def get_rslres(self, rsldb, lid, avg=False):
"""Get RSL residual.
rsldb: RSL database
lid: location id.
avg: set to True to get average"""
# check if residuals are cached
if lid not in self.__rslres:
# get coordinates
cu = rsldb.db.cursor()
cu.execute("SELECT longitude,latitude FROM location WHERE location_id == %i", (lid))
loc = cu.fetchone()
# get data
times = []
obs = []
cu.execute("SELECT time,rsl FROM measurement WHERE location_id == %i", (lid))
for o in cu.fetchall():
times.append(o[0] * self.timescale)
obs.append(o[1])
ti = [self.timeslice(min(times) - 2.0, "d"), self.timeslice(max(times), "u")]
ts = spline.cspline(ti[1] - ti[0] + 1)
ts.init(self.time(ti), self.getRSL(list(loc), ti, clip=False))
residuals = []
for i in range(0, len(times)):
residuals.append(obs[i] - ts.eval(times[i]))
self.__rslres[lid] = (times, residuals)
if avg:
r = 0.0
if len(self.__rslres[lid][1]) > 0:
r = sum(self.__rslres[lid][1]) / float(len(self.__rslres[lid][1]))
return r
else:
return self.__rslres[lid]
def get_rslres(self,rsldb,lid):
"""Get RSL residual.
rsldb: RSL database
lid: location id."""
# check if residuals are cached
if lid not in self.__rslres:
# get coordinates
cu = rsldb.db.cursor()
cu.execute('SELECT longitude,latitude FROM location WHERE location_id == %i',(lid))
loc = cu.fetchone()
# get data
times = []
obs = []
cu.execute('SELECT time,rsl FROM measurement WHERE location_id == %i',(lid))
for o in cu.fetchall():
times.append(o[0]*self.timescale)
obs.append(o[1])
ti = [self.timeslice(min(times)-2.,'d'), self.timeslice(max(times),'u')]
ts = spline.cspline(ti[1]-ti[0]+1)
ts.init(self.time(ti),self.getRSL(list(loc),ti))
residuals = []
for i in range(0,len(times)):
residuals.append(obs[i]-ts.eval(times[i]))
self.__rslres[lid] = (times,residuals)
return self.__rslres[lid]
def spline(self,pos,time,level=0):
"""Interpolate 2D field using cubic splines.
pos: [xloc,yloc]
time: time slice
level: horizontal slice."""
data = self.get2Dfield(time,level=level)
# interpolate along columns
r = []
for c in range(0,data.shape[0]):
col = spline.cspline(data.shape[1])
col.init(self.ydim[:],data[c,:])
r.append(col.eval(pos[1]))
# interpolate row
row = spline.cspline(data.shape[0])
row.init(self.xdim[:],r)
return row.eval(pos[0])
"""
from pygsl import spline, errors, init
from pygsl import _numobj as numx
print ("#m=0,S=2")
n = 10
a = numx.arange(n)
x = a + 0.5 * numx.sin(a)
y = a + numx.cos(a**2)
for i in a:
print (x[i], y[i])
print ("#m=1,S=0")
# Generation of the spline object ... Acceleration is handled internally
myspline = spline.cspline(n)
myspline = spline.linear(n)
#acc = myspline._object.get_accel_object()
#print "Accel object", dir(acc)
# initalise with the vector of the independent and the dependent
init.add_c_traceback_frames(1)
#init.set_debug_level(10)
myspline.init(x, y[:3])
#print("Saved error state", init.error_handler_state_get())
x1 = numx.arange(n * 20) / 20.
for xi in x1:
#print xi, myspline.eval(xi)
pass
# Faster: eval_vector
"""
from pygsl import spline, errors
from pygsl import _numobj as numx
print "#m=0,S=2"
n = 10
a = numx.arange(n)
x = a + 0.5 * numx.sin(a)
y = a + numx.cos(a**2)
for i in a:
print x[i], y[i]
print "#m=1,S=0"
# Generation of the spline object ... Acceleration is handled internally
myspline = spline.cspline(n)
myspline = spline.linear(n)
acc = myspline._object.get_accel_object()
#print "Accel object", dir(acc)
# initalise with the vector of the independent and the dependent
myspline.init(x,y)
x1 = numx.arange(n * 20) / 20.
for xi in x1:
#print xi, myspline.eval(xi)
pass
# Faster: eval_vector
myspline.eval_vector(x1)
# Faster: eval_vector but use gsl_spline_eval_e to get errors back
# This should fail with gsl_DomainError
xtest = 10.5
def spectrum(y_final, y, u_s, u_t, N, derivs1, scalarsys, tensorsys):
i = None
h = 0.01
h2 = 1.e-6 # init step size for mode integration
abserr1 = 1.e-8 # absolute error tolerance - DO NOT ADJUST THESE VALUES!
relerr1 = 1.e-8 # relative error tolerance
abserr2 = 1e-10 # absolute error tolerance
relerr2 = 1e-10 # relative error tolerance
spec_params = params()
# Read in k files
k = None
ks = np.empty(knos)
kis = np.empty(kinos)
try:
ks = np.loadtxt(k_file)
except IOError as e:
print(f"Could not open file {k_file}, errno = {e}.")
sys.exit()
try:
kis = np.loadtxt(ki_file)
except IOError as e:
print(f"Could not open file {ki_file}, errno = {e}.")
sys.exit()
realu_init = np.empty(2)
imu_init = np.empty(2)
realu_s = np.empty(kmax)
realu_t = np.empty(kmax)
imu_s = np.empty(kmax)
imu_t = np.empty(kmax)
P_s = np.empty(kinos)
P_t = np.empty(kinos)
j = None
l = None
m = None
o = None
status = None
countback = 0
count = 0
ydoub = np.empty(NEQS)
Ninit = None # N_obs from flow integration
Nfinal = None # Smallest N value from flow integration
spec_norm = None
ru_init = None
dru_init = None
iu_init = None
diu_init = None
nu = None
Yeff = None
Phi = None
# Buffers for interpolations
Nefoldsback = np.empty(kmax)
flowback = np.empty((5, kmax))
Nordered = np.empty(kmax)
uordered_s = np.empty(kmax)
uordered_t = np.empty(kmax)
"""
Initialize/allocate gsl stepper routines and variable
step-size routines. Define ode system.
"""
s = odeiv.step_rk4(NEQS, derivs1)
c = odeiv.control_y_new(s, abserr1, relerr1)
e = odeiv.evolve(s, c, NEQS)
"""
Set the initial value of the scale factor. This is chosen
so that k = aH (with k corresponding to the quadrupole) at the
value N_obs from the path file. The scale factor as a
function of N is a(N) = a_init*exp(-# of efolds).
Units are hM_PL
"""
Ninit = N
spec_params.a_init = (1.73e-61 / y[1]) * np.exp(Ninit)
spec_params.k = k
"""
To improve stability/efficiency, we first generate
an interpolating function for H, epsilon, sigma and xi^2. We then pass these values
as parameters to the mode equation, rather than solving the mode equation along with
the full set of flow equations each time.
"""
"""
Integrate backwards from end of inflation to the earliest time needed in order to initialize the
largest scale fluctuations in the BD limlt.
"""
ydoub[:] = y_final[:NEQS].copy()
N = y_final[NEQS]
Nfinal = N
while (kis[0] * 5.41e-58) / (spec_params.a_init * np.exp(-N) *
ydoub[1]) < Y:
flowback[:, countback] = ydoub[:5].copy()
Nefoldsback[countback] = N
try:
N, h2, ydoub = e.apply(N, 1000, h2, ydoub)
except:
status = 0
return status
else:
status = 0
countback += 1
Nefoldsback[countback] = N
flowback[:, countback] = ydoub[:5].copy()
H = np.empty(countback + 1)
eps = np.empty(countback + 1)
sig = np.empty(countback + 1)
xi = np.empty(countback + 1)
Nefolds = np.empty(kmax)
# Nefolds = np.empty(countback+1)
phi = np.empty(countback + 1)
H[:] = flowback[1, :countback + 1].copy()
eps[:] = flowback[2, :countback + 1].copy()
sig[:] = flowback[3, :countback + 1].copy()
xi[:] = flowback[4, :countback + 1].copy()
phi[:] = flowback[0, :countback + 1].copy()
Nefolds[:countback + 1] = Nefoldsback[:countback + 1].copy()
# Generate interpolating functions for H, eps, sig, xi and phi (for path gen. only)
spline1 = spline.cspline(countback + 1)
spline1.init(Nefolds[:countback + 1], H)
spline2 = spline.cspline(countback + 1)
spline2.init(Nefolds[:countback + 1], eps)
spline3 = spline.cspline(countback + 1)
spline3.init(Nefolds[:countback + 1], sig)
spline4 = spline.cspline(countback + 1)
spline4.init(Nefolds[:countback + 1], xi)
spline0 = spline.cspline(countback + 1)
spline0.init(Nefolds[:countback + 1], phi)
h2 = -h2
"""
Find scalar spectra first.
"""
for m in range(kinos):
print(m)
k = kis[m] * 5.41e-58 # converts to Planck from hMpc^-1
kis[m] = k
N = Ninit
ydoub[1] = spline1.eval(N)
ydoub[2] = spline2.eval(N)
count = 0
"""
First, check to see if the given k value is in the
Bunch-Davies limit at the start of inflation. This limit is
set by the #define Y=k/aH. If the given k value yields a
larger Y than the BD limit, then we must integrate forward
(to smaller N) until we reach the proper value for Y. If it is
smaller, we must integrate backwards (to larger N). These
integrators are given a fixed stepsize to ensure that we don't
inadvertently step too far beyond Y.
"""
if k / 1.73e-61 > Y: # 1.73e-61 is the present Hubble radius (~3.2e-4 hMpc^-1) in Planck units
while k / (spec_params.a_init * np.exp(-N) * ydoub[1] *
(1 - ydoub[2])) > Y:
N += -0.01
ydoub[1] = spline1.eval(N)
ydoub[2] = spline2.eval(N)
else:
while k / (spec_params.a_init * np.exp(-N) * ydoub[1] *
(1 - ydoub[2])) < Y:
N += 0.01
ydoub[1] = spline1.eval(N)
ydoub[2] = spline2.eval(N)
spec_params.k = k
nu = (3 - spline2.eval(N)) / (2 * (1 - spline2.eval(N)))
# print(nu)
Yeff = k / (spec_params.a_init *
(np.exp(-N) * (spline1.eval(N) * (1. - spline2.eval(N)))))
# print(Yeff)
if spline2.eval(N) < 1.:
ru_init = realu_init[0] = 0.5 * np.sqrt(
np.pi / k) * np.sqrt(Yeff) * _ufuncs.sf_bessel_Jnu(nu, Yeff)
dru_init = realu_init[1] = 0.5 * np.sqrt(np.pi / k) * (
k / (spec_params.a_init * np.exp(-N) * spline1.eval(N))
) * (_ufuncs.sf_bessel_Jnu(nu, Yeff) / (2. * np.sqrt(Yeff)) +
(np.sqrt(Yeff) *
(-_ufuncs.sf_bessel_Jnu(nu + 1., Yeff) +
(nu *
(1. - spline2.eval(N)) * _ufuncs.sf_bessel_Jnu(nu, Yeff)) /
(Yeff * (1. - spline2.eval(N))))))
iu_init = imu_init[0] = 0.5 * np.sqrt(
np.pi / k) * np.sqrt(Yeff) * _ufuncs.sf_bessel_Ynu(nu, Yeff)
diu_init = imu_init[1] = 0.5 * np.sqrt(np.pi / k) * (
k / (spec_params.a_init * np.exp(-N) * spline1.eval(N))
) * (_ufuncs.sf_bessel_Ynu(nu, Yeff) / (2. * np.sqrt(Yeff)) +
(np.sqrt(Yeff) *
(-_ufuncs.sf_bessel_Ynu(nu + 1., Yeff) +
(nu *
(1. - spline2.eval(N)) * _ufuncs.sf_bessel_Ynu(nu, Yeff)) /
(Yeff * (1. - spline2.eval(N))))))
else:
ru_init = realu_init[0] = -0.5 * np.sqrt(
np.pi / k) * np.sqrt(Yeff) * _ufuncs.sf_bessel_Ynu(nu, Yeff)
dru_init = realu_init[1] = -0.5 * np.sqrt(np.pi / k) * (
k / (spec_params.a_init * np.exp(-N) * spline1.eval(N))
) * (_ufuncs.sf_bessel_Ynu(nu, Yeff) / (2. * np.sqrt(Yeff)) +
(np.sqrt(Yeff) *
(-_ufuncs.sf_bessel_Ynu(nu + 1., Yeff) +
(nu *
(1. - spline2.eval(N)) * _ufuncs.sf_bessel_Ynu(nu, Yeff)) /
(Yeff * (1. - spline2.eval(N))))))
iu_init = imu_init[0] = 0.5 * np.sqrt(
np.pi / k) * np.sqrt(Yeff) * _ufuncs.sf_bessel_Jnu(nu, Yeff)
diu_init = imu_init[1] = 0.5 * np.sqrt(np.pi / k) * (
k / (spec_params.a_init * np.exp(-N) * spline1.eval(N))
) * (_ufuncs.sf_bessel_Jnu(nu, Yeff) / (2. * np.sqrt(Yeff)) +
(np.sqrt(Yeff) *
(-_ufuncs.sf_bessel_Jnu(nu + 1., Yeff) +
(nu *
(1. - spline2.eval(N)) * _ufuncs.sf_bessel_Jnu(nu, Yeff)) /
(Yeff * (1. - spline2.eval(N))))))
"""
Solve for real part of u first.
"""
s2 = odeiv.step_rkf45(2, scalarsys, args=spec_params)
c2 = odeiv.control_y_new(s2, abserr2, relerr2)
while N > Nfinal:
realu_s[count] = realu_init[0] * realu_init[0]
Nefolds[count] = N
spec_params.H = spline1.eval(N)
spec_params.eps = spline2.eval(N)
spec_params.sig = spline3.eval(N)
spec_params.xi = spline4.eval(N)
Phi = spline0.eval(N)
e2 = odeiv.evolve(s2, c2, 2) # mode eqs
try:
N, h2, realu_init = e2.apply(N, 0, h2, realu_init)
except:
status = 0
return status
else:
status = 0
count += 1
if count == kmax:
status = 0
return status
realu_s[count] = realu_init[0] * realu_init[0]
Nefolds[count] = N
for j in range(count + 1):
Nordered[j] = Nefolds[count - j]
uordered_s[j] = realu_s[count - j]
"""
Generate interpolating function for realu(N)
"""
spline5 = spline.cspline(count + 1)
spline5.init(Nordered[:count + 1], uordered_s[:count + 1])
"""
Imaginary part
"""
count = 0
N = Nefolds[0]
s2 = odeiv.step_rkf45(2, scalarsys, args=spec_params)
c2 = odeiv.control_y_new(s2, abserr2, relerr2)
e2 = odeiv.evolve(s2, c2, 2) # mode eqs
while N > Nfinal:
imu_s[count] = imu_init[0] * imu_init[0]
Nefolds[count] = N
spec_params.H = spline1.eval(N)
spec_params.eps = spline2.eval(N)
spec_params.sig = spline3.eval(N)
spec_params.xi = spline4.eval(N)
try:
N, h2, imu_init = e2.apply(N, 0, h2, imu_init)
except:
status = 0
return status
else:
status = 0
count += 1
if count == kmax:
status = 0
return status
imu_s[count] = imu_init[0] * imu_init[0]
Nefolds[count] = N
count -= 1
P_s[m] = (k**3. / (2. * (np.pi**2.))) * (
spline5.eval(Nefolds[count]) + imu_s[count]) / (
(spec_params.a_init * np.exp(-Nefolds[count]) *
spec_params.a_init * np.exp(-Nefolds[count]) *
spline2.eval(Nefolds[count])) / (4 * np.pi))
"""
Tensor spectra
"""
count = 0
N = Nefolds[0]
realu_init[0] = ru_init
realu_init[1] = dru_init
s2 = odeiv.step_rkf45(2, tensorsys, args=spec_params)
c2 = odeiv.control_y_new(s2, abserr2, relerr2)
while N > Nfinal:
realu_t[count] = realu_init[0] * realu_init[0]
Nefolds[count] = N
spec_params.H = spline1.eval(N)
spec_params.eps = spline2.eval(N)
e2 = odeiv.evolve(s2, c2, 2) # mode eqs
try:
N, h2, realu_init = e2.apply(N, 0, h2, realu_init)
except:
status = 0
return status
else:
status = 0
count += 1
if count == kmax:
status = 0
return status
realu_t[count] = realu_init[0] * realu_init[0]
Nefolds[count] = N
for j in range(count + 1):
Nordered[j] = Nefolds[count - j]
uordered_t[j] = realu_t[count - j]
spline7 = spline.cspline(count + 1)
spline7.init(Nordered[:count + 1], uordered_t[:count + 1])
"""
Imaginary part
"""
count = 0
N = Nefolds[0]
imu_init[0] = iu_init
imu_init[1] = diu_init
s2 = odeiv.step_rkf45(2, tensorsys, args=spec_params)
c2 = odeiv.control_y_new(s2, abserr2, relerr2)
while N > Nfinal:
imu_t[count] = imu_init[0] * imu_init[0]
Nefolds[count] = N
spec_params.H = spline1.eval(N)
spec_params.eps = spline2.eval(N)
e2 = odeiv.evolve(s2, c2, 2) # mode eqs
try:
N, h2, imu_init = e2.apply(N, 0, h2, imu_init)
except:
status = 0
return status
else:
status = 0
count += 1
if count == kmax:
status = 0
return status
imu_t[count] = imu_init[0] * imu_init[0]
Nefolds[count] = N
count -= 1
P_t[m] = 64. * np.pi * (k**3. / (2. * np.pi**2.)) * (
spline7.eval(Nefolds[count]) + imu_t[count]) / (
(spec_params.a_init * np.exp(-Nefolds[count]) *
spec_params.a_init * np.exp(-Nefolds[count])))
if kis[m] == knorm * 5.41e-58: # normalize here
spec_norm = Amp / (P_s[m] + P_t[m])
"""
This is a little different from the C code,
because the y[1] change is outside the if statement
"""
y[1] = np.sqrt(spec_norm) # normalize H for later recon
"""
Now that we have finished calculating the spectra, interpolate each spectrum and evaluate at k-values of interest
"""
spline8 = spline.cspline(kinos)
spline8.init(kis, P_t)
spline6 = spline.cspline(kinos)
spline6.init(kis, P_s)
for i in range(knos):
u_s[0, i] = ks[i]
u_s[1, i] = spec_norm * spline6.eval(ks[i] * 5.41e-58)
u_t[0, i] = ks[i]
u_t[1, i] = spec_norm * spline8.eval(ks[i] * 5.41e-58)
return status