def _is_close(a, b, rtol=1e-05, atol=1e-08):
# np.isclose for mp.mpf, i.e. absolute(a - b) <= (atol + rtol * absolute(b))
try:
return [
mp.almosteq(le, ri, rel_eps=rtol, abs_eps=atol)
for le, ri in itertools.zip_longest(a, b)
]
except TypeError:
return mp.almosteq(a, b, rel_eps=rtol, abs_eps=atol)
def dTk(x):
with mp.extradps(extradps):
x = clip(x, -1.0, 1.0)
if mp.almosteq(x, mp.one): return pos
if mp.almosteq(x, -mp.one): return neg
moredps = max(
0,
int(-math.log10(
min(abs(x - mp.one), abs(x + mp.one))) / 2))
moredps = min(moredps, 100)
with mp.extradps(moredps):
t = mp.acos(x)
return k * mp.sin(k * t) / mp.sin(t)
def _filter_corners(self, pts, basis):
r"""A generator to return only those points not on corner positions.
Does nothing (i.e. no filtering) in the 1D case.
"""
if self._dim == 1:
for x in pts: yield x
domains = [basis.get_basis(d).domain() for d in range(self._dim)]
for i, p in pts:
is_corner = True
for d in range(self._dim):
if d != self._idx and not (mp.almosteq(p[d], domains[d][0]) or mp.almosteq(p[d], domains[d][1])):
is_corner = False
if not is_corner:
yield i, p
def ddTk(x):
with mp.extradps(extradps):
x = clip(x, -1.0, 1.0)
if mp.almosteq(x, mp.one): return pos
if mp.almosteq(x, -mp.one): return neg
moredps = max(
0,
int(-math.log10(
min(abs(x - mp.one), abs(x + mp.one))) * 1.5) +
2)
moredps = min(moredps, 100)
with mp.extradps(moredps):
t = mp.acos(x)
s = mp.sin(t)
return -k**2 * mp.cos(k * t) / s**2 + k * mp.cos(
t) * mp.sin(k * t) / s**3
def get_seq(self, n):
seq = np.zeros(n, dtype=np.longlong)
number = self.number
for i in range(n):
a = mp.floor(number)
frac = number - a
seq[i] = a
if mp.almosteq(number, a):
number = 0
else:
number = mp.fdiv(1, frac)
return seq
def isclose(a, b, rel_tol=None, abs_tol=None, use_mp=False):
r"""Test if two numbers agree within an absolute/relative tolerance.
For floating point comparison (i.e. if `use_mp==False`), the default
relative tolerance is `1e-9` and the absolute one `0.0`.
"""
if use_mp:
return mp.almosteq(a, b, rel_eps=rel_tol, abs_eps=abs_tol)
if rel_tol is None:
rel_tol = 1e-9
if abs_tol is None:
abs_tol = 0.0
return abs(a - b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)
def _is_close(a, b, rtol=1e-05, atol=1e-08):
# np.isclose for mp.mpf, i.e. absolute(a - b) <= (atol + rtol * absolute(b))
return mp.almosteq(a, b, rel_eps=rtol, abs_eps=atol)