def eqn_s(max_deg, order=2, num_item=1, t_order_max=15, prefix=''):
"""
"""
from pyranha.math import partial, truncate_degree
if order == 1:
index = ''
if order > 1:
pbrackets = ['t1h1'] if order == 2 else [
't1h2', 't2h1_h2', 't2h1_t1a1', 't2h1_t1h1', 't1t1h1', 't1t1a1'
]
if num_item == 1: index = '_' + str(order)
if num_item > 1:
index = '_' + pbrackets[num_item -
2] + '_tor' + str(t_order_max).rjust(
2, '0')
PATH = PREFIX + 'HDM/SUMS/HAM/HAM' + str(order) + prefix + '/'
for file2 in os.listdir(PATH):
if index in file2 and file2[0] == 'h':
series = epst(0)
lf(series, PATH + file2, df.boost_portable, cf.bzip2)
for i in range(8, len(pq_list)):
motion = -partial(series, pq_list[i]) if (
pq_list[i][0] in 'qyv') else partial(series, pq_list[i])
if max_deg > 0:
motion = truncate_degree(motion, max_deg, pq_list[8:])
PATH_SAVE = PREFIX + 'HDM/SUMS/EQN/EQN' + str(
order) + prefix + '/'
sf(
motion.trim(), PATH_SAVE + 'e' + file2[1:-16] + '_' +
qp_list[i] + '.epst.boostp.bz2', df.boost_portable,
cf.bzip2)
def eqn_1(out_post='', pair=''):
"""
"""
from pyranha.math import partial
out_post = out_post if out_post == '' else '_' + out_post
PATH = PREFIX + 'HDM/HAM1/H1' + out_post + '/'
for file2 in os.listdir(PATH):
if pair in file2 or pair == '':
start = time.time()
series = epst(0)
lf(series, PATH + file2, df.boost_portable, cf.bzip2)
for i in range(len(pq_list)):
motion = -partial(series, pq_list[i]) if (
pq_list[i][0] in 'qyv') else partial(series, pq_list[i])
motion = motion.trim()
if motion != epst(0):
PATH_SAVE = PREFIX + 'HDM/EQN1/H1' + out_post + '/' + qp_list[
i] + '/'
if not os.path.exists(PATH_SAVE): os.makedirs(PATH_SAVE)
sf(
motion, PATH_SAVE + 'e' + file2[1:-16] + '_' +
pq_list[i] + '.epst.boostp.bz2', df.boost_portable,
cf.bzip2)
print file2[:-16], qp_list[i], sum([
len(item.list)
for item in [jtem[0].list[0][0] for jtem in motion.list]
]), str('%.1f' % (time.time() - start)).rjust(4, ' '), 's'
def chn_N(N, num_item=1, t_order_max=15, isDouble=False):
"""
"""
from pyranha.math import partial
if N == 1:
PATH_INT = [
PREFIX + 'HDM/INT' + str(i + 1) + '/H' + str(i + 1) + '/'
for i in range(3)
]
else:
BRACKETS = ['T1H1', 'T1A1'] if N == 2 else [
'T1H2', 'T1A2', 'T2H1_H2', 'T2H1_T1A1', 'T2H1_T1H1', 'T2A1_H2',
'T2A1_T1A1', 'T2A1_T1H1', 'T1T1H1', 'T1T1A1'
]
PATH_INT = PREFIX + 'HDM/INT' + str(N) + '/' + BRACKETS[
num_item - 1] + '_TOR' + str(t_order_max).rjust(2, '0')
(type2, epst2) = ('d', epsd) if isDouble else ('t', epst)
for j in range(len(PATHS_INT)):
list_dir = os.listdir(PATHS_INT[j]) if N > 1 else ['']
for subdir in list_dir:
for file2 in os.listdir(PATHS_INT[j] + subdir + '/'):
start = time.time()
order = int(file2[1])
series = epst2(0)
lf(series, PATHS_INT[j] + subdir + '/' + file2,
df.boost_portable, cf.bzip2)
for i in range(len(pq_list)):
if i in range(4):
s_prev = epst2('s' + str(i)) if i != 0 else 1
part_diff_nu = -3 * epst2('K0')**2 * (
epst2('m' + str(i + 1))**3 * s_prev *
epst2('s' + str(i + 1))**
-1) * epst2('L' + str(i + 1))**-4
epst2.register_custom_derivative(
pq_list[i], lambda temp: temp.partial(pq_list[i]) +
temp.partial(r'\nu_{' + qp_list[i] + r'}'
) * part_diff_nu)
change = partial(series, pq_list[i])
epst2.unregister_all_custom_derivatives()
else:
change = -partial(series, pq_list[i]) if (
pq_list[i][0] in 'qyv') else partial(
series, pq_list[i])
if change != epst2(0):
PATH_SAVE = PREFIX + 'HDM/CHN' + str(
order) + '/' + INT_DIRS[j] + '/' + qp_list[
i] + '/' + subdir + '/'
if not os.path.exists(PATH_SAVE):
os.makedirs(PATH_SAVE)
sf(
change.trim(), PATH_SAVE + 'c' + file2[1:-16] +
'_' + pq_list[i] + '.eps' + type2 + '.boostp.bz2',
df.boost_portable, cf.bzip2)
print PATHS_INT[j] + subdir + '/' + file2[:-16], str(
'%.1f' % (time.time() - start)).rjust(4, ' '), 's'
def d_phi1(out_post='', pair=''):
"""
"""
from pyranha.math import partial
out_post = out_post if out_post == '' else '_' + out_post
PATH_PHI = PREFIX + 'HDM/PHI1/H1' + out_post + '/'
for file2 in os.listdir(PATH_PHI):
if pair in file2 or pair == '':
start = time.time()
series = epst(0)
lf(series, PATH_PHI + file2, df.boost_portable, cf.bzip2)
for i in range(len(pq_list)):
diff = partial(series, pq_list[i])
diff = diff.trim()
if diff != epst(0):
PATH_SAVE = PREFIX + 'HDM/D_PHI1/H1' + out_post + '/' + pq_list[
i] + '/'
if not os.path.exists(PATH_SAVE): os.makedirs(PATH_SAVE)
sf(
diff, PATH_SAVE + file2[:-16] + '_' + pq_list[i] +
'.epst.boostp.bz2', df.boost_portable, cf.bzip2)
print file2[:-16], pq_list[i], sum([
len(item.list)
for item in [jtem[0].list[0][0] for jtem in diff.list]
]), str('%.1f' % (time.time() - start)).rjust(4, ' '), 's'
def d_phi1():
"""
"""
from pyranha.math import partial
PATHS_PHI = [
PREFIX + 'HDM/PHI' + str(i + 1) + '/H' + str(i + 1) + '/'
for i in range(3)
]
for PATH_PHI in PATHS_PHI:
if os.path.isdir(PATH_PHI):
for file2 in os.listdir(PATH_PHI):
start = time.time()
order = int(file2[1])
series = epst(0)
lf(series, PATH_PHI + file2, df.boost_portable, cf.bzip2)
for i in range(len(pq_list)):
diff = partial(series, pq_list[i])
if diff != epst(0):
PATH_SAVE = PREFIX + 'HDM/DIF1/PHI' + str(
order) + '/H' + str(order) + '/' + pq_list[i] + '/'
if not os.path.exists(PATH_SAVE):
os.makedirs(PATH_SAVE)
sf(
diff.trim(), PATH_SAVE + file2[:-16] + '_' +
pq_list[i] + '.epst.boostp.bz2', df.boost_portable,
cf.bzip2)
print '/PHI' + str(order) + '/H' + str(
order) + '/' + file2[:-16], str(
'%.1f' % (time.time() - start)).rjust(4, ' '), 's'
def chn_1(out_post='', pair=''):
"""
"""
from pyranha.math import partial
out_post = out_post if out_post == '' else '_' + out_post
PATH = PREFIX + 'HDM/INT1/H1' + out_post + '/'
for file2 in os.listdir(PATH):
if pair in file2 or pair == '':
start = time.time()
series = epst(0)
lf(series, PATH + file2, df.boost_portable, cf.bzip2)
for i in range(len(pq_list)):
if i in range(4):
s_prev = epst('s' + str(i)) if i != 0 else 1
part_diff_nu = -3 * epst('K0')**2 * (
epst('m' + str(i + 1))**3 * s_prev *
epst('s' + str(i + 1))**-1) * epst('L' +
str(i + 1))**-4
epst.register_custom_derivative(
pq_list[i],
lambda temp: temp.partial(pq_list[i]) + temp.partial(
r'\nu_{' + qp_list[i] + r'}') * part_diff_nu)
change = partial(series, pq_list[i])
epst.unregister_all_custom_derivatives()
else:
change = -partial(series, pq_list[i]) if (
pq_list[i][0] in 'qyv') else partial(
series, pq_list[i])
change = change.trim()
if change != epst(0):
PATH_SAVE = PREFIX + 'HDM/CHN1/H1' + out_post + '/' + qp_list[
i] + '/'
if not os.path.exists(PATH_SAVE): os.makedirs(PATH_SAVE)
sf(
change, PATH_SAVE + 'c' + file2[1:-16] + '_' +
pq_list[i] + '.epst.boostp.bz2', df.boost_portable,
cf.bzip2)
print file2[:-16], qp_list[i], sum([
len(item.list)
for item in [jtem[0].list[0][0] for jtem in change.list]
]), str('%.1f' % (time.time() - start)).rjust(4, ' '), 's'
def eqn_s(max_deg, order=2, out_save=''):
"""
"""
from pyranha.math import partial, truncate_degree
out_save = out_save if out_save == '' else '_' + out_save
PATH = PREFIX + 'SUM/HAM/HAM' + str(order) + out_save + '/'
for file2 in os.listdir(PATH):
if index in file2 and file2[0] == 'h':
series = epst(0)
lf(series, PATH + file2, df.boost_portable, cf.bzip2)
for i in range(8, len(pq_list)):
motion = -partial(series, pq_list[i]) if (
pq_list[i][0] in 'qyv') else partial(series, pq_list[i])
if max_deg > 0:
motion = truncate_degree(motion, max_deg, pq_list[8:])
PATH_SAVE = PREFIX + 'SUM/EQN/EQN' + str(
order) + out_save + '/'
if not os.path.exists(PATH_SAVE): os.makedirs(PATH_SAVE)
sf(
motion.trim(), PATH_SAVE + 'e' + file2[1:-16] + '_' +
qp_list[i] + '.epst.boostp.bz2', df.boost_portable,
cf.bzip2)
def __init__(self,params = __default_params):
from numpy import dot
from mpmath import mpf
from fractions import Fraction as Frac
import sympy
from IPython.parallel import Client
# Set up constants.
self.__eps_val = (1./mpf(299792458.))**2
self.__GG_val = mpf(6.673E-11)
# Various variables.
Gt,I1,GG,m2,L,r,a,v2,Gtxy,ht,Ht,Gxy,h,H,J2,g,G,f,e,E,eps,hs,Hts,Gtxys = [pt(name) for name in ['\\tilde{G}','\\mathcal{I}_1',\
'\\mathcal{G}','m_2','L','r','a','v2','\\tilde{G}_{xy}','\\tilde{h}','\\tilde{H}','G_{xy}','h','H','J_2','g','G','f','e','E',\
'\\varepsilon','h_\\ast','\\tilde{H}_\\ast','\\tilde{G}_{xy\\ast}']]
# The unperturbed Hamiltonian.
H0 = Gt**2 * I1 / 2 - GG**2 * m2**2 * L**-2 / 2
self.__HH0 = H0
# Pieces of the perturbed Hamiltonian.
Gt_vec = [Gtxy * math.sin(ht),-Gtxy * math.cos(ht),Ht]
J2_vec = [0,0,J2]
r_vec = dot(celmec.orbitalR([math.cos(g),math.sin(g),H*G**-1,Gxy*G**-1,math.cos(h),math.sin(h)]),[r*math.cos(f),r*math.sin(f),0])
r_cross_v = [Gxy * math.sin(h),-Gxy * math.cos(h),H]
H1 = -Frac(1,8) * v2 ** 2 - Frac(3,2) * v2 * GG * m2 * r ** -1 + Frac(1,2) * GG**2 * m2**2 * r**-2 +\
Frac(3,2) * GG * m2 * r**-3 * dot(Gt_vec,r_cross_v) + 2 * GG * r**-3 * dot(J2_vec,r_cross_v) +\
GG * r**-3 * (3 * dot(Gt_vec,r_vec) * dot(J2_vec,r_vec) * r**-2 - dot(Gt_vec,J2_vec))
H1 = H1.subs('v2',GG * m2 * (2 * r**-1 - a ** -1)).subs('a',L ** 2 * (GG * m2)**-1)
# Verify formula in the paper.
assert(-Frac(1,8)*GG**4*m2**4*L**-4+r**-1*2*GG**3*m2**3*L**-2-r**-2*3*GG**2*m2**2+GG*r**-3*(\
2*J2*H+3*J2*Gxy**2*Ht*(G**-2)/2+3*m2*Ht*H/2-J2*Ht+(3*m2/2*Gtxy*Gxy-3*J2/2*H*Gxy*Gtxy*G**-2)*math.cos(ht-h)+\
3*J2*(-Frac(1,2)*Gxy**2*Ht*G**-2*math.cos(2*f+2*g)-Frac(1,4)*Gxy*Gtxy*G**-1*(1-H*G**-1)*math.cos(2*f+2*g+ht-h)+\
Frac(1,4)*Gxy*Gtxy*G**-1*(1+H*G**-1)*math.cos(2*f+2*g-ht+h))) == H1)
# Split the Hamiltonian in parts.
A0 = H1.transform(lambda t: (t[0].filter(lambda t: t[1].degree(['r']) == 0),t[1])).filter(lambda t: t[1] == pt(1)).subs('r',pt(1))
A1 = H1.transform(lambda t: (t[0].filter(lambda t: t[1].degree(['r']) == -1),t[1])).filter(lambda t: t[1] == pt(1)).subs('r',pt(1))
A2 = H1.transform(lambda t: (t[0].filter(lambda t: t[1].degree(['r']) == -2),t[1])).filter(lambda t: t[1] == pt(1)).subs('r',pt(1))
A3a = H1.transform(lambda t: (t[0].filter(lambda t: t[1].degree(['r']) == -3),t[1])).filter(lambda t: t[1] == pt(1)).subs('r',pt(1))
A3b = H1.filter(lambda t: t[1] == math.cos(ht - h)).transform(lambda t: (t[0],pt(1))).subs('r',pt(1))
B0 = H1.filter(lambda t: t[1] == math.cos(2*f + 2*g)).transform(lambda t: (t[0],pt(1))).subs('r',pt(1))
B1 = H1.filter(lambda t: t[1] == math.cos(2*f + 2*g + ht - h)).transform(lambda t: (t[0],pt(1))).subs('r',pt(1))
B2 = H1.filter(lambda t: t[1] == math.cos(2*f + 2*g - ht + h)).transform(lambda t: (t[0],pt(1))).subs('r',pt(1))
# Make sure we got them right.
assert(A0 + A1 * r**-1 + A2 * r**-2 + r**-3 * (A3a + A3b * math.cos(ht - h)) + r**-3 * (B0 * math.cos(2*f + 2*g) +\
B1 * math.cos(2*f + 2*g + ht - h) + B2 * math.cos(2*f + 2*g - ht + h)) == H1)
# This is the integrand in f (without the part that is integrated in E).
f_int = A2 * r**-2 + r**-3 * (A3a + A3b * math.cos(ht - h)) + r**-3 * (B0 * math.cos(2*f + 2*g) + B1 * math.cos(2*f + 2*g + ht - h) + B2 * math.cos(2*f + 2*g - ht + h))
# Change the integration variable to f (with the constant parts already taken out of the integral).
f_int *= r**2
# Substitute the definition of 1/r in terms of f.
f_int = f_int.subs('r',pt('rm1')**-1).subs('rm1',GG*m2*G**-2*(1+e*math.cos(f)))
# This is the integrand in E.
E_int = A1 * r**-1
# Change the integration variable to f.
E_int *= r**2
# Change the integration variable to E.
E_int *= L*G*r**-1*GG**-1*m2**-1
assert(E_int == A1*G*L*GG**-1*m2**-1)
# K1.
K1 = GG**2 * m2**2 * G**-1 * L**-3 * (f_int + E_int).filter(lambda t: t[1].t_degree(['f']) == 0)
# K.
K = K1 + A0
# The generator.
chi = G**-1 * (E_int.integrate('E') + f_int.integrate('f')) - L**3 * GG**-2 * m2**-2 * K1.integrate('l')
# Verifiy that chi satisfies the homological equation, yielding K.
assert((math.pbracket(H0,chi,['L','G','H','\\tilde{G}','\\tilde{H}'],['l','g','h','\\tilde{g}','\\tilde{h}']) + H1)\
.subs('r',pt('rm1')**-1).subs('rm1',GG*m2*G**-2*(1+e*math.cos(f))) == K)
# This is the complete Hamiltonian, with the two coordinates compressed into a single one.
HHp = H0 + eps * K.subs('h',ht+hs).subs('\\tilde{H}',Hts-H).subs('\\tilde{G}_{xy}',Gtxys)
# Record it as a member.
self.__HHp = HHp
# F0 and F1.
F0 = HHp.filter(lambda t: t[1].t_degree(['h_\\ast']) == 0).transform(lambda t: (t[0].filter(lambda t: t[1].degree(['\\varepsilon']) == 1),t[1])).subs('\\varepsilon',pt(1))
F1 = HHp.filter(lambda t: t[1].t_degree(['h_\\ast']) == 1).transform(lambda t: (t[0].filter(lambda t: t[1].degree(['\\varepsilon']) == 1),t[1])).subs('\\varepsilon',pt(1)).subs('h_\\ast',pt(0))
assert(H0 + eps * F0 + eps * F1 * math.cos(pt('h_\\ast')) == H0 + eps * K.subs('h',ht+hs).subs('\\tilde{H}',Hts-H).subs('\\tilde{G}_{xy}',Gtxys))
self.__F0 = F0
self.__F1 = F1
# Quartic polynomial.
f4H = (eps**2 * F1 ** 2 - (pt('\\mathcal{H}^\\prime') - H0 - eps * F0)**2)\
.ipow_subs('G_{xy}',2,G**2-H**2)\
.ipow_subs('\\tilde{G}_{xy\\ast}',2,Gt**2-(Hts-H)**2)
a4 = f4H.transform(lambda t: (t[0].filter(lambda t: t[1].degree(['H']) == 0),t[1]))
a3 = f4H.transform(lambda t: (t[0].filter(lambda t: t[1].degree(['H']) == 1),t[1])).subs('H',pt(1)) / 4
a2 = f4H.transform(lambda t: (t[0].filter(lambda t: t[1].degree(['H']) == 2),t[1])).subs('H',pt(1)) / 6
a1 = f4H.transform(lambda t: (t[0].filter(lambda t: t[1].degree(['H']) == 3),t[1])).subs('H',pt(1)) / 4
a0 = f4H.transform(lambda t: (t[0].filter(lambda t: t[1].degree(['H']) == 4),t[1])).subs('H',pt(1))
# NOTE: these are not the polynomial coefficient strictly speaking, they are normalised by 4, 6 and 4
# as shown above and in the assert below.
self.__f4_cf = (a0,a1,a2,a3,a4)
# Check we got them right.
assert(a4+4*a3*H+6*a2*H**2+4*a1*H**3+a0*H**4 == f4H)
# Store the coefficients - from high degree to low.
self.__f4_coeffs = [t[0] * t[1].trim() for t in zip([1,4,6,4,1],self.__f4_cf)]
# Derivatives of the quartic poly.
f4Hp = math.partial(f4H,'H')
f4Hpp = math.partial(f4Hp,'H')
f4Hppp = math.partial(f4Hpp,'H')
f4Hpppp = math.partial(f4Hppp,'H')
# Check the derivatives for consistency.
assert(f4Hp == 4*a3 + 12*a2*H + 12*a1*H**2 + 4*a0*H**3)
assert(f4Hpp == 12*a2 + 24*a1*H + 12*a0*H**2)
assert(f4Hppp == 24*a1 + 24*a0*H)
assert(f4Hpppp == 24*a0)
self.__f4 = [f4H, f4Hp, f4Hpp, f4Hppp, f4Hpppp]
# Invariants for wp.
g2 = a0*a4 - 4*a1*a3 + 3*a2**2
g3 = a0*a2*a4 + 2*a1*a2*a3 - (a2**3) - (a0*a3**2) - (a1**2*a4)
self.__g2 = g2
self.__g3 = g3
# Solve the angles.
# Extract cosine of h_s.
#chs = sympy.solve((spin_gr_theory.__to_sympy(self.HHp.trim())-sympy.Symbol('\\mathcal{H}^\\prime')).replace(sympy.cos(sympy.Symbol('h_\\ast')),sympy.Symbol('chs')),sympy.Symbol('chs'))[0]
#ipy_view = Client().load_balanced_view()
#g_sol = ipy_view.apply_async(spin_gr_theory.__solve_g,chs,spin_gr_theory.__to_sympy(math.partial(self.HHp.trim(),'G')))
#hs_sol = ipy_view.apply_async(spin_gr_theory.__solve_hs,chs,spin_gr_theory.__to_sympy(math.partial(self.HHp.trim(),'H')))
#ht_sol = ipy_view.apply_async(spin_gr_theory.__solve_ht,chs,spin_gr_theory.__to_sympy(math.partial(self.HHp.trim(),'\\tilde{H}_\\ast')))
#self.__g_sol = g_sol.get()
#self.__hs_sol = hs_sol.get()
#self.__ht_sol = ht_sol.get()
import pickle
self.__g_sol = pickle.load(open('g_sol.pickle','rb'))
self.__hs_sol = pickle.load(open('hs_sol.pickle','rb'))
self.__ht_sol = pickle.load(open('ht_sol.pickle','rb'))
# Set the parameters of the theory.
self.__set_params(params)
# Some sanity checks.
HHp,G,L,H,GG,eps,m2,Hts,Gt,J2,hs,Gxy,Gtxys = [sympy.Symbol(s) for s in ['\\mathcal{H}^\\prime','G','L','H','\\mathcal{G}',\
'\\varepsilon','m_2','\\tilde{H}_\\ast','\\tilde{G}','J_2','h_\\ast','G_{xy}','\\tilde{G}_{xy\\ast}']]
# Phi_g^4 going to zero in the equilibrium point.
assert(self.g_sol[0][3][1].subs(HHp,spin_gr_theory.__to_sympy(self.HHp.ipow_subs('G_{xy}',2,pt('G')**2\
-pt('H')**2).subs('H',pt('G')**2*pt('m_2')*pt('J_2')**-1))).ratsimp() == 0)
# Reduction to Einstein precession.
simpl_HHp_ein = spin_gr_theory.__to_sympy(self.HHp.subs('J_2',0).subs('\\tilde{G}_{xy\\ast}',0).subs('\\tilde{H}_\\ast',pt('H'))\
.subs('\\tilde{G}',0))
ein_prec = sum([t[0]*t[1] for t in self.g_sol[0]]).subs('J_2',0).subs(Hts,H).subs(Gt,0)\
.subs(HHp,simpl_HHp_ein).ratsimp()
assert(ein_prec == 3 * eps * GG**4 * m2**4/(G**2*L**3))
# Lense-Thirring precession for g.
simpl_HHp_lt = spin_gr_theory.__to_sympy(self.HHp.subs('\\tilde{G}_{xy\\ast}',0).subs('\\tilde{H}_\\ast',pt('H'))\
.subs('\\tilde{G}',0))
lt_prec = sum([t[0]*t[1] for t in self.g_sol[0]]).subs(Hts,H).subs(Gt,0).subs(HHp,simpl_HHp_lt).ratsimp()
assert(lt_prec == (eps * ((-6*H*J2*GG**4*m2**3)/(G**4*L**3)+3*GG**4*m2**4/(G**2*L**3))).ratsimp())
# Geodetic effect on g.
simpl_HHp_ge = spin_gr_theory.__to_sympy(self.HHp.subs('J_2',0)).subs(sympy.cos(hs),-1).subs(Gxy,sympy.sqrt(G**2-H**2))\
.subs(Gtxys,sympy.sqrt(Gt**2-(Hts-H)**2)).subs(H,(Hts**2+G**2-Gt**2)/(2*Hts))
ge_g = sum([t[0]*t[1] for t in self.g_sol[0]]).subs(J2,0).subs(Gxy,sympy.sqrt(G**2-H**2))\
.subs(Gtxys,sympy.sqrt(Gt**2-(Hts-H)**2)).subs(H,(Hts**2+G**2-Gt**2)/(2*Hts)).subs(HHp,simpl_HHp_ge).ratsimp()
assert(ge_g == (1 / (4*G**4*L**3) * (15*G**2*GG**4*eps*m2**4+9*GG**4*Gt**2*eps*m2**4-9*GG**4*Hts**2*eps*m2**4)).ratsimp())
# No precession in h for Einstein case.
assert((sum([t[0]*t[1] for t in self.hs_sol[0]]) + sum([t[0]*t[1] for t in self.ht_sol[0]])).subs(HHp,simpl_HHp_ein)\
.subs('J_2',0).subs(Hts,H).ratsimp().subs(Gt,0) == 0)
# h precession in LT.
assert((sum([t[0]*t[1] for t in self.hs_sol[0]]) + sum([t[0]*t[1] for t in self.ht_sol[0]])).subs(HHp,simpl_HHp_lt)\
.subs(Hts,H).ratsimp().subs(Gt,0).ratsimp() == 2*eps*J2*GG**4*m2**3/(G**3*L**3))
# Geodetic effect for h and ht.
assert((sum([t[0]*t[1] for t in self.hs_sol[0]]) + sum([t[0]*t[1] for t in self.ht_sol[0]])).subs(HHp,simpl_HHp_ge)\
.subs(J2,0).subs(H,(Hts**2+G**2-Gt**2)/(2*Hts)).ratsimp() == 3*GG**4*Hts*eps*m2**4/(2*G**3*L**3))
assert((sum([t[0]*t[1] for t in self.ht_sol[0]])).subs(HHp,simpl_HHp_ge)\
.subs(J2,0).subs(H,(Hts**2+G**2-Gt**2)/(2*Hts)).ratsimp() == 3*GG**4*Hts*eps*m2**4/(2*G**3*L**3))
def pb_t1t1f1(f=0,
m=4,
num_br=0,
num_subr=0,
t_order_max=20,
in1_post='',
in2_post='',
out_post='',
isAver=True,
isDouble=False,
isPrint=True):
"""
Poisson brackets {T_1, {T_1, H_1}} and {T_1, {T_1, A_1}}.
"""
from pyranha.math import cos, sin, degree, ldegree, t_degree, t_ldegree, t_order, t_lorder, partial, truncate_degree
in1_post = in1_post if in1_post == '' else '_' + in1_post
in2_post = in2_post if in2_post == '' else '_' + in2_post
out_post = out_post if out_post == '' else '_' + out_post
if f == 0: c = -1. / 6. if isDouble else F(-1, 6)
if f == 1: c = 1. / 6. if isDouble else F(1, 6)
TYPE2 = 'A' if f == 0 else 'H'
PATH_CHN = PREFIX + 'HDM/CHN1/H1' + in1_post + '/'
PATH_BRA = PREFIX + 'HDM/PHI2/T1' + TYPE2 + '1' + in2_post + '_TOR' + str(
t_order_max).rjust(2, '0') + '/'
(one, max_m, type2, pt2,
epst2) = (1., m, 'd', pd, epsd) if isDouble else (1, F(m), 't', pt, epst)
for i in range(len(pq_list))[num_bracket:num_bracket + 1]:
TYPE = 'HAM' if isAver else 'PHI'
PATH_SAVE = PREFIX + 'HDM/' + TYPE + '3/T1T1' + TYPE2 + '1' + out_post + '_TOR' + str(
t_order_max).rjust(2,
'0') + '/' + pq_list[i] + '_' + qp_list[i] + '/'
for file1 in os.listdir(PATH_CHN + qp_list[i]): # diff L,q (chn q,L)
diff1 = epst(0)
lf(diff1, PATH_CHN + qp_list[i] + '/' + file1, df.boost_portable,
cf.bzip2)
diff1 = truncate_degree(diff1, F(m), pq_list[8:])
new_diff1 = epst2(0)
for item1 in diff1.list:
if t_order(item1[1]) <= t_order_max:
new_diff1 += one * (item1[0] * item1[1])
#new_diff1 = epst(0)
#lf(new_diff1, PATH_CHN + qp_list[i]+'/'+file1, df.boost_portable, cf.bzip2)
#new_diff1 = truncate_degree(new_diff1, F(m), pq_list[8:])
if isPrint:
print file1[:
-16] #+':', sum([len(item.list) for item in [jtem[0].list[0][0] for jtem in new_diff1.list]]), len(new_diff1.list)
for subdir in os.listdir(PATH_BRA)[num_subr:num_subr + 1]:
for file2 in os.listdir(PATH_BRA + subdir + '/'):
CHECK_FILE = PATH_SAVE + '/' + TYPE[0].lower(
) + '3_' + file1[3:5] + '_(' + subdir + '_' + file2[
3:8] + ').eps' + type2 + '.boostp.bz2'
if not os.path.isfile(CHECK_FILE):
if '44' in file2[3:8]:
num_list = range(1, 5)
else:
num_list = range(int(file2[4:5]),
int(file2[3:4]) + 1)
num_list += range(int(file2[7:8]),
int(file2[6:7]) + 1)
if int(pq_list[i][1]) in num_list:
start = time.time()
diff2 = epst(0)
lf(diff2, PATH_BRA + subdir + '/' + file2,
df.boost_portable, cf.bzip2)
diff2 = truncate_degree(diff2, F(m), pq_list[8:])
new_diff2 = epst2(0)
for item1 in diff2.list:
if t_order(item1[1]) <= t_order_max:
new_diff2 += one * (item1[0] * item1[1])
#new_diff2 = epst(0)
#lf(new_diff2, PATH_BRA + subdir+'/'+file2, df.boost_portable, cf.bzip2)
#new_diff2 = truncate_degree(new_diff2, F(m), pq_list[8:])
if i in range(4, 8):
s_prev = epst2('s' +
str(i - 4)) if i != 4 else 1
part_diff_nu = -3 * epst2('K0')**2 * (
epst2('m' + str(i - 4 + 1))**3 * s_prev *
epst2('s' + str(i - 4 + 1))**
-1) * epst2('L' + str(i - 4 + 1))**-4
epst2.register_custom_derivative(
qp_list[i],
lambda temp: temp.partial(qp_list[
i]) + temp.partial(r'\nu_{' + pq_list[
i] + r'}') * part_diff_nu)
new_diff2 = partial(new_diff2, qp_list[i])
epst2.unregister_all_custom_derivatives()
else:
new_diff2 = partial(new_diff2, qp_list[i])
if isPrint:
print subdir, file2[:
-16] #+':', sum([len(item.list) for item in [jtem[0].list[0][0] for jtem in new_diff2.list]]), len(new_diff2.list)
pt2.set_auto_truncate_degree(max_m, pq_list[8:])
if isAver:
count = 0
new_result = epst2(0)
for item in new_diff1.list:
for jtem in new_diff2.list:
trig = item[1] * jtem[1]
for ktem in trig.list:
if ktem[1] == 1:
temp_result = c * (item[0] *
jtem[0] *
ktem[0])
new_result = new_result + temp_result
print c, item[1]
count += 1
else:
result = c * new_diff1 * new_diff2
pt2.unset_auto_truncate_degree()
if not isAver:
new_result = epst2(0)
for item1 in result.list:
if t_order(item1[1]) <= t_order_max:
new_result += item1[0] * item1[1]
if new_result != epst2(0):
if not os.path.exists(PATH_SAVE):
os.makedirs(PATH_SAVE)
sf(
new_result.trim(), PATH_SAVE + '/' +
TYPE[0].lower() + '3_' + file1[3:5] +
'_(' + subdir + '_' + file2[3:8] +
').eps' + type2 + '.boostp.bz2',
df.boost_portable, cf.bzip2)
print 'bracket:', pq_list[i] + '_' + qp_list[
i], file1[:-16], file2[:-16], str(
'%.1f' % (time.time() - start)).rjust(
4, ' '), 's'
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 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()