def evalf_sum(expr, prec, options):
func = expr.function
limits = expr.limits
if len(limits) != 1 or not isinstance(limits[0], Tuple) or \
len(limits[0]) != 3:
raise NotImplementedError
prec2 = prec + 10
try:
n, a, b = limits[0]
if b != S.Infinity or a != int(a):
raise NotImplementedError
# Use fast hypergeometric summation if possible
v = hypsum(func, n, int(a), prec2)
delta = prec - fastlog(v)
if fastlog(v) < -10:
v = hypsum(func, n, int(a), delta)
return v, None, min(prec, delta), None
except NotImplementedError:
# Euler-Maclaurin summation for general series
eps = C.Float(2.0)**(-prec)
for i in range(1, 5):
m = n = 2**i * prec
s, err = expr.euler_maclaurin(m=m, n=n, eps=eps, \
eval_integral=False)
err = err.evalf()
if err <= eps:
break
err = fastlog(evalf(abs(err), 20, options)[0])
re, im, re_acc, im_acc = evalf(s, prec2, options)
re_acc = max(re_acc, -err)
im_acc = max(im_acc, -err)
return re, im, re_acc, im_acc
def _eval_evalf(self, prec):
# Lookup mpmath function based on name
fname = self.func.__name__
try:
if not hasattr(mpmath, fname):
from sympy.utilities.lambdify import MPMATH_TRANSLATIONS
fname = MPMATH_TRANSLATIONS[fname]
func = getattr(mpmath, fname)
except (AttributeError, KeyError):
try:
return C.Float(self._imp_(*self.args), prec)
except (AttributeError, TypeError):
return
# Convert all args to mpf or mpc
try:
args = [arg._to_mpmath(prec) for arg in self.args]
except ValueError:
return
# Set mpmath precision and apply. Make sure precision is restored
# afterwards
orig = mpmath.mp.prec
try:
mpmath.mp.prec = prec
v = func(*args)
finally:
mpmath.mp.prec = orig
return Expr._from_mpmath(v, prec)
def evalf_piecewise(expr, prec, options):
if 'subs' in options:
expr = expr.subs(options['subs'])
del options['subs']
if hasattr(expr, 'func'):
return evalf(expr, prec, options)
if type(expr) == float:
return evalf(C.Float(expr), prec, options)
if type(expr) == int:
return evalf(C.Integer(expr), prec, options)
# We still have undefined symbols
raise NotImplementedError
def evalf_sum(expr, prec, options):
func = expr.function
limits = expr.limits
if len(limits) != 1 or len(limits[0]) != 3:
raise NotImplementedError
prec2 = prec + 10
try:
n, a, b = limits[0]
if b != S.Infinity or a != int(a):
raise NotImplementedError
# Use fast hypergeometric summation if possible
v = hypsum(func, n, int(a), prec2)
delta = prec - fastlog(v)
if fastlog(v) < -10:
v = hypsum(func, n, int(a), delta)
return v, None, min(prec, delta), None
except NotImplementedError:
# Euler-Maclaurin summation for general series
eps = C.Float(2.0)**(-prec)
for i in range(1, 5):
m = n = 2**i * prec
s, err = expr.euler_maclaurin(m=m,
n=n,
eps=eps,
eval_integral=False)
err = err.evalf()
if err <= eps:
break
err = fastlog(evalf(abs(err), 20, options)[0])
try:
re, im, re_acc, im_acc = evalf(s, prec2, options)
except TypeError: # issue 3174
# when should it try subs if they are in options?
raise NotImplementedError
if re_acc is None:
re_acc = -err
if im_acc is None:
im_acc = -err
return re, im, re_acc, im_acc
