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