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"""Real and complex elements. """
from sympy.external.gmpy import MPQ
from sympy.polys.domains.domainelement import DomainElement
from sympy.utilities import public
from mpmath.ctx_mp_python import PythonMPContext, _mpf, _mpc, _constant
from mpmath.libmp import (MPZ_ONE, fzero, fone, finf, fninf, fnan,
round_nearest, mpf_mul, repr_dps, int_types,
from_int, from_float, from_str, to_rational)
@public
class RealElement(_mpf, DomainElement):
"""An element of a real domain. """
__slots__ = ('__mpf__',)
def _set_mpf(self, val):
self.__mpf__ = val
_mpf_ = property(lambda self: self.__mpf__, _set_mpf)
def parent(self):
return self.context._parent
@public
class ComplexElement(_mpc, DomainElement):
"""An element of a complex domain. """
__slots__ = ('__mpc__',)
def _set_mpc(self, val):
self.__mpc__ = val
_mpc_ = property(lambda self: self.__mpc__, _set_mpc)
def parent(self):
return self.context._parent
new = object.__new__
@public
class MPContext(PythonMPContext):
def __init__(ctx, prec=53, dps=None, tol=None, real=False):
ctx._prec_rounding = [prec, round_nearest]
if dps is None:
ctx._set_prec(prec)
else:
ctx._set_dps(dps)
ctx.mpf = RealElement
ctx.mpc = ComplexElement
ctx.mpf._ctxdata = [ctx.mpf, new, ctx._prec_rounding]
ctx.mpc._ctxdata = [ctx.mpc, new, ctx._prec_rounding]
if real:
ctx.mpf.context = ctx
else:
ctx.mpc.context = ctx
ctx.constant = _constant
ctx.constant._ctxdata = [ctx.mpf, new, ctx._prec_rounding]
ctx.constant.context = ctx
ctx.types = [ctx.mpf, ctx.mpc, ctx.constant]
ctx.trap_complex = True
ctx.pretty = True
if tol is None:
ctx.tol = ctx._make_tol()
elif tol is False:
ctx.tol = fzero
else:
ctx.tol = ctx._convert_tol(tol)
ctx.tolerance = ctx.make_mpf(ctx.tol)
if not ctx.tolerance:
ctx.max_denom = 1000000
else:
ctx.max_denom = int(1/ctx.tolerance)
ctx.zero = ctx.make_mpf(fzero)
ctx.one = ctx.make_mpf(fone)
ctx.j = ctx.make_mpc((fzero, fone))
ctx.inf = ctx.make_mpf(finf)
ctx.ninf = ctx.make_mpf(fninf)
ctx.nan = ctx.make_mpf(fnan)
def _make_tol(ctx):
hundred = (0, 25, 2, 5)
eps = (0, MPZ_ONE, 1-ctx.prec, 1)
return mpf_mul(hundred, eps)
def make_tol(ctx):
return ctx.make_mpf(ctx._make_tol())
def _convert_tol(ctx, tol):
if isinstance(tol, int_types):
return from_int(tol)
if isinstance(tol, float):
return from_float(tol)
if hasattr(tol, "_mpf_"):
return tol._mpf_
prec, rounding = ctx._prec_rounding
if isinstance(tol, str):
return from_str(tol, prec, rounding)
raise ValueError("expected a real number, got %s" % tol)
def _convert_fallback(ctx, x, strings):
raise TypeError("cannot create mpf from " + repr(x))
@property
def _repr_digits(ctx):
return repr_dps(ctx._prec)
@property
def _str_digits(ctx):
return ctx._dps
def to_rational(ctx, s, limit=True):
p, q = to_rational(s._mpf_)
# Needed for GROUND_TYPES=flint if gmpy2 is installed because mpmath's
# to_rational() function returns a gmpy2.mpz instance and if MPQ is
# flint.fmpq then MPQ(p, q) will fail.
p = int(p)
if not limit or q <= ctx.max_denom:
return p, q
p0, q0, p1, q1 = 0, 1, 1, 0
n, d = p, q
while True:
a = n//d
q2 = q0 + a*q1
if q2 > ctx.max_denom:
break
p0, q0, p1, q1 = p1, q1, p0 + a*p1, q2
n, d = d, n - a*d
k = (ctx.max_denom - q0)//q1
number = MPQ(p, q)
bound1 = MPQ(p0 + k*p1, q0 + k*q1)
bound2 = MPQ(p1, q1)
if not bound2 or not bound1:
return p, q
elif abs(bound2 - number) <= abs(bound1 - number):
return bound2.numerator, bound2.denominator
else:
return bound1.numerator, bound1.denominator
def almosteq(ctx, s, t, rel_eps=None, abs_eps=None):
t = ctx.convert(t)
if abs_eps is None and rel_eps is None:
rel_eps = abs_eps = ctx.tolerance or ctx.make_tol()
if abs_eps is None:
abs_eps = ctx.convert(rel_eps)
elif rel_eps is None:
rel_eps = ctx.convert(abs_eps)
diff = abs(s-t)
if diff <= abs_eps:
return True
abss = abs(s)
abst = abs(t)
if abss < abst:
err = diff/abst
else:
err = diff/abss
return err <= rel_eps
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