#  extract Skyrme parameters from PRC82 024313 (2010)
#  mac:skyrme/unedf0.py
import sys,os
from math import *

h2m = 20.73553

#first, the explicit C parameters  (UNEDF0)
Cgrad_0 = -55.2606
Cgrad_1 = -55.6226
CgradJ_0 = -79.5308
CgradJ_1 = 45.6302

#next, the variables implicitly defining other C parameters
rho = 0.160526
B = -16.0559
Knm = 230.
a_sym = 30.5429
L_sym = 45.0804
Minv_0 = 0.9
Minv_1 = 1.249                                    #in text below Eq. (42)


#now some formulas
Ctau_0 = h2m*(Minv_0 - 1)/rho                      # Eq. (19)
Ctau_1 = Ctau_0 - h2m*(Minv_1 -1)/rho              # Eq. (30)
tau = (3./5.) * (3*pi**2*rho/2.)**(2./3.)          # Eq. (10)
temp1 = h2m*(4*Minv_0 - 3) *tau
temp2 = h2m*(6*Minv_0 - 9) * tau
gm = (temp1 - Knm - 9*B)/(temp2 + 9*B)          # Eq. (20)
temp3 = h2m*((2-3*gm)*Minv_0 - 3)*tau
Crho_0 = (temp3 + 3*(1+gm)*B)/(3*gm*rho)     # Eq. (17)
temp4 = h2m*(3- 2*Minv_0)*tau
Crho_0D = (temp4 - 3*B)/(3*gm*rho**(1+gm))   # Eq. (18)
temp5 = tau*(Ctau_0 + 3*Ctau_1) * rho
temp6  = (27*(1 + gm)*a_sym - 9* L_sym +5*(2-3*gm)*temp5-5*tau*(1+3*gm)*h2m)
Crho_1 = temp6/(27*gm*rho)                   # Eq. (31),(32)
Crho_1D = (-27*a_sym + 9* L_sym + 5*(h2m*tau -2*temp5))/(27*gm*rho**(1+gm))
#convert to standard Skyrme, augmented by W_q  from NP A 584 467.
def c2xt(In):
    """Converts C-form skyr params to XT-form skyr params
    Symbolically, 
    In=['Crho_0','Crho_1','Crho_0D','Crho_1D','Cgrad_0','Cgrad_1','Ctau_0','Ctau_1','CgradJ_0','CgradJ_1']
    out =['x0','x1','x2','x3','t0','t1','t2','t3','W','Wq']"""
    out = [None]*10
    out[0] = -(In[0]+3.0*In[1])/(2.0*In[0])
    out[1] = (-4.0*In[4]-12.0*In[5]+In[6]+3.0*In[7])/(8.0*In[4]-2.0*In[6])
    out[2] = (4.0*In[4]-20.0*In[5]+3.0*In[6]-15.0*In[7])/(-8.0*In[4]+16.0*In[5]-6.0*In[6]+12.0*In[7])
    out[3] = -(In[2]+3*In[3])/(2*In[2])
    out[4] = 8*In[0]/3
    out[5] = (-16*In[4]+4*In[6])/3
    out[6] = (16*In[4]-32*In[5]+12*In[6]-24*In[7])/3
    out[7] = 16*In[2]
    out[8] = -2*In[8]+2*In[9]
    out[9] = -4*In[9]
    return out

In=[Crho_0,Crho_1,Crho_0D,Crho_1D,Cgrad_0,Cgrad_1,Ctau_0,Ctau_1,CgradJ_0,CgradJ_1]
In_label=['Crho_0','Crho_1','Crho_0D','Crho_1D','Cgrad_0','Cgrad_1','Ctau_0','Ctau_1','CgradJ_0','CgradJ_1']
out_label =['x0','x1','x2','x3','t0','t1','t2','t3','W','Wq']

out = c2xt(In)
print 'C format'
for i in range(len(out)) :
  print In_label[i], In[i]
print 'xt format'
for i in range(len(out)) :
  print out_label[i], out[i]