def plot_critical_lines():
ell = 0.45167959731417684
a = math.sqrt(1.0/(1.0 - ell))
b = math.sqrt(1.0 - ell)
tst = {'x1' : 0.3, 'x2' : 0.2, \
'radial' : 0.36055512754639896, 'theta': 0.5880026035475676, \
'u' : 0.5, 'a' : 1.414213562, 'b' : 0.707106781, 'u' : 0.5, \
'kappa_s' : 0.1}
lens_apro_num = em.KappaGammaEll( rm.EnfwAprox() )
lens_exact = em.KappaGammaEll( rm.NfwLens() )
comp_aprox_num = em.LensComputation(lens_apro_num)
comp_lens_exact = em.LensComputation(lens_exact)
npts = 25
thetha_vec = np.linspace(0.0, cn.pi/2.0, npts)
aprox_num_vec = []
exact = []
aprox_ana_vec = []
for i in thetha_vec:
#print i
aprox_num_vec.append(comp_aprox_num.find_cc_tan(i, tst['a'], tst['b'], \
tst['kappa_s'])[0] )
exact.append(comp_lens_exact.find_cc_tan(i, tst['a'], tst['b'], \
tst['kappa_s'])[0])
aprox_ana_vec.append(cs.critica_curve_tangential(i, tst['a'], tst['b'],\
tst['kappa_s']))
plt.plot(exact*np.cos(thetha_vec), exact*np.sin(thetha_vec), \
label='ENFW Numeric', linewidth = 3)
plt.plot(aprox_num_vec*np.cos(thetha_vec), \
aprox_num_vec*np.sin(thetha_vec), 'm--', label='Aprox Numeric', \
linewidth = 3)
plt.plot(aprox_ana_vec*np.cos(thetha_vec), \
aprox_ana_vec*np.sin(thetha_vec), 'o', label='Aprox Analytic')
plt.legend( loc='botton left' )
plt.suptitle(r'\Tex $\kappa_s='+str(tst['kappa_s']) + '$', y = 0.94)
plt.xlabel('$x_1$')
plt.ylabel('$x_2$')
plt.show()
def cross_section_computation():
ell = 0.4
a = math.sqrt(1.0/(1.0 - ell))
b = math.sqrt(1.0 - ell)
tst = {'x1' : 0.3, 'x2' : 0.2, \
'radial' : 0.36055512754639896, 'theta': 0.5880026035475676, \
'u' : 0.5, 'a' : a, 'b' : b, 'u' : 0.5, \
'kappa_s' : 0.1}
lens_apro_num = em.KappaGammaEll( rm.EnfwAprox() )
lens_exact = em.KappaGammaEll( rm.NfwLens() )
comp_aprox_num = em.LensComputation(lens_apro_num)
comp_lens_exact = em.LensComputation(lens_exact)
r_lambda = 10.0
def plot_magnifications_thetafix():
ell = 0.45167959731417684
a = math.sqrt(1.0/(1.0 - ell))
b = math.sqrt(1.0 - ell)
tst = {'x1' : 0.3, 'x2' : 0.2, \
'radial' : 0.36055512754639896, 'theta': 0.5880026035475676, \
'u' : 0.5, 'a' : 1.414213562, 'b' : 0.707106781, 'u' : 0.5, \
'kappa_s' : 1.0}
lens_apro_num = em.KappaGammaEll( rm.EnfwAprox() )
lens_exact = em.KappaGammaEll( rm.NfwLens() )
comp_aprox_num = em.LensComputation(lens_apro_num)
comp_lens_exact = em.LensComputation(lens_exact)
npts = 200
radial_vec = np.linspace(1E-5, 1.5, npts)
mag_ratio = []
arg_find = []
mag_radial = []
mag_tan = []
for i in radial_vec:
mag_radial.append( 1.0/comp_aprox_num.mag_rad_inv_polar(i, 0.0, tst['a'], \
tst['b'], tst['kappa_s']) )
mag_tan.append( 1.0/comp_aprox_num.mag_tan_inv_polar(i, 0.0, tst['a'], \
tst['b'], tst['kappa_s']) )
mag_ratio.append(comp_aprox_num.mag_rad_over_mag_tan(i, 0.0, tst['a'], \
tst['b'], tst['kappa_s']))
arg_find.append(comp_aprox_num.arg_find_constant_distortion(i, 0.0, tst['a'], \
tst['b'], tst['kappa_s'], -10) )
plt.plot(radial_vec, mag_ratio, linewidth = 3, label='mag ratio')
#plt.plot(radial_vec, arg_find, linewidth = 3)
plt.plot(radial_vec, mag_radial, linewidth = 3, label='mag radial')
plt.plot(radial_vec, mag_tan, linewidth = 3, label='mag tan')
plt.plot([0,1.5], [0,0], color = 'Black')
plt.plot([0,1.5], [.1,.1], color = 'Black')
plt.plot([0,1.5], [-.1,-.1], color = 'Black')
plt.legend( loc='lower left' )
plt.ylim( (-1, 1) )
plt.show()
def compare2(ell_str):
lens_exact = em.KappaGammaEll( rm.NfwLens() )
comp_lens_exact = em.LensComputation(lens_exact)
file_path = 'input_enfw_novo/input_enfw_e' + ell_str + '.dat'
ks_pnfw, e_enfw, e_gk, ks_ef, ks_gk, sigma_q = \
np.loadtxt(file_path, unpack = True)
r_lambda = 10.0
path_file_out1 = 'sigma_enfw_e' + ell_str + '_2.dat'
path_file_out2 = 'dif_sigma_e' + ell_str + '_2.dat'
file_out1 = open(path_file_out1, 'w')
file_out2 = open(path_file_out2, 'w')
#print file_path, file_out1, file_out2
for i in range(len(e_enfw)):
a_enfw = math.sqrt(1.0/(1.0 - e_enfw[i]))
b_enfw = math.sqrt(1.0 - e_enfw[i])
a_gk = math.sqrt(1.0/(1.0 - e_gk[i]))
b_gk = math.sqrt(1.0 - e_gk[i])
#kappa_s = ks_ef[i]
if ks_ef[i] < 10.1:
sigma_ef = cs.sigma(a_enfw, b_enfw, ks_ef[i], r_lambda)
else:
sigma_ef = comp_lens_exact.sigma(a_enfw, b_enfw, ks_ef[i], r_lambda)
if ks_gk[i] < 10.1:
sigma_gk1 = cs.sigma(a_gk, b_gk, ks_gk[i], r_lambda)
else:
sigma_gk1 = comp_lens_exact.sigma(a_gk, b_gk, ks_gk[i], r_lambda)
#print ks_pnfw[i], sigma_ef, sigma_gk1
diff_rel_ef = math.fabs( (sigma_ef - sigma_q[i])/sigma_ef )
dif_rel_gk1 = math.fabs( (sigma_gk1 - sigma_q[i])/sigma_gk1 )
#print ks_pnfw[i], diff_rel_ef, dif_rel_gk1
print '----------'
str1 = str(ks_pnfw[i]) + ' ' + str(sigma_q[i]) + ' ' + str(sigma_ef) + \
' ' + str(sigma_gk1) + '\n'
print str1
file_out1.write(str1)
str2 = str(ks_pnfw[i]) + ' ' + str(diff_rel_ef) + ' ' + str(dif_rel_gk1) + '\n'
print str2
file_out2.write(str2)
print ks_pnfw[i], ks_ef[i], ks_gk[i], sigma_q[i]
file_out1.close()
file_out2.close()
def test_PotentialDerivatives():
tst = {'x1' : 0.3, 'x2' : 0.2, \
'radial' : 0.36055512754639896, 'theta': 0.5880026035475676, \
'u' : 0.5, 'a' : 1.414213562, 'b' : 0.707106781, 'u' : 0.5, \
'kappa_s' : 0.05}
ENFW = rm.EnfwAprox()
PD = em.LensPotDrivatives(ENFW)
#print dir(PD)
print cs.pot_xx(tst['radial'], tst['theta'], tst['a'], tst['b'], \
tst['kappa_s'])
print cs.pot_xy(tst['theta'], tst['a'], tst['b'], tst['kappa_s'])
print tst['a']*tst['b']*tst['x1']*\
cs.j0_function(tst['radial'], tst['theta'], tst['a'], tst['b'], \
tst['kappa_s'])
print 'pot_x = ', PD.pot_x(tst['x1'], tst['x2'], tst['a'], tst['b'], \
tst['kappa_s'])
print 'pot_y = ', PD.pot_y(tst['x1'], tst['x2'], tst['a'], tst['b'], \
tst['kappa_s'])
print 'pot_xx = ', PD.pot_xx(tst['x1'], tst['x2'], tst['a'], tst['b'], \
tst['kappa_s'])
print 'pot_yy = ', PD.pot_yy(tst['x1'], tst['x2'], tst['a'], tst['b'], \
tst['kappa_s'])
print 'pot_xy = ', PD.pot_xy(tst['x1'], tst['x2'], tst['a'], tst['b'], \
tst['kappa_s'])
KG = em.KappaGammaEll(ENFW)
print 'kappa_num = ', KG.kappa_numeric(tst['x1'], tst['x2'], tst['a'], \
tst['b'], tst['kappa_s'])
print 'kappa_ell = ', KG.kappa_ell(tst['x1'], tst['x2'], tst['a'], \
tst['b'], tst['kappa_s'])
print 'gamma1 = ', KG.gamma1(tst['x1'], tst['x2'], tst['a'], tst['b'], \
tst['kappa_s'])
print 'gamma2 = ', KG.gamma2(tst['x1'], tst['x2'], tst['a'], tst['b'], \
tst['kappa_s'])
print 'gamma = ', KG.gamma(tst['x1'], tst['x2'], tst['a'], tst['b'], \
tst['kappa_s'])
print 'mag_tot = ', KG.mag_total(tst['x1'], tst['x2'], tst['a'], \
tst['b'], tst['kappa_s'])
print 'mag_all = ', KG.mag_all(tst['x1'], tst['x2'], tst['a'], tst['b'], \
tst['kappa_s'])
print 'mag_inv = ', KG.mag_inv_all(tst['x1'], tst['x2'], tst['a'], \
tst['b'], tst['kappa_s'])
def plot_constant_distortion():
ell = 0.1
a = math.sqrt(1.0/(1.0 - ell))
b = math.sqrt(1.0 - ell)
tst = {'x1' : 0.3, 'x2' : 0.2, \
'radial' : 0.36055512754639896, 'theta': 0.5880026035475676, \
'u' : 0.5, 'a' : a, 'b' : b, 'kappa_s' : 0.125}
lens_apro_num = em.KappaGammaEll( rm.EnfwAprox() )
lens_exact = em.KappaGammaEll( rm.NfwLens() )
comp_aprox_num = em.LensComputation(lens_apro_num)
comp_lens_exact = em.LensComputation(lens_exact)
npts = 10
thetha_vec = np.linspace(0.0, cn.pi/2.0, npts)
raz = 10.0
cc_tan = []
cc_rad = []
dist_p = []
dist_m = []
cc_tan2 = []
cc_rad2 = []
dist_p2 = []
dist_m2 = []
dist_p3 = []
dist_m3 = []
cc_tan3 = []
for i in thetha_vec:
if tst['kappa_s'] >= 0.1:
curves = comp_aprox_num.find_constant_distortion(i, tst['a'], tst['b'], \
tst['kappa_s'], raz)
cc_tan.append(curves[0])
cc_rad.append(curves[1])
dist_m.append(curves[2])
dist_p.append(curves[3])
curves2 = comp_lens_exact.find_constant_distortion(i, tst['a'], tst['b'], \
tst['kappa_s'], raz)
cc_tan2.append(curves2[0])
cc_rad2.append(curves2[1])
dist_m2.append(curves2[2])
dist_p2.append(curves2[3])
dist_p3.append( cs.const_dist_curve(i, tst['a'], tst['b'], \
tst['kappa_s'], 1.0/raz)[1] )
dist_m3.append( cs.const_dist_curve(i, tst['a'], tst['b'], \
tst['kappa_s'], -1.0/raz)[1] )
cc_tan3.append( cs.critica_curve_tangential(i, tst['a'], tst['b'],\
tst['kappa_s']) )
if tst['kappa_s'] >= 0.1:
plt.plot( dist_p2*np.cos(thetha_vec), dist_p2*np.sin(thetha_vec), \
'b-', linewidth = 3)
plt.plot( dist_m2*np.cos(thetha_vec), dist_m2*np.sin(thetha_vec), \
'b-', linewidth = 3)
plt.plot( cc_tan2*np.cos(thetha_vec), cc_tan2*np.sin(thetha_vec), \
'b-', label=r'\Tex $\rm ENFW Numeric$', linewidth = 3)
plt.plot( dist_m*np.cos(thetha_vec), dist_m*np.sin(thetha_vec), \
'm--', linewidth = 3)
plt.plot( dist_p*np.cos(thetha_vec), dist_p*np.sin(thetha_vec), \
'm--', linewidth = 3)
plt.plot( cc_tan*np.cos(thetha_vec), cc_tan*np.sin(thetha_vec), \
'm--', label=r'\Tex $\rm Aprox Numeric$', linewidth = 3)
plt.plot( dist_m3*np.cos(thetha_vec), dist_m3*np.sin(thetha_vec), \
'go', linewidth = 3)
plt.plot( cc_tan3*np.cos(thetha_vec), cc_tan3*np.sin(thetha_vec), \
'go', label=r'\Tex $\rm Aprox Analytic$', linewidth = 3)
plt.plot( dist_p3*np.cos(thetha_vec), dist_p3*np.sin(thetha_vec), \
'go', linewidth = 3)
plt.legend(loc='lower left')# left')#'center' 'lower left'
plt.suptitle(r'\Tex $\kappa_s='+str(tst['kappa_s']) + r', \;\;\varepsilon=' + \
str(ell) + '$', y = 0.94)
plt.xlabel('$x_1$')
plt.ylabel('$x_2$')
plt.show()
print comp_lens_exact.sigma(tst['a'], tst['b'], tst['kappa_s'], 10.0)