def evl_f(elmass, series_input, series_type):
"""
Evaluation of the series.
"""
from mpmath import mpf
from pyranha.math import evaluate
# -------- coordinates & masses --------
num_pl = len(elmass[0])
gmj, mpj, km = jacobiAMass(elmass[1], elmass[2])
mm = massesRatio(elmass[1], elmass[2])
mp = [1. / elmass[2]] + [
elmass[1][i] / elmass[1][0] / elmass[2] for i in range(len(elmass[1]))
][1:]
sp = [1. + elmass[2] * sum(mp[1:i + 1]) for i in range(len(elmass[1]))]
# -------- dictionaries --------
evaldict = {'K0': mpf(elmass[1][0])}
evaldict.update({'m' + str(i + 1): mpf(mp[i + 1]) for i in range(num_pl)})
evaldict.update({'s' + str(i + 1): mpf(sp[i + 1]) for i in range(num_pl)})
evaldict.update(
{'L' + str(i + 1): mpf(elmass[0][i][0])
for i in range(num_pl)})
evaldict.update(
{'x' + str(i + 1): mpf(elmass[0][i][1])
for i in range(num_pl)})
evaldict.update(
{'y' + str(i + 1): mpf(elmass[0][i][2])
for i in range(num_pl)})
evaldict.update(
{'u' + str(i + 1): mpf(elmass[0][i][3])
for i in range(num_pl)})
evaldict.update(
{'v' + str(i + 1): mpf(elmass[0][i][4])
for i in range(num_pl)})
evaldict.update(
{'q' + str(i + 1): mpf(elmass[0][i][5])
for i in range(num_pl)})
evaldict.update({
r'\nu_{q' + str(i + 1) + '}':
mpf(gmj[i]**2 * mpj[i]**3 * elmass[0][i][0]**-3)
for i in range(num_pl)
})
if type(series_input) == str:
series = series_type
lf(series, series_input, df.boost_portable, cf.bzip2)
series_eval = evaluate(series, evaldict)
else:
series_eval = evaluate(series_input, evaldict)
return float(series_eval)
def check_items(elmass, series2, isPrint):
"""
Checking accuracy of items of the hamiltonian.
"""
from math import fabs
from mpmath import mpf
from pyranha.math import evaluate
from eps.tools import kepler2cart, kepler2poincare, poincare2kepler, jacobiAMass
elements, gmass, mu = elmass
# -------- masses --------
mp = [1. / mu] + [gmass[i] / gmass[0] / mu for i in range(len(gmass))][1:]
sp = [1. + mu * sum(mp[1:i + 1]) for i in range(len(gmass))]
gmj, mpj, km = jacobiAMass(gmass, mu)
# -------- coordinates --------
rlen1 = range(len(elements))
kepler = [poincare2kepler(elements[i], km[i]) for i in rlen1]
x, y, z = [0. for i in rlen1], [0. for i in rlen1], [0. for i in rlen1]
for i in rlen1:
x[i], y[i], z[i] = kepler2cart(kepler[i], km[i])[:3]
r = [(x[i]**2 + y[i]**2 + z[i]**2)**0.5 for i in rlen1]
PE = [kepler2poincare(kepler[i], km[i]) for i in rlen1]
# pairs 21, 32, 43, 31, 42, 41:
rr = {
'21': r[0] / r[1],
'32': r[1] / r[2],
'43': r[2] / r[3],
'31': r[0] / r[2],
'42': r[1] / r[3],
'41': r[0] / r[3]
}
sc = {
'21': (x[0] * x[1] + y[0] * y[1] + z[0] * z[1]),
'32': (x[1] * x[2] + y[1] * y[2] + z[1] * z[2]),
'43': (x[2] * x[3] + y[2] * y[3] + z[2] * z[3]),
'31': (x[0] * x[2] + y[0] * y[2] + z[0] * z[2]),
'42': (x[1] * x[3] + y[1] * y[3] + z[1] * z[3]),
'41': (x[0] * x[3] + y[0] * y[3] + z[0] * z[3])
}
cs = {
'21': (x[0] * x[1] + y[0] * y[1] + z[0] * z[1]) / r[0] / r[1],
'32': (x[1] * x[2] + y[1] * y[2] + z[1] * z[2]) / r[1] / r[2],
'43': (x[2] * x[3] + y[2] * y[3] + z[2] * z[3]) / r[2] / r[3],
'31': (x[0] * x[2] + y[0] * y[2] + z[0] * z[2]) / r[0] / r[2],
'42': (x[1] * x[3] + y[1] * y[3] + z[1] * z[3]) / r[1] / r[3],
'41': (x[0] * x[3] + y[0] * y[3] + z[0] * z[3]) / r[0] / r[3]
}
dd = {
'21': ((x[1] - x[0])**2 + (y[1] - y[0])**2 + (z[1] - z[0])**2)**-0.5,
'32': ((x[2] - x[1])**2 + (y[2] - y[1])**2 + (z[2] - z[1])**2)**-0.5,
'43': ((x[3] - x[2])**2 + (y[3] - y[2])**2 + (z[3] - z[2])**2)**-0.5,
'31': ((x[2] - x[0])**2 + (y[2] - y[0])**2 + (z[2] - z[0])**2)**-0.5,
'42': ((x[3] - x[1])**2 + (y[3] - y[1])**2 + (z[3] - z[1])**2)**-0.5,
'41': ((x[3] - x[0])**2 + (y[3] - y[0])**2 + (z[3] - z[0])**2)**-0.5
}
# -------- dictionaries --------
evaldict = {'K0': mpf(gmass[0]), 'm1': mpf(mp[1]), 'm2': mpf(mp[2]), 'm3': mpf(mp[3]), 'm4': mpf(mp[4]), 's1': mpf(sp[1]), 's2': mpf(sp[2]), 's3': mpf(sp[3]), 's4': mpf(sp[4]),\
'K1': mpf(gmj[0]**0.5), 'M1': mpf(mpj[0]), 'L1': mpf(PE[0][0]), 'x1': mpf(PE[0][1]), 'y1': mpf(PE[0][2]), 'u1': mpf(PE[0][3]), 'v1': mpf(PE[0][4]), 'q1': mpf(PE[0][5]),\
'K2': mpf(gmj[1]**0.5), 'M2': mpf(mpj[1]), 'L2': mpf(PE[1][0]), 'x2': mpf(PE[1][1]), 'y2': mpf(PE[1][2]), 'u2': mpf(PE[1][3]), 'v2': mpf(PE[1][4]), 'q2': mpf(PE[1][5]),\
'K3': mpf(gmj[2]**0.5), 'M3': mpf(mpj[2]), 'L3': mpf(PE[2][0]), 'x3': mpf(PE[2][1]), 'y3': mpf(PE[2][2]), 'u3': mpf(PE[2][3]), 'v3': mpf(PE[2][4]), 'q3': mpf(PE[2][5]),\
'K4': mpf(gmj[3]**0.5), 'M4': mpf(mpj[3]), 'L4': mpf(PE[3][0]), 'x4': mpf(PE[3][1]), 'y4': mpf(PE[3][2]), 'u4': mpf(PE[3][3]), 'v4': mpf(PE[3][4]), 'q4': mpf(PE[3][5])}
# -------- evaluation --------
temp1_all, temp2_all, length1_all = 0, 0, 0
tmp1, tmp2 = [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]
for file2, series1, length1 in series2:
if file2[0] != 'A':
temp1, temp2 = 0, 0
length1_all += length1
if isPrint: print file2[:-16] + ':',
if file2[:2] == 'H0':
temp1 = evaluate(series1, evaldict)
temp2 = -F(1, 2) * (mpj[0]**3 * gmj[0]**2 * PE[0][0]**-2 +
mpj[1]**3 * gmj[1]**2 * PE[1][0]**-2 +
mpj[2]**3 * gmj[2]**2 * PE[2][0]**-2 +
mpj[3]**3 * gmj[3]**2 * PE[3][0]**-2)
temp1_h0, temp2_h0 = temp1, temp2
if '_21_' in file2:
temp1 = evaluate(series1, evaldict)
if 'H1' in file2:
temp2 = -mp[1] * mp[2] * dd['21']
temp1_all += temp1
temp2_all += temp2
tmp1[0] += temp1
tmp2[0] += temp2
if 'H2' in file2:
temp2 = mp[1] * mp[2] * (mm[1] * sc['21'] -
mm[1] * r[0]**2) * dd['21']**3
temp1_all += mu * temp1
temp2_all += mu * temp2
tmp1[0] += mu * temp1
tmp2[0] += mu * temp2
if 'H3' in file2:
temp2 = -1.5 * mp[1] * mp[2] * (
mm[1] * sc['21'] - mm[1] *
r[0]**2)**2 * dd['21']**5 + 0.5 * mp[1] * mp[2] * (
mm[1] * r[0])**2 * dd['21']**3
temp1_all += mu**2 * temp1
temp2_all += mu**2 * temp2
tmp1[0] += mu**2 * temp1
tmp2[0] += mu**2 * temp2
if '_32_' in file2:
temp1 = evaluate(series1, evaldict)
if 'H1' in file2:
temp2 = -mp[2] * mp[3] * dd['32']
temp1_all += temp1
temp2_all += temp2
tmp1[1] += temp1
tmp2[1] += temp2
if 'H2' in file2:
temp2 = mp[2] * mp[3] * (mm[2] * sc['32'] -
mm[2] * r[1]**2) * dd['32']**3
temp1_all += mu * temp1
temp2_all += mu * temp2
tmp1[1] += mu * temp1
tmp2[1] += mu * temp2
if 'H3' in file2:
temp2 = -1.5 * mp[2] * mp[3] * (
mm[2] * sc['32'] - mm[2] *
r[1]**2)**2 * dd['32']**5 + 0.5 * mp[2] * mp[3] * (
mm[2] * r[1])**2 * dd['32']**3
temp1_all += mu**2 * temp1
temp2_all += mu**2 * temp2
tmp1[1] += mu**2 * temp1
tmp2[1] += mu**2 * temp2
if '_43_' in file2:
temp1 = evaluate(series1, evaldict)
if 'H1' in file2:
temp2 = -mp[3] * mp[4] * dd['43']
temp1_all += temp1
temp2_all += temp2
tmp1[2] += temp1
tmp2[2] += temp2
if 'H2' in file2:
temp2 = mp[3] * mp[4] * (mm[3] * sc['43'] -
mm[3] * r[2]**2) * dd['43']**3
temp1_all += mu * temp1
temp2_all += mu * temp2
tmp1[2] += mu * temp1
tmp2[2] += mu * temp2
if 'H3' in file2:
temp2 = -1.5 * mp[3] * mp[4] * (
mm[3] * sc['43'] - mm[3] *
r[2]**2)**2 * dd['43']**5 + 0.5 * mp[3] * mp[4] * (
mm[3] * r[2])**2 * dd['43']**3
temp1_all += mu**2 * temp1
temp2_all += mu**2 * temp2
tmp1[2] += mu**2 * temp1
tmp2[2] += mu**2 * temp2
if '_31_' in file2:
temp1 = evaluate(series1, evaldict)
if 'H1' in file2:
temp2 = -mp[1] * mp[3] * dd['31']
temp1_all += temp1
temp2_all += temp2
tmp1[3] += temp1
tmp2[3] += temp2
if 'H2' in file2:
temp2 = mp[1] * mp[3] * (
mm[1] * sc['31'] - mm[1] * r[0]**2 + mm[2] * sc['32'] -
mm[2] * sc['21']) * dd['31']**3
temp1_all += mu * temp1
temp2_all += mu * temp2
tmp1[3] += mu * temp1
tmp2[3] += mu * temp2
if 'H3' in file2:
temp2 = -1.5*mp[1]*mp[3]*(mm[1]*sc['31'] - mm[1]*r[0]**2 + mm[2]*sc['32'] - mm[2]*sc['21'])**2 * dd['31']**5 +\
0.5*mp[1]*mp[3]*((mm[1]*r[0])**2 + (mm[2]*r[1])**2 + 2*mm[1]*mm[2]*sc['21']) * dd['31']**3
temp1_all += mu**2 * temp1
temp2_all += mu**2 * temp2
tmp1[3] += mu**2 * temp1
tmp2[3] += mu**2 * temp2
if '_42_' in file2:
temp1 = evaluate(series1, evaldict)
if 'H1' in file2:
temp2 = -mp[2] * mp[4] * dd['42']
temp1_all += temp1
temp2_all += temp2
tmp1[4] += temp1
tmp2[4] += temp2
if 'H2' in file2:
temp2 = mp[2] * mp[4] * (
mm[2] * sc['42'] - mm[2] * r[1]**2 + mm[3] * sc['43'] -
mm[3] * sc['32']) * dd['42']**3
temp1_all += mu * temp1
temp2_all += mu * temp2
tmp1[4] += mu * temp1
tmp2[4] += mu * temp2
if 'H3' in file2:
temp2 = -1.5*mp[2]*mp[4]*(mm[2]*sc['42'] - mm[2]*r[1]**2 + mm[3]*sc['43'] - mm[3]*sc['32'])**2 * dd['42']**5 +\
0.5*mp[2]*mp[4]*((mm[2]*r[1])**2 + (mm[3]*r[2])**2 + 2*mm[2]*mm[3]*sc['32']) * dd['42']**3
temp1_all += mu**2 * temp1
temp2_all += mu**2 * temp2
tmp1[4] += mu**2 * temp1
tmp2[4] += mu**2 * temp2
if '_41_' in file2:
temp1 = evaluate(series1, evaldict)
if 'H1' in file2:
temp2 = -mp[1] * mp[4] * dd['41']
temp1_all += temp1
temp2_all += temp2
tmp1[5] += temp1
tmp2[5] += temp2
if 'H2' in file2:
temp2 = mp[1] * mp[4] * (
mm[1] * sc['41'] - mm[1] * r[0]**2 + mm[2] * sc['42'] -
mm[2] * sc['21'] + mm[3] * sc['43'] -
mm[3] * sc['31']) * dd['41']**3
temp1_all += mu * temp1
temp2_all += mu * temp2
tmp1[5] += mu * temp1
tmp2[5] += mu * temp2
if 'H3' in file2:
temp2 = -1.5*mp[1]*mp[4]*(mm[1]*sc['41'] - mm[1]*r[0]**2 + mm[2]*sc['42'] - mm[2]*sc['21'] + mm[3]*sc['43'] - mm[3]*sc['31'])**2 * dd['41']**5 +\
0.5*mp[1]*mp[4]*((mm[1]*r[0])**2 + (mm[2]*r[1])**2 + (mm[3]*r[2])**2 + 2*mm[1]*mm[2]*sc['21'] + 2*mm[1]*mm[3]*sc['31'] + 2*mm[2]*mm[3]*sc['32']) * dd['41']**3
temp1_all += mu**2 * temp1
temp2_all += mu**2 * temp2
tmp1[5] += mu**2 * temp1
tmp2[5] += mu**2 * temp2
if 'H1_44_' in file2:
temp1 = evaluate(series1, evaldict)
temp2 = mp[2] * (mm[1] * sc['21']) * r[1]**-3 + mp[3] * (
mm[1] * sc['31'] + mm[2] * sc['32']) * r[2]**-3 + mp[4] * (
mm[1] * sc['41'] + mm[2] * sc['42'] +
mm[3] * sc['43']) * r[3]**-3
temp1_all += temp1
temp2_all += temp2
tmp1[6] += temp1
tmp2[6] += temp2
if 'H2_44_' in file2:
temp1 = evaluate(series1, evaldict)
temp2 = mp[2]*(-1.5*(mm[1]*sc['21'])**2*r[1]**-5 + 0.5*(mm[1]*r[0])**2 * r[1]**-3) + \
mp[3]*(-1.5*(mm[1]*sc['31'] + mm[2]*sc['32'])**2 * r[2]**-5 + 0.5*((mm[1]*r[0])**2 + (mm[2]*r[1])**2 + 2*mm[1]*mm[2]*sc['21']) * r[2]**-3) + \
mp[4]*(-1.5*(mm[1]*sc['41'] + mm[2]*sc['42'] + mm[3]*sc['43'])**2 * r[3]**-5 + \
0.5*((mm[1]*r[0])**2 + (mm[2]*r[1])**2 + (mm[3]*r[2])**2 + 2*mm[1]*mm[2]*sc['21'] + 2*mm[2]*mm[3]*sc['32'] + 2*mm[1]*mm[3]*sc['31']) * r[3]**-3)
temp1_all += mu * temp1
temp2_all += mu * temp2
tmp1[6] += mu * temp1
tmp2[6] += mu * temp2
if 'H3_44_' in file2:
temp1 = evaluate(series1, evaldict)
temp2 = mp[2]*(2.5*(mm[1]*sc['21'])**3 * r[1]**-7 - 1.5*(mm[1]*sc['21'])*(mm[1]*r[0])**2 * r[1]**-5) + \
mp[3]*(2.5*(mm[1]*sc['31'] + mm[2]*sc['32'])**3 * r[2]**-7 - 1.5*(mm[1]*sc['31'] + mm[2]*sc['32'])*((mm[1]*r[0])**2 + (mm[2]*r[1])**2 + 2*mm[1]*mm[2]*sc['21']) * r[2]**-5) + \
mp[4]*(2.5*(mm[1]*sc['41'] + mm[2]*sc['42'] + mm[3]*sc['43'])**3 * r[3]**-7 - \
1.5*(mm[1]*sc['41'] + mm[2]*sc['42'] + mm[3]*sc['43'])* \
((mm[1]*r[0])**2 + (mm[2]*r[1])**2 + (mm[3]*r[2])**2 + 2*mm[1]*mm[2]*sc['21'] + 2*mm[2]*mm[3]*sc['32'] + 2*mm[1]*mm[3]*sc['31']) * r[3]**-5)
temp1_all += mu**2 * temp1
temp2_all += mu**2 * temp2
tmp1[6] += mu**2 * temp1
tmp2[6] += mu**2 * temp2
if isPrint:
if file2[:2] != 'H0':
print '%.12e' % temp1, '%.12e' % temp2, '%.1e' % fabs(
(temp1 - temp2) / temp2), length1
else:
print '%.12e' % temp1, '%.12e' % temp2, '%.1e' % 0, length1
print '\n'
for i in range(7):
if isPrint:
print i + 1, '%.12e' % tmp1[i], '%.12e' % tmp2[i], '%.1e' % fabs(
(tmp1[i] - tmp2[i]) / tmp2[i])
h0_1 = temp1_h0 + gmass[0] * mu * temp1_all
h0_2 = temp2_h0 + gmass[0] * mu * temp2_all
prec = fabs((h0_2 - h0_1) / h0_2)
if isPrint:
print '%.12e' % temp1_all, '%.12e' % temp2_all, '%.1e' % fabs(
(temp1_all - temp2_all) / temp2_all), length1_all
print '%.12e' % h0_1, '%.12e' % h0_2, '%.1e' % prec, length1_all + 4
return h0_1, h0_2, prec
def check_base(elmass, num=0, p=1, q=2, c_max=25, deg=1):
"""
Checking accuracy of base series.
"""
from math import fabs
from mpmath import mpf
from pyranha.math import evaluate
from eps.tools import kepler2cart, kepler2poincare, jacobiAMass
elements, gmass, mu = elmass
# -------- masses --------
mp = [1. / mu] + [gmass[i] / gmass[0] / mu for i in range(len(gmass))][1:]
sp = [1. + mu * sum(mp[1:i + 1]) for i in range(len(gmass))]
gmj, mpj, km = jacobiAMass(gmass, mu)
# -------- coordinates --------
rlen1 = range(len(elements))
x, y, z = [0. for i in rlen1], [0. for i in rlen1], [0. for i in rlen1]
for i in rlen1:
x[i], y[i], z[i] = kepler2cart(elements[i], km[i])[:3]
r = [(x[i]**2 + y[i]**2 + z[i]**2)**0.5 for i in rlen1]
PE = [kepler2poincare(elements[i], km[i]) for i in rlen1]
# pairs 21, 32, 43, 31, 42, 41:
rr = {
'21': r[0] / r[1],
'32': r[1] / r[2],
'43': r[2] / r[3],
'31': r[0] / r[2],
'42': r[1] / r[3],
'41': r[0] / r[3]
}
cs = {
'21': (x[0] * x[1] + y[0] * y[1] + z[0] * z[1]) / r[0] / r[1],
'32': (x[1] * x[2] + y[1] * y[2] + z[1] * z[2]) / r[1] / r[2],
'43': (x[2] * x[3] + y[2] * y[3] + z[2] * z[3]) / r[2] / r[3],
'31': (x[0] * x[2] + y[0] * y[2] + z[0] * z[2]) / r[0] / r[2],
'42': (x[1] * x[3] + y[1] * y[3] + z[1] * z[3]) / r[1] / r[3],
'41': (x[0] * x[3] + y[0] * y[3] + z[0] * z[3]) / r[0] / r[3]
}
dd = {
'21': ((x[1] - x[0])**2 + (y[1] - y[0])**2 + (z[1] - z[0])**2)**-0.5,
'32': ((x[2] - x[1])**2 + (y[2] - y[1])**2 + (z[2] - z[1])**2)**-0.5,
'43': ((x[3] - x[2])**2 + (y[3] - y[2])**2 + (z[3] - z[2])**2)**-0.5,
'31': ((x[2] - x[0])**2 + (y[2] - y[0])**2 + (z[2] - z[0])**2)**-0.5,
'42': ((x[3] - x[1])**2 + (y[3] - y[1])**2 + (z[3] - z[1])**2)**-0.5,
'41': ((x[3] - x[0])**2 + (y[3] - y[0])**2 + (z[3] - z[0])**2)**-0.5
}
# -------- dictionaries --------
evaldict = {'K0': mpf(gmass[0]), 'm1': mpf(mp[1]), 'm2': mpf(mp[2]), 'm3': mpf(mp[3]), 'm4': mpf(mp[4]), 's1': mpf(sp[1]), 's2': mpf(sp[2]), 's3': mpf(sp[3]), 's4': mpf(sp[4]),\
'K1': mpf(gmj[0]**0.5), 'M1': mpf(mpj[0]), 'L1': mpf(PE[0][0]), 'x1': mpf(PE[0][1]), 'y1': mpf(PE[0][2]), 'u1': mpf(PE[0][3]), 'v1': mpf(PE[0][4]), 'q1': mpf(PE[0][5]),\
'K2': mpf(gmj[1]**0.5), 'M2': mpf(mpj[1]), 'L2': mpf(PE[1][0]), 'x2': mpf(PE[1][1]), 'y2': mpf(PE[1][2]), 'u2': mpf(PE[1][3]), 'v2': mpf(PE[1][4]), 'q2': mpf(PE[1][5]),\
'K3': mpf(gmj[2]**0.5), 'M3': mpf(mpj[2]), 'L3': mpf(PE[2][0]), 'x3': mpf(PE[2][1]), 'y3': mpf(PE[2][2]), 'u3': mpf(PE[2][3]), 'v3': mpf(PE[2][4]), 'q3': mpf(PE[2][5]),\
'K4': mpf(gmj[3]**0.5), 'M4': mpf(mpj[3]), 'L4': mpf(PE[3][0]), 'x4': mpf(PE[3][1]), 'y4': mpf(PE[3][2]), 'u4': mpf(PE[3][3]), 'v4': mpf(PE[3][4]), 'q4': mpf(PE[3][5])}
# -------- evaluation x, y, z --------
if num in [0, 1]:
for n in range(1, 17):
start = time.time()
coord_s = xyz(p, n)
coord_e = [x[p - 1], y[p - 1], z[p - 1]]
accuracy = [0, 0, 0]
sum_items = [0, 0, 0]
finish = time.time() - start
for i in range(len(coord_s)):
for item in coord_s[i].list:
for jtem in item[0].list:
sum_items[i] += len(jtem[0].list)
accuracy[i] = fabs(
(coord_e[i] - evaluate(coord_s[i], evaldict)) / coord_e[i])
print 'n =', str(n).rjust(2, ' '), '|x ', ('%.2f'%finish).rjust(5, ' '), str(sum_items[0]).rjust(5, ' '), '%.1e'%accuracy[0], ' ',\
'|y ', ('%.2f'%finish).rjust(5, ' '), str(sum_items[1]).rjust(5, ' '), '%.1e'%accuracy[1], ' ',\
'|z ', ('%.2f'%finish).rjust(5, ' '), str(sum_items[2]).rjust(5, ' '), '%.1e'%accuracy[2]
# -------- evaluation r, 1/r', r/r' --------
if num in [0, 2]:
for n in range(1, 17):
temp, finish, accuracy = [], [], [0, 0, 0]
start = time.time()
temp.append(rrr(p, n, deg))
finish.append(time.time() - start)
start = time.time()
temp.append(one_r(q, n, deg))
finish.append(time.time() - start)
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)
])
start = time.time()
temp.append(rrr(p, n, deg) * one_r(q, n, deg))
finish.append(time.time() - start)
pt.unset_auto_truncate_degree()
sum_items = [0, 0, 0]
for i in range(3):
for item in temp[i].list:
for jtem in item[0].list:
sum_items[i] += len(jtem[0].list)
accuracy[0] = fabs(
(r[p - 1]**deg - evaluate(temp[0], evaldict)) / r[p - 1]**deg)
accuracy[1] = fabs((r[q - 1]**-deg - evaluate(temp[1], evaldict)) /
r[q - 1]**-deg)
accuracy[2] = fabs(
((rr[str(q) + str(p)])**deg - evaluate(temp[2], evaldict)) /
rr[str(q) + str(p)]**deg)
print 'n =', str(n).rjust(2, ' '), '|r ', ('%.2f'%finish[0]).rjust(5, ' '), str(sum_items[0]).rjust(5, ' '), '%.1e'%accuracy[0], ' ',\
'|1/r', ('%.2f'%finish[1]).rjust(5, ' '), str(sum_items[1]).rjust(5, ' '), '%.1e'%accuracy[1], ' ',\
'|r/r', ('%.2f'%finish[2]).rjust(5, ' '), str(sum_items[2]).rjust(5, ' '), '%.1e'%accuracy[2]
# -------- evaluation cos --------
if num in [0, 3]:
for n in range(1, 17):
start = time.time()
temp = cosine(p, q, n, deg)
finish = time.time() - start
sum_items = 0
for item in temp.list:
for jtem in item[0].list:
sum_items += len(jtem[0].list)
accuracy = fabs(
(cs[str(q) + str(p)]**deg - evaluate(temp, evaldict)) /
cs[str(q) + str(p)]**deg)
print 'n =', str(n).rjust(
2, ' '), '|cos', '%.2f' % finish, str(sum_items).rjust(
8, ' '), '%.1e' % accuracy
# -------- evaluation 1/d --------
if num in [0, 4]:
for i in range(1, 17):
start = time.time()
temp = one_delta(p, q, i, c_max, deg, isPrint=False)
finish = time.time() - start
sum_items = 0
for item in temp.list:
for jtem in item[0].list:
sum_items += len(jtem[0].list)
evaluated = evaluate(temp, evaldict)
accuracy = fabs((dd[str(q) + str(p)]**deg - evaluated) /
dd[str(q) + str(p)]**deg)
print 'n =', str(n).rjust(
2, ' '), '|1/d', '%.2f' % finish, str(sum_items).rjust(
8, ' '), '%.16e' % dd[str(q) + str(
p)]**deg, '%.16e' % evulated, '%.1e' % accuracy
def evl_s(elmass=[[], [], 0],
num_pl=4,
order=2,
max_n=0,
func='eqn',
prefix='',
is_q=False):
"""
Evaluation of the constructed series.
"""
from mpmath import mpf
from pyranha.math import evaluate, truncate_degree
from eps.tools import jacobiAMass
# -------- coordinates & masses --------
gmj, mpj, km = jacobiAMass(elmass[1], elmass[2])
mp = [1. / elmass[2]] + [
elmass[1][i] / elmass[1][0] / elmass[2] for i in range(len(elmass[1]))
][1:]
sp = [1. + elmass[2] * sum(mp[1:i + 1]) for i in range(len(elmass[1]))]
# -------- dictionaries --------
evaldict = {'K0': mpf(elmass[1][0]),\
'L1': mpf(elmass[0][0][0]), 'm1': mpf(mp[1]), 's1': mpf(sp[1]), r'\nu_{q1}': mpf(gmj[0]**2*mpj[0]**3*elmass[0][0][0]**-3),\
'L2': mpf(elmass[0][1][0]), 'm2': mpf(mp[2]), 's2': mpf(sp[2]), r'\nu_{q2}': mpf(gmj[1]**2*mpj[1]**3*elmass[0][1][0]**-3),\
'L3': mpf(elmass[0][2][0]), 'm3': mpf(mp[3]), 's3': mpf(sp[3]), r'\nu_{q3}': mpf(gmj[2]**2*mpj[2]**3*elmass[0][2][0]**-3),\
'L4': mpf(elmass[0][3][0]), 'm4': mpf(mp[4]), 's4': mpf(sp[4]), r'\nu_{q4}': mpf(gmj[3]**2*mpj[3]**3*elmass[0][3][0]**-3),\
'x1': mpf(elmass[0][0][1]), 'y1': mpf(elmass[0][0][2]), 'u1': mpf(elmass[0][0][3]), 'v1': mpf(elmass[0][0][4]), 'q1': mpf(elmass[0][0][5]),\
'x2': mpf(elmass[0][1][1]), 'y2': mpf(elmass[0][1][2]), 'u2': mpf(elmass[0][1][3]), 'v2': mpf(elmass[0][1][4]), 'q2': mpf(elmass[0][1][5]),\
'x3': mpf(elmass[0][2][1]), 'y3': mpf(elmass[0][2][2]), 'u3': mpf(elmass[0][2][3]), 'v3': mpf(elmass[0][2][4]), 'q3': mpf(elmass[0][2][5]),\
'x4': mpf(elmass[0][3][1]), 'y4': mpf(elmass[0][3][2]), 'u4': mpf(elmass[0][3][3]), 'v4': mpf(elmass[0][3][4]), 'q4': mpf(elmass[0][3][5])}
for i in range(num_pl, 4):
evaldict.update({'m' + str(i + 1): 0.})
# -------- loop --------
return_temp = {}
for file2 in os.listdir(PREFIX + 'SUM/' + func.upper() + '/' +
func.upper() + str(order) + prefix + '/'):
if func[0] in file2[0]:
if order == 1:
c = (elmass[2] * elmass[1][0])
if order == 2:
c = elmass[1][0] * elmass[2]**order if file2[3] == str(
order) else (elmass[1][0] * elmass[2])**order
if order == 3:
c = elmass[1][0]**2 * elmass[2]**order if (
('_t1h2' in file2[:-16]) or
('_t2h1_h2' in file2[:-16])) else (elmass[1][0] *
elmass[2])**order
series = epst(0)
if is_q or (not is_q
and file2.split('.')[0].split('_')[-1][0] != 'q'):
lf(
series, PREFIX + 'SUM/' + func.upper() + '/' +
func.upper() + str(order) + prefix + '/' + file2,
df.boost_portable, cf.bzip2)
#if max_n > 0:
# series = truncate_degree(series, max_n, pq_list[8:])
if num_pl in [2, 3]:
for key3 in ['m1', 'm2', 'm3', 'm4']:
series = series.subs(key3, F(evaldict[key3]))
series = series.trim()
eval_series = c * evaluate(series, evaldict)
sum_items = 0
for item in series.list:
for jtem in item[0].list:
sum_items += len(jtem[0].list)
print file2[:-16] + ':', '%.16e' % eval_series, sum_items
return_temp.update({file2.split('.')[0]: eval_series})
return return_temp
def txt_q(elmass=[[], [], 0],
PROBLEM='',
paths=['', '', ''],
isDouble=False,
isEval=False):
'''
Writing text-files for the integration process (the fast variables).
'''
from mpmath import mpf
from pyranha.math import degree, evaluate, partial, subs
from eps.tools import jacobiAMass
# -------- elements & masses --------
gmj, mpj, km = jacobiAMass(elmass[1], elmass[2])
mp = [1. / elmass[2]] + [
elmass[1][i] / elmass[1][0] / elmass[2] for i in range(len(elmass[1]))
][1:]
sp = [1. + elmass[2] * sum(mp[1:i + 1]) for i in range(len(elmass[1]))]
list_elem = [jtem + item for item in '1234' for jtem in 'xyuv']
num_pl = len(elmass[0])
order = 2 if (paths[1] != '' and paths[2] != '') else 1
max_range = num_pl * 4 if num_pl in [2, 3] else 16
epst2 = epsd if isDouble else epst
typef = mpf if isEval else float
series = [epst(0) for key in range(len(paths))]
series2 = [0 for key in range(num_pl)]
# -------- dictionaries & lists --------
evaldict = {'K0': typef(elmass[1][0])}
evaldict.update(
{'m' + str(i + 1): typef(mp[i + 1])
for i in range(num_pl)})
evaldict.update(
{'s' + str(i + 1): typef(sp[i + 1])
for i in range(num_pl)})
evaldict.update(
{'L' + str(i + 1): typef(elmass[0][i][0])
for i in range(num_pl)})
const = [
elmass[1][0] * elmass[2], (elmass[1][0] * elmass[2])**2,
elmass[1][0] * elmass[2]**2
]
# -------- hamiltonian --------
for i in range(len(paths[:2 * order - 1])):
lf(series[i], PREFIX + 'SUM/HAM/' + paths[i] + '.epst.boostp.bz2',
df.boost_portable, cf.bzip2)
if num_pl < 4:
for key in paths[:2 * order - 1]:
for key2 in ['m' + str(i + 1) for i in range(num_pl, 4)]:
series[key] = subs(series[key], key2, 0)
series[key] = series[key].trim()
# -------- evaluation of motion equations --------
start = time.time()
for i in range(num_pl):
for key in range(len(paths[:2 * order - 1])):
temp_q = partial(series[key], 'L' + str(i + 1))
if isEval:
c, temp = 0, 0
for item in temp_q.list:
for jtem in item[0].list:
for ktem in jtem[0].list:
c += 1
poly = 1
for j in range(max_range):
poly *= pt(pq_list[num_pl * 2 + j])**degree(
ktem[1],
pq_list[num_pl * 2 + j:num_pl * 2 + 1 + j])
temp += float(
evaluate((ktem[0] * ktem[1] * poly**-1).trim(),
evaldict)) * poly
if c % 100000 == 0: print c
temp_q = const[key] * temp
print 'q' + str(i + 1), '->', c, 'terms for', int(time.time() -
start), 's'
else:
for key2 in evaldict.keys():
temp_q = subs(temp_q, key2, evaldict[key2])
temp_q = const[key] * (temp_q.trim())
print 'q' + str(i + 1), 'for', int(time.time() - start), 's'
series2[i] += temp_q
# -------- write to files equations --------
PATH_SAVE = PREFIX + 'EVL/TXTS/TXT_' + PROBLEM + '/'
if not os.path.exists(PATH_SAVE): os.makedirs(PATH_SAVE)
lines = ['' for key in range(num_pl)]
length = [0 for key in range(num_pl)]
for i in range(num_pl):
for item in series2[i].list:
if type(item[0]) != float:
for jtem in item[0].list:
for ktem in jtem[0].list:
lines[i] += str('%.16e' % ktem[0]).rjust(24, ' ')
length[i] += 1
for elem in list_elem[:max_range]:
deg_elem = degree(ktem[1], [elem])
lines[i] += str(deg_elem).rjust(3, ' ')
lines[i] += '\n'
else:
lines[i] += str('%.16e' % item[0]).rjust(24, ' ')
length[i] += 1
for elem in list_elem[:max_range]:
deg_elem = degree(item[1], [elem])
lines[i] += str(deg_elem).rjust(3, ' ')
lines[i] += '\n'
f2 = open(PATH_SAVE + 'q' + str(i + 1) + '.txt', 'w')
f2.write(str(length[i]) + '\n' + lines[i])
print 'q' + str(i + 1) + ':', length[i]
def sub_h(elmass=[[], [], 0],
PROBLEM='',
prefix='',
postfix='',
part=0,
isDouble=False,
isEval=False):
'''
The substitution mass parameters, denominators and L-elements (semi-major axes) into the Hamiltonian expansion.
'''
from mpmath import mpf
from pyranha.math import degree, evaluate, subs
from eps.tools import jacobiAMass
# -------- elements & masses --------
gmj, mpj, km = jacobiAMass(elmass[1], elmass[2])
mp = [1. / elmass[2]] + [
elmass[1][i] / elmass[1][0] / elmass[2] for i in range(len(elmass[1]))
][1:]
sp = [1. + elmass[2] * sum(mp[1:i + 1]) for i in range(len(elmass[1]))]
list_elem = [jtem + item for item in '1234' for jtem in 'xyuv']
num_pl = len(elmass[0])
max_range = num_pl * 4 if num_pl in [2, 3] else 16
(epst2, type2) = (epsd, 'd') if isDouble else (epst, 't')
typef = mpf if isEval else float
# -------- dictionaries --------
evaldict = {'K0': typef(elmass[1][0])}
evaldict.update(
{'m' + str(i + 1): typef(mp[i + 1])
for i in range(num_pl)})
evaldict.update(
{'s' + str(i + 1): typef(sp[i + 1])
for i in range(num_pl)})
evaldict.update(
{'L' + str(i + 1): typef(elmass[0][i][0])
for i in range(num_pl)})
eval_dnu = {
r'\nu_{q' + str(i + 1) + '}':
typef(gmj[i]**2 * mpj[i]**3 * elmass[0][i][0]**-3)
for i in range(num_pl)
}
# -------- evaluation --------
order = [0, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3]
#index = {0: '', 1: '', 2: '_t1h1_tor', 3: '_2', 4: '_t1h2', 5: '_t2h1_h2', 6: '_t2h1_t1a1', 7: '_t2h1_t1h1', 8: '_t1t1a1', 9: '_t1t1h1', 10: '_3'}
const = [
1., elmass[1][0] * elmass[2], (elmass[2] * elmass[1][0])**2,
elmass[1][0] * elmass[2]**2
]
const += [elmass[1][0]**2 * elmass[2]**3 for i in range(2)] + [
(elmass[1][0] * elmass[2])**3 for i in range(4)
] + [elmass[1][0] * elmass[2]**3]
# -------- hamiltonian --------
start = time.time()
series_sum = 0
PATH_DIR = PREFIX + 'SUM/HAM/HAM' + str(order[part]) + prefix + '/'
for file2 in os.listdir(PATH_DIR):
if postfix == '' or postfix in file2[:-16]:
series = epst2(0)
lf(series, PATH_DIR + file2, df.boost_portable, cf.bzip2)
if num_pl < 4:
for key in ['m' + str(i + 1) for i in range(num_pl, 4)]:
series = subs(series, key, 0)
series = series.trim()
if isEval:
c, stemp = 0, 0
for item in series.list:
for jtem in item[0].list:
c += 1
stemp += jtem[0] * float(evaluate(jtem[1], eval_dnu))
if type(stemp) == int:
temp = stemp
else:
stemp = stemp.trim()
print c, 'denominators'
c, temp = 0, 0
length = len(stemp)
for item in stemp.list:
c += 1
poly = 1
for j in range(max_range):
poly *= pd(pq_list[2 * num_pl + j])**degree(
item[1],
pq_list[2 * num_pl + j:2 * num_pl + 1 + j])
temp += float(
evaluate((item[0] * item[1] * poly**-1).trim(),
evaldict)) * poly
if c % 10000 == 0:
print str(c) + '/' + str(length)
temp = temp.trim()
else:
c, temp = 0, 0
for item in series.list:
for jtem in item[0].list:
c += 1
temp += jtem[0] * evaluate(jtem[1], eval_dnu)
if type(temp) != int:
for key in evaldict.keys():
temp = subs(temp, key, evaldict[key])
print key
temp = temp.trim()
series_sum += const[part] * temp
print str(file2[:-16]) + ':', c, 'terms for', int(time.time() -
start), 's'
# -------- write to file --------
PATH_SAVE = PREFIX + 'EVL/SUMS/SUMS_' + PROBLEM + '/'
if not os.path.exists(PATH_SAVE): os.makedirs(PATH_SAVE)
sf(
series_sum.trim(), PATH_SAVE + '/h' + str(order[part]) +
prefix.lower() + postfix + '.epsd.boostp.bz2', df.boost_portable,
cf.bzip2)
def txt_N(elmass=[[], [], 0], PROBLEM='', order=1, eps=1):
'''
Writing text-files for the integration process (the slow variables).
'''
from math import fabs
from pyranha.math import degree, evaluate, partial
list_elem = [jtem + item for item in '1234' for jtem in 'xyuv']
num_pl = len(elmass[0])
max_range = num_pl * 4 if num_pl in [2, 3] else 16
series = {key: pd(0) for key in ['hm'] + pq_list[2 * num_pl:]}
postfix = ''
# -------- loop --------
for file2 in os.listdir(PREFIX + 'EVL/SUMS/SUMS_' + PROBLEM + '/'):
if int(file2[1]) <= order:
temp = pd(0)
lf(temp, PREFIX + 'EVL/SUMS/SUMS_' + PROBLEM + '/' + file2,
df.boost_portable, cf.bzip2)
series['hm'] += temp
if eps != 1:
postfix = '_' + str(eps)
evaldict = {'x1': elmass[0][0][1], 'y1': elmass[0][0][2], 'u1': elmass[0][0][3], 'v1': elmass[0][0][4],\
'x2': elmass[0][1][1], 'y2': elmass[0][1][2], 'u2': elmass[0][1][3], 'v2': elmass[0][1][4],\
'x3': elmass[0][2][1], 'y3': elmass[0][2][2], 'u3': elmass[0][2][3], 'v3': elmass[0][2][4],\
'x4': elmass[0][3][1], 'y4': elmass[0][3][2], 'u4': elmass[0][3][3], 'v4': elmass[0][3][4]}
temp_sum = 0
for jtem in series['hm'].list:
temp = jtem[0] * jtem[1]
if degree(temp, pq_list[2 * num_pl:]) <= 4:
temp_sum += temp
continue
if fabs(evaluate(temp, evaldict)) > eps:
temp_sum += temp
series['hm'] = temp_sum
# -------- motion equations --------
for item in list_elem[:max_range]:
dict_key = {'x': 'y', 'y': 'x', 'u': 'v', 'v': 'u'}
for key in dict_key.keys():
if item[0] == key:
jtem = item.replace(item[0], dict_key[key])
series[item] = -partial(series['hm'], jtem) if (
jtem[0] in 'qyv') else partial(series['hm'], jtem)
# -------- write to files hamiltonian and equations --------
PATH_SAVE = PREFIX + 'EVL/TXTS/TXT_' + PROBLEM + postfix + '/'
if not os.path.exists(PATH_SAVE): os.makedirs(PATH_SAVE)
lines = {key: '' for key in ['hm'] + pq_list[2 * num_pl:]}
length = {key: 0 for key in ['hm'] + pq_list[2 * num_pl:]}
for what in ['hm'] + pq_list[2 * num_pl:]:
for item in series[what].list:
if type(item[0]) != float:
for jtem in item[0].list:
for ktem in jtem[0].list:
lines[what] += str('%.16e' % ktem[0]).rjust(24, ' ')
length[what] += 1
for elem in list_elem[:max_range]:
deg_elem = degree(ktem[1], [elem])
lines[what] += str(deg_elem).rjust(3, ' ')
lines[what] += '\n'
else:
lines[what] += str('%.16e' % item[0]).rjust(24, ' ')
length[what] += 1
for elem in list_elem[:max_range]:
deg_elem = degree(item[1], [elem])
lines[what] += str(deg_elem).rjust(3, ' ')
lines[what] += '\n'
f2 = open(PATH_SAVE + what + '.txt', 'w')
f2.write(str(length[what]) + '\n' + lines[what])
print what + ':', length[what]
# -------- write to files masses and elements --------
f3 = open(PATH_SAVE + 'el.txt', 'w')
for planet in elmass[0][:num_pl]:
for elem in planet:
f3.write(str('%.16e' % elem).rjust(24, ' '))
f3.write('\n')
f3.close()
f4 = open(PATH_SAVE + 'gm.txt', 'w')
for item in [elmass[2]] + elmass[1][:num_pl + 1]:
f4.write(str('%.16e' % item).rjust(24, ' ') + '\n')
f4.close()
