def plot_one(rates, plotname, *p, frac=0.05, age=13.6):
brates = u.gimme_rebinned_data(rates,
splits=arange(0, 1.167, 0.167).tolist())
scale_k = quad(imf.salpeter, 3, 8)[0] / quad(imf.salpeter1, 0.1, 125)[0]
scale = scale_k * 0.7**2. * 1e4 ## factors of h...
dt = 0.05
tt = arange(0.1, age, dt) ## forward time
lbt = age - tt
zz = [ct.cosmoz(x) for x in lbt]
sfh = rz.sfr_behroozi_12(tt)
dtd = step_dtd(tt, *p)
norm_dtd = sum(step_dtd(tt, *p)) * dt
dtd = dtd / norm_dtd
tmp = convolve(
sfh, dtd,
'full') * dt * frac * scale ## now convolved result in forward time
rate_fn = tmp[:len(dtd)]
clf()
ax = subplot(111)
ax2 = ax.twinx()
ax2.plot(zz, sfh, 'r-')
ax.plot(zz, rate_fn, 'k-')
ax.errorbar(rates[:, 0],
rates[:, 1],
yerr=[rates[:, 3], rates[:, 2]],
fmt='o',
color='0.6')
ax.errorbar(brates[:, 0],
brates[:, 1],
yerr=[brates[:, 3], brates[:, 2]],
xerr=[brates[:, 5], brates[:, 4]],
fmt='o',
color='0.0',
zorder=10)
pwrl = (-1.0, 1.0)
ax.set_xlim(0, 2.5)
ax.set_xlabel('Redshift')
ax.set_ylabel(r'SN Ia Rate')
ax.set_ylabel(r'$10^{-4}$ SNe Ia per year per Mpc$^3$')
ax2.set_ylabel(r'SF Rate')
ax3 = axes([0.65, 0.6, 0.23, 0.2])
ax3.plot(tt, dtd, 'b-',
label='Fit') #label='Norm = %1.1f' %(simps(dtd,x=time)))
ax3.plot(tt, rz.powerdtd(tt, *pwrl), 'b:', label=r'$t^{%.1f}$' % (pwrl[0]))
pn = (-20, 8.8, 11)
ax3.plot(tt, rz.dtdfunc(tt, *pn), 'b--', label='Best model')
ax.set_title(r' $k=%.4f$ M$_{\odot}^{-1}$, $f=%2.1f\%%$' %
(scale_k, frac * 100))
ax3.set_ylabel('$\Phi$')
ax3.set_xlabel('Delay Time (Gyr)')
ax3.set_xlim(0, 12)
ax3.set_ylim(0, 1.3)
ax3.legend(frameon=False)
savefig(plotname)
return ()
def run_model(tt, *p):
ddt = average(diff(tt))
sfh = rz.csfh_time(tt, *csfh_model)
dtd = rz.dtdfunc(tt, *p[1:])
tmp = convolve(sfh, dtd, 'full') * ddt * np.exp(
p[0]) #*frac*scale ## now convolved result in forward time
rate_fn = tmp[:len(dtd)]
return (rate_fn)
def run_model(tt, *p):
ddt = average(diff(tt))
sfh = rz.csfh_time(tt, *csfh_model)
dtd = rz.dtdfunc(tt, *p[1:])
tmp = convolve(sfh, dtd, 'full')*ddt*p[0]#*frac*scale ## now convolved result in forward time
rate_fn=tmp[:len(dtd)]
## print(p,sum(rate_fn))
## if sum(rate_fn)==0.:
## pdb.set_trace()
return(rate_fn)
def dtdfit(time, *p):
ff, aa, bb, cc = p
scale = quad(imf.salpeter, 3, 8)[0] / quad(imf.salpeter1, 0.1, 125)[0]
scale = scale * 0.7**2. * 1e4
par_model = [0.0134, 2.55, 3.3, 6.1]
sfh = rz.csfh_time(time, *par_model)
dt = sum(diff(time)) / (len(time) - 1)
p1 = (aa, bb, cc)
res = rz.dtdfunc(time, *p1, norm=True)
tmp = convolve(sfh, res, 'full')
return (ff * tmp[:len(time)] * dt * scale)
def dtdfit(time, *p):
ff, m, w, k = p
scale = quad(imf.salpeter, 3, 8)[0] / quad(imf.salpeter1, 0.1, 125)[0]
scale = scale * 0.7**2. * 1e4
par_model = [0.0134, 2.55, 3.3, 6.1] ## Compendium
## par_model = [0.013, 2.6, 3.2, 6.1] ## MD14
## par_model = [0.009, 2.7, 2.5, 4.1] ## Driver18
sfh = rz.csfh_time(time, *par_model)
dt = sum(diff(time)) / (len(time) - 1)
p1 = (m, w, k)
res = rz.dtdfunc(time, *p1, norm=True)
tmp = convolve(sfh, res, 'full')
return (np.exp(ff) * tmp[:len(time)] * dt * scale)
def rate_per_galaxy(
sfh_data,
lbu=13.65,
lbl=0.05,
p0=None,
frac_ia=0.05,
):
scale = quad(imf.salpeter, 3, 8)[0] / quad(imf.salpeter1, 0.1, 125)[0]
scale = scale * 0.70**2.
if not tuple(p0):
p0 = (-1.4, 3.5, -1.0)
ii = where((sfh_data[:, 0] > lbl) &
(sfh_data[:, 0] <= lbu)) # cuts the data range
sfh_data = sfh_data[ii]
sfh_data[:, 0] = lbu - sfh_data[:, 0][::-1]
sfh_data[:, 1] = sfh_data[:, 1][::-1] ## now in forward time
warnings.simplefilter('ignore', RuntimeWarning)
dtd = rz.dtdfunc(sfh_data[:, 0], *p0)
if sum(dtd) == 0.0:
return (-np.inf)
dt = sum(diff(sfh_data[:, 0])) / (len(sfh_data[:, 0]) - 1)
rate_fn = zeros((len(sfh_data), 2), )
tmp = convolve(
sfh_data[:, 1], dtd,
'full') * dt * scale * frac_ia ## now convolved result in forward time
rate_fn[:, 1] = tmp[:len(dtd)]
rate_fn[:, 0] = sfh_data[:, 0]
rate_fn[:, 1] = rate_fn[:, 1]
rate = rate_fn[-1, 1] ## only need the current value
return (rate_fn[-1, 1])
#!/usr/bin/env python
import os,sys,pdb,scipy,glob
from pylab import *
from strolger_util import util as u
from strolger_util import rates_z as rz
if __name__=='__main__':
p0 = (3.5, 2.5, 2.5)
tt = arange(-10.0, 13.6, 0.1)
ax1 = subplot(131)
for mm in arange(-2.5, 12.5, 3):
p = (mm,p0[1],p0[2])
ax1.plot(tt, rz.dtdfunc(tt,*p, norm=False))
ax1.set_xlim(0,10)
ax2 = subplot(132)
for ww in [1.0, 2.0, 2.5, 5.0, 7.5]:
p = (p0[0],ww,p0[2])
ax2.plot(tt, rz.dtdfunc(tt,*p, norm=False))
ax2.set_xlim(0,10)
ax3 = subplot(133)
for kk in arange(-5.0, 7.5, 2.5):
p = (p0[0],p0[1],kk)
ax3.plot(tt, rz.dtdfunc(tt,*p, norm=False))
ax3.set_xlim(0,10)
u.adjust_spines(ax1,['left','bottom'])
u.adjust_spines(ax2,['bottom'])
def plot_one(rates, plotname, *p, frac=0.05, age=13.6):
brates = u.gimme_rebinned_data(rates,
splits=arange(0, 1.125, 0.125).tolist())
scale_k = quad(imf.salpeter, 3, 8)[0] / quad(imf.salpeter1, 0.1, 125)[0]
scale = scale_k * 0.7**2. * 1e4 ## factors of h...
dt = 0.05
tt = arange(dt, age, dt)
lbt = age - tt
zz = [ct.cosmoz(x, ho=70) for x in lbt]
par_model = [0.0134, 2.55, 3.3, 6.1]
sfh = rz.csfh_time(tt, *par_model)
dtd = rz.dtdfunc(tt, *p)
pwrl = (-1.0, 1.0)
dud = rz.powerdtd(tt, *pwrl)
tmp = convolve(
sfh, dtd,
'full') * dt * frac * scale ## now convolved result in forward time
rate_fn = tmp[:len(dtd)]
jdud = convolve(sfh, dud, 'full') * dt * scale * 0.065
jdud = jdud[:len(dtd)]
clf()
ax = subplot(111)
ax2 = ax.twinx()
ax2.plot(zz, sfh, 'r-', label='CSFH')
ax.plot(zz, rate_fn, 'k-', label='Fit', zorder=3)
ax.plot(zz, jdud, 'k:', label=r'$t^{%.1f}$' % (pwrl[0]))
ax.errorbar(rates[:, 0],
rates[:, 1],
yerr=[rates[:, 3], rates[:, 2]],
fmt='o',
color='0.6',
alpha=0.4)
ax.errorbar(brates[:, 0],
brates[:, 1],
yerr=[brates[:, 3], brates[:, 2]],
xerr=[brates[:, 5], brates[:, 4]],
fmt='o',
color='0.0',
zorder=10)
pwrl = (-1.0, 1.0)
ax.set_xlim(0, 2.6)
ax.set_ylim(0, 1.8)
ax2.set_ylim(0, 0.16)
ax3 = axes([0.65, 0.62, 0.23, 0.2])
## ax3 = axes([0.55, 0.6, 0.33, 0.25])
ax3.plot(tt, log10(dtd), 'b-',
label='Fit') #label='Norm = %1.1f' %(simps(dtd,x=time)))
ax3.plot(tt,
log10(rz.powerdtd(tt, *pwrl)),
'b:',
label=r'$t^{%.1f}$' % (pwrl[0]))
ax3.set_ylabel('$\log(\Phi)$')
ax3.set_xlabel('Delay Time (Gyr)')
ax3.set_xlim(0, 12)
ax3.set_ylim(-3, 0.5)
##ax3.set_ylim(0,1)
## ax3.legend(loc=1,ncol=1,frameon=False, fontsize=8)
ax.set_xlabel('Redshift')
ax.set_ylabel(r'$10^{-4}$ SNe Ia per year per Mpc$^3$')
ax2.set_ylabel(r'M$_{\odot}$ per year per Mpc$^3$')
## ax.set_title(r' $k=%.4f$ M$_{\odot}^{-1}$, $f=%2.1f\%%$' %(scale_k,frac*100))
ax.set_title(r'$k=%.4f\,M_{\odot}^{-1},\,\,\varepsilon=%2.1f\%%$' %
(scale_k, frac * 100))
ax.legend(loc=2, frameon=False)
ax2.legend(loc=4, frameon=False)
savefig(plotname)
return ()
def func(x, *p):
aa = p
return (aa * rz.dtdfunc(x, *p0) * scale)
#!/usr/bin/env python
import os, sys, pdb, scipy, glob
from pylab import *
from strolger_util import util as u
from strolger_util import rates_z as rz
from scipy.optimize import curve_fit
from scipy.stats import chisquare
import pickle
scale = (0.0210) * 0.062 * (0.7)**2
ax = subplot(111)
p0 = [-1257.93, 59.32, 248.88] ## from MCMC
time = arange(0.05, 13.5, 0.1)
dtd = rz.dtdfunc(time, *p0)
def func(x, *p):
aa = p
return (aa * rz.dtdfunc(x, *p0) * scale)
p_t = [1.0]
color = '#4BADFF'
## pwrl = (-1.0,1.0)
## ax.plot(time,rz.powerdtd(time, *pwrl, normed=False)*(1.3e-3), 'b--', label=r'$t^{%.1f}$'%(pwrl[0]))
pwrl = (-1.10, 1.0)
perr = (0.09, 0.0)
cov = diag(array(perr)**2)
'''
if __name__ == '__main__':
xx = arange(0, 10, 0.1)
ax1 = subplot(131)
ax2 = subplot(132)
ax3 = subplot(133)
p0 = [-2.1, 0.4, -12.8]
p = p0
cnt = 0
for i in arange(-12, 9, 3.0):
p[0] = i
ax1.plot(xx, cnt + rz.dtdfunc(xx, *p, norm=False), 'k-', alpha=0.3)
cnt += 0.1
p = p0
cnt = 0
for i in arange(0.1, 12., 0.5):
p[1] = i
ax2.plot(xx, cnt + rz.dtdfunc(xx, *p), 'k-', alpha=0.3)
cnt += 0.1
p = p0
cnt = 0
for i in arange(-12, 9, 3.0):
p[2] = i
ax3.plot(xx, cnt + rz.dtdfunc(xx, *p), 'k-', alpha=0.3)
cnt += 0.1
rate_fn = tmp[:len(dtd)]
return (rate_fn)
if __name__ == '__main__':
dt = 0.05
age = 13.6
tt = arange(dt, age, dt)
## p_val = [-2.810, -1518.39108091, 51.06020462, 49.98728772] ## from optimized fit
p_val = [-2.814, -1257.93, 59.32, 248.88] ## from MCMC
ax = subplot(111)
ax2 = axes([0.55, 0.6, 0.33, 0.25])
## ax2 = axes([0.65, 0.62, 0.23, 0.2])
ax2.plot(tt, log10(rz.dtdfunc(tt, *p_val[1:])), 'b-')
files = glob.glob('mc_sfd_*.pkl')
tot = 0
for file in files:
samples = pickle.load(open(file, 'rb'))
samples = samples[:, 50:, :].reshape((-1, 5))
print('adding %d samples from %s... ' % (len(samples), file))
try:
temp = concatenate((temp, samples), axis=0)
except:
temp = samples
#tta = linspace(min(tt), max(tt), 100)
tta = tt
print('%d total samples' % len(temp))
def plot_one(rates, plotname, *p, frac=0.05, age=13.6):
brates = u.gimme_rebinned_data(rates,
splits=arange(0, 1.125, 0.125).tolist())
scale_k = quad(imf.salpeter, 3, 8)[0] / quad(imf.salpeter1, 0.1, 125)[0]
scale = scale_k * 0.7**2. * 1e4 ## factors of h...
dt = 0.05
tt = arange(dt, age, dt) ## forward time
lbt = age - tt
zz = [ct.cosmoz(x) for x in lbt]
par_model = [0.0134, 2.55, 3.3, 6.1]
sfh = rz.csfh_time(tt, *par_model)
dtd = rz.dtdfunc(tt, *p)
pwrl = (-1.0, 1.0)
dud = rz.powerdtd(tt, *pwrl)
tmp = convolve(
sfh, dtd,
'full') * dt * frac * scale ## now convolved result in forward time
rate_fn = tmp[:len(dtd)]
jdud = convolve(sfh, dud, 'full') * dt * scale * 0.065
jdud = jdud[:len(dtd)]
clf()
ax = subplot(111)
ax2 = ax.twinx()
ax2.plot(zz, sfh, 'r-')
ax.plot(zz, rate_fn, 'k-')
ax.plot(zz, jdud, 'k:')
ax.errorbar(rates[:, 0],
rates[:, 1],
yerr=[rates[:, 3], rates[:, 2]],
fmt='o',
color='0.6')
ax.errorbar(brates[:, 0],
brates[:, 1],
yerr=[brates[:, 3], brates[:, 2]],
xerr=[brates[:, 5], brates[:, 4]],
fmt='o',
color='0.0',
zorder=10)
ax.set_xlim(0, 2.5)
ax.set_ylim(0, 1.8)
ax.set_xlabel('Redshift')
ax.set_ylabel(r'SN Ia Rate')
ax.set_ylabel(r'$10^{-4}$ SNe Ia per year per Mpc$^3$')
ax2.set_ylabel(r'SF Rate')
ax3 = axes([0.65, 0.6, 0.23, 0.2])
ax3.plot(tt, dtd, 'b-',
label='Fit') #label='Norm = %1.1f' %(simps(dtd,x=time)))
ax3.plot(tt, dud, 'b:', label=r'$t^{%.1f}$' % (pwrl[0]))
ax3.set_ylabel('$\Phi$')
ax3.set_xlabel('Delay Time (Gyr)')
ax3.set_xlim(0, 12)
ax3.set_ylim(0, 1.3)
ax3.legend(frameon=False)
savefig(plotname)
return ()
dt = 0.05
age=13.6
tt = arange(dt,age,dt)
## p_val = [0.060, -1156., 58., 220.]
p_val = [0.060, -1500., 58., 220.]
p_err = [[0.003, -0.004],
[839., -596.],
[14., -16.],
[191., -186.]
]
## fout, (ax, ax2) = plt.subplots(1,2, gridspec_kw = {'width_ratios':[3, 1]})
ax = subplot(111)
ax2 = axes([0.55, 0.6, 0.33, 0.25])
ax2.plot(tt, rz.dtdfunc(tt, *p_val[1:]), 'b-')
p_err=sqrt(array(p_err)[:,1]**2.)
## p_err=sqrt(p_err[:,0]**2.+p_err[:,1]**2.)
tta = linspace(min(tt), max(tt), 300)
cov = diag(array(p_err)**2.)
## ps = np.random.multivariate_normal(p_val, cov, 10000)
outfile = 'bfres0.pkl'
if os.path.isfile(outfile):
print ('%s exists' %outfile)
ps=pickle.load(open(outfile,'rb'))
else:
ps = np.random.multivariate_normal(p_val, cov, 100)
def rate_per_galaxy(
sfh,
lbu=13.65,
lbl=0.05,
p0=None,
frac_ia=0.05,
plotit=True,
title=None,
testing=False,
):
scale = quad(imf.salpeter, 3, 8)[0] / quad(imf.salpeter1, 0.1, 125)[0]
scale = scale * 0.70**2.
if not p0:
p0 = (-1.4, 3.5, -1.0)
sfh_data = loadtxt(sfh)
ii = where((sfh_data[:, 0] > lbl) &
(sfh_data[:, 0] <= lbu)) # cuts the data range
sfh_data = sfh_data[ii]
sfh_data[:, 0] = lbu - sfh_data[:, 0][::-1]
sfh_data[:, 1] = sfh_data[:, 1][::-1] ## now in forward time
if testing:
## reframes everything in a more continuous time.
n_out = IUS(sfh_data[:, 0], sfh_data[:, 1])
time = arange(0, lbu + 0.1, 0.1)
sfh_data = zeros((len(time), 2), )
sfh_data[:, 0] = time
sfh_data[:, 1] = n_out(
time) ## now continuous, evenly spaced, not sure that's important.
if testing:
## just makes a SFH box
box_ll = 4.
ii = where((sfh_data[:, 0] > box_ll) & (sfh_data[:, 0] < box_ll + 2.))
sfh_data[:, 1] = 0.0
sfh_data[:, 1][ii] = 10.
#warnings.simplefilter('ignore',RuntimeWarning)
dtd = rz.dtdfunc(sfh_data[:, 0], *p0)
if testing:
## makes the dtd function gaussian
p1 = (1., 4.0, 0.01)
dtd = u.gauss(sfh_data[:, 0], *p1)
dt = sum(diff(sfh_data[:, 0])) / (len(sfh_data[:, 0]) - 1)
rate_fn = zeros((len(sfh_data), 2), )
tmp = convolve(
sfh_data[:, 1], dtd,
'full') * dt * scale * frac_ia ## now convolved result in forward time
rate_fn[:, 1] = tmp[:len(
dtd)] #*concatenate((array([0.]),diff(sfh_data[:,0])),)
rate_fn[:, 0] = sfh_data[:, 0]
rate_fn[:, 1] = rate_fn[:, 1]
rate = rate_fn[-1, 1]
if testing:
## a check of the shift in the effective time on each
tmp1 = sum((sfh_data[:, 0]) * sfh_data[:, 1]) / sum(sfh_data[:, 1])
tmp2 = sum(rate_fn[:, 1] * (rate_fn[:, 0])) / sum(rate_fn[:, 1])
print(tmp1, tmp2, tmp2 - tmp1)
if plotit:
clf()
ax1 = subplot(111)
ax1.plot(lbu - sfh_data[:, 0], sfh_data[:, 1], '--',
color='0.25') #,alpha=0.3)
ax1.set_xlabel('Lookback Time (Gyr)')
ax1.set_ylabel('$\psi(M_{\odot}\,yr^{-1})$')
if title: ax1.set_title(title)
## ax1.axvline(x=0, color='r')
ax3 = ax1.twinx()
ax3.plot(lbu - rate_fn[:, 0],
rate_fn[:, 1] * 1.e3,
'k-',
label='$R_{Ia}(0)=%2.2f\, (1000\, yr)^{-1}$' % (rate * 1.e3),
alpha=0.3)
ax3.set_ylabel('$R_{Ia}[\#\,(1000\, yr)^{-1}]$')
ax3.legend(frameon=False)
ttt, ddd = rz.greggio()
ttt = array(ttt)
ddd = array(ddd)
ii = where(ttt > 0)
ttt = ttt[ii]
ddd = ddd[ii]
time = arange(0.1, 15, 0.1)
dtd = rz.dtdfunc(time, *p0)
pwrl = (-1.0, 1.0)
ax2 = axes([0.6, 0.55, 0.25, 0.25])
ax2.plot(time, dtd, 'r-',
label='Best Fit') #label='Norm = %1.1f' %(simps(dtd,x=time)))
ax2.plot(time,
rz.powerdtd(time, *pwrl),
'b--',
label=r'$t^{%.1f}$' % (pwrl[0]))
## ax2.plot(ttt,ddd,'b--', label='Greggio')
ax2.set_ylabel('$\Phi$')
ax2.set_xlabel('Delay Time (Gyr)')
ax2.set_xlim(0, 12)
ax2.set_ylim(0, 1.3)
ax2.legend(frameon=False)
#tight_layout()
ax4 = axes([0.6, 0.2, 0.25, 0.25])
img = mpimg.imread('107.jpg') ## Thoth
ax4.imshow(img[75:135, 50:140])
#img = mpimg.imread('206.jpg') ## Borg
#ax4.imshow(img[75:135,70:160])
ax4.set_yticks([])
ax4.set_xticks([])
if title:
savefig(title + '.png')
else:
savefig('figure_sfh_demo.png')
return (rate)