def modified_round(w, p=0):
"""
sympy expr.round() function modified so that gives extra digits
in it representation when p <= 0
"""
try:
from mpmath.libmp import prec_to_dps
except ImportError:
from sympy.mpmath.libmp import prec_to_dps
from sympy.core.expr import _mag
from sympy import Pow, Rational, Integer
x = w
if not x.is_number:
raise TypeError('%s is not a number' % type(x))
if x in (S.NaN, S.Infinity, S.NegativeInfinity, S.ComplexInfinity):
return x
if not x.is_real:
i, r = x.as_real_imag()
return i.round(p) + S.ImaginaryUnit*r.round(p)
if not x:
return x
p = int(p)
precs = [f._prec for f in x.atoms(Float)]
dps = prec_to_dps(max(precs)) if precs else None
mag_first_dig = _mag(x)
allow = digits_needed = mag_first_dig + p
if p <= 0:
allow += 1
digits_needed += 1
if dps is not None and allow > dps:
allow = dps
mag = Pow(10, p) # magnitude needed to bring digit p to units place
xwas = x
x += 1/(2*mag) # add the half for rounding
i10 = 10*mag*x.n((dps if dps is not None else digits_needed) + 1)
if i10.is_negative:
x = xwas - 1/(2*mag) # should have gone the other way
i10 = 10*mag*x.n((dps if dps is not None else digits_needed) + 1)
rv = -(Integer(-i10)//10)
else:
rv = Integer(i10)//10
q = 1
if p > 0:
q = mag
elif p < 0:
rv /= mag
rv = Rational(rv, q)
if rv.is_Integer:
# use str or else it won't be a float
return Float(str(rv), digits_needed)
else:
if not allow and rv > w:
allow += 1
return Float(rv, allow)
def evalf(self, n=15, subs=None, maxn=100, chop=False, strict=False, quad=None, verbose=False):
"""
Evaluate the given formula to an accuracy of n digits.
Optional keyword arguments:
subs=<dict>
Substitute numerical values for symbols, e.g.
subs={x:3, y:1+pi}.
maxn=<integer>
Allow a maximum temporary working precision of maxn digits
(default=100)
chop=<bool>
Replace tiny real or imaginary parts in subresults
by exact zeros (default=False)
strict=<bool>
Raise PrecisionExhausted if any subresult fails to evaluate
to full accuracy, given the available maxprec
(default=False)
quad=<str>
Choose algorithm for numerical quadrature. By default,
tanh-sinh quadrature is used. For oscillatory
integrals on an infinite interval, try quad='osc'.
verbose=<bool>
Print debug information (default=False)
"""
# for sake of sage that doesn't like evalf(1)
if n == 1 and isinstance(self, C.Number):
from sympy.core.expr import _mag
rv = self.evalf(2, subs, maxn, chop, strict, quad, verbose)
m = _mag(rv)
rv = rv.round(1 - m)
return rv
if not evalf_table:
_create_evalf_table()
prec = dps_to_prec(n)
options = {"maxprec": max(prec, int(maxn * LG10)), "chop": chop, "strict": strict, "verbose": verbose}
if subs is not None:
options["subs"] = subs
if quad is not None:
options["quad"] = quad
try:
result = evalf(self, prec + 4, options)
except NotImplementedError:
# Fall back to the ordinary evalf
v = self._eval_evalf(prec)
if v is None:
return self
try:
# If the result is numerical, normalize it
result = evalf(v, prec, options)
except NotImplementedError:
# Probably contains symbols or unknown functions
return v
re, im, re_acc, im_acc = result
if re:
p = max(min(prec, re_acc), 1)
# re = mpf_pos(re, p, rnd)
re = C.Float._new(re, p)
else:
re = S.Zero
if im:
p = max(min(prec, im_acc), 1)
# im = mpf_pos(im, p, rnd)
im = C.Float._new(im, p)
return re + im * S.ImaginaryUnit
else:
return re
def evalf(self, n=15, subs=None, maxn=100, chop=False, strict=False, quad=None, verbose=False):
"""
Evaluate the given formula to an accuracy of n digits.
Optional keyword arguments:
subs=<dict>
Substitute numerical values for symbols, e.g.
subs={x:3, y:1+pi}. The substitutions must be given as a
dictionary.
maxn=<integer>
Allow a maximum temporary working precision of maxn digits
(default=100)
chop=<bool>
Replace tiny real or imaginary parts in subresults
by exact zeros (default=False)
strict=<bool>
Raise PrecisionExhausted if any subresult fails to evaluate
to full accuracy, given the available maxprec
(default=False)
quad=<str>
Choose algorithm for numerical quadrature. By default,
tanh-sinh quadrature is used. For oscillatory
integrals on an infinite interval, try quad='osc'.
verbose=<bool>
Print debug information (default=False)
"""
n = n if n is not None else 15
if subs and is_sequence(subs):
raise TypeError('subs must be given as a dictionary')
# for sake of sage that doesn't like evalf(1)
if n == 1 and isinstance(self, C.Number):
from sympy.core.expr import _mag
rv = self.evalf(2, subs, maxn, chop, strict, quad, verbose)
m = _mag(rv)
rv = rv.round(1 - m)
return rv
if not evalf_table:
_create_evalf_table()
prec = dps_to_prec(n)
options = {'maxprec': max(prec, int(maxn*LG10)), 'chop': chop,
'strict': strict, 'verbose': verbose}
if subs is not None:
options['subs'] = subs
if quad is not None:
options['quad'] = quad
try:
result = evalf(self, prec + 4, options)
except NotImplementedError:
# Fall back to the ordinary evalf
v = self._eval_evalf(prec)
if v is None:
return self
try:
# If the result is numerical, normalize it
result = evalf(v, prec, options)
except NotImplementedError:
# Probably contains symbols or unknown functions
return v
re, im, re_acc, im_acc = result
if re:
p = max(min(prec, re_acc), 1)
#re = mpf_pos(re, p, rnd)
re = C.Float._new(re, p)
else:
re = S.Zero
if im:
p = max(min(prec, im_acc), 1)
#im = mpf_pos(im, p, rnd)
im = C.Float._new(im, p)
return re + im*S.ImaginaryUnit
else:
return re
