def fasterMCMC(self, niter, nburn, nthin=1, grid=False):
from Sampler import SimpleSample as sample
import pymc, numpy, ndinterp
axn = [a for a in self.model.axes_names]
axes = self.model.axes
pmags = []
lpModel = None
magModel = None
Modaxes = None
magUC = 0.
order = None
for i in range(len(self.data)):
f = self.data[i]['filter']
z = self.data[i]['redshift']
pmags.append(self.model.models[f][z].z)
if magModel is None:
magModel = self.model.models[f][z].z * 0.
lpModel = magModel.copy()
Modaxes = self.model.models[f][z].axes
order = self.model.models[f][z].order
m, me = self.data[i]['mag'], self.data[i]['error']**2
d = (m - pmags[-1])
lpModel += -0.5 * d**2 / me
magModel += d / me
magUC += -0.5 / me
for i in range(len(self.data) - 1):
d1 = self.data[i]
d2 = self.data[i + 1]
f1, m1, me1 = d1['filter'], d1['mag'], d1['error']
f2, m2, me2 = d2['filter'], d2['mag'], d2['error']
c = pmags[i] - pmags[i + 1]
dc = m1 - m2
if i == 0:
logp = (c - dc)**2 / (me1**2 + me2**2)
else:
logp += (c - dc)**2 / (me1**2 + me2**2)
indx = numpy.unravel_index(logp.argmin(), logp.shape)
m = 0.
w = 0.
for i in range(len(self.data)):
d, e = self.data[i]['mag'], self.data[i]['error']
M = (pmags[i][indx] - d) / 2.5
m += M / e**2
w += 1. / e**2
m /= w
M = numpy.linspace(m - 0.6, m + 0.6, 13)
a = []
for i in range(len(self.model.axes_names)):
a.append(
self.model.axes[self.model.axes_names[i]]['points'].copy())
for key in self.names:
p = self.priors[key]['prior']
if key.find('mass') >= 0:
continue
if key.find('log') == 0:
key = key[3:]
a[axn.index(key)] = numpy.log10(a[axn.index(key)])
i = axn.index(key)
for j in range(len(a[i])):
p.value = a[i][j]
try:
a[i][j] = p.logp
except:
a[i][j] = -1e300
logp = lpModel + ndinterp.create_axes_array(a).sum(0)
logp = numpy.expand_dims(logp, logp.ndim).repeat(M.size, logp.ndim)
for i in range(M.size):
M0 = M[i] * -2.5
logp[:, :, :, :, i] += magModel * M0 + M0**2 * magUC
logp -= logp.max()
wt = numpy.exp(logp)
wt /= wt.sum()
a = []
for i in range(len(self.model.axes_names)):
a.append(self.model.axes[self.model.axes_names[i]]['points'])
a.append(M)
for key in self.names:
if key.find('mass') >= 0:
if key.find('log') != 0:
a[-1] == 10**a[-1]
axn.append('mass')
elif key.find('log') == 0:
key = key[3:]
a[axn.index(key)] = numpy.log10(a[axn.index(key)])
vals = ndinterp.create_axes_array(a)
if grid == True:
m = (wt * vals[-1]).sum()
st = ((wt * (vals[-1] - m)**2).sum())**0.5
return m, st
pars = []
cov = []
for key in self.names:
pars.append(self.priors[key]['prior'])
if key.find('log') == 0:
key = key[3:]
i = axn.index(key)
m = (wt * vals[i]).sum()
st = ((wt * (vals[i] - m)**2).sum())**0.5
pars[-1].value = m
cov.append(st)
for key in self.names:
continue
pars.append(self.priors[key]['prior'])
if key == 'logmass':
pars[-1].value = m
cov.append(0.03)
elif key == 'mass':
pars[-1].value = 10**m
cov.append(self.priors[key]['prior'].value / 20.)
else:
if key.find('log') != 0:
i = axn.index(key)
mn = (vals[i] * wt).sum()
cov.append(((wt * (vals[i] - mn)**2).sum())**0.5)
pars[-1].value = mn
else:
key = key.split('log')[1]
i = axn.index(key)
mn = (numpy.log10(vals[i]) * wt).sum()
cov.append(
((wt * (numpy.log10(vals[i]) - mn)**2).sum())**0.5)
pars[-1].value = mn
for key in self.names:
continue
pars.append(self.priors[key]['prior'])
if key == 'logmass':
pars[-1].value = m
cov.append(0.03)
elif key == 'mass':
pars[-1].value = 10**m
cov.append(self.priors[key]['prior'].value / 20.)
elif key == 'age':
pars[-1].value = axes['age']['points'][indx[axn.index('age')]]
cov.append(0.5)
elif key == 'logage':
pars[-1].value = numpy.log10(
axes['age']['points'][indx[axn.index('age')]])
cov.append(0.03)
elif key == 'tau':
pars[-1].value = axes['tau']['points'][indx[axn.index('tau')]]
cov.append(0.2)
elif key == 'logtau':
pars[-1].value = numpy.log10(
axes['tau']['points'][indx[axn.index('tau')]])
cov.append(0.03)
elif key == 'tau_V':
pars[-1].value = axes['tau_V']['points'][indx[axn.index(
'tau_V')]]
cov.append(self.priors[key]['prior'].value / 20.)
elif key == 'logtau_V':
pars[-1].value = numpy.log10(
axes['tau_V']['points'][indx[axn.index('tau_V')]])
cov.append(0.1)
elif key == 'Z':
pars[-1].value = axes['Z']['points'][indx[axn.index('Z')]]
cov.append(self.priors[key]['prior'].value / 20.)
elif key == 'logZ':
pars[-1].value = numpy.log10(
axes['Z']['points'][indx[axn.index('Z')]])
cov.append(0.05)
lpModel = ndinterp.ndInterp(Modaxes, lpModel, order)
magModel = ndinterp.ndInterp(Modaxes, magModel, order)
cov = numpy.array(cov)
@pymc.observed
def loglikelihood(value=0., pars=pars):
from math import log10
points = numpy.zeros((1, len(pars) - 1))
i = 0
for key in self.names:
if key == 'mass':
M = -2.5 * log10(pars[i])
elif key == 'logmass':
M = -2.5 * pars[i]
elif key.find('log') == 0:
key = key.split('log')[1]
points[0, axn.index(key)] = 10**pars[i]
else:
points[0, axn.index(key)] = pars[i]
i += 1
lp = lpModel.eval(points)
if lp == 0:
return -1e300 # Short circuit if out of range
lp += magModel.eval(points) * M + M**2 * magUC
return lp
costs = [loglikelihood]
logps, trace, dets = sample(pars,
costs, [],
nburn / 2,
cov=cov,
jump=[0., 0.])
# cov = numpy.cov(trace.T)
logps, trace, dets = sample(pars,
costs, [],
nburn / 2,
cov=cov,
jump=[0., 0.])
cov = numpy.cov(trace.T)
logps, trace, dets = sample(pars,
costs, [],
niter,
cov=cov,
jump=[0., 0.])
self.proposal_cov = cov
self.trace = trace
self.logp = logps
cnt = 0
o = {'logp': logps}
for key in self.names:
o[key] = trace[:, cnt].copy()
cnt += 1
return o
from pylens import MassModels
import numpy,pylab
import indexTricks as iT
from scipy import interpolate
from scipy.special import gamma,gammainc
import ndinterp,time
import sersic
import cPickle
x0 = numpy.logspace(-4.,1.,51)
n0 = numpy.linspace(0.5,6.,12)
q0 = numpy.linspace(0.1,1.,19)
x,y,n,q = ndinterp.create_axes_array([x0,x0,n0,q0])
yout = x*0.
xout = y*0.
for i in range(x.shape[2]):
for j in range(x.shape[3]):
X = x[:,:,i,j]
Y = y[:,:,i,j]
N = n[0,0,i,j]
Q = q[0,0,i,j]
k = 2.*N-1./3+4./(405.*N)+46/(25515.*N**2)
amp = k**(2*N)/(2*N*gamma(2*N))
yi,xi = sersic.sersicdeflections(-Y.ravel(),X.ravel(),amp,1.,N,Q)
yout[:,:,i,j] = -1*yi.reshape(Y.shape)
xout[:,:,i,j] = xi.reshape(X.shape)
axes = {}
axes[0] = interpolate.splrep(x0,numpy.arange(x0.size))
axes[1] = interpolate.splrep(x0,numpy.arange(x0.size))
def fasterMCMC(self,niter,nburn,nthin=1,grid=False):
from Sampler import SimpleSample as sample
import pymc,numpy,ndinterp
axn = [a for a in self.model.axes_names]
axes = self.model.axes
pmags = []
lpModel = None
magModel = None
Modaxes = None
magUC = 0.
order = None
for i in range(len(self.data)):
f = self.data[i]['filter']
z = self.data[i]['redshift']
pmags.append(self.model.models[f][z].z)
if magModel is None:
magModel = self.model.models[f][z].z*0.
lpModel = magModel.copy()
Modaxes = self.model.models[f][z].axes
order = self.model.models[f][z].order
m,me = self.data[i]['mag'],self.data[i]['error']**2
d = (m-pmags[-1])
lpModel += -0.5*d**2/me
magModel += d/me
magUC += -0.5/me
for i in range(len(self.data)-1):
d1 = self.data[i]
d2 = self.data[i+1]
f1,m1,me1 = d1['filter'],d1['mag'],d1['error']
f2,m2,me2 = d2['filter'],d2['mag'],d2['error']
c = pmags[i]-pmags[i+1]
dc = m1-m2
if i==0:
logp = (c-dc)**2/(me1**2+me2**2)
else:
logp += (c-dc)**2/(me1**2+me2**2)
indx = numpy.unravel_index(logp.argmin(),logp.shape)
m = 0.
w = 0.
for i in range(len(self.data)):
d,e = self.data[i]['mag'],self.data[i]['error']
M = (pmags[i][indx]-d)/2.5
m += M/e**2
w += 1./e**2
m /= w
M = numpy.linspace(m-0.6,m+0.6,13)
a = []
for i in range(len(self.model.axes_names)):
a.append(self.model.axes[self.model.axes_names[i]]['points'].copy())
for key in self.names:
p = self.priors[key]['prior']
if key.find('mass')>=0:
continue
if key.find('log')==0:
key = key[3:]
a[axn.index(key)] = numpy.log10(a[axn.index(key)])
i = axn.index(key)
for j in range(len(a[i])):
p.value = a[i][j]
try:
a[i][j] = p.logp
except:
a[i][j] = -1e300
logp = lpModel+ndinterp.create_axes_array(a).sum(0)
logp = numpy.expand_dims(logp,logp.ndim).repeat(M.size,logp.ndim)
for i in range(M.size):
M0 = M[i]*-2.5
logp[:,:,:,:,i] += magModel*M0 + M0**2*magUC
logp -= logp.max()
wt = numpy.exp(logp)
wt /= wt.sum()
a = []
for i in range(len(self.model.axes_names)):
a.append(self.model.axes[self.model.axes_names[i]]['points'])
a.append(M)
for key in self.names:
if key.find('mass')>=0:
if key.find('log')!=0:
a[-1] == 10**a[-1]
axn.append('mass')
elif key.find('log')==0:
key = key[3:]
a[axn.index(key)] = numpy.log10(a[axn.index(key)])
vals = ndinterp.create_axes_array(a)
if grid==True:
m = (wt*vals[-1]).sum()
st = ((wt*(vals[-1]-m)**2).sum())**0.5
return m,st
pars = []
cov = []
for key in self.names:
pars.append(self.priors[key]['prior'])
if key.find('log')==0:
key = key[3:]
i = axn.index(key)
m = (wt*vals[i]).sum()
st = ((wt*(vals[i]-m)**2).sum())**0.5
pars[-1].value = m
cov.append(st)
for key in self.names:
continue
pars.append(self.priors[key]['prior'])
if key=='logmass':
pars[-1].value = m
cov.append(0.03)
elif key=='mass':
pars[-1].value = 10**m
cov.append(self.priors[key]['prior'].value/20.)
else:
if key.find('log')!=0:
i = axn.index(key)
mn = (vals[i]*wt).sum()
cov.append(((wt*(vals[i]-mn)**2).sum())**0.5)
pars[-1].value = mn
else:
key = key.split('log')[1]
i = axn.index(key)
mn = (numpy.log10(vals[i])*wt).sum()
cov.append(((wt*(numpy.log10(vals[i])-mn)**2).sum())**0.5)
pars[-1].value = mn
for key in self.names:
continue
pars.append(self.priors[key]['prior'])
if key=='logmass':
pars[-1].value = m
cov.append(0.03)
elif key=='mass':
pars[-1].value = 10**m
cov.append(self.priors[key]['prior'].value/20.)
elif key=='age':
pars[-1].value = axes['age']['points'][indx[axn.index('age')]]
cov.append(0.5)
elif key=='logage':
pars[-1].value = numpy.log10(axes['age']['points'][indx[axn.index('age')]])
cov.append(0.03)
elif key=='tau':
pars[-1].value = axes['tau']['points'][indx[axn.index('tau')]]
cov.append(0.2)
elif key=='logtau':
pars[-1].value = numpy.log10(axes['tau']['points'][indx[axn.index('tau')]])
cov.append(0.03)
elif key=='tau_V':
pars[-1].value = axes['tau_V']['points'][indx[axn.index('tau_V')]]
cov.append(self.priors[key]['prior'].value/20.)
elif key=='logtau_V':
pars[-1].value = numpy.log10(axes['tau_V']['points'][indx[axn.index('tau_V')]])
cov.append(0.1)
elif key=='Z':
pars[-1].value = axes['Z']['points'][indx[axn.index('Z')]]
cov.append(self.priors[key]['prior'].value/20.)
elif key=='logZ':
pars[-1].value = numpy.log10(axes['Z']['points'][indx[axn.index('Z')]])
cov.append(0.05)
lpModel = ndinterp.ndInterp(Modaxes,lpModel,order)
magModel = ndinterp.ndInterp(Modaxes,magModel,order)
cov = numpy.array(cov)
@pymc.observed
def loglikelihood(value=0.,pars=pars):
from math import log10
points = numpy.zeros((1,len(pars)-1))
i = 0
for key in self.names:
if key=='mass':
M = -2.5*log10(pars[i])
elif key=='logmass':
M = -2.5*pars[i]
elif key.find('log')==0:
key = key.split('log')[1]
points[0,axn.index(key)] = 10**pars[i]
else:
points[0,axn.index(key)] = pars[i]
i += 1
lp = lpModel.eval(points)
if lp==0:
return -1e300 # Short circuit if out of range
lp += magModel.eval(points)*M + M**2*magUC
return lp
costs = [loglikelihood]
logps,trace,dets = sample(pars,costs,[],nburn/2,cov=cov,jump=[0.,0.])
# cov = numpy.cov(trace.T)
logps,trace,dets = sample(pars,costs,[],nburn/2,cov=cov,jump=[0.,0.])
cov = numpy.cov(trace.T)
logps,trace,dets = sample(pars,costs,[],niter,cov=cov,jump=[0.,0.])
self.proposal_cov = cov
self.trace= trace
self.logp = logps
cnt = 0
o = {'logp':logps}
for key in self.names:
o[key] = trace[:,cnt].copy()
cnt += 1
return o
import pylab,numpy import indexTricks as iT from scipy import ndimage import ndinterp from scipy.special import gamma,gammainc import sersic from pylens import powerlaw x0 = numpy.logspace(-4.,1.,51) #x0 = numpy.linspace(0.1,15.,151) x,y = ndinterp.create_axes_array([x0,x0]) N = 3.7 Q = 0.73 k = 2.*N-1./3+4./(405.*N)+46/(25515.*N**2) amp = k**(2*N)/(2*N*gamma(2*N)) print amp,x.size amp = 1. import time t = time.time() yi,xi = sersic.sersicdeflections(-y.ravel(),x.ravel(),amp,1.,N,Q) yi *= -1 print time.time()-t t = time.time() yy,xx = powerlaw.powerlawdeflections(x.ravel(),y.ravel(),2.4,1.1,1e-5,0.73) print time.time()-t xr = x.ravel() yr = y.ravel() t = time.time() gam = 1.1/2.
from pylens import MassModels
import numpy, pylab
import indexTricks as iT
from scipy import interpolate
from scipy.special import gamma, gammainc
import ndinterp, time
import sersic
import cPickle
x0 = numpy.logspace(-4., 1., 51)
n0 = numpy.linspace(0.5, 6., 12)
q0 = numpy.linspace(0.1, 1., 19)
x, y, n, q = ndinterp.create_axes_array([x0, x0, n0, q0])
yout = x * 0.
xout = y * 0.
for i in range(x.shape[2]):
for j in range(x.shape[3]):
X = x[:, :, i, j]
Y = y[:, :, i, j]
N = n[0, 0, i, j]
Q = q[0, 0, i, j]
k = 2. * N - 1. / 3 + 4. / (405. * N) + 46 / (25515. * N**2)
amp = k**(2 * N) / (2 * N * gamma(2 * N))
yi, xi = sersic.sersicdeflections(-Y.ravel(), X.ravel(), amp, 1., N, Q)
yout[:, :, i, j] = -1 * yi.reshape(Y.shape)
xout[:, :, i, j] = xi.reshape(X.shape)
axes = {}
axes[0] = interpolate.splrep(x0, numpy.arange(x0.size))
axes[1] = interpolate.splrep(x0, numpy.arange(x0.size))