EQUADidx[tag] = []
EQUAD = float(md.__dict__['T2EQUAD ' + tag])
EQUADlist.append(EQUAD)
for i, toa in enumerate(tf.toalist):
SIGMA.append(float(toa.TOAsigma))
TOAflags = [('-%s %s' % (f,toa.flags[f])) for f in toa.flags]
try:
key = (set(EFACtags) & set(TOAflags)).pop()
EFACidx[key].append(i)
except:
EFAC = EFAC_default
key = (set(EQUADtags) & set(TOAflags)).pop()
EQUADidx[key].append(i)
"""Setup red noise Fourier matrix, Fr"""
f, F = get_rr_rep(toas, Tspan, 1./Tspan/4.7, 50, 20)
#fyr = 1./secperyear
p0 = [float(md.__dict__[p]) for p in T2EFAC]
p1 = [np.log(float(md.__dict__[p])) for p in T2EQUAD]
p2 = [np.log(float(md.__dict__[p])) for p in T2ECORR]
p3 = [np.log(RNAMP), RNIDX]
np0 = len(p0)
np1 = np0 + len(p1)
np2 = np1 + len(p2)
np3 = np2 + len(p3)
plist = np.array(p0 + p1 + p2 + p3)
def loglikelihood(plist, logspace=True):
for tag in EQUADtags:
EQUADidx[tag] = []
EQUAD = float(md.__dict__['T2EQUAD ' + tag])
EQUADlist.append(EQUAD)
for i, toa in enumerate(tf.toalist):
SIGMA.append(float(toa.TOAsigma))
TOAflags = [('-%s %s' % (f, toa.flags[f])) for f in toa.flags]
try:
key = (set(EFACtags) & set(TOAflags)).pop()
EFACidx[key].append(i)
except:
EFAC = EFAC_default
key = (set(EQUADtags) & set(TOAflags)).pop()
EQUADidx[key].append(i)
"""Setup red noise Fourier matrix, Fr"""
f, F = get_rr_rep(toas, Tspan, 1. / Tspan / 4.7, 50, 20)
#fyr = 1./secperyear
p0 = [float(md.__dict__[p]) for p in T2EFAC]
p1 = [np.log(float(md.__dict__[p])) for p in T2EQUAD]
p2 = [np.log(float(md.__dict__[p])) for p in T2ECORR]
p3 = [np.log(RNAMP), RNIDX]
np0 = len(p0)
np1 = np0 + len(p1)
np2 = np1 + len(p2)
np3 = np2 + len(p3)
plist = np.array(p0 + p1 + p2 + p3)
def loglikelihood(plist, logspace=True):
tstart = time.time()
def getRNreal(md, tf, t, w, M, r, n):
T2EFAC = [par for par in md.__dict__ if par.startswith('T2EFAC')]
T2EQUAD = [par for par in md.__dict__ if par.startswith('T2EQUAD')]
T2ECORR = [par for par in md.__dict__ if par.startswith('ECORR')]
if 'RNAMP' in md.__dict__:
RNAMP = np.abs(float(md.RNAMP))
else:
RNAMP = np.abs(0.06)
md.manifest.append('RNAMP')
if 'RNIDX' in md.__dict__:
RNIDX = float(md.RNIDX)
else:
RNIDX = -2.17
md.manifest.append('RNIDX')
#groups = {}
#flaglist = []
#for par in T2EQUAD:
#flag = ' '.join(par.split()[1:3])
#groups[flag] = tf.othergroups[flag]
#flaglist.append(flag)
""" Setup matrix U and epoch-avearging matrix EA"""
ECORRtags = [' '.join(tag.split()[1:3]) for tag in T2ECORR]
S_idx = []
stack = []
aveeph = []
ECORRlist = []
for key in T2ECORR:
flag = ' '.join(key.split()[1:3])
if key in md.__dict__:
ECORRlist.append(float(md.__dict__[key]))
S_idx.append(0)
for epochs in sorted(md.toagrps[flag].keys()):
aveeph.append(epochs)
idx = md.toagrps[flag][epochs]
S_idx[-1] += 1
l = np.zeros(n)
l[idx] = 1.
stack.append(l)
S_idx[-1] = np.array(S_idx[-1])
S_ele = np.hstack([ ECORRlist[i]**2 *np.ones(k) for i,k in enumerate(S_idx)])
U = (np.vstack(stack)).T
UT = U.T
""" Setup EFAC, EQUAD"""
EFACtags = [' '.join(tag.split()[1:3]) for tag in T2EFAC]
EQUADtags = [' '.join(tag.split()[1:3]) for tag in T2EQUAD]
EFACidx = {}
EQUADidx = {}
SIGMA = []
EFAClist = []
EQUADlist = []
for tag in EFACtags:
EFACidx[tag] = []
EFAC = float(md.__dict__['T2EFAC ' + tag])
EFAClist.append(EFAC)
for tag in EQUADtags:
EQUADidx[tag] = []
EQUAD = float(md.__dict__['T2EQUAD ' + tag])
EQUADlist.append(EQUAD)
for i, toa in enumerate(tf.toalist):
SIGMA.append(float(toa.TOAsigma))
TOAflags = [('-%s %s' % (f,toa.flags[f])) for f in toa.flags]
try:
key = (set(EFACtags) & set(TOAflags)).pop()
EFACidx[key].append(i)
except:
EFAC = EFAC_default
key = (set(EQUADtags) & set(TOAflags)).pop()
EQUADidx[key].append(i)
"""Setup red noise Fourier matrix, Fr"""
freq , F = get_rr_rep(toas, Tspan, 1./Tspan/4.7, 50, 20)
p0 = [float(md.__dict__[p]) for p in T2EFAC]
p1 = [np.log(float(md.__dict__[p])) for p in T2EQUAD]
p2 = [np.log(float(md.__dict__[p])) for p in T2ECORR]
p3 = [np.log(RNAMP), RNIDX]
np0 = len(p0)
np1 = np0 + len(p1)
np2 = np1 + len(p2)
np3 = np2 + len(p3)
plist = np.array(p0 + p1 + p2 + p3)
#def plotRN(plist, logspace=True):
tstart = time.time()
"""setup parameters"""
p0 = np.array(plist[:np0])
p1 = np.array(plist[np0:np1])
p2 = np.array(plist[np1:np2])
p3 = np.array(plist[np2:np3])
if logspace:
CoordTransTerm = (np.sum(p1) + np.sum(p2) + p3[0]) #sume all the logterm for coordinate transformation dz = z d (ln(z))
p1 = np.exp(p1)
p2 = np.exp(p2)
p3[0] = np.exp(p3[0])
else:
CoordTransTerm = 0.
"""Load parameters"""
efac = np.ones(n)
for i,tag in enumerate(EFACtags):
efac[EFACidx[tag]] = p0[i]
Nvec = np.array(SIGMA * efac)**2
equad = np.zeros(n)
for i,tag in enumerate(EQUADtags):
equad[EQUADidx[tag]] = p1[i]
Nvec += (equad**2)
S_ele = np.hstack([ p2[i]**2. *np.ones(k) for i,k in enumerate(S_idx)])
RNAMP = np.abs(p3[0]) #/ ampfac
RNIDX = p3[1]
#phi = (RNAMP**2)/12/np.pi/np.pi *fyr**(-3-RNIDX) * f**RNIDX
phi = (RNAMP**2) * freq ** RNIDX #assuming f is is 1/yr units.
"""Putting the noise models together"""
T = np.hstack((M, F, U))
"""Putting the timing and noise parameters together """
m = M.shape[1]
n_f = F.shape[1]
n_j = U.shape[1]
n_p = T.shape[1]
Phi_I = np.zeros((n_p, n_p))
Pars = [LARGE_NUMBER for i in range(m)]
Pars += list(phi)
Pars += list(S_ele)
Pi = 1./np.array(Pars)
np.fill_diagonal(Phi_I, Pi)
"""compute likelyhood"""
d = dot(T.T, r/Nvec)
Sigma = Phi_I + dot(T.T, (1./Nvec * T.T).T)
#print d.shape, Sigma.shape
try:
cfSigma = sl.cho_factor(Sigma)
#except LinAlgError:
except :
print Sigma
logdetSigma = 2.*np.sum(np.log(np.diag(cfSigma[0])))
Sid = sl.cho_solve(cfSigma, d)
dSid = np.dot(d.T, Sid)
logdetCt = np.sum(np.log(np.array(Pars[m:])))
logdetN = np.sum(np.log(Nvec))
Nir = r / Nvec
LogLike1 = 0.5 * ( dot(r.T, Nir) - dSid)
LogLike2 = 0.5 * ( logdetN + logdetSigma + logdetCt)
LogLike = LogLike1 + LogLike2 - CoordTransTerm
b = sl.cho_solve(cfSigma, d.T)
bphi = b[m:m+n_f]
phi_I = np.zeros((n_f, n_f))
np.fill_diagonal(phi_I, 1./phi)
FT = F.T
sigma = phi_I #+ dot(FT, (1./Nvec * FT).T)
cfsigma = sl.cho_factor(sigma)
y = dot(F, bphi.T)
yerr = np.sqrt(np.diag(dot(F, sl.cho_solve(cfsigma, FT))))
return y, yerr
def getRNreal(md, tf, t, w, M, r, n):
T2EFAC = [par for par in md.__dict__ if par.startswith('T2EFAC')]
T2EQUAD = [par for par in md.__dict__ if par.startswith('T2EQUAD')]
T2ECORR = [par for par in md.__dict__ if par.startswith('ECORR')]
if 'RNAMP' in md.__dict__:
RNAMP = np.abs(float(md.RNAMP))
else:
RNAMP = np.abs(0.06)
md.manifest.append('RNAMP')
if 'RNIDX' in md.__dict__:
RNIDX = float(md.RNIDX)
else:
RNIDX = -2.17
md.manifest.append('RNIDX')
#groups = {}
#flaglist = []
#for par in T2EQUAD:
#flag = ' '.join(par.split()[1:3])
#groups[flag] = tf.othergroups[flag]
#flaglist.append(flag)
""" Setup matrix U and epoch-avearging matrix EA"""
ECORRtags = [' '.join(tag.split()[1:3]) for tag in T2ECORR]
S_idx = []
stack = []
aveeph = []
ECORRlist = []
for key in T2ECORR:
flag = ' '.join(key.split()[1:3])
if key in md.__dict__:
ECORRlist.append(float(md.__dict__[key]))
S_idx.append(0)
for epochs in sorted(md.toagrps[flag].keys()):
aveeph.append(epochs)
idx = md.toagrps[flag][epochs]
S_idx[-1] += 1
l = np.zeros(n)
l[idx] = 1.
stack.append(l)
S_idx[-1] = np.array(S_idx[-1])
S_ele = np.hstack(
[ECORRlist[i]**2 * np.ones(k) for i, k in enumerate(S_idx)])
U = (np.vstack(stack)).T
UT = U.T
""" Setup EFAC, EQUAD"""
EFACtags = [' '.join(tag.split()[1:3]) for tag in T2EFAC]
EQUADtags = [' '.join(tag.split()[1:3]) for tag in T2EQUAD]
EFACidx = {}
EQUADidx = {}
SIGMA = []
EFAClist = []
EQUADlist = []
for tag in EFACtags:
EFACidx[tag] = []
EFAC = float(md.__dict__['T2EFAC ' + tag])
EFAClist.append(EFAC)
for tag in EQUADtags:
EQUADidx[tag] = []
EQUAD = float(md.__dict__['T2EQUAD ' + tag])
EQUADlist.append(EQUAD)
for i, toa in enumerate(tf.toalist):
SIGMA.append(float(toa.TOAsigma))
TOAflags = [('-%s %s' % (f, toa.flags[f])) for f in toa.flags]
try:
key = (set(EFACtags) & set(TOAflags)).pop()
EFACidx[key].append(i)
except:
EFAC = EFAC_default
key = (set(EQUADtags) & set(TOAflags)).pop()
EQUADidx[key].append(i)
"""Setup red noise Fourier matrix, Fr"""
freq, F = get_rr_rep(toas, Tspan, 1. / Tspan / 4.7, 50, 20)
p0 = [float(md.__dict__[p]) for p in T2EFAC]
p1 = [np.log(float(md.__dict__[p])) for p in T2EQUAD]
p2 = [np.log(float(md.__dict__[p])) for p in T2ECORR]
p3 = [np.log(RNAMP), RNIDX]
np0 = len(p0)
np1 = np0 + len(p1)
np2 = np1 + len(p2)
np3 = np2 + len(p3)
plist = np.array(p0 + p1 + p2 + p3)
#def plotRN(plist, logspace=True):
tstart = time.time()
"""setup parameters"""
p0 = np.array(plist[:np0])
p1 = np.array(plist[np0:np1])
p2 = np.array(plist[np1:np2])
p3 = np.array(plist[np2:np3])
if logspace:
CoordTransTerm = (
np.sum(p1) + np.sum(p2) + p3[0]
) #sume all the logterm for coordinate transformation dz = z d (ln(z))
p1 = np.exp(p1)
p2 = np.exp(p2)
p3[0] = np.exp(p3[0])
else:
CoordTransTerm = 0.
"""Load parameters"""
efac = np.ones(n)
for i, tag in enumerate(EFACtags):
efac[EFACidx[tag]] = p0[i]
Nvec = np.array(SIGMA * efac)**2
equad = np.zeros(n)
for i, tag in enumerate(EQUADtags):
equad[EQUADidx[tag]] = p1[i]
Nvec += (equad**2)
S_ele = np.hstack([p2[i]**2. * np.ones(k) for i, k in enumerate(S_idx)])
RNAMP = np.abs(p3[0]) #/ ampfac
RNIDX = p3[1]
#phi = (RNAMP**2)/12/np.pi/np.pi *fyr**(-3-RNIDX) * f**RNIDX
phi = (RNAMP**2) * freq**RNIDX #assuming f is is 1/yr units.
"""Putting the noise models together"""
T = np.hstack((M, F, U))
"""Putting the timing and noise parameters together """
m = M.shape[1]
n_f = F.shape[1]
n_j = U.shape[1]
n_p = T.shape[1]
Phi_I = np.zeros((n_p, n_p))
Pars = [LARGE_NUMBER for i in range(m)]
Pars += list(phi)
Pars += list(S_ele)
Pi = 1. / np.array(Pars)
np.fill_diagonal(Phi_I, Pi)
"""compute likelyhood"""
d = dot(T.T, r / Nvec)
Sigma = Phi_I + dot(T.T, (1. / Nvec * T.T).T)
#print d.shape, Sigma.shape
try:
cfSigma = sl.cho_factor(Sigma)
#except LinAlgError:
except:
print Sigma
logdetSigma = 2. * np.sum(np.log(np.diag(cfSigma[0])))
Sid = sl.cho_solve(cfSigma, d)
dSid = np.dot(d.T, Sid)
logdetCt = np.sum(np.log(np.array(Pars[m:])))
logdetN = np.sum(np.log(Nvec))
Nir = r / Nvec
LogLike1 = 0.5 * (dot(r.T, Nir) - dSid)
LogLike2 = 0.5 * (logdetN + logdetSigma + logdetCt)
LogLike = LogLike1 + LogLike2 - CoordTransTerm
b = sl.cho_solve(cfSigma, d.T)
bphi = b[m:m + n_f]
phi_I = np.zeros((n_f, n_f))
np.fill_diagonal(phi_I, 1. / phi)
FT = F.T
sigma = phi_I #+ dot(FT, (1./Nvec * FT).T)
cfsigma = sl.cho_factor(sigma)
y = dot(F, bphi.T)
yerr = np.sqrt(np.diag(dot(F, sl.cho_solve(cfsigma, FT))))
return y, yerr