def test_cosm1_opt():
x = Symbol('x')
expr1 = cos(x) - 1
opt1 = optimize(expr1, [cosm1_opt])
assert cosm1(x) - opt1 == 0
assert opt1.rewrite(cos) == expr1
expr2 = 3*cos(x) - 3
opt2 = optimize(expr2, [cosm1_opt])
assert 3*cosm1(x) == opt2
assert opt2.rewrite(cos) == expr2
expr3 = 3*cos(x) - 5
assert expr3 == optimize(expr3, [cosm1_opt])
expr4 = 3*cos(x) + log(x) - 3
opt4 = optimize(expr4, [cosm1_opt])
assert 3*cosm1(x) + log(x) == opt4
assert opt4.rewrite(cos) == expr4
expr5 = 3*cos(2*x) - 3
opt5 = optimize(expr5, [cosm1_opt])
assert 3*cosm1(2*x) == opt5
assert opt5.rewrite(cos) == expr5
def test_cosm1():
cm1_xy = cosm1(x * y)
ref_xy = cos(x * y) - 1
for wrt, deriv_order in product([x, y, z], range(0, 3)):
assert (cm1_xy.diff(wrt, deriv_order) -
ref_xy.diff(wrt, deriv_order)).rewrite(cos).simplify() == 0
expr_minus2 = cosm1(pi)
assert expr_minus2.rewrite(cos) == -2
assert cosm1(3.14).simplify() == cosm1(3.14) # cannot simplify with 3.14
def test_cosm1_opt():
x = Symbol('x')
expr1 = cos(x) - 1
opt1 = optimize(expr1, [cosm1_opt])
assert cosm1(x) - opt1 == 0
assert opt1.rewrite(cos) == expr1
expr2 = 3 * cos(x) - 3
opt2 = optimize(expr2, [cosm1_opt])
assert 3 * cosm1(x) == opt2
assert opt2.rewrite(cos) == expr2
expr3 = 3 * cos(x) - 5
opt3 = optimize(expr3, [cosm1_opt])
assert 3 * cosm1(x) - 2 == opt3
assert opt3.rewrite(cos) == expr3
cosm1_opt_non_opportunistic = FuncMinusOneOptim(cos,
cosm1,
opportunistic=False)
assert expr3 == optimize(expr3, [cosm1_opt_non_opportunistic])
assert opt1 == optimize(expr1, [cosm1_opt_non_opportunistic])
assert opt2 == optimize(expr2, [cosm1_opt_non_opportunistic])
expr4 = 3 * cos(x) + log(x) - 3
opt4 = optimize(expr4, [cosm1_opt])
assert 3 * cosm1(x) + log(x) == opt4
assert opt4.rewrite(cos) == expr4
expr5 = 3 * cos(2 * x) - 3
opt5 = optimize(expr5, [cosm1_opt])
assert 3 * cosm1(2 * x) == opt5
assert opt5.rewrite(cos) == expr5
expr6 = 2 - 2 * cos(x)
opt6 = optimize(expr6, [cosm1_opt])
assert -2 * cosm1(x) == opt6
assert opt6.rewrite(cos) == expr6
def test_numerical_accuracy_functions():
prntr = SciPyPrinter()
assert prntr.doprint(expm1(x)) == 'numpy.expm1(x)'
assert prntr.doprint(log1p(x)) == 'numpy.log1p(x)'
assert prntr.doprint(cosm1(x)) == 'scipy.special.cosm1(x)'
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
def test_expm1_cosm1_mixed():
x = Symbol('x')
expr1 = exp(x) + cos(x) - 2
opt1 = optimize(expr1, [expm1_opt, cosm1_opt]) # need a combined opt pass?
assert opt1 == cosm1(x) + expm1(x)
def test_cosm1_two_cos_terms():
x, y = map(Symbol, 'x y'.split())
expr1 = cos(x) + cos(y) - 2
opt1 = optimize(expr1, [cosm1_opt])
assert opt1 == cosm1(x) + cosm1(y)
def test_expm1_cosm1_mixed():
x = Symbol('x')
expr1 = exp(x) + cos(x) - 2
opt1 = optimize(expr1, [expm1_opt, cosm1_opt])
assert opt1 == cosm1(x) + expm1(x)
