def H_eff_n(self, n): # k<=m => j<=(n)/2 r = 0 for j in xrange(1, int(math.ceil( n/2. )) + 1 ): b = 2*(2**(2*j)-1)*mpmath.bernoulli(2*j)/mpmath.factorial(2*j) r += b*self.P_0.dot(self.S_k(2*j-1,n-1)).dot(self.P_0) return r
def stirling_series(N):
with mpmath.workdps(100):
coeffs = [
mpmath.bernoulli(2 * n) / (2 * n * (2 * n - 1))
for n in range(1, N + 1)
]
return coeffs
def H_eff_n(self, n):
# k<=m => j<=(n)/2
r = 0
for j in xrange(1, int(math.ceil(n / 2.)) + 1):
b = 2 * (2**(2 * j) - 1) * mpmath.bernoulli(
2 * j) / mpmath.factorial(2 * j)
r += b * self.P_0.dot(self.S_k(2 * j - 1, n - 1)).dot(self.P_0)
return r
def zeta_even_integers(N):
values = []
for n in range(0, N + 1):
zeta_2n = (
(-1)**(n + 1)
* mpmath.bernoulli(2 * n)
* (2 * mpmath.pi)**(2 * n)
/ (2 * mpmath.factorial(2 * n))
)
values.append(zeta_2n)
return values
def bernoulli_num(n):
"""
Returns n'th bernoulli number
Parameters
----------
n : int
positive integer value
return : float
returns bernoulli number
"""
return mp.bernoulli(n)
def _S(self, n):
if n < 1:
raise ValueError("i must be greater than or equal to zero.")
elif n == 1:
return self.L(self.V_od)
elif n == 2:
return -self.L(self.hat(self.V_d, self.S(1)))
else:
r = -self.L(self.hat(self.V_d, self.S(n-1)))
# k<=m => j<=(n-1)/2
for j in xrange(1, int(math.ceil( (n-1)/2 )) + 1 ):
a = 2**(2*j) * mpmath.bernoulli(2*j) / mpmath.factorial(2*j)
r += a * self.L(self.S_k(2*j, n-1))
return r
def _S(self, n):
if n < 1:
raise ValueError("i must be greater than or equal to zero.")
elif n == 1:
return self.L(self.V_od)
elif n == 2:
return -self.L(self.hat(self.V_d, self.S(1)))
else:
r = -self.L(self.hat(self.V_d, self.S(n - 1)))
# k<=m => j<=(n-1)/2
for j in xrange(1, int(math.ceil((n - 1) / 2)) + 1):
a = 2**(2 * j) * mpmath.bernoulli(2 * j) / mpmath.factorial(
2 * j)
r += a * self.L(self.S_k(2 * j, n - 1))
return r
def stirling_series(N):
coeffs = []
with mpmath.workdps(100):
for n in range(1, N + 1):
coeffs.append(mpmath.bernoulli(2 * n) / (2 * n * (2 * n - 1)))
return coeffs
def stirling_series(N):
with mpmath.workdps(100):
coeffs = [mpmath.bernoulli(2*n)/(2*n*(2*n - 1))
for n in range(1, N + 1)]
return coeffs
def test_bernoulli(self):
assert_mpmath_equal(lambda n: sc.bernoulli(int(n))[int(n)],
lambda n: float(mpmath.bernoulli(int(n))),
[IntArg(0, 13000)],
rtol=1e-9, n=13000)
def test_bernoulli(self):
assert_mpmath_equal(lambda n: sc.bernoulli(int(n))[int(n)],
lambda n: float(mpmath.bernoulli(int(n))),
[IntArg(0, 13000)],
rtol=1e-9,
n=13000)
def getNthBernoulli( n ):
return bernoulli( n )
def stirling_series(N):
coeffs = []
with mpmath.workdps(100):
for n in range(1, N + 1):
coeffs.append(mpmath.bernoulli(2 * n) / (2 * n * (2 * n - 1)))
return coeffs
def getNthBernoulliNumberOperator(n):
return bernoulli(n)