x, y < 1), (1 / x, True))
|
|
f = lambdify([x, y], p, modules='numpy')
|
|
numpy.seterr(divide='ignore')
|
|
assert float(f(numpy.array([0]),numpy.array([0.5]))) == 0
|
|
assert str(float(f(numpy.array([0]),numpy.array([1])))) == 'inf'
|
|
numpy.seterr(divide='warn')
|
|
|
|
|
|
def test_issue9474():
|
|
mods = [None, 'math']
|
|
if numpy:
|
|
mods.append('numpy')
|
|
if mpmath:
|
|
mods.append('mpmath')
|
|
for mod in mods:
|
|
f = lambdify(x, S.One/x, modules=mod)
|
|
assert f(2) == 0.5
|
|
f = lambdify(x, floor(S.One/x), modules=mod)
|
|
assert f(2) == 0
|
|
|
|
for absfunc, modules in product([Abs, abs], mods):
|
|
f = lambdify(x, absfunc(x), modules=modules)
|
|
assert f(-1) == 1
|
|
assert f(1) == 1
|
|
assert f(3+4j) == 5
|
|
|
|
|
|
def test_issue_9871():
|
|
if not numexpr:
|
|
skip("numexpr not installed.")
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
|
|
r = sqrt(x**2 + y**2)
|
|
expr = diff(1/r, x)
|
|
|
|
xn = yn = numpy.linspace(1, 10, 16)
|
|
# expr(xn, xn) = -xn/(sqrt(2)*xn)^3
|
|
fv_exact = -numpy.sqrt(2.)**-3 * xn**-2
|
|
|
|
fv_numpy = lambdify((x, y), expr, modules='numpy')(xn, yn)
|
|
fv_numexpr = lambdify((x, y), expr, modules='numexpr')(xn, yn)
|
|
numpy.testing.assert_allclose(fv_numpy, fv_exact, rtol=1e-10)
|
|
numpy.testing.assert_allclose(fv_numexpr, fv_exact, rtol=1e-10)
|
|
|
|
|
|
def test_numpy_piecewise():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
pieces = Piecewise((x, x < 3), (x**2, x > 5), (0, True))
|
|
f = lambdify(x, pieces, modules="numpy")
|
|
numpy.testing.assert_array_equal(f(numpy.arange(10)),
|
|
numpy.array([0, 1, 2, 0, 0, 0, 36, 49, 64, 81]))
|
|
# If we evaluate somewhere all conditions are False, we should get back NaN
|
|
nodef_func = lambdify(x, Piecewise((x, x > 0), (-x, x < 0)))
|
|
numpy.testing.assert_array_equal(nodef_func(numpy.array([-1, 0, 1])),
|
|
numpy.array([1, numpy.nan, 1]))
|
|
|
|
|
|
def test_numpy_logical_ops():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
and_func = lambdify((x, y), And(x, y), modules="numpy")
|
|
and_func_3 = lambdify((x, y, z), And(x, y, z), modules="numpy")
|
|
or_func = lambdify((x, y), Or(x, y), modules="numpy")
|
|
or_func_3 = lambdify((x, y, z), Or(x, y, z), modules="numpy")
|
|
not_func = lambdify((x), Not(x), modules="numpy")
|
|
arr1 = numpy.array([True, True])
|
|
arr2 = numpy.array([False, True])
|
|
arr3 = numpy.array([True, False])
|
|
numpy.testing.assert_array_equal(and_func(arr1, arr2), numpy.array([False, True]))
|
|
numpy.testing.assert_array_equal(and_func_3(arr1, arr2, arr3), numpy.array([False, False]))
|
|
numpy.testing.assert_array_equal(or_func(arr1, arr2), numpy.array([True, True]))
|
|
numpy.testing.assert_array_equal(or_func_3(arr1, arr2, arr3), numpy.array([True, True]))
|
|
numpy.testing.assert_array_equal(not_func(arr2), numpy.array([True, False]))
|
|
|
|
|
|
def test_numpy_matmul():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
xmat = Matrix([[x, y], [z, 1+z]])
|
|
ymat = Matrix([[x**2], [Abs(x)]])
|
|
mat_func = lambdify((x, y, z), xmat*ymat, modules="numpy")
|
|
numpy.testing.assert_array_equal(mat_func(0.5, 3, 4), numpy.array([[1.625], [3.5]]))
|
|
numpy.testing.assert_array_equal(mat_func(-0.5, 3, 4), numpy.array([[1.375], [3.5]]))
|
|
# Multiple matrices chained together in multiplication
|
|
f = lambdify((x, y, z), xmat*xmat*xmat, modules="numpy")
|
|
numpy.testing.assert_array_equal(f(0.5, 3, 4), numpy.array([[72.125, 119.25],
|
|
[159, 251]]))
|
|
|
|
|
|
def test_numpy_numexpr():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
if not numexpr:
|
|
skip("numexpr not installed.")
|
|
a, b, c = numpy.random.randn(3, 128, 128)
|
|
# ensure that numpy and numexpr return same value for complicated expression
|
|
expr = sin(x) + cos(y) + tan(z)**2 + Abs(z-y)*acos(sin(y*z)) + \
|
|
Abs(y-z)*acosh(2+exp(y-x))- sqrt(x**2+I*y**2)
|
|
npfunc = lambdify((x, y, z), expr, modules='numpy')
|
|
nefunc = lambdify((x, y, z), expr, modules='numexpr')
|
|
assert numpy.allclose(npfunc(a, b, c), nefunc(a, b, c))
|
|
|
|
|
|
def test_numexpr_userfunctions():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
if not numexpr:
|
|
skip("numexpr not installed.")
|
|
a, b = numpy.random.randn(2, 10)
|
|
uf = type('uf', (Function, ),
|
|
{'eval' : classmethod(lambda x, y : y**2+1)})
|
|
func = lambdify(x, 1-uf(x), modules='numexpr')
|
|
assert numpy.allclose(func(a), -(a**2))
|
|
|
|
uf = implemented_function(Function('uf'), lambda x, y : 2*x*y+1)
|
|
func = lambdify((x, y), uf(x, y), modules='numexpr')
|
|
assert numpy.allclose(func(a, b), 2*a*b+1)
|
|
|
|
|
|
def test_tensorflow_basic_math():
|
|
if not tensorflow:
|
|
skip("tensorflow not installed.")
|
|
expr = Max(sin(x), Abs(1/(x+2)))
|
|
func = lambdify(x, expr, modules="tensorflow")
|
|
|
|
with tensorflow.compat.v1.Session() as s:
|
|
a = tensorflow.constant(0, dtype=tensorflow.float32)
|
|
assert func(a).eval(session=s) == 0.5
|
|
|
|
|
|
def test_tensorflow_placeholders():
|
|
if not tensorflow:
|
|
skip("tensorflow not installed.")
|
|
expr = Max(sin(x), Abs(1/(x+2)))
|
|
func = lambdify(x, expr, modules="tensorflow")
|
|
|
|
with tensorflow.compat.v1.Session() as s:
|
|
a = tensorflow.compat.v1.placeholder(dtype=tensorflow.float32)
|
|
assert func(a).eval(session=s, feed_dict={a: 0}) == 0.5
|
|
|
|
|
|
def test_tensorflow_variables():
|
|
if not tensorflow:
|
|
skip("tensorflow not installed.")
|
|
expr = Max(sin(x), Abs(1/(x+2)))
|
|
func = lambdify(x, expr, modules="tensorflow")
|
|
|
|
with tensorflow.compat.v1.Session() as s:
|
|
a = tensorflow.Variable(0, dtype=tensorflow.float32)
|
|
s.run(a.initializer)
|
|
assert func(a).eval(session=s, feed_dict={a: 0}) == 0.5
|
|
|
|
|
|
def test_tensorflow_logical_operations():
|
|
if not tensorflow:
|
|
skip("tensorflow not installed.")
|
|
expr = Not(And(Or(x, y), y))
|
|
func = lambdify([x, y], expr, modules="tensorflow")
|
|
|
|
with tensorflow.compat.v1.Session() as s:
|
|
assert func(False, True).eval(session=s) == False
|
|
|
|
|
|
def test_tensorflow_piecewise():
|
|
if not tensorflow:
|
|
skip("tensorflow not installed.")
|
|
expr = Piecewise((0, Eq(x,0)), (-1, x < 0), (1, x > 0))
|
|
func = lambdify(x, expr, modules="tensorflow")
|
|
|
|
with tensorflow.compat.v1.Session() as s:
|
|
assert func(-1).eval(session=s) == -1
|
|
assert func(0).eval(session=s) == 0
|
|
assert func(1).eval(session=s) == 1
|
|
|
|
|
|
def test_tensorflow_multi_max():
|
|
if not tensorflow:
|
|
skip("tensorflow not installed.")
|
|
expr = Max(x, -x, x**2)
|
|
func = lambdify(x, expr, modules="tensorflow")
|
|
|
|
with tensorflow.compat.v1.Session() as s:
|
|
assert func(-2).eval(session=s) == 4
|
|
|
|
|
|
def test_tensorflow_multi_min():
|
|
if not tensorflow:
|
|
skip("tensorflow not installed.")
|
|
expr = Min(x, -x, x**2)
|
|
func = lambdify(x, expr, modules="tensorflow")
|
|
|
|
with tensorflow.compat.v1.Session() as s:
|
|
assert func(-2).eval(session=s) == -2
|
|
|
|
|
|
def test_tensorflow_relational():
|
|
if not tensorflow:
|
|
skip("tensorflow not installed.")
|
|
expr = x >= 0
|
|
func = lambdify(x, expr, modules="tensorflow")
|
|
|
|
with tensorflow.compat.v1.Session() as s:
|
|
assert func(1).eval(session=s) == True
|
|
|
|
|
|
def test_tensorflow_complexes():
|
|
if not tensorflow:
|
|
skip("tensorflow not installed")
|
|
|
|
func1 = lambdify(x, re(x), modules="tensorflow")
|
|
func2 = lambdify(x, im(x), modules="tensorflow")
|
|
func3 = lambdify(x, Abs(x), modules="tensorflow")
|
|
func4 = lambdify(x, arg(x), modules="tensorflow")
|
|
|
|
with tensorflow.compat.v1.Session() as s:
|
|
# For versions before
|
|
# https://github.com/tensorflow/tensorflow/issues/30029
|
|
# resolved, using Python numeric types may not work
|
|
a = tensorflow.constant(1+2j)
|
|
assert func1(a).eval(session=s) == 1
|
|
assert func2(a).eval(session=s) == 2
|
|
|
|
tensorflow_result = func3(a).eval(session=s)
|
|
sympy_result = Abs(1 + 2j).evalf()
|
|
assert abs(tensorflow_result-sympy_result) < 10**-6
|
|
|
|
tensorflow_result = func4(a).eval(session=s)
|
|
sympy_result = arg(1 + 2j).evalf()
|
|
assert abs(tensorflow_result-sympy_result) < 10**-6
|
|
|
|
|
|
def test_tensorflow_array_arg():
|
|
# Test for issue 14655 (tensorflow part)
|
|
if not tensorflow:
|
|
skip("tensorflow not installed.")
|
|
|
|
f = lambdify([[x, y]], x*x + y, 'tensorflow')
|
|
|
|
with tensorflow.compat.v1.Session() as s:
|
|
fcall = f(tensorflow.constant([2.0, 1.0]))
|
|
assert fcall.eval(session=s) == 5.0
|
|
|
|
|
|
#================== Test symbolic ==================================
|
|
|
|
|
|
def test_sym_single_arg():
|
|
f = lambdify(x, x * y)
|
|
assert f(z) == z * y
|
|
|
|
|
|
def test_sym_list_args():
|
|
f = lambdify([x, y], x + y + z)
|
|
assert f(1, 2) == 3 + z
|
|
|
|
|
|
def test_sym_integral():
|
|
f = Lambda(x, exp(-x**2))
|
|
l = lambdify(x, Integral(f(x), (x, -oo, oo)), modules="sympy")
|
|
assert l(y) == Integral(exp(-y**2), (y, -oo, oo))
|
|
assert l(y).doit() == sqrt(pi)
|
|
|
|
|
|
def test_namespace_order():
|
|
# lambdify had a bug, such that module dictionaries or cached module
|
|
# dictionaries would pull earlier namespaces into themselves.
|
|
# Because the module dictionaries form the namespace of the
|
|
# generated lambda, this meant that the behavior of a previously
|
|
# generated lambda function could change as a result of later calls
|
|
# to lambdify.
|
|
n1 = {'f': lambda x: 'first f'}
|
|
n2 = {'f': lambda x: 'second f',
|
|
'g': lambda x: 'function g'}
|
|
f = sympy.Function('f')
|
|
g = sympy.Function('g')
|
|
if1 = lambdify(x, f(x), modules=(n1, "sympy"))
|
|
assert if1(1) == 'first f'
|
|
if2 = lambdify(x, g(x), modules=(n2, "sympy"))
|
|
# previously gave 'second f'
|
|
assert if1(1) == 'first f'
|
|
|
|
assert if2(1) == 'function g'
|
|
|
|
|
|
def test_imps():
|
|
# Here we check if the default returned functions are anonymous - in
|
|
# the sense that we can have more than one function with the same name
|
|
f = implemented_function('f', lambda x: 2*x)
|
|
g = implemented_function('f', lambda x: math.sqrt(x))
|
|
l1 = lambdify(x, f(x))
|
|
l2 = lambdify(x, g(x))
|
|
assert str(f(x)) == str(g(x))
|
|
assert l1(3) == 6
|
|
assert l2(3) == math.sqrt(3)
|
|
# check that we can pass in a Function as input
|
|
func = sympy.Function('myfunc')
|
|
assert not hasattr(func, '_imp_')
|
|
my_f = implemented_function(func, lambda x: 2*x)
|
|
assert hasattr(my_f, '_imp_')
|
|
# Error for functions with same name and different implementation
|
|
f2 = implemented_function("f", lambda x: x + 101)
|
|
raises(ValueError, lambda: lambdify(x, f(f2(x))))
|
|
|
|
|
|
def test_imps_errors():
|
|
# Test errors that implemented functions can return, and still be able to
|
|
# form expressions.
|
|
# See: https://github.com/sympy/sympy/issues/10810
|
|
#
|
|
# XXX: Removed AttributeError here. This test was added due to issue 10810
|
|
# but that issue was about ValueError. It doesn't seem reasonable to
|
|
# "support" catching AttributeError in the same context...
|
|
for val, error_class in product((0, 0., 2, 2.0), (TypeError, ValueError)):
|
|
|
|
def myfunc(a):
|
|
if a == 0:
|
|
raise error_class
|
|
return 1
|
|
|
|
f = implemented_function('f', myfunc)
|
|
expr = f(val)
|
|
assert expr == f(val)
|
|
|
|
|
|
def test_imps_wrong_args():
|
|
raises(ValueError, lambda: implemented_function(sin, lambda x: x))
|
|
|
|
|
|
def test_lambdify_imps():
|
|
# Test lambdify with implemented functions
|
|
# first test basic (sympy) lambdify
|
|
f = sympy.cos
|
|
assert lambdify(x, f(x))(0) == 1
|
|
assert lambdify(x, 1 + f(x))(0) == 2
|
|
assert lambdify((x, y), y + f(x))(0, 1) == 2
|
|
# make an implemented function and test
|
|
f = implemented_function("f", lambda x: x + 100)
|
|
assert lambdify(x, f(x))(0) == 100
|
|
assert lambdify(x, 1 + f(x))(0) == 101
|
|
assert lambdify((x, y), y + f(x))(0, 1) == 101
|
|
# Can also handle tuples, lists, dicts as expressions
|
|
lam = lambdify(x, (f(x), x))
|
|
assert lam(3) == (103, 3)
|
|
lam = lambdify(x, [f(x), x])
|
|
assert lam(3) == [103, 3]
|
|
lam = lambdify(x, [f(x), (f(x), x)])
|
|
assert lam(3) == [103, (103, 3)]
|
|
lam = lambdify(x, {f(x): x})
|
|
assert lam(3) == {103: 3}
|
|
lam = lambdify(x, {f(x): x})
|
|
assert lam(3) == {103: 3}
|
|
lam = lambdify(x, {x: f(x)})
|
|
assert lam(3) == {3: 103}
|
|
# Check that imp preferred to other namespaces by default
|
|
d = {'f': lambda x: x + 99}
|
|
lam = lambdify(x, f(x), d)
|
|
assert lam(3) == 103
|
|
# Unless flag passed
|
|
lam = lambdify(x, f(x), d, use_imps=False)
|
|
assert lam(3) == 102
|
|
|
|
|
|
def test_dummification():
|
|
t = symbols('t')
|
|
F = Function('F')
|
|
G = Function('G')
|
|
#"\alpha" is not a valid Python variable name
|
|
#lambdify should sub in a dummy for it, and return
|
|
#without a syntax error
|
|
alpha = symbols(r'\alpha')
|
|
some_expr = 2 * F(t)**2 / G(t)
|
|
lam = lambdify((F(t), G(t)), some_expr)
|
|
assert lam(3, 9) == 2
|
|
lam = lambdify(sin(t), 2 * sin(t)**2)
|
|
assert lam(F(t)) == 2 * F(t)**2
|
|
#Test that \alpha was properly dummified
|
|
lam = lambdify((alpha, t), 2*alpha + t)
|
|
assert lam(2, 1) == 5
|
|
raises(SyntaxError, lambda: lambdify(F(t) * G(t), F(t) * G(t) + 5))
|
|
raises(SyntaxError, lambda: lambdify(2 * F(t), 2 * F(t) + 5))
|
|
raises(SyntaxError, lambda: lambdify(2 * F(t), 4 * F(t) + 5))
|
|
|
|
|
|
def test_curly_matrix_symbol():
|
|
# Issue #15009
|
|
curlyv = sympy.MatrixSymbol("{v}", 2, 1)
|
|
lam = lambdify(curlyv, curlyv)
|
|
assert lam(1)==1
|
|
lam = lambdify(curlyv, curlyv, dummify=True)
|
|
assert lam(1)==1
|
|
|
|
|
|
def test_python_keywords():
|
|
# Test for issue 7452. The automatic dummification should ensure use of
|
|
# Python reserved keywords as symbol names will create valid lambda
|
|
# functions. This is an additional regression test.
|
|
python_if = symbols('if')
|
|
expr = python_if / 2
|
|
f = lambdify(python_if, expr)
|
|
assert f(4.0) == 2.0
|
|
|
|
|
|
def test_lambdify_docstring():
|
|
func = lambdify((w, x, y, z), w + x + y + z)
|
|
ref = (
|
|
"Created with lambdify. Signature:\n\n"
|
|
"func(w, x, y, z)\n\n"
|
|
"Expression:\n\n"
|
|
"w + x + y + z"
|
|
).splitlines()
|
|
assert func.__doc__.splitlines()[:len(ref)] == ref
|
|
syms = symbols('a1:26')
|
|
func = lambdify(syms, sum(syms))
|
|
ref = (
|
|
"Created with lambdify. Signature:\n\n"
|
|
"func(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15,\n"
|
|
" a16, a17, a18, a19, a20, a21, a22, a23, a24, a25)\n\n"
|
|
"Expression:\n\n"
|
|
"a1 + a10 + a11 + a12 + a13 + a14 + a15 + a16 + a17 + a18 + a19 + a2 + a20 +..."
|
|
).splitlines()
|
|
assert func.__doc__.splitlines()[:len(ref)] == ref
|
|
|
|
|
|
#================== Test special printers ==========================
|
|
|
|
|
|
def test_special_printers():
|
|
from sympy.printing.lambdarepr import IntervalPrinter
|
|
|
|
def intervalrepr(expr):
|
|
return IntervalPrinter().doprint(expr)
|
|
|
|
expr = sqrt(sqrt(2) + sqrt(3)) + S.Half
|
|
|
|
func0 = lambdify((), expr, modules="mpmath", printer=intervalrepr)
|
|
func1 = lambdify((), expr, modules="mpmath", printer=IntervalPrinter)
|
|
func2 = lambdify((), expr, modules="mpmath", printer=IntervalPrinter())
|
|
|
|
mpi = type(mpmath.mpi(1, 2))
|
|
|
|
assert isinstance(func0(), mpi)
|
|
assert isinstance(func1(), mpi)
|
|
assert isinstance(func2(), mpi)
|
|
|
|
# To check Is lambdify loggamma works for mpmath or not
|
|
exp1 = lambdify(x, loggamma(x), 'mpmath')(5)
|
|
exp2 = lambdify(x, loggamma(x), 'mpmath')(1.8)
|
|
exp3 = lambdify(x, loggamma(x), 'mpmath')(15)
|
|
exp_ls = [exp1, exp2, exp3]
|
|
|
|
sol1 = mpmath.loggamma(5)
|
|
sol2 = mpmath.loggamma(1.8)
|
|
sol3 = mpmath.loggamma(15)
|
|
sol_ls = [sol1, sol2, sol3]
|
|
|
|
assert exp_ls == sol_ls
|
|
|
|
|
|
def test_true_false():
|
|
# We want exact is comparison here, not just ==
|
|
assert lambdify([], true)() is True
|
|
assert lambdify([], false)() is False
|
|
|
|
|
|
def test_issue_2790():
|
|
assert lambdify((x, (y, z)), x + y)(1, (2, 4)) == 3
|
|
assert lambdify((x, (y, (w, z))), w + x + y + z)(1, (2, (3, 4))) == 10
|
|
assert lambdify(x, x + 1, dummify=False)(1) == 2
|
|
|
|
|
|
def test_issue_12092():
|
|
f = implemented_function('f', lambda x: x**2)
|
|
assert f(f(2)).evalf() == Float(16)
|
|
|
|
|
|
def test_issue_14911():
|
|
class Variable(sympy.Symbol):
|
|
def _sympystr(self, printer):
|
|
return printer.doprint(self.name)
|
|
|
|
_lambdacode = _sympystr
|
|
_numpycode = _sympystr
|
|
|
|
x = Variable('x')
|
|
y = 2 * x
|
|
code = LambdaPrinter().doprint(y)
|
|
assert code.replace(' ', '') == '2*x'
|
|
|
|
|
|
def test_ITE():
|
|
assert lambdify((x, y, z), ITE(x, y, z))(True, 5, 3) == 5
|
|
assert lambdify((x, y, z), ITE(x, y, z))(False, 5, 3) == 3
|
|
|
|
|
|
def test_Min_Max():
|
|
# see gh-10375
|
|
assert lambdify((x, y, z), Min(x, y, z))(1, 2, 3) == 1
|
|
assert lambdify((x, y, z), Max(x, y, z))(1, 2, 3) == 3
|
|
|
|
|
|
def test_Indexed():
|
|
# Issue #10934
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
|
|
a = IndexedBase('a')
|
|
i, j = symbols('i j')
|
|
b = numpy.array([[1, 2], [3, 4]])
|
|
assert lambdify(a, Sum(a[x, y], (x, 0, 1), (y, 0, 1)))(b) == 10
|
|
|
|
|
|
def test_issue_12173():
|
|
#test for issue 12173
|
|
expr1 = lambdify((x, y), uppergamma(x, y),"mpmath")(1, 2)
|
|
expr2 = lambdify((x, y), lowergamma(x, y),"mpmath")(1, 2)
|
|
assert expr1 == uppergamma(1, 2).evalf()
|
|
assert expr2 == lowergamma(1, 2).evalf()
|
|
|
|
|
|
def test_issue_13642():
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
f = lambdify(x, sinc(x))
|
|
assert Abs(f(1) - sinc(1)).n() < 1e-15
|
|
|
|
|
|
def test_sinc_mpmath():
|
|
f = lambdify(x, sinc(x), "mpmath")
|
|
assert Abs(f(1) - sinc(1)).n() < 1e-15
|
|
|
|
|
|
def test_lambdify_dummy_arg():
|
|
d1 = Dummy()
|
|
f1 = lambdify(d1, d1 + 1, dummify=False)
|
|
assert f1(2) == 3
|
|
f1b = lambdify(d1, d1 + 1)
|
|
assert f1b(2) == 3
|
|
d2 = Dummy('x')
|
|
f2 = lambdify(d2, d2 + 1)
|
|
assert f2(2) == 3
|
|
f3 = lambdify([[d2]], d2 + 1)
|
|
assert f3([2]) == 3
|
|
|
|
|
|
def test_lambdify_mixed_symbol_dummy_args():
|
|
d = Dummy()
|
|
# Contrived example of name clash
|
|
dsym = symbols(str(d))
|
|
f = lambdify([d, dsym], d - dsym)
|
|
assert f(4, 1) == 3
|
|
|
|
|
|
def test_numpy_array_arg():
|
|
# Test for issue 14655 (numpy part)
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
|
|
f = lambdify([[x, y]], x*x + y, 'numpy')
|
|
|
|
assert f(numpy.array([2.0, 1.0])) == 5
|
|
|
|
|
|
def test_scipy_fns():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
|
|
single_arg_sympy_fns = [Ei, erf, erfc, factorial, gamma, loggamma, digamma, Si, Ci]
|
|
single_arg_scipy_fns = [scipy.special.expi, scipy.special.erf, scipy.special.erfc,
|
|
scipy.special.factorial, scipy.special.gamma, scipy.special.gammaln,
|
|
scipy.special.psi, scipy.special.sici, scipy.special.sici]
|
|
numpy.random.seed(0)
|
|
for (sympy_fn, scipy_fn) in zip(single_arg_sympy_fns, single_arg_scipy_fns):
|
|
f = lambdify(x, sympy_fn(x), modules="scipy")
|
|
for i in range(20):
|
|
tv = numpy.random.uniform(-10, 10) + 1j*numpy.random.uniform(-5, 5)
|
|
# SciPy thinks that factorial(z) is 0 when re(z) < 0 and
|
|
# does not support complex numbers.
|
|
# SymPy does not think so.
|
|
if sympy_fn == factorial:
|
|
tv = numpy.abs(tv)
|
|
# SciPy supports gammaln for real arguments only,
|
|
# and there is also a branch cut along the negative real axis
|
|
if sympy_fn == loggamma:
|
|
tv = numpy.abs(tv)
|
|
# SymPy's digamma evaluates as polygamma(0, z)
|
|
# which SciPy supports for real arguments only
|
|
if sympy_fn == digamma:
|
|
tv = numpy.real(tv)
|
|
sympy_result = sympy_fn(tv).evalf()
|
|
scipy_result = scipy_fn(tv)
|
|
# SciPy's sici returns a tuple with both Si and Ci present in it
|
|
# which needs to be unpacked
|
|
if sympy_fn == Si:
|
|
scipy_result = scipy_fn(tv)[0]
|
|
if sympy_fn == Ci:
|
|
scipy_result = scipy_fn(tv)[1]
|
|
assert abs(f(tv) - sympy_result) < 1e-13*(1 + abs(sympy_result))
|
|
assert abs(f(tv) - scipy_result) < 1e-13*(1 + abs(sympy_result))
|
|
|
|
double_arg_sympy_fns = [RisingFactorial, besselj, bessely, besseli,
|
|
besselk, polygamma]
|
|
double_arg_scipy_fns = [scipy.special.poch, scipy.special.jv,
|
|
scipy.special.yv, scipy.special.iv, scipy.special.kv, scipy.special.polygamma]
|
|
for (sympy_fn, scipy_fn) in zip(double_arg_sympy_fns, double_arg_scipy_fns):
|
|
f = lambdify((x, y), sympy_fn(x, y), modules="scipy")
|
|
for i in range(20):
|
|
# SciPy supports only real orders of Bessel functions
|
|
tv1 = numpy.random.uniform(-10, 10)
|
|
tv2 = numpy.random.uniform(-10, 10) + 1j*numpy.random.uniform(-5, 5)
|
|
# SciPy requires a real valued 2nd argument for: poch, polygamma
|
|
if sympy_fn in (RisingFactorial, polygamma):
|
|
tv2 = numpy.real(tv2)
|
|
if sympy_fn == polygamma:
|
|
tv1 = abs(int(tv1)) # first argument to polygamma must be a non-negative integral.
|
|
sympy_result = sympy_fn(tv1, tv2).evalf()
|
|
assert abs(f(tv1, tv2) - sympy_result) < 1e-13*(1 + abs(sympy_result))
|
|
assert abs(f(tv1, tv2) - scipy_fn(tv1, tv2)) < 1e-13*(1 + abs(sympy_result))
|
|
|
|
|
|
def test_scipy_polys():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
numpy.random.seed(0)
|
|
|
|
params = symbols('n k a b')
|
|
# list polynomials with the number of parameters
|
|
polys = [
|
|
(chebyshevt, 1),
|
|
(chebyshevu, 1),
|
|
(legendre, 1),
|
|
(hermite, 1),
|
|
(laguerre, 1),
|
|
(gegenbauer, 2),
|
|
(assoc_legendre, 2),
|
|
(assoc_laguerre, 2),
|
|
(jacobi, 3)
|
|
]
|
|
|
|
msg = \
|
|
"The random test of the function {func} with the arguments " \
|
|
"{args} had failed because the SymPy result {sympy_result} " \
|
|
"and SciPy result {scipy_result} had failed to converge " \
|
|
"within the tolerance {tol} " \
|
|
"(Actual absolute difference : {diff})"
|
|
|
|
for sympy_fn, num_params in polys:
|
|
args = params[:num_params] + (x,)
|
|
f = lambdify(args, sympy_fn(*args))
|
|
for _ in range(10):
|
|
tn = numpy.random.randint(3, 10)
|
|
tparams = tuple(numpy.random.uniform(0, 5, size=num_params-1))
|
|
tv = numpy.random.uniform(-10, 10) + 1j*numpy.random.uniform(-5, 5)
|
|
# SciPy supports hermite for real arguments only
|
|
if sympy_fn == hermite:
|
|
tv = numpy.real(tv)
|
|
# assoc_legendre needs x in (-1, 1) and integer param at most n
|
|
if sympy_fn == assoc_legendre:
|
|
tv = numpy.random.uniform(-1, 1)
|
|
tparams = tuple(numpy.random.randint(1, tn, size=1))
|
|
|
|
vals = (tn,) + tparams + (tv,)
|
|
scipy_result = f(*vals)
|
|
sympy_result = sympy_fn(*vals).evalf()
|
|
atol = 1e-9*(1 + abs(sympy_result))
|
|
diff = abs(scipy_result - sympy_result)
|
|
try:
|
|
assert diff < atol
|
|
except TypeError:
|
|
raise AssertionError(
|
|
msg.format(
|
|
func=repr(sympy_fn),
|
|
args=repr(vals),
|
|
sympy_result=repr(sympy_result),
|
|
scipy_result=repr(scipy_result),
|
|
diff=diff,
|
|
tol=atol)
|
|
)
|
|
|
|
|
|
def test_lambdify_inspect():
|
|
f = lambdify(x, x**2)
|
|
# Test that inspect.getsource works but don't hard-code implementation
|
|
# details
|
|
assert 'x**2' in inspect.getsource(f)
|
|
|
|
|
|
def test_issue_14941():
|
|
x, y = Dummy(), Dummy()
|
|
|
|
# test dict
|
|
f1 = lambdify([x, y], {x: 3, y: 3}, 'sympy')
|
|
assert f1(2, 3) == {2: 3, 3: 3}
|
|
|
|
# test tuple
|
|
f2 = lambdify([x, y], (y, x), 'sympy')
|
|
assert f2(2, 3) == (3, 2)
|
|
f2b = lambdify([], (1,)) # gh-23224
|
|
assert f2b() == (1,)
|
|
|
|
# test list
|
|
f3 = lambdify([x, y], [y, x], 'sympy')
|
|
assert f3(2, 3) == [3, 2]
|
|
|
|
|
|
def test_lambdify_Derivative_arg_issue_16468():
|
|
f = Function('f')(x)
|
|
fx = f.diff()
|
|
assert lambdify((f, fx), f + fx)(10, 5) == 15
|
|
assert eval(lambdastr((f, fx), f/fx))(10, 5) == 2
|
|
raises(SyntaxError, lambda:
|
|
eval(lambdastr((f, fx), f/fx, dummify=False)))
|
|
assert eval(lambdastr((f, fx), f/fx, dummify=True))(10, 5) == 2
|
|
assert eval(lambdastr((fx, f), f/fx, dummify=True))(S(10), 5) == S.Half
|
|
assert lambdify(fx, 1 + fx)(41) == 42
|
|
assert eval(lambdastr(fx, 1 + fx, dummify=True))(41) == 42
|
|
|
|
|
|
def test_imag_real():
|
|
f_re = lambdify([z], sympy.re(z))
|
|
val = 3+2j
|
|
assert f_re(val) == val.real
|
|
|
|
f_im = lambdify([z], sympy.im(z)) # see #15400
|
|
assert f_im(val) == val.imag
|
|
|
|
|
|
def test_MatrixSymbol_issue_15578():
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
A = MatrixSymbol('A', 2, 2)
|
|
A0 = numpy.array([[1, 2], [3, 4]])
|
|
f = lambdify(A, A**(-1))
|
|
assert numpy.allclose(f(A0), numpy.array([[-2., 1.], [1.5, -0.5]]))
|
|
g = lambdify(A, A**3)
|
|
assert numpy.allclose(g(A0), numpy.array([[37, 54], [81, 118]]))
|
|
|
|
|
|
def test_issue_15654():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
from sympy.abc import n, l, r, Z
|
|
from sympy.physics import hydrogen
|
|
nv, lv, rv, Zv = 1, 0, 3, 1
|
|
sympy_value = hydrogen.R_nl(nv, lv, rv, Zv).evalf()
|
|
f = lambdify((n, l, r, Z), hydrogen.R_nl(n, l, r, Z))
|
|
scipy_value = f(nv, lv, rv, Zv)
|
|
assert abs(sympy_value - scipy_value) < 1e-15
|
|
|
|
|
|
def test_issue_15827():
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
A = MatrixSymbol("A", 3, 3)
|
|
B = MatrixSymbol("B", 2, 3)
|
|
C = MatrixSymbol("C", 3, 4)
|
|
D = MatrixSymbol("D", 4, 5)
|
|
k=symbols("k")
|
|
f = lambdify(A, (2*k)*A)
|
|
g = lambdify(A, (2+k)*A)
|
|
h = lambdify(A, 2*A)
|
|
i = lambdify((B, C, D), 2*B*C*D)
|
|
assert numpy.array_equal(f(numpy.array([[1, 2, 3], [1, 2, 3], [1, 2, 3]])), \
|
|
numpy.array([[2*k, 4*k, 6*k], [2*k, 4*k, 6*k], [2*k, 4*k, 6*k]], dtype=object))
|
|
|
|
assert numpy.array_equal(g(numpy.array([[1, 2, 3], [1, 2, 3], [1, 2, 3]])), \
|
|
numpy.array([[k + 2, 2*k + 4, 3*k + 6], [k + 2, 2*k + 4, 3*k + 6], \
|
|
[k + 2, 2*k + 4, 3*k + 6]], dtype=object))
|
|
|
|
assert numpy.array_equal(h(numpy.array([[1, 2, 3], [1, 2, 3], [1, 2, 3]])), \
|
|
numpy.array([[2, 4, 6], [2, 4, 6], [2, 4, 6]]))
|
|
|
|
assert numpy.array_equal(i(numpy.array([[1, 2, 3], [1, 2, 3]]), numpy.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]]), \
|
|
numpy.array([[1, 2, 3, 4, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5]])), numpy.array([[ 120, 240, 360, 480, 600], \
|
|
[ 120, 240, 360, 480, 600]]))
|
|
|
|
|
|
def test_issue_16930():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
|
|
x = symbols("x")
|
|
f = lambda x: S.GoldenRatio * x**2
|
|
f_ = lambdify(x, f(x), modules='scipy')
|
|
assert f_(1) == scipy.constants.golden_ratio
|
|
|
|
def test_issue_17898():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
x = symbols("x")
|
|
f_ = lambdify([x], sympy.LambertW(x,-1), modules='scipy')
|
|
assert f_(0.1) == mpmath.lambertw(0.1, -1)
|
|
|
|
def test_issue_13167_21411():
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
f1 = lambdify(x, sympy.Heaviside(x))
|
|
f2 = lambdify(x, sympy.Heaviside(x, 1))
|
|
res1 = f1([-1, 0, 1])
|
|
res2 = f2([-1, 0, 1])
|
|
assert Abs(res1[0]).n() < 1e-15 # First functionality: only one argument passed
|
|
assert Abs(res1[1] - 1/2).n() < 1e-15
|
|
assert Abs(res1[2] - 1).n() < 1e-15
|
|
assert Abs(res2[0]).n() < 1e-15 # Second functionality: two arguments passed
|
|
assert Abs(res2[1] - 1).n() < 1e-15
|
|
assert Abs(res2[2] - 1).n() < 1e-15
|
|
|
|
def test_single_e():
|
|
f = lambdify(x, E)
|
|
assert f(23) == exp(1.0)
|
|
|
|
def test_issue_16536():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
|
|
a = symbols('a')
|
|
f1 = lowergamma(a, x)
|
|
F = lambdify((a, x), f1, modules='scipy')
|
|
assert abs(lowergamma(1, 3) - F(1, 3)) <= 1e-10
|
|
|
|
f2 = uppergamma(a, x)
|
|
F = lambdify((a, x), f2, modules='scipy')
|
|
assert abs(uppergamma(1, 3) - F(1, 3)) <= 1e-10
|
|
|
|
|
|
def test_issue_22726():
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
|
|
x1, x2 = symbols('x1 x2')
|
|
f = Max(S.Zero, Min(x1, x2))
|
|
g = derive_by_array(f, (x1, x2))
|
|
G = lambdify((x1, x2), g, modules='numpy')
|
|
point = {x1: 1, x2: 2}
|
|
assert (abs(g.subs(point) - G(*point.values())) <= 1e-10).all()
|
|
|
|
|
|
def test_issue_22739():
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
|
|
x1, x2 = symbols('x1 x2')
|
|
f = Heaviside(Min(x1, x2))
|
|
F = lambdify((x1, x2), f, modules='numpy')
|
|
point = {x1: 1, x2: 2}
|
|
assert abs(f.subs(point) - F(*point.values())) <= 1e-10
|
|
|
|
|
|
def test_issue_22992():
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
|
|
a, t = symbols('a t')
|
|
expr = a*(log(cot(t/2)) - cos(t))
|
|
F = lambdify([a, t], expr, 'numpy')
|
|
|
|
point = {a: 10, t: 2}
|
|
|
|
assert abs(expr.subs(point) - F(*point.values())) <= 1e-10
|
|
|
|
# Standard math
|
|
F = lambdify([a, t], expr)
|
|
|
|
assert abs(expr.subs(point) - F(*point.values())) <= 1e-10
|
|
|
|
|
|
def test_issue_19764():
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
|
|
expr = Array([x, x**2])
|
|
f = lambdify(x, expr, 'numpy')
|
|
|
|
assert f(1).__class__ == numpy.ndarray
|
|
|
|
def test_issue_20070():
|
|
if not numba:
|
|
skip("numba not installed")
|
|
|
|
f = lambdify(x, sin(x), 'numpy')
|
|
assert numba.jit(f)(1)==0.8414709848078965
|
|
|
|
|
|
def test_fresnel_integrals_scipy():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
|
|
f1 = fresnelc(x)
|
|
f2 = fresnels(x)
|
|
F1 = lambdify(x, f1, modules='scipy')
|
|
F2 = lambdify(x, f2, modules='scipy')
|
|
|
|
assert abs(fresnelc(1.3) - F1(1.3)) <= 1e-10
|
|
assert abs(fresnels(1.3) - F2(1.3)) <= 1e-10
|
|
|
|
|
|
def test_beta_scipy():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
|
|
f = beta(x, y)
|
|
F = lambdify((x, y), f, modules='scipy')
|
|
|
|
assert abs(beta(1.3, 2.3) - F(1.3, 2.3)) <= 1e-10
|
|
|
|
|
|
def test_beta_math():
|
|
f = beta(x, y)
|
|
F = lambdify((x, y), f, modules='math')
|
|
|
|
assert abs(beta(1.3, 2.3) - F(1.3, 2.3)) <= 1e-10
|
|
|
|
|
|
def test_betainc_scipy():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
|
|
f = betainc(w, x, y, z)
|
|
F = lambdify((w, x, y, z), f, modules='scipy')
|
|
|
|
assert abs(betainc(1.4, 3.1, 0.1, 0.5) - F(1.4, 3.1, 0.1, 0.5)) <= 1e-10
|
|
|
|
|
|
def test_betainc_regularized_scipy():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
|
|
f = betainc_regularized(w, x, y, z)
|
|
F = lambdify((w, x, y, z), f, modules='scipy')
|
|
|
|
assert abs(betainc_regularized(0.2, 3.5, 0.1, 1) - F(0.2, 3.5, 0.1, 1)) <= 1e-10
|
|
|
|
|
|
def test_numpy_special_math():
|
|
if not numpy:
|
|
skip("numpy not installed")
|
|
|
|
funcs = [expm1, log1p, exp2, log2, log10, hypot, logaddexp, logaddexp2]
|
|
for func in funcs:
|
|
if 2 in func.nargs:
|
|
expr = func(x, y)
|
|
args = (x, y)
|
|
num_args = (0.3, 0.4)
|
|
elif 1 in func.nargs:
|
|
expr = func(x)
|
|
args = (x,)
|
|
num_args = (0.3,)
|
|
else:
|
|
raise NotImplementedError("Need to handle other than unary & binary functions in test")
|
|
f = lambdify(args, expr)
|
|
result = f(*num_args)
|
|
reference = expr.subs(dict(zip(args, num_args))).evalf()
|
|
assert numpy.allclose(result, float(reference))
|
|
|
|
lae2 = lambdify((x, y), logaddexp2(log2(x), log2(y)))
|
|
assert abs(2.0**lae2(1e-50, 2.5e-50) - 3.5e-50) < 1e-62 # from NumPy's docstring
|
|
|
|
|
|
def test_scipy_special_math():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
|
|
cm1 = lambdify((x,), cosm1(x), modules='scipy')
|
|
assert abs(cm1(1e-20) + 5e-41) < 1e-200
|
|
|
|
have_scipy_1_10plus = tuple(map(int, scipy.version.version.split('.')[:2])) >= (1, 10)
|
|
|
|
if have_scipy_1_10plus:
|
|
cm2 = lambdify((x, y), powm1(x, y), modules='scipy')
|
|
assert abs(cm2(1.2, 1e-9) - 1.82321557e-10) < 1e-17
|
|
|
|
|
|
def test_scipy_bernoulli():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
|
|
bern = lambdify((x,), bernoulli(x), modules='scipy')
|
|
assert bern(1) == 0.5
|
|
|
|
|
|
def test_scipy_harmonic():
|
|
if not scipy:
|
|
skip("scipy not installed")
|
|
|
|
hn = lambdify((x,), harmonic(x), modules='scipy')
|
|
assert hn(2) == 1.5
|
|
hnm = lambdify((x, y), harmonic(x, y), modules='scipy')
|
|
assert hnm(2, 2) == 1.25
|
|
|
|
|
|
def test_cupy_array_arg():
|
|
if not cupy:
|
|
skip("CuPy not installed")
|
|
|
|
f = lambdify([[x, y]], x*x + y, 'cupy')
|
|
result = f(cupy.array([2.0, 1.0]))
|
|
assert result == 5
|
|
assert "cupy" in str(type(result))
|
|
|
|
|
|
def test_cupy_array_arg_using_numpy():
|
|
# numpy functions can be run on cupy arrays
|
|
# unclear if we can "officially" support this,
|
|
# depends on numpy __array_function__ support
|
|
if not cupy:
|
|
skip("CuPy not installed")
|
|
|
|
f = lambdify([[x, y]], x*x + y, 'numpy')
|
|
result = f(cupy.array([2.0, 1.0]))
|
|
assert result == 5
|
|
assert "cupy" in str(type(result))
|
|
|
|
def test_cupy_dotproduct():
|
|
if not cupy:
|
|
skip("CuPy not installed")
|
|
|
|
A = Matrix([x, y, z])
|
|
f1 = lambdify([x, y, z], DotProduct(A, A), modules='cupy')
|
|
f2 = lambdify([x, y, z], DotProduct(A, A.T), modules='cupy')
|
|
f3 = lambdify([x, y, z], DotProduct(A.T, A), modules='cupy')
|
|
f4 = lambdify([x, y, z], DotProduct(A, A.T), modules='cupy')
|
|
|
|
assert f1(1, 2, 3) == \
|
|
f2(1, 2, 3) == \
|
|
f3(1, 2, 3) == \
|
|
f4(1, 2, 3) == \
|
|
cupy.array([14])
|
|
|
|
|
|
def test_jax_array_arg():
|
|
if not jax:
|
|
skip("JAX not installed")
|
|
|
|
f = lambdify([[x, y]], x*x + y, 'jax')
|
|
result = f(jax.numpy.array([2.0, 1.0]))
|
|
assert result == 5
|
|
assert "jax" in str(type(result))
|
|
|
|
|
|
def test_jax_array_arg_using_numpy():
|
|
if not jax:
|
|
skip("JAX not installed")
|
|
|
|
f = lambdify([[x, y]], x*x + y, 'numpy')
|
|
result = f(jax.numpy.array([2.0, 1.0]))
|
|
assert result == 5
|
|
assert "jax" in str(type(result))
|
|
|
|
|
|
def test_jax_dotproduct():
|
|
if not jax:
|
|
skip("JAX not installed")
|
|
|
|
A = Matrix([x, y, z])
|
|
f1 = lambdify([x, y, z], DotProduct(A, A), modules='jax')
|
|
f2 = lambdify([x, y, z], DotProduct(A, A.T), modules='jax')
|
|
f3 = lambdify([x, y, z], DotProduct(A.T, A), modules='jax')
|
|
f4 = lambdify([x, y, z], DotProduct(A, A.T), modules='jax')
|
|
|
|
assert f1(1, 2, 3) == \
|
|
f2(1, 2, 3) == \
|
|
f3(1, 2, 3) == \
|
|
f4(1, 2, 3) == \
|
|
jax.numpy.array([14])
|
|
|
|
|
|
def test_lambdify_cse():
|
|
def dummy_cse(exprs):
|
|
return (), exprs
|
|
|
|
def minmem(exprs):
|
|
from sympy.simplify.cse_main import cse_release_variables, cse
|
|
return cse(exprs, postprocess=cse_release_variables)
|
|
|
|
class Case:
|
|
def __init__(self, *, args, exprs, num_args, requires_numpy=False):
|
|
self.args = args
|
|
self.exprs = exprs
|
|
self.num_args = num_args
|
|
subs_dict = dict(zip(self.args, self.num_args))
|
|
self.ref = [e.subs(subs_dict).evalf() for e in exprs]
|
|
self.requires_numpy = requires_numpy
|
|
|
|
def lambdify(self, *, cse):
|
|
return lambdify(self.args, self.exprs, cse=cse)
|
|
|
|
def assertAllClose(self, result, *, abstol=1e-15, reltol=1e-15):
|
|
if self.requires_numpy:
|
|
assert all(numpy.allclose(result[i], numpy.asarray(r, dtype=float),
|
|
rtol=reltol, atol=abstol)
|
|
for i, r in enumerate(self.ref))
|
|
return
|
|
|
|
for i, r in enumerate(self.ref):
|
|
abs_err = abs(result[i] - r)
|
|
if r == 0:
|
|
assert abs_err < abstol
|
|
else:
|
|
assert abs_err/abs(r) < reltol
|
|
|
|
cases = [
|
|
Case(
|
|
args=(x, y, z),
|
|
exprs=[
|
|
x + y + z,
|
|
x + y - z,
|
|
2*x + 2*y - z,
|
|
(x+y)**2 + (y+z)**2,
|
|
],
|
|
num_args=(2., 3., 4.)
|
|
),
|
|
Case(
|
|
args=(x, y, z),
|
|
exprs=[
|
|
x + sympy.Heaviside(x),
|
|
y + sympy.Heaviside(x),
|
|
z + sympy.Heaviside(x, 1),
|
|
z/sympy.Heaviside(x, 1)
|
|
],
|
|
num_args=(0., 3., 4.)
|
|
),
|
|
Case(
|
|
args=(x, y, z),
|
|
exprs=[
|
|
x + sinc(y),
|
|
y + sinc(y),
|
|
z - sinc(y)
|
|
],
|
|
num_args=(0.1, 0.2, 0.3)
|
|
),
|
|
Case(
|
|
args=(x, y, z),
|
|
exprs=[
|
|
Matrix([[x, x*y], [sin(z) + 4, x**z]]),
|
|
x*y+sin(z)-x**z,
|
|
Matrix([x*x, sin(z), x**z])
|
|
],
|
|
num_args=(1.,2.,3.),
|
|
requires_numpy=True
|
|
),
|
|
Case(
|
|
args=(x, y),
|
|
exprs=[(x + y - 1)**2, x, x + y,
|
|
(x + y)/(2*x + 1) + (x + y - 1)**2, (2*x + 1)**(x + y)],
|
|
num_args=(1,2)
|
|
)
|
|
]
|
|
for case in cases:
|
|
if not numpy and case.requires_numpy:
|
|
continue
|
|
for cse in [False, True, minmem, dummy_cse]:
|
|
f = case.lambdify(cse=cse)
|
|
result = f(*case.num_args)
|
|
case.assertAllClose(result)
|
|
|
|
def test_deprecated_set():
|
|
with warns_deprecated_sympy():
|
|
lambdify({x, y}, x + y)
|
|
|
|
def test_issue_13881():
|
|
if not numpy:
|
|
skip("numpy not installed.")
|
|
|
|
X = MatrixSymbol('X', 3, 1)
|
|
|
|
f = lambdify(X, X.T*X, 'numpy')
|
|
assert f(numpy.array([1, 2, 3])) == 14
|
|
assert f(numpy.array([3, 2, 1])) == 14
|
|
|
|
f = lambdify(X, X*X.T, 'numpy')
|
|
assert f(numpy.array([1, 2, 3])) == 14
|
|
assert f(numpy.array([3, 2, 1])) == 14
|
|
|
|
f = lambdify(X, (X*X.T)*X, 'numpy')
|
|
arr1 = numpy.array([[1], [2], [3]])
|
|
arr2 = numpy.array([[14],[28],[42]])
|
|
|
|
assert numpy.array_equal(f(arr1), arr2)
|
|
|
|
|
|
def test_23536_lambdify_cse_dummy():
|
|
|
|
f = Function('x')(y)
|
|
g = Function('w')(y)
|
|
expr = z + (f**4 + g**5)*(f**3 + (g*f)**3)
|
|
expr = expr.expand()
|
|
eval_expr = lambdify(((f, g), z), expr, cse=True)
|
|
ans = eval_expr((1.0, 2.0), 3.0) # shouldn't raise NameError
|
|
assert ans == 300.0 # not a list and value is 300
|
|
|
|
|
|
class LambdifyDocstringTestCase:
|
|
SIGNATURE = None
|
|
EXPR = None
|
|
SRC = None
|
|
|
|
def __init__(self, docstring_limit, expected_redacted):
|
|
self.docstring_limit = docstring_limit
|
|
self.expected_redacted = expected_redacted
|
|
|
|
@property
|
|
def expected_expr(self):
|
|
expr_redacted_msg = 'EXPRESSION REDACTED DUE TO LENGTH'
|
|
return self.EXPR if not self.expected_redacted else expr_redacted_msg
|
|
|
|
@property
|
|
def expected_src(self):
|
|
src_redacted_msg = 'SOURCE CODE REDACTED DUE TO LENGTH'
|
|
return self.SRC if not self.expected_redacted else src_redacted_msg
|
|
|
|
@property
|
|
def expected_docstring(self):
|
|
expected_docstring = (
|
|
f'Created with lambdify. Signature:\n\n'
|
|
f'func({self.SIGNATURE})\n\n'
|
|
f'Expression:\n\n'
|
|
f'{self.expected_expr}\n\n'
|
|
f'Source code:\n\n'
|
|
f'{self.expected_src}\n\n'
|
|
f'Imported modules:\n\n'
|
|
)
|
|
return expected_docstring
|
|
|
|
def __len__(self):
|
|
return len(self.expected_docstring)
|
|
|
|
def __repr__(self):
|
|
return (
|
|
f'{self.__class__.__name__}('
|
|
f'docstring_limit={self.docstring_limit}, '
|
|
f'expected_redacted={self.expected_redacted})'
|
|
)
|
|
|
|
|
|
def test_lambdify_docstring_size_limit_simple_symbol():
|
|
|
|
class SimpleSymbolTestCase(LambdifyDocstringTestCase):
|
|
SIGNATURE = 'x'
|
|
EXPR = 'x'
|
|
SRC = (
|
|
'def _lambdifygenerated(x):\n'
|
|
' return x\n'
|
|
)
|
|
|
|
x = symbols('x')
|
|
|
|
test_cases = (
|
|
SimpleSymbolTestCase(docstring_limit=None, expected_redacted=False),
|
|
SimpleSymbolTestCase(docstring_limit=100, expected_redacted=False),
|
|
SimpleSymbolTestCase(docstring_limit=1, expected_redacted=False),
|
|
SimpleSymbolTestCase(docstring_limit=0, expected_redacted=True),
|
|
SimpleSymbolTestCase(docstring_limit=-1, expected_redacted=True),
|
|
)
|
|
for test_case in test_cases:
|
|
lambdified_expr = lambdify(
|
|
[x],
|
|
x,
|
|
'sympy',
|
|
docstring_limit=test_case.docstring_limit,
|
|
)
|
|
assert lambdified_expr.__doc__ == test_case.expected_docstring
|
|
|
|
|
|
def test_lambdify_docstring_size_limit_nested_expr():
|
|
|
|
class ExprListTestCase(LambdifyDocstringTestCase):
|
|
SIGNATURE = 'x, y, z'
|
|
EXPR = (
|
|
'[x, [y], z, x**3 + 3*x**2*y + 3*x**2*z + 3*x*y**2 + 6*x*y*z '
|
|
'+ 3*x*z**2 +...'
|
|
)
|
|
SRC = (
|
|
'def _lambdifygenerated(x, y, z):\n'
|
|
' return [x, [y], z, x**3 + 3*x**2*y + 3*x**2*z + 3*x*y**2 '
|
|
'+ 6*x*y*z + 3*x*z**2 + y**3 + 3*y**2*z + 3*y*z**2 + z**3]\n'
|
|
)
|
|
|
|
x, y, z = symbols('x, y, z')
|
|
expr = [x, [y], z, ((x + y + z)**3).expand()]
|
|
|
|
test_cases = (
|
|
ExprListTestCase(docstring_limit=None, expected_redacted=False),
|
|
ExprListTestCase(docstring_limit=200, expected_redacted=False),
|
|
ExprListTestCase(docstring_limit=50, expected_redacted=True),
|
|
ExprListTestCase(docstring_limit=0, expected_redacted=True),
|
|
ExprListTestCase(docstring_limit=-1, expected_redacted=True),
|
|
)
|
|
for test_case in test_cases:
|
|
lambdified_expr = lambdify(
|
|
[x, y, z],
|
|
expr,
|
|
'sympy',
|
|
docstring_limit=test_case.docstring_limit,
|
|
)
|
|
assert lambdified_expr.__doc__ == test_case.expected_docstring
|
|
|
|
|
|
def test_lambdify_docstring_size_limit_matrix():
|
|
|
|
class MatrixTestCase(LambdifyDocstringTestCase):
|
|
SIGNATURE = 'x, y, z'
|
|
EXPR = (
|
|
'Matrix([[0, x], [x + y + z, x**3 + 3*x**2*y + 3*x**2*z + 3*x*y**2 '
|
|
'+ 6*x*y*z...'
|
|
)
|
|
SRC = (
|
|
'def _lambdifygenerated(x, y, z):\n'
|
|
' return ImmutableDenseMatrix([[0, x], [x + y + z, x**3 '
|
|
'+ 3*x**2*y + 3*x**2*z + 3*x*y**2 + 6*x*y*z + 3*x*z**2 + y**3 '
|
|
'+ 3*y**2*z + 3*y*z**2 + z**3]])\n'
|
|
)
|
|
|
|
x, y, z = symbols('x, y, z')
|
|
expr = Matrix([[S.Zero, x], [x + y + z, ((x + y + z)**3).expand()]])
|
|
|
|
test_cases = (
|
|
MatrixTestCase(docstring_limit=None, expected_redacted=False),
|
|
MatrixTestCase(docstring_limit=200, expected_redacted=False),
|
|
MatrixTestCase(docstring_limit=50, expected_redacted=True),
|
|
MatrixTestCase(docstring_limit=0, expected_redacted=True),
|
|
MatrixTestCase(docstring_limit=-1, expected_redacted=True),
|
|
)
|
|
for test_case in test_cases:
|
|
lambdified_expr = lambdify(
|
|
[x, y, z],
|
|
expr,
|
|
'sympy',
|
|
docstring_limit=test_case.docstring_limit,
|
|
)
|
|
assert lambdified_expr.__doc__ == test_case.expected_docstring
|