def test_logaddexp2_opt():
x, y = map(Symbol, 'x y'.split())
expr1 = log(2**x + 2**y) / log(2)
opt1 = optimize(expr1, [logaddexp2_opt])
assert logaddexp2(x, y) - opt1 == 0
assert logaddexp2(y, x) - opt1 == 0
assert opt1.rewrite(log) == expr1
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_logaddexp2():
lae2_xy = logaddexp2(x, y)
ref2_xy = log(2**x + 2**y) / log(2)
for wrt, deriv_order in product([x, y, z], range(0, 3)):
assert (lae2_xy.diff(wrt, deriv_order) -
ref2_xy.diff(wrt, deriv_order)).rewrite(log).simplify() == 0
def lb(x):
return log(x) / log(2)
two_thirds = S.One * 2 / 3
four_thirds = 2 * two_thirds
lbTwoThirds = lb(two_thirds)
lbFourThirds = lb(four_thirds)
lae2_sum_to_2 = logaddexp2(lbTwoThirds, lbFourThirds)
assert lae2_sum_to_2.rewrite(log) == 1
assert lae2_sum_to_2.simplify() == 1
assert logaddexp2(x, y).simplify() == logaddexp2(
x, y) # cannot simplify with x, y
# Optimization procedures for turning A**(-1) * x into MatrixSolve(A, x)
def _matinv_predicate(expr):
# TODO: We should be able to support more than 2 elements
if expr.is_MatMul and len(expr.args) == 2:
left, right = expr.args
if left.is_Inverse and right.shape[1] == 1:
inv_arg = left.arg
if isinstance(inv_arg, MatrixSymbol):
return bool(ask(Q.fullrank(left.arg)))
return False
def _matinv_transform(expr):
left, right = expr.args
inv_arg = left.arg
return MatrixSolve(inv_arg, right)
matinv_opt = ReplaceOptim(_matinv_predicate, _matinv_transform)
logaddexp_opt = ReplaceOptim(log(exp(_v)+exp(_w)), logaddexp(_v, _w))
logaddexp2_opt = ReplaceOptim(log(Pow(2, _v)+Pow(2, _w)), logaddexp2(_v, _w)*log(2))
# Collections of optimizations:
optims_c99 = (expm1_opt, log1p_opt, exp2_opt, log2_opt, log2const_opt)
optims_numpy = optims_c99 + (logaddexp_opt, logaddexp2_opt,) + sinc_opts
optims_scipy = (cosm1_opt,)
left, right = expr.args
if left.is_Inverse and right.shape[1] == 1:
inv_arg = left.arg
if isinstance(inv_arg, MatrixSymbol):
return bool(ask(Q.fullrank(left.arg)))
return False
def _matinv_transform(expr):
left, right = expr.args
inv_arg = left.arg
return MatrixSolve(inv_arg, right)
matinv_opt = ReplaceOptim(_matinv_predicate, _matinv_transform)
logaddexp_opt = ReplaceOptim(log(exp(_v) + exp(_w)), logaddexp(_v, _w))
logaddexp2_opt = ReplaceOptim(log(Pow(2, _v) + Pow(2, _w)),
logaddexp2(_v, _w) * log(2))
# Collections of optimizations:
optims_c99 = (expm1_opt, log1p_opt, exp2_opt, log2_opt, log2const_opt)
optims_numpy = optims_c99 + (
logaddexp_opt,
logaddexp2_opt,
) + sinc_opts
optims_scipy = (cosm1_opt, )
def test_numpy_logaddexp():
lae = logaddexp(a, b)
assert NumPyPrinter().doprint(lae) == 'numpy.logaddexp(a, b)'
lae2 = logaddexp2(a, b)
assert NumPyPrinter().doprint(lae2) == 'numpy.logaddexp2(a, b)'
