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Estrellas.py
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#!/usr/bin/env python
print(" ")
print("**********************************************")
print("*** Solucion numerica ***")
print("*** para las estrellas de bosones ***")
print("*** utilizando metodos espectrales ***")
print("*** en la base de Chebyshev ***")
print("*** ***")
print("*** Victor Jaramillo: Septiembre 2020 ***")
print("*** X O C H I M I L C O MX ***")
print("**********************************************")
print(" ")
import numpy as np
import matplotlib.pyplot as plt
import numpy.polynomial.chebyshev as pch
import os
N=24
gg = 0.0 #THIS IS g
hh = 0.0 #THIS IS h
Ns=np.linspace(0.91,0.4,40) # g=0 h=0, g=-1 h=0,
#Ns=np.linspace(0.91,0.7,40) # g=-5 h=0
#Ns=np.linspace(0.91,0.85,40) # g=-10 h=0
#Ns=np.linspace(0.91,0.95,40) # g=-20 h=0
#Ns=np.linspace(0.91,0.1,60) # with h=10, and g=-0,-1,-5 and -7.5
# also h=20, and g=0,-1,-5 and -7.5, -20
# also h=-5, and g=0,-1
#Ns=np.linspace(0.91,0.1,80) # with h=-20, and g=-5 and
#Ns=np.linspace(0.91,0.162,60) # with h=-20, and g=-10 and
Ns=np.linspace(0.99,0.06,100) # g=0 h=0, g=-1 h=0,
#Colocar N0!=N si queremos construir un dato inicial a partir de otro con N menor
N0=18
# HERE SUBSTITUTE " " with an specific file, to construct family of solutions starting from it
#datafile_N0=" "
#datafile_N0="g0.00_h0.00/lapse_9.10e-01.dat"
datafile_N0="solutions_varying_omega/start_point/omega_9.95e-01.dat"
#datafile_N0="g0.00_h0.00_TEMP/lapse_1.01e-01.dat"
#
phi0_semilla=0.02/np.sqrt(2) * np.sqrt(8*3.14159265) #gg=0
solution_folder="g"+"{:.2f}".format(gg)+"_h"+"{:.2f}".format(hh)
os.mkdir(solution_folder)
omega_inicial=0.95
r_m1=0.1
r_m2=2.5
r_m2m=5.0
r_m3=25.0
dV=1.0e-10 #ojo antes era 1e-10
tolf=5.0e-11
epsilon=5e-10 #antes 1e-10
M=int(N/2)
sigmax =64 #gg=0
uc_a=np.zeros(len(Ns))
omega_a=np.zeros(len(Ns))
MADM_a=np.zeros(len(Ns))
MKomar_a=np.zeros(len(Ns))
R99_a=np.zeros(len(Ns))
C99_a=np.zeros(len(Ns))
Rtest_a=np.zeros(len(Ns))
Ctest_a=np.zeros(len(Ns))
for i in np.arange(len(Ns)):
if i==0 and datafile_N0==" ":
dato_inicial="gaussiana"
omegamanual=omega_inicial
if i==0 and datafile_N0!=" ":
dato_inicial="archivo"
omegamanual=0.0
if i!=0:
dato_inicial="archivo"
datafile_N0=" "
omegamanual=0.0
datafile=solution_folder+"/lapse_"+"{:.2e}".format(Ns[i-1])+".dat"
N00=Ns[i]
#Numero de coeficientes, puntos de colocacion y pesos:
pi=3.14159265359
x=np.zeros(N+1)
w=np.zeros(N+1)
##Gauss-Lobato##
for ii in range(N+1):
x[ii]=np.cos(pi*ii/N)
if ii==0 or ii==N:
w[ii]=pi/(2.*N)
else:
w[ii]=pi/N
#Interpolante (ojo: TODOS en N+1 coeficientes)
# de f(x)
def I_f(f):
sum1=np.zeros(N+1)
sum2=np.zeros(N+1)
for nn in range(N+1):
a=np.zeros(N+1)
a[nn]=1
for ii in range(N+1):
cheba=pch.Chebyshev(a)(x[ii])
wii=w[ii]
sum1[nn]=f[ii]*cheba*wii+sum1[nn]
sum2[nn]=cheba**2*wii+sum2[nn]
return sum1/sum2
##
##Formulas exactas en el espacio de coeficientes
##
#1/x * funcion impar# #mejorado#
def rm1f(un):
d=np.zeros(N+1)
d[N-2]=2*un[N-1]
for ii in N-2-np.arange(len(un)-3):
if ii!=1 and ii%2!=0:
d[ii-1]=2.*un[ii]-d[ii+1]
if ii==1:
d[ii-1]=0.5*(2.*un[ii]-d[ii+1])
return d
##
##Formulas aproximadas en el espacio de funciones
##
#Derivada
def fd(un):
H=np.append(pch.Chebyshev.deriv(pch.Chebyshev(un), m=1).coef,0)
return H
#Segunda derivada
def fdd(un):
H=np.append(pch.Chebyshev.deriv(pch.Chebyshev(un), m=2).coef,[0,0])
return H
#############################
#############################
#Representacion espectral del "lado derecho" de las ecuaciones para, Estrellas de Bosones
#DOMINIO 1
def Psi_d_1(un,vn,wn,omega):
phi=pch.Chebyshev(un)(x)
NN=pch.Chebyshev(vn)(x)
Psi=pch.Chebyshev(wn)(x)
dphi=pch.Chebyshev.deriv(pch.Chebyshev(un), m=1)(x)
sigma=0.25*Psi**5*((omega*phi/NN)**2+dphi**2/(r_m1**2*Psi**4)+phi**2+0.5*gg*phi**4+(1.0/3.0)*hh*phi**6)
return sigma
def N_d_1(un,vn,wn,omega):
phi=pch.Chebyshev(un)(x)
NN=pch.Chebyshev(vn)(x)
Psi=pch.Chebyshev(wn)(x)
dphi=pch.Chebyshev.deriv(pch.Chebyshev(un), m=1)(x)
dNN=pch.Chebyshev.deriv(pch.Chebyshev(vn), m=1)(x)
dPsi=pch.Chebyshev.deriv(pch.Chebyshev(wn), m=1)(x)
sigma= 2.*dNN*dPsi/(r_m1**2*Psi)-NN*Psi**4*(2.0*omega**2*phi**2/NN**2-phi**2-0.5*gg*phi**4-(1.0/3.0)*hh*phi**6)
return sigma
def phi_d_1(un,vn,wn,omega):
phi=pch.Chebyshev(un)(x)
NN=pch.Chebyshev(vn)(x)
Psi=pch.Chebyshev(wn)(x)
dphi=pch.Chebyshev.deriv(pch.Chebyshev(un), m=1)(x)
dNN=pch.Chebyshev.deriv(pch.Chebyshev(vn), m=1)(x)
dPsi=pch.Chebyshev.deriv(pch.Chebyshev(wn), m=1)(x)
sigma=-Psi**4*(1.0+gg*phi**2+hh*phi**4-omega**2/NN**2)*phi+dphi*dNN/(r_m1**2*NN)+2.0*dphi*dPsi/(r_m1**2*Psi)
return sigma
#DOMINIO 2
rr2=0.5*(r_m2-r_m1)*x+0.5*(r_m2+r_m1)
rr2d=0.5*(r_m2-r_m1)
def DOS(un,vn,wn,omega):
phi=pch.Chebyshev(un)(x)
NN=pch.Chebyshev(vn)(x)
Psi=pch.Chebyshev(wn)(x)
dphi=(pch.Chebyshev.deriv(pch.Chebyshev(un), m=1)(x))
dNN=pch.Chebyshev.deriv(pch.Chebyshev(vn), m=1)(x)
dPsi=(pch.Chebyshev.deriv(pch.Chebyshev(wn), m=1)(x))
ddphi=pch.Chebyshev.deriv(pch.Chebyshev(un), m=2)(x)
ddNN=pch.Chebyshev.deriv(pch.Chebyshev(vn), m=2)(x)
ddPsi=(pch.Chebyshev.deriv(pch.Chebyshev(wn), m=2)(x))
sigma1=ddPsi/rr2d**2+2.0*dPsi/(rr2*rr2d)+0.25*Psi**5*((omega*phi/NN)**2+(dphi/rr2d)**2/(Psi**4)+(1.0+0.5*gg*phi**2+(1.0/3.0)*hh*phi**4)*phi**2)
sigma2=ddNN/rr2d**2+2.0*dNN/(rr2*rr2d)+2.*dNN*dPsi/(rr2d**2*Psi)-NN*Psi**4*(2.0*omega**2*phi**2/NN**2-phi**2-0.5*gg*phi**4-(1.0/3.0)*hh*phi**6)
sigma3=ddphi/rr2d**2+2.0*dphi/(rr2*rr2d)-Psi**4*(1.0+gg*phi**2+hh*phi**4-omega**2/NN**2)*phi+dphi*dNN/(rr2d**2*NN)+2.0*dphi*dPsi/(rr2d**2*Psi)
return sigma3, sigma2, sigma1
#DOMINIO 2m
rr2m=0.5*(r_m2m-r_m2)*x+0.5*(r_m2m+r_m2)
rr2dm=0.5*(r_m2m-r_m2)
def DOSm(un,vn,wn,omega):
phi=pch.Chebyshev(un)(x)
NN=pch.Chebyshev(vn)(x)
Psi=pch.Chebyshev(wn)(x)
dphi=(pch.Chebyshev.deriv(pch.Chebyshev(un), m=1)(x))
dNN=pch.Chebyshev.deriv(pch.Chebyshev(vn), m=1)(x)
dPsi=(pch.Chebyshev.deriv(pch.Chebyshev(wn), m=1)(x))
ddphi=pch.Chebyshev.deriv(pch.Chebyshev(un), m=2)(x)
ddNN=pch.Chebyshev.deriv(pch.Chebyshev(vn), m=2)(x)
ddPsi=(pch.Chebyshev.deriv(pch.Chebyshev(wn), m=2)(x))
sigma1=ddPsi/rr2dm**2+2.0*dPsi/(rr2m*rr2dm)+0.25*Psi**5*((omega*phi/NN)**2+(dphi/rr2dm)**2/(Psi**4)+(1.0+0.5*gg*phi**2+(1.0/3.0)*hh*phi**4)*phi**2)
sigma2=ddNN/rr2dm**2+2.0*dNN/(rr2m*rr2dm)+2.*dNN*dPsi/(rr2dm**2*Psi)-NN*Psi**4*(2.0*omega**2*phi**2/NN**2-phi**2-0.5*gg*phi**4-(1.0/3.0)*hh*phi**6)
sigma3=ddphi/rr2dm**2+2.0*dphi/(rr2m*rr2dm)-Psi**4*(1.0+gg*phi**2+hh*phi**4-omega**2/NN**2)*phi+dphi*dNN/(rr2dm**2*NN)+2.0*dphi*dPsi/(rr2dm**2*Psi)
return sigma3, sigma2, sigma1
#DOMINIO 3
rr3=0.5*(r_m3-r_m2m)*x+0.5*(r_m3+r_m2m)
rr3d=0.5*(r_m3-r_m2m)
def TRES(un,vn,wn,omega):
phi=pch.Chebyshev(un)(x)
NN=pch.Chebyshev(vn)(x)
Psi=pch.Chebyshev(wn)(x)
dphi=(pch.Chebyshev.deriv(pch.Chebyshev(un), m=1)(x))
dNN=pch.Chebyshev.deriv(pch.Chebyshev(vn), m=1)(x)
dPsi=(pch.Chebyshev.deriv(pch.Chebyshev(wn), m=1)(x))
ddphi=pch.Chebyshev.deriv(pch.Chebyshev(un), m=2)(x)
ddNN=pch.Chebyshev.deriv(pch.Chebyshev(vn), m=2)(x)
ddPsi=(pch.Chebyshev.deriv(pch.Chebyshev(wn), m=2)(x))
sigma1=ddPsi/rr3d**2+2.0*dPsi/(rr3*rr3d)+0.25*Psi**5*((omega*phi/NN)**2+(dphi/rr3d)**2/(Psi**4)+(1.0+0.5*gg*phi**2+(1.0/3.0)*hh*phi**4)*phi**2)
sigma2=ddNN/rr3d**2+2.0*dNN/(rr3*rr3d)+2.*dNN*dPsi/(rr3d**2*Psi)-NN*Psi**4*(2.0*omega**2*phi**2/NN**2-phi**2-0.5*gg*phi**4-(1.0/3.0)*hh*phi**6)
sigma3=ddphi/rr3d**2+2.0*dphi/(rr3*rr3d)-Psi**4*(1.0+gg*phi**2+hh*phi**4-omega**2/NN**2)*phi+dphi*dNN/(rr3d**2*NN)+2.0*dphi*dPsi/(rr3d**2*Psi)
return sigma3, sigma2, sigma1
#DOMINIO4
srr=(1.0-x)/(2.0*r_m3)
def CUATRO(un,vn,wn,omega):
phi=pch.Chebyshev(un)(x)
NN=pch.Chebyshev(vn)(x)
Psi=pch.Chebyshev(wn)(x)
dphi=pch.Chebyshev.deriv(pch.Chebyshev(un), m=1)(x)
dNN=pch.Chebyshev.deriv(pch.Chebyshev(vn), m=1)(x)
dPsi=pch.Chebyshev.deriv(pch.Chebyshev(wn), m=1)(x)
ddPsi=pch.Chebyshev.deriv(pch.Chebyshev(wn), m=2)(x)
ddNN=pch.Chebyshev.deriv(pch.Chebyshev(vn), m=2)(x)
ddphi=pch.Chebyshev.deriv(pch.Chebyshev(un), m=2)(x)
sigma1=0.25*(1.0-x)**4*ddPsi/r_m3**2+0.25*Psi**5*((omega*phi/NN)**2+srr**(2)*((1.0-x)*dphi)**2/(Psi**4)+(1.0+0.5*gg*phi**2+(1.0/3.0)*hh*phi**4)*phi**2)
sigma2=0.25*(1.0-x)**4*ddNN/r_m3**2+0.5*(1.0-x)**4*dNN*dPsi/(Psi*r_m3**2)-NN*Psi**4*(2.0*omega**2*phi**2/NN**2-phi**2-0.5*gg*phi**4-(1.0/3.0)*hh*phi**6)
sigma3=0.25*(1.0-x)**4*ddphi/r_m3**2-Psi**4*(1.0+gg*phi**2+hh*phi**4-omega**2/NN**2)*phi+0.25*(1.0-x)**4*dphi*dNN/(r_m3**2*NN)+0.5*(1.0-x)**4*dphi*dPsi/(r_m3**2*Psi)
return sigma3, sigma2, sigma1
#############################
#############################
#############################
#############################
def R(o):
un1=o[0:M+1]
un2=o[M+1:M+1+N+1]
un2m=o[M+1+N+1:M+1+2*N+2]
un3=o[M+1+2*N+2:M+1+3*N+3]
un4=o[M+1+3*N+3:M+1+4*N+4]
vn1=o[M+1+4*N+4:2*M+2+4*N+4]
vn2=o[2*M+2+4*N+4:2*M+2+5*N+5]
vn2m=o[2*M+2+5*N+5:2*M+2+6*N+6]
vn3=o[2*M+2+6*N+6:2*M+2+7*N+7]
vn4=o[2*M+2+7*N+7:2*M+2+8*N+8]
wn1=o[2*M+2+8*N+8:3*M+3+8*N+8]
wn2=o[3*M+3+8*N+8:3*M+3+9*N+9]
wn2m=o[3*M+3+9*N+9:3*M+3+10*N+10]
wn3=o[3*M+3+10*N+10:3*M+3+11*N+11]
wn4=o[3*M+3+11*N+11:3*M+3+12*N+12]
omega=o[3*M+3+12*N+12]
un1_f=np.zeros(N+1)
vn1_f=np.zeros(N+1)
wn1_f=np.zeros(N+1)
for ii in np.arange(M+1):
un1_f[2*ii]=un1[ii]
vn1_f[2*ii]=vn1[ii]
wn1_f[2*ii]=wn1[ii]
#definicion de coeficientes para terminos mezclados que involucran a 1/r
phi_d_2,N_d_2,Psi_d_2=DOS(un2,vn2,wn2,omega)
phi_d_2m,N_d_2m,Psi_d_2m=DOSm(un2m,vn2m,wn2m,omega)
phi_d_3,N_d_3,Psi_d_3=TRES(un3,vn3,wn3,omega)
phi_d_4,N_d_4,Psi_d_4=CUATRO(un4,vn4,wn4,omega)
Lu1_f=pch.Chebyshev(fdd(un1_f)/r_m1**2+2.0*rm1f(fd(un1_f))/r_m1**2)(x)+phi_d_1(un1_f,vn1_f,wn1_f,omega)
Lu2=phi_d_2
Lu2m=phi_d_2m
Lu3=phi_d_3
Lu4=phi_d_4
Lv1_f=pch.Chebyshev(fdd(vn1_f)/r_m1**2+2.0*rm1f(fd(vn1_f))/r_m1**2)(x)+N_d_1(un1_f,vn1_f,wn1_f,omega)
Lv2=N_d_2
Lv2m=N_d_2m
Lv3=N_d_3
Lv4=N_d_4
Lw1_f=pch.Chebyshev(fdd(wn1_f)/r_m1**2+2.0*rm1f(fd(wn1_f))/r_m1**2)(x)+Psi_d_1(un1_f,vn1_f,wn1_f,omega)
Lw2=Psi_d_2
Lw2m=Psi_d_2m
Lw3=Psi_d_3
Lw4=Psi_d_4
Lu1=np.zeros(M+1)
Lv1=np.zeros(M+1)
Lw1=np.zeros(M+1)
for ii in np.arange(M+1):
Lu1[ii]=Lu1_f[M+ii]
Lv1[ii]=Lv1_f[M+ii]
Lw1[ii]=Lw1_f[M+ii]
residuou1=Lu1
residuou2=Lu2
residuou2m=Lu2m
residuou3=Lu3
residuou4=Lu4
residuov1=Lv1
residuov2=Lv2
residuov2m=Lv2m
residuov3=Lv3
residuov4=Lv4
residuow1=Lw1
residuow2=Lw2
residuow2m=Lw2m
residuow3=Lw3
residuow4=Lw4
#############################
#############################
#############################
#############################
residuou1[M]=pch.Chebyshev(un1_f)(+1)-pch.Chebyshev(un2)(-1)
residuou2[0]=pch.Chebyshev.deriv(pch.Chebyshev(un1_f), m=1)(+1)-(2.*r_m1/(r_m2-r_m1))*pch.Chebyshev.deriv(pch.Chebyshev(un2), m=1)(-1)
residuou2[N]=pch.Chebyshev(un2)(+1)-pch.Chebyshev(un2m)(-1)
residuou2m[0]=(1./(r_m2-r_m1))*pch.Chebyshev.deriv(pch.Chebyshev(un2), m=1)(+1)-(1./(r_m2m-r_m2))*pch.Chebyshev.deriv(pch.Chebyshev(un2m), m=1)(-1)
residuou2m[N]=pch.Chebyshev(un2m)(+1)-pch.Chebyshev(un3)(-1)
residuou3[0]=(1./(r_m2m-r_m2))*pch.Chebyshev.deriv(pch.Chebyshev(un2m), m=1)(+1)-(1./(r_m3-r_m2m))*pch.Chebyshev.deriv(pch.Chebyshev(un3), m=1)(-1)
residuou3[N]=pch.Chebyshev(un3)(+1)-pch.Chebyshev(un4)(-1)
residuou4[0]=pch.Chebyshev.deriv(pch.Chebyshev(un3), m=1)(+1)-((r_m3-r_m2m)/r_m3)*pch.Chebyshev.deriv(pch.Chebyshev(un4), m=1)(-1)
residuou4[N]=pch.Chebyshev(un4)(+1)
residuov1[M]=pch.Chebyshev(vn1_f)(+1)-pch.Chebyshev(vn2)(-1)
residuov2[0]=pch.Chebyshev.deriv(pch.Chebyshev(vn1_f), m=1)(+1)-(2.*r_m1/(r_m2-r_m1))*pch.Chebyshev.deriv(pch.Chebyshev(vn2), m=1)(-1)
residuov2[N]=pch.Chebyshev(vn2)(+1)-pch.Chebyshev(vn2m)(-1)
residuov2m[0]=(1./(r_m2-r_m1))*pch.Chebyshev.deriv(pch.Chebyshev(vn2), m=1)(+1)-(1./(r_m2m-r_m2))*pch.Chebyshev.deriv(pch.Chebyshev(vn2m), m=1)(-1)
residuov2m[N]=pch.Chebyshev(vn2m)(+1)-pch.Chebyshev(vn3)(-1)
residuov3[0]=(1./(r_m2m-r_m2))*pch.Chebyshev.deriv(pch.Chebyshev(vn2m), m=1)(+1)-(1./(r_m3-r_m2m))*pch.Chebyshev.deriv(pch.Chebyshev(vn3), m=1)(-1)
residuov3[N]=pch.Chebyshev(vn3)(+1)-pch.Chebyshev(vn4)(-1)
residuov4[0]=pch.Chebyshev.deriv(pch.Chebyshev(vn3), m=1)(+1)-((r_m3-r_m2m)/r_m3)*pch.Chebyshev.deriv(pch.Chebyshev(vn4), m=1)(-1)
residuov4[N]=pch.Chebyshev(vn4)(+1)-1.0
residuow1[M]=pch.Chebyshev(wn1_f)(+1)-pch.Chebyshev(wn2)(-1)
residuow2[0]=pch.Chebyshev.deriv(pch.Chebyshev(wn1_f), m=1)(+1)-(2.*r_m1/(r_m2-r_m1))*pch.Chebyshev.deriv(pch.Chebyshev(wn2), m=1)(-1)
residuow2[N]=pch.Chebyshev(wn2)(+1)-pch.Chebyshev(wn2m)(-1)
residuow2m[0]=(1./(r_m2-r_m1))*pch.Chebyshev.deriv(pch.Chebyshev(wn2), m=1)(+1)-(1./(r_m2m-r_m2))*pch.Chebyshev.deriv(pch.Chebyshev(wn2m), m=1)(-1)
residuow2m[N]=pch.Chebyshev(wn2m)(+1)-pch.Chebyshev(wn3)(-1)
residuow3[0]=(1./(r_m2m-r_m2))*pch.Chebyshev.deriv(pch.Chebyshev(wn2m), m=1)(+1)-(1./(r_m3-r_m2m))*pch.Chebyshev.deriv(pch.Chebyshev(wn3), m=1)(-1)
residuow3[N]=pch.Chebyshev(wn3)(+1)-pch.Chebyshev(wn4)(-1)
residuow4[0]=pch.Chebyshev.deriv(pch.Chebyshev(wn3), m=1)(+1)-((r_m3-r_m2m)/r_m3)*pch.Chebyshev.deriv(pch.Chebyshev(wn4), m=1)(-1)
residuow4[N]=pch.Chebyshev(wn4)(+1)-1.0
residuoomega=pch.Chebyshev(vn1_f)(0.0)-N00
residuo=np.concatenate((residuou1,residuou2,residuou2m,residuou3,residuou4,residuov1,residuov2,residuov2m,residuov3,residuov4,residuow1,residuow2,residuow2m,residuow3,residuow4,residuoomega), axis=None)
return residuo
#############################
#############################
def NR(f,x0, dV,tolf):
T=12*(N+1)+3*(M+1)+1
#T=M+1
J=np.zeros((T,T))
y=x0
errf=sum(abs(f(y)))
i=1
while errf>tolf:
print(" --------------------------------------------")
print("| i="+str(i)+" | sum(|R_n|)="+"{:.2e}".format(errf)+" | omega_i="+"{:.4f}".format(y[-1])+" |")
fy=f(y)
for jj in np.arange(T):
dy=np.zeros(T)
dy[jj]=dV
fy_dy=f(y+dy)
for ii in np.arange(T):
J[ii,jj]=(fy_dy[ii]-fy[ii])/dV
Jinv=np.linalg.inv(J)
deltay=np.zeros(T)
for ii in np.arange(T):
for jj in np.arange(T):
deltay[ii]=deltay[ii]-Jinv[ii,jj]*fy[jj]
y=y+deltay
errf2=sum(abs(f(y)))
i=i+1
if errf2>errf:
print("no parece estar convergiendo")
#break
else:
errf=errf2
return y
#Construccion de estimacion inicial a partir de cero
if dato_inicial=="gaussiana":
#############################
#############################
r1=r_m1*x
r2=0.5*(r_m2-r_m1)*x+0.5*(r_m2+r_m1)
r2m=0.5*(r_m2m-r_m2)*x+0.5*(r_m2m+r_m2)
r3=0.5*(r_m3-r_m2m)*x+0.5*(r_m3+r_m2m)
r4=2.0*r_m3/(1.0-x+epsilon)
u_ini1=phi0_semilla*np.exp(-r1**2/sigmax)
v_ini1=-(1.0-N00)*np.exp(-r1**2)+1.0
w_ini1=0.0*np.exp(-r1**2/sigmax)+1.0
u_ini2=phi0_semilla*np.exp(-r2**2/sigmax)
v_ini2=-(1.0-N00)*np.exp(-r2**2)+1.0
w_ini2=0.0*np.exp(-r2**2/sigmax)+1.0
u_ini2m=phi0_semilla*np.exp(-r2m**2/sigmax)
v_ini2m=-(1.0-N00)*np.exp(-r2m**2)+1.0
w_ini2m=0.0*np.exp(-r2m**2/sigmax)+1.0
u_ini3=phi0_semilla*np.exp(-r3**2/sigmax)
v_ini3=-(1.0-N00)*np.exp(-r3**2)+1.0
w_ini3=0.0*np.exp(-r3**2/sigmax)+1.0
u_ini4=phi0_semilla*np.exp(-r4**2/sigmax)
v_ini4=-(1.0-N00)*np.exp(-r4**2)+1.0
w_ini4=0.0*np.exp(-r4**2/sigmax)+1.0
#############################
#############################
#Construccion de estimacion inicial a partir de otra solucion
if dato_inicial=="archivo" and datafile_N0==" ":
g=np.loadtxt(datafile)
M0=int(N0/2)
u10=np.zeros(N0+1)
for ii in np.arange(M0+1):
u10[2*ii]=g[ii]
u20=g[M0+1:M0+1+N0+1]
u20m=g[M0+1+N0+1:M0+1+2*N0+2]
u30=g[M0+1+2*N0+2:M0+1+3*N0+3]
u40=g[M0+1+3*N0+3:M0+1+4*N0+4]
v10=np.zeros(N0+1)
for ii in np.arange(M0+1):
v10[2*ii]=g[ii+M0+1+4*N0+4]
v20=g[2*M0+2+4*N0+4:2*M0+2+5*N0+5]
v20m=g[2*M0+2+5*N0+5:2*M0+2+6*N0+6]
v30=g[2*M0+2+6*N0+6:2*M0+2+7*N0+7]
v40=g[2*M0+2+7*N0+7:2*M0+2+8*N0+8]
w10=np.zeros(N0+1)
for ii in np.arange(M0+1):
w10[2*ii]=g[ii+2*M0+2+8*N0+8]
w20=g[3*M0+3+8*N0+8:3*M0+3+9*N0+9]
w20m=g[3*M0+3+9*N0+9:3*M0+3+10*N0+10]
w30=g[3*M0+3+10*N0+10:3*M0+3+11*N0+11]
w40=g[3*M0+3+11*N0+11:3*M0+3+12*N0+12]
#Cambio de N
#############################
#############################
u_ini1=pch.Chebyshev(u10)(x)
v_ini1=pch.Chebyshev(v10)(x)
w_ini1=pch.Chebyshev(w10)(x)
u_ini2=pch.Chebyshev(u20)(x)
v_ini2=pch.Chebyshev(v20)(x)
w_ini2=pch.Chebyshev(w20)(x)
u_ini2m=pch.Chebyshev(u20m)(x)
v_ini2m=pch.Chebyshev(v20m)(x)
w_ini2m=pch.Chebyshev(w20m)(x)
u_ini3=pch.Chebyshev(u30)(x)
v_ini3=pch.Chebyshev(v30)(x)
w_ini3=pch.Chebyshev(w30)(x)
u_ini4=pch.Chebyshev(u40)(x)
v_ini4=pch.Chebyshev(v40)(x)
w_ini4=pch.Chebyshev(w40)(x)
#############################
#############################
#Construccion de estimacion inicial a partir de otra solucion con menor N
#SOLO FUNCIONA PARESSSS OJO
if dato_inicial=="archivo" and datafile_N0!=" ":
g=np.loadtxt(datafile_N0)
M0=int(N0/2)
u10=np.zeros(N0+1)
for ii in np.arange(M0+1):
u10[2*ii]=g[ii]
u20=g[M0+1:M0+1+N0+1]
u20m=g[M0+1+N0+1:M0+1+2*N0+2]
u30=g[M0+1+2*N0+2:M0+1+3*N0+3]
u40=g[M0+1+3*N0+3:M0+1+4*N0+4]
v10=np.zeros(N0+1)
for ii in np.arange(M0+1):
v10[2*ii]=g[ii+M0+1+4*N0+4]
v20=g[2*M0+2+4*N0+4:2*M0+2+5*N0+5]
v20m=g[2*M0+2+5*N0+5:2*M0+2+6*N0+6]
v30=g[2*M0+2+6*N0+6:2*M0+2+7*N0+7]
v40=g[2*M0+2+7*N0+7:2*M0+2+8*N0+8]
w10=np.zeros(N0+1)
for ii in np.arange(M0+1):
w10[2*ii]=g[ii+2*M0+2+8*N0+8]
w20=g[3*M0+3+8*N0+8:3*M0+3+9*N0+9]
w20m=g[3*M0+3+9*N0+9:3*M0+3+10*N0+10]
w30=g[3*M0+3+10*N0+10:3*M0+3+11*N0+11]
w40=g[3*M0+3+11*N0+11:3*M0+3+12*N0+12]
#Cambio de N
#############################
#############################
u_ini1=pch.Chebyshev(u10)(x)
v_ini1=pch.Chebyshev(v10)(x)
w_ini1=pch.Chebyshev(w10)(x)
u_ini2=pch.Chebyshev(u20)(x)
v_ini2=pch.Chebyshev(v20)(x)
w_ini2=pch.Chebyshev(w20)(x)
u_ini2m=pch.Chebyshev(u20m)(x)
v_ini2m=pch.Chebyshev(v20m)(x)
w_ini2m=pch.Chebyshev(w20m)(x)
u_ini3=pch.Chebyshev(u30)(x)
v_ini3=pch.Chebyshev(v30)(x)
w_ini3=pch.Chebyshev(w30)(x)
u_ini4=pch.Chebyshev(u40)(x)
v_ini4=pch.Chebyshev(v40)(x)
w_ini4=pch.Chebyshev(w40)(x)
#############################
#############################
u10_f=I_f(u_ini1)
v10_f=I_f(v_ini1)
w10_f=I_f(w_ini1)
u10=np.zeros(M+1)
v10=np.zeros(M+1)
w10=np.zeros(M+1)
for ii in np.arange(M+1):
u10[ii]=u10_f[2*ii]
v10[ii]=v10_f[2*ii]
w10[ii]=w10_f[2*ii]
#Dominio 2
u20=I_f(u_ini2)
v20=I_f(v_ini2)
w20=I_f(w_ini2)
#Dominio 2m
u20m=I_f(u_ini2m)
v20m=I_f(v_ini2m)
w20m=I_f(w_ini2m)
#Dominio 3
u30=I_f(u_ini3)
v30=I_f(v_ini3)
w30=I_f(w_ini3)
#Dominio 4
u40=I_f(u_ini4)
v40=I_f(v_ini4)
w40=I_f(w_ini4)
if omegamanual!=0:
omega0=omegamanual
else:
omega0=g[3*M0+3+12*N0+12]
N0=N # Para asegurar que despues del primer paso, lea la omega de la iteracion anterior
x0=np.concatenate((u10,u20,u20m,u30,u40,v10,v20,v20m,v30,v40,w10,w20,w20m,w30,w40,omega0), axis=None)
#x0=Un
print(" ")
Un=NR(R,x0,dV, tolf)
print(" ")
print("omega: "+str(Un[-1]))
np.savetxt(solution_folder+"/lapse_"+"{:.2e}".format(N00)+".dat", Un)
#### output ####
u1=np.zeros(N+1)
for ii in np.arange(M+1):
u1[2*ii]=Un[ii]
u2=Un[M+1:M+1+N+1]
u2m=Un[M+1+N+1:M+1+2*N+2]
u3=Un[M+1+2*N+2:M+1+3*N+3]
u4=Un[M+1+3*N+3:M+1+4*N+4]
v1=np.zeros(N+1)
for ii in np.arange(M+1):
v1[2*ii]=Un[ii+M+1+4*N+4]
v2=Un[2*M+2+4*N+4:2*M+2+5*N+5]
v2m=Un[2*M+2+5*N+5:2*M+2+6*N+6]
v3=Un[2*M+2+6*N+6:2*M+2+7*N+7]
v4=Un[2*M+2+7*N+7:2*M+2+8*N+8]
w1=np.zeros(N+1)
for ii in np.arange(M+1):
w1[2*ii]=Un[ii+2*M+2+8*N+8]
w2=Un[3*M+3+8*N+8:3*M+3+9*N+9]
w2m=Un[3*M+3+9*N+9:3*M+3+10*N+10]
w3=Un[3*M+3+10*N+10:3*M+3+11*N+11]
w4=Un[3*M+3+11*N+11:3*M+3+12*N+12]
xx=np.linspace(-1,1,1000)
################################
#Masas ADM y Komar
omega_a[i]=Un[-1]
uc_a[i]=pch.Chebyshev.deriv(pch.Chebyshev(u1), m=0)(0.0)
MADM_a[i]=-4.*r_m3*pch.Chebyshev.deriv(pch.Chebyshev(w4), m=1)(xx)[-1]
MKomar_a[i]=2.*r_m3*pch.Chebyshev.deriv(pch.Chebyshev(v4), m=1)(xx)[-1]
#Radios y Compacidades
rr2=0.5*(r_m2-r_m1)*xx+0.5*(r_m2+r_m1)
rr2m=0.5*(r_m2m-r_m2)*xx+0.5*(r_m2m+r_m2)
rr3=0.5*(r_m3-r_m2m)*xx+0.5*(r_m3+r_m2m)
rr4=2.0*r_m3/(1.0-xx+epsilon)
rr=np.concatenate((rr2,rr2m,rr3,rr4), axis=None)
Psi2=pch.Chebyshev(w2)(xx)
Psi2m=pch.Chebyshev(w2m)(xx)
Psi3=pch.Chebyshev(w3)(xx)
Psi4=pch.Chebyshev(w4)(xx)
Psirr=np.concatenate((Psi2,Psi2m,Psi3,Psi4), axis=None)
N2=pch.Chebyshev(v2)(xx)
N2m=pch.Chebyshev(v2m)(xx)
N3=pch.Chebyshev(v3)(xx)
N4=pch.Chebyshev(v4)(xx)
Nrr=np.concatenate((N2,N2m,N3,N4), axis=None)
dPsi2=(2.0/(r_m2-r_m1))*pch.Chebyshev.deriv(pch.Chebyshev(w2), m=1)(xx)
dPsi2m=(2.0/(r_m2m-r_m2))*pch.Chebyshev.deriv(pch.Chebyshev(w2m), m=1)(xx)
dPsi3=(2.0/(r_m3-r_m2m))*pch.Chebyshev.deriv(pch.Chebyshev(w3), m=1)(xx)
dPsi4=((1.-xx)**2/(2.*r_m3))*pch.Chebyshev.deriv(pch.Chebyshev(w4), m=1)(xx)
dPsirr=np.concatenate((dPsi2,dPsi2m,dPsi3,dPsi4), axis=None)
Mms=-2.*rr**2*dPsirr*(Psirr+rr*dPsirr)
noventaynueve=Mms-0.99*MADM_a[i]
ii99=np.argmin(abs(noventaynueve))
R99_a[i]=rr[ii99]*Psirr[ii99]**2
C99_a[i]=MADM_a[i]/R99_a[i]
#Mmsrmax=Mms/(rr*Psirr**2)
#iimax=np.argmax(Mmsrmax)
#Rtest_a[i]=rr[iimax]*Psirr[iimax]**2
#Ctest_a[i]=Mmsrmax[iimax]
###################################
#if i!=0 and Un[-1]>omega0:
# break
print(" ")
print("rel. err. MADM MKomar= "+str(abs(MADM_a[i]-MKomar_a[i])/(MADM_a[i]+MKomar_a[i])))
print("(the number above should be << 1)")
print(" ")
print("phi(r=0) = "+str(uc_a[i]))
print("MADM = "+str(MADM_a[i]))
#print("MKom = "+str(MKomar_a[i]))
print("R99 = "+str(R99_a[i]))
#print("C99 = "+str(C99_a[i]))
#print("Rtest = "+str(Rtest_a[i]))
#print("Ctest = "+str(Ctest_a[i]))
#print(" ")
#if i!=0 and MADM_a[i-1]>MADM_a[i]:
# break
#if i!=0 and omega_a[i-1]<omega_a[i]:
# break
uc_a_i=uc_a[0:i+1]
omega_a_i=omega_a[0:i+1]
MADM_a_i=MADM_a[0:i+1]
MKomar_a_i=MKomar_a[0:i+1]
R99_a_i=R99_a[0:i+1]
C99_a_i=C99_a[0:i+1]
#Rtest_a_i=Rtest_a[0:i+1]
#Ctest_a_i=Ctest_a[0:i+1]
np.savetxt(solution_folder+"/phi_0.dat", uc_a_i)
np.savetxt(solution_folder+"/omega.dat", omega_a_i)
np.savetxt(solution_folder+"/MADM.dat", MADM_a_i)
np.savetxt(solution_folder+"/MKomar.dat", MKomar_a_i)
np.savetxt(solution_folder+"/R99.dat", R99_a_i)
np.savetxt(solution_folder+"/C99.dat", C99_a_i)
#np.savetxt("Rtest.dat", Rtest_a_i)
#np.savetxt("Ctest.dat", Ctest_a_i)
plt.plot(omega_a_i,MADM_a_i, color="k")
plt.plot(omega_a_i,MKomar_a_i, color="g")
plt.savefig(solution_folder+'/omega_vs_M.png', dpi=400)
print(" ")
print(" listo ")
print(" ")