def causAmp(uvec, rF2, lc, ax, ay):
""" Returns an approximation to the amplitude at the caustic, using the formula from Cooke 1982. """
ux, uy = uvec
psi20, psi02, psi11 = lensh(ux, uy)
phi20 = ax**2 / rF2 + lc * psi20
phi02 = ay**2 / rF2 + lc * psi02
phi11 = lc * psi11
phi30, phi21, phi12, phi03 = lc * np.asarray(lensgh(ux, uy))
B = phi20**3 * phi03 - 3 * phi20**2 * phi11 * phi12 + 3 * phi20 * phi11**2 * phi21 - phi11**3 * phi30
amp = ax * ay / (2 * pi * rF2) * 2.**(5. / 6.) * pi**(1. / 2.) * gfunc(
1. / 3.) * np.abs(phi20)**0.5 / (3.**(1. / 6.) * np.abs(B)**(1. / 3.))
# G = 2./(pi*np.abs(phi20))*(ax*ay*gfunc(1./3.)*np.cos(pi/6.)/(rF2*(9*np.abs(phi03))**(1./3.)))**2.
# G = (ax*ay/(2*pi*rF2))**2/3 * (gfunc(0.5)*gfunc(1./3.)/(np.abs(phi20)**0.5*np.abs(phi03)**(1./3.)))**2
return amp**2
def L(nser, reff):
return reff**2 * 2 * np.pi * nser / b(nser)**(2 * nser) * gfunc(2 * nser)
def rho(r, r2, alpha):
h = r2 / (2. / alpha)**(1 / alpha)
mtot = 4. * np.pi * h**3 * np.exp(2. / alpha) / alpha * gfunc(3. / alpha)
return np.exp(-2. / alpha * ((r / r2)**alpha - 1.)) / mtot
def M2d(R, gamma):
return 2 * np.pi**1.5 / (3. - gamma) * gfunc(
(gamma - 1.) / 2.) / gfunc(gamma / 2.) * R**(3 - gamma)
def L(n, Re):
return Re**2 * 2 * np.pi * n / b(n)**(2 * n) * gfunc(2 * n)
def L(n,Re):
return Re**2*2*np.pi*n/b(n)**(2*n)*gfunc(2*n)
def Sigma(R, gamma):
return R**(1 - gamma) * np.pi**0.5 * gfunc(
(gamma - 1.) / 2.) / gfunc(gamma / 2.)
def main():
theta_E = 1.25
# check if all the output files are created #
str = []
nl = 0
for line in open('sig_files/list', 'r'):
str.append(line)
nl += 1
print nl
for j in range(nl):
string_ = str[j]
str[j] = string_[41:-5]
print len(str)
num = map(int, str)
num = sort(num)
print num
# finding the missing file index #
nmiss = 0
missings = []
for i in range(nl):
if i != num[i]:
print i
missings.append(i)
num = insert(num, i, i)
nmiss += 1
f = open('missing_idx', 'w')
for i in range(nmiss):
f.write('%s\n' % (missings[i]))
f.close()
print nmiss
print nmiss + nl
# return
ngam = 121
nbout = 13
nbin = 13
nrani = 121
re = 1.85
gamma_arr = linspace(1.01, 2.99, ngam)
rani_arr = logspace(log10(0.5 * re), log10(5. * re), nrani)
bin_arr = linspace(-0.6, 0.6, nbin)
bout_arr = linspace(-0.6, 0.6, nbout)
np = 32
nsamp = 13 * 13
data_grid = zeros((ngam, nrani, nbin, nbout), 'float64')
asec_to_rad = 4.84e-6
# i is the index of vdisp file #
for i in range(77323):
nline = 0
if i % 1000 == 0:
print '...reading %d th file...' % i
vdisp_file = 'sig_files/log_grid_spl_idx_fft_vdisp_out_fine_full_%d.txt' % (
i)
for line in open(vdisp_file, 'r'):
nline += 1
# if i%100 ==0:
# print '...number of lines : %d...'%nline
vdisp_data = zeros((nline, 3), 'float64')
count = 0
for line in open(vdisp_file, 'r'):
if (line.find('#') == -1):
vdisp_data[count] = line.split()
count += 1
gal_idx = vdisp_data[:, 0]
vdisp_norm = vdisp_data[:, 1]
vdisp_raw = vdisp_data[:, 2]
idxs = i * np
idxf = (i + 1) * np - 1
if idxf > ngam * nrani * nbin * nbout:
idxf = ngam * nrani * nbin * nbout - 1
# nfiles is the index of param file #
nfiles = idxs / nsamp
nfilef = idxf / nsamp
iis = nfiles / ngam
jjs = nfiles % ngam
iif = nfilef / ngam
jjf = nfilef % ngam
idx_offset = idxs - nfiles * nsamp
file = 'param/grid_gam%03drani%03d.dat' % (iis, jjs)
data2 = zeros((nsamp, 8), 'float64')
data = zeros((nsamp, 8), 'float64')
count = 0
for line in open(file, 'r'):
if (line.find('#') == -1):
data[count] = line.split()
count += 1
file2 = 'param/grid_gam%03drani%03d.dat' % (iif, jjf)
data2 = zeros((nsamp, 8), 'float64')
count = 0
for line in open(file2, 'r'):
if (line.find('#') == -1):
data2[count] = line.split()
count += 1
if jjs != jjf:
data = concatenate((data, data2), axis=0)
Dd = data[:, 0] * 1000000.
gamma = data[:, 1]
kext = data[:, 2]
theta_E = data[:, 3]
mE = data[:, 4]
mass = mE * (1. - kext)
if iis == 0 and jjs == 0:
print mE
from scipy.special import gamma as gfunc
rho = -mass * theta_E**(gamma - 3) * gfunc(
gamma / 2.) * pi**(-1.5) / gfunc(0.5 * (gamma - 3))
norm = 4. * pi * rho / (3. - gamma)
# data = zeros((nsamp,8),'float64')
# count = 0
# for line in open(file,'r'):
# if(line.find('#')==-1):
# data[count] = line.split()
# count += 1
gal_idx = gal_idx.astype(int)
gamma_idx = gal_idx / (nbout * nbin * nrani)
rani_idx = (gal_idx / (nbout * nbin)) % nrani
bin_idx = (gal_idx / nbout) % nbin
bout_idx = gal_idx % nbout
# data grid is guaranteed to be positive #
# check what's happening with interpolation #
for m in range(nline):
#data_grid[gamma_idx[m],rani_idx[m],bin_idx[m],bout_idx[m]] = (vdisp_raw[m])**2./norm[idx_offset+m]/(asec_to_rad*Dd[idx_offset+m])
data_grid[gamma_idx[m], rani_idx[m], bin_idx[m],
bout_idx[m]] = (vdisp_norm[m])**2. / norm[
idx_offset + m] * (Dd[idx_offset + m])
print 'data grid created'
import ndinterp
from scipy import interpolate
axes = {}
axes[0] = interpolate.splrep(gamma_arr, arange(ngam), k=3, s=0)
axes[1] = interpolate.splrep(rani_arr, arange(nrani), k=3, s=0)
axes[2] = interpolate.splrep(bin_arr, arange(nbin), k=3, s=0)
axes[3] = interpolate.splrep(bout_arr, arange(nbout), k=3, s=0)
model = ndinterp.ndInterp(axes, data_grid)
filesigv = 'filesigv_adriparam'
import cPickle
f = open(filesigv, 'wb')
cPickle.dump(model, f, 2)
f.close()
print '1 grid interpolated and saved'
model2 = interpolate.RegularGridInterpolator(
(gamma_arr, rani_arr, bin_arr, bout_arr), data_grid, method='nearest')
filesigv = 'filesigv_adriparam_reg_grid_norm_1115'
import cPickle
f = open(filesigv, 'wb')
cPickle.dump(model2, f, 2)
f.close()
print '2 grid interpolated and saved'
return
numpy.random.seed(10)
c = 8.39e-10
Grav = 6.67408e-11 * (3.086e22)**-3. * 1.989e30 / (1.157e-5)**2.
zl = 0.6304
zs = 1.394
reff = 0.58
######## number of beta_in and beta_out : each has 13 sample points in [-0.6,0.6] ########
nbin = 13
nbout = 13
######## number of samples in each parameter file ########
nsamp = nbin * nbout
######## for grid creation, pick a single value ########
Ddmax = 2100
Ddmin = 700
Dd_samp = numpy.random.random(nsamp) * (Ddmax - Ddmin) + Ddmin
DdsDsmax = 0.70
DdsDsmin = 0.30
DdsDs_samp = numpy.random.random(nsamp) * (DdsDsmax - DdsDsmin) + DdsDsmin
SigCrit_samp = c**2. / (4. * pi * Grav * Dd_samp * DdsDs_samp)
# SigCrit = c**2./(4.*pi*Grav*Dd*DdsDs)
thE_samp = [0.826 for i in range(nsamp)]
# thE = 0.826
mE_samp = SigCrit_samp * pi * thE_samp * thE_samp * Dd_samp * Dd_samp * asec_to_rad * asec_to_rad
# mE = SigCrit * pi * thE * thE * Dd * Dd * asec_to_rad * asec_to_rad
# number of desired gamma / rani for the grid #
ngam = 121
nrani = 121
count = 0
kextfile = 'kextcounts_for_Inh_16-0623.dat'
for line in open(kextfile, 'r'):
count += 1
kext = numpy.zeros(count)
kext_samp = numpy.zeros(nsamp)
m = 0
for line in open(kextfile, 'r'):
kext[m] = line
m += 1
gam_samp = numpy.linspace(1.01, 2.99, ngam)
rani_samp = numpy.logspace(log10(0.5 * reff), log10(5 * reff), nrani)
bi_samp = numpy.linspace(-0.6, 0.6, nbin)
bo_samp = numpy.linspace(-0.6, 0.6, nbout)
# give a random seed to numpy random so that one can reproduce the same results #
for i2 in range(nsamp):
idx = numpy.random.randint(low=0, high=m)
kext_samp[i2] = kext[idx]
mass_samp = (1 - kext_samp) * mE_samp
for i1 in range(ngam):
gam = gam_samp[i1]
for j1 in range(nrani):
rani = rani_samp[j1]
paramfile = 'param/grid_gam%03drani%03d.dat' % (i1, j1)
f = open(paramfile, 'w')
f.write(
"# Dd, gamma, kext, theta_E, m_E, rani, beta_in, beta_out\n")
# model_Inh = numpy.load('filesigv_Inh_100CF')
for i3 in range(nbin):
bin = bi_samp[i3]
for j3 in range(nbout):
bout = bo_samp[j3]
idxp = i3 * nbout + j3
# sig_ref = numpy.sqrt(2.)*sm.getSigmaFromGrid2(mass_samp,thE_samp, gam_samp, rani_samp, model_Inh, Dd_samp)
f.write("%le\t%le\t%le\t%le\t%le\t%le\t%le\t%le\n" %
(Dd_samp[idxp], gam, kext_samp[idxp],
thE_samp[idxp], mE_samp[idxp], rani, bin, bout))
f.close()
def sersic_sb(rvals, lp_pars):
# Sersic surface brightness profile, normalized to unit luminosity
reff, nser = lp_pars
L = reff**2 * 2 * np.pi * nser / sersic_bfunc(nser)**(2 * nser) * gfunc(
2 * nser)
return np.exp(-sersic_bfunc(nser) * (rvals / reff)**(1. / nser)) / L
def physField(uvec, rF2, lc, ax, ay):
""" Returns an approximation of the field at the caustic, using the formula from Cooke 1982. """
ux, uy = uvec
alp = rF2*lc
phi20, phi02 = ax**2/rF2 + lc*gauss20(ux, uy), ay**2/rF2 + lc*gauss02(ux, uy)
phi11 = lc*gauss11(ux, uy)
phi30 = lc*gauss30(ux, uy)
phi21 = lc*gauss21(ux, uy)
phi12 = lc*gauss12(ux, uy)
phi03 = lc*gauss03(ux, uy)
B = phi20**3*phi03 - 3*phi20**2*phi11*phi12 + 3*phi20*phi11**2*phi21 - phi11**3*phi30
U = ax*ay/(2*pi*rF2) * exp(1j*(phi(uvec, rF2, lc, ax, ay) + 0.25*pi*np.sign(phi20))) * 2.**(5./6.) * pi**(1./3.) * gfunc(1./3.) * np.abs(phi20)**0.5/(3.**(1./6.) * np.abs(B)**(1./3.))
return U
def M2d(R, nser, Re):
return 2.*np.pi*Re**2*nser/b(nser)**(2.*nser)*gammainc(2*nser, b(nser)*(R/Re)**(1./nser))/L(nser, Re)*gfunc(2.*nser)
def L(nser, Re):
return Re**2*2*np.pi*nser/b(nser)**(2*nser)*gfunc(2*nser)
