def besselJ(n, x, order):
"""
Bessel functions.
"""
from pyranha.math import factorial
from fractions import Fraction as F
temp = 0
for m in range(0, int((order - n) / 2) + 1):
temp = temp + F((-1)**m,
factorial(m) * factorial(m + n)) * (x / 2)**(2 * m + n)
return temp
def legendrePn(n, x):
"""
Legendre polynomials.
"""
from pyranha.math import factorial
from fractions import Fraction as F
temp = 0
for k in range(0, int(n / 2) + 1):
temp = temp + (-1)**k * F(
factorial(2 * (n - k)), 2**n * factorial(k) * factorial(n - k) *
factorial(n - 2 * k)) * x**(n - 2 * k)
return temp
def one_delta(p, q, n, c_max, deg, isAver, isCalc, isPrint):
"""
Construction of the expansion 1/DELTA through cosines between radius vectors.
- n is maximum degree of variables;
- c_max is maximum power of cosines;
- deg is degree of 1/DELTA.
"""
from pyranha.math import factorial
start = time.time()
ra = rrr(p, n, 1)
br = one_r(q, n, 1)
if isAver and deg == 1:
for item in br.list:
if item[1] == epst(1):
delta = item[0] * item[1]
else:
delta = br
cos_deg = [1]
for i in range(1, c_max + 1):
if isCalc:
cos_deg.append(cosine(p, q, n, i))
else:
cos_temp = epst()
lf(
cos_temp, PREFIX + 'COS/' + str(n) + '/' + str(i) +
'/cosine_' + str(q) + str(p) + '.epst.boostp.bz2',
df.boost_portable, cf.bzip2)
cos_deg.append(cos_temp)
if isPrint:
if isCalc:
print 'cosine with power of', i, 'is calculated for %.2f' % (
time.time() - start), 's'
else:
print 'cosine with power of', i, 'is read for %.2f' % (
time.time() - start), 's'
##################################################
pt.set_auto_truncate_degree(F(n), [
'x' + str(p), 'y' + str(p), 'u' + str(p), 'v' + str(p), 'x' + str(q),
'y' + str(q), 'u' + str(q), 'v' + str(q)
])
rr = ra * br
for c in range(1, c_max + 1):
legPn = 0
for k in range(0, int(c / 2) + 1):
legPn = legPn + (-1)**k * F(
factorial(2 * (c - k)), 2**c * factorial(k) *
factorial(c - k) * factorial(c - 2 * k)) * cos_deg[c - 2 * k]
rr_n = br * rr**c
if isAver and deg == 1:
temp = 0
for item in rr_n.list:
for jtem in legPn.list:
trig = item[1] * jtem[1]
for ktem in trig.list:
if ktem[1] == 1:
temp = temp + item[0] * jtem[0] * ktem[0]
else:
temp = rr_n * legPn
delta = delta + temp
if isPrint:
print 'Legendre polynomial with power of', c, 'is added for %.2f' % (
time.time() - start), 's'
if deg > 1: delta = delta**deg
pt.unset_auto_truncate_degree()
return delta