from scipy.stats import norm, ks_2samp
from scipy.integrate import quad
##import functions
import sys
sys.path.insert(0, 'C:\Python34\masters\graphs')
import functions as fun
def HubbleCalculate(z, dist):
##Calculates the distance modulus to an object at z redshift. Assesses the integral
##between 0 and z
##To find the value in MPc, use fun.D(fun.HubbleIntegrate(0.2))
def integrand(z, m, de):
return 1/np.sqrt((m*(1+z)**3)+de)
m=0.22
de=0.7205
H0 = 69.79
a = 3*10**5/dist
I = quad(integrand, 0, z, args=(m,de))
H = I[0]*a*(1+z)
return H
d = fun.D(fun.HubbleIntegrate(0.06))
#d = 260.90498780322844
x=HubbleCalculate(0.06, d)
print(x)
def deltaH(SNered, SNedist):
return (fun.D(fun.HubbleIntegrate(float(SNered))) -
(float(SNedist))) / fun.D(fun.HubbleIntegrate(float(SNered)))
voidRA = fun.minvoidRA + fun.isovoidRA
voiddec = fun.minvoiddec + fun.isovoiddec
voidz = fun.minvoidz + fun.isovoidz
voidRadii = fun.minvoidradius + fun.isovoidradius
scin = []
scout = []
i = 0
k = 0
j = 0
while k < len(SNered): ##Find the nearest sc for each k Supernova
while i < len(clusterz):
distancesNew = fun.polar_dist_comp(
SNeRA[k], clusterRA[i], SNedec[k], clusterdec[i], SNered[k],
clusterz[i]) ##Keep SN constant, loop over supercluster
if fun.D(fun.HubbleIntegrate(distancesNew)) < clusterRadii[i]:
scin.append([
SNedist[k], SNedisterror[k], SNered[k], clusterRadii[i],
fun.D(fun.HubbleIntegrate(distancesNew)) - clusterRadii[i]
])
i = len(clusterz) + 1
j = len(voidRA) + 1
i += 1
while j < len(voidRA):
distancesNew = fun.polar_dist_comp(SNeRA[k], voidRA[j], SNedec[k],
voiddec[j], SNered[k], voidz[j])
if fun.D(fun.HubbleIntegrate(distancesNew)) < voidRadii[j]:
scout.append([
SNedist[k], SNedisterror[k], SNered[k], voidRadii[j],
fun.D(fun.HubbleIntegrate(distancesNew)) - voidRadii[j]
])
scName = fun.scName
scRadius = [float(x) for x in fun.R]
confirmedSC = [] ##[0] is SNe number, [1] is corresponding SC
unconfirmedSC = []
i = 0
z = 0
k = 0
while k < len(SNered): ##Find the nearest sc for each k Supernova
if SNered[k] < max(scz) + 0.02 and SNedec[k] < max(scdec) + 5:
while i < len(scz):
distancesNew = fun.polar_dist_comp(
SNeRA[k], scRA[i], SNedec[k], scdec[i], SNered[k],
scz[i]) ##Keep SN constant, loop over supercluster
if fun.D(fun.HubbleIntegrate(distancesNew)) < scRadius[i]:
print(SNeRA[k], scRA[i], SNedec[k], scdec[i], SNered[k],
scz[i], i, k)
confirmedSC.append(k)
i = len(scz)
if i == len(scz) - 1:
unconfirmedSC.append(k)
i += 1
i = 0
k += 1
else:
if SNered[k] < max(scz) + 0.02 and SNedec[k] > max(scdec) + 5:
z += 1
del SNered[k]
del SNeRA[k]
del SNedec[k]
plt.axis([
min(np.append(largered, smallred)) * 0.9,
max(np.append(largered, smallred)) * 1.1,
min(np.append(large_H, small_H)) * 0.9,
max(np.append(large_H, small_H)) * 1.1
])
plt.legend()
plt.show()
##Histogram of dH
large_dH = []
small_dH = []
i = 0
while i < len(largered):
large_dH.append((fun.D(fun.HubbleIntegrate(largered[i])) - largedist[i]) /
fun.D(fun.HubbleIntegrate(largered[i])))
i += 1
i = 0
while i < len(smallred):
small_dH.append((fun.D(fun.HubbleIntegrate(smallred[i])) - smalldist[i]) /
fun.D(fun.HubbleIntegrate(smallred[i])))
i += 1
print(ks_2samp(large_dH, small_dH))
largehist = plt.hist(large_dH,
bins=binno,
alpha=0.5,
label='large',
color='blue')
ascRadius = fun.abelscradii
##Combine Clusters
clusterRA = scRA + ascRA
clusterdec = scdec + ascdec
clusterz = scz + ascz
clusterRadii = scRadius + ascRadius
scin = []
scout = []
i=0
k=0
while k < len(SNered): ##Find the nearest sc for each k Supernova
while i < len(clusterz):
distancesNew = fun.polar_dist_comp(SNeRA[k], clusterRA[i], SNedec[k], clusterdec[i], SNered[k], clusterz[i]) ##Keep SN constant, loop over supercluster
if fun.D(fun.HubbleIntegrate(distancesNew)) < clusterRadii[i]:
scin.append([SNedist[k], SNedisterror[k], SNered[k], clusterRadii[i], fun.D(fun.HubbleIntegrate(distancesNew)) - clusterRadii[i]])
i = len(clusterz)+1
if i == len(clusterz) - 1:
scout.append([SNedist[k], SNedisterror[k], SNered[k]])
i+=1
i=0
k+=1
##Calculate dH for each supernovae
dHin = []
i=0
while i < len(scin):
dHin.append(deltaH(scin[i][2], scin[i][0]))
i+=1
while i < len(clusterz):
distancesNew = fun.polar_dist_comp(
SNeRA[k], clusterRA[i], SNedec[k], clusterdec[i], SNered[k],
clusterz[i]) ##Keep SN constant, loop over supercluster
if distancesNew < distancescluster[k]:
distancescluster[k] = fun.polar_dist_comp(SNeRA[k], clusterRA[i],
SNedec[k], clusterdec[i],
SNered[k], clusterz[i])
i += 1
i = 0
k += 1
distancesMpc = []
i = 0
while i < len(distancescluster):
distancesMpc.append(fun.D(fun.HubbleIntegrate(distancescluster[i])))
i += 1
##Supernovae numbers 566, 567, 569, 571, 576 confirmed to reside in cluster
distancesMpc[566] = 1
distancesMpc[567] = 1.1
distancesMpc[569] = 1.2
distancesMpc[571] = 1.3
distancesMpc[576] = 1.4
##Calculate dH for each supernovae
dH = []
i = 0
while i < len(SNeRA):
dH.append(deltaH(SNered[i], SNedist[i]))
i += 1
voidz = fun.minvoidz + fun.isovoidz
voidRadii = fun.minvoidradius + fun.isovoidradius
distancescluster = len(SNered) * [1000000]
distancevoid = len(SNered) * [1000000]
SNSC = len(SNered) * [0]
SNVoid = len(SNered) * [0]
i = 0
j = 0
k = 0
while k < len(SNered): ##Find the nearest sc for each k Supernova
while i < len(clusterz):
distancesNew = fun.D(
fun.HubbleIntegrate(
fun.polar_dist_comp(
SNeRA[k], clusterRA[i], SNedec[k], clusterdec[i],
SNered[k],
clusterz[i]))) ##Keep SN constant, loop over supercluster
if distancesNew < clusterRadii[i]:
SNSC[k] = 1
if distancesNew < distancescluster[k]:
distancescluster[k] = distancesNew
i += 1
while j < len(voidRA):
distancesNew = fun.D(
fun.HubbleIntegrate(
fun.polar_dist_comp(
SNeRA[k], voidRA[j], SNedec[k], voiddec[j], SNered[k],
voidz[j]))) ##Keep SN constant, loop over supercluster
if distancesNew < voidRA[j]:
SNVoid[k] = 1
plt.plot(redshiftrange, 10 * [66.9 - 1.6], ':', color="red", alpha=0.3)
plt.legend(loc="upper left")
plt.xlabel('Redshift')
plt.ylabel('Hubble constant (km s$^{-1}$ Mpc$^{-1}$)')
plt.title('Hubble values for SGC and its corresponding dipole')
plt.legend()
plt.show()
##Histogram of dH
NGC_dH = []
SGC_dH = []
i = 0
while i < len(NGCred):
NGC_dH.append((fun.D(fun.HubbleIntegrate(NGCred[i])) - NGCdist[i]) /
fun.D(fun.HubbleIntegrate(NGCred[i])))
i += 1
i = 0
while i < len(SGCred):
SGC_dH.append((fun.D(fun.HubbleIntegrate(SGCred[i])) - SGCdist[i]) /
fun.D(fun.HubbleIntegrate(SGCred[i])))
i += 1
print(ks_2samp(NGC_dH, SGC_dH))
plt.plot(SGCred, SGC_dH, '.')
plt.plot([min(SGCred), max(SGCred)], [0, 0])
plt.show()
NGChist = plt.hist(NGC_dH, bins=binno, alpha=0.5, label='NGC', color='blue')
Alldec = [x[4] for x in All]
minres = 100000
NGCH = 0
i = 0
while i < 1000:
h = 65 + i / 100
res = fun.residual(fun.dmod(NGCdist), fun.dmod(NGCdisterror), NGCred, h,
0.2807, 0.7193)
if res < minres:
minres = res
NGCH = h
i += 1
redshiftrange = np.linspace(minredshift, maxredshift, 10)
expectedH = [fun.D(fun.HubbleIntegrate(x)) for x in redshiftrange]
##Graph for redshift vs distance
plt.figure()
plt.errorbar(NGCred,
NGCdist,
yerr=NGCdisterror,
fmt='.',
markersize=5,
color="blue",
label='Maximal Acceleration')
plt.errorbar(SGCred,
SGCdist,
yerr=SGCdisterror,
fmt='.',
markersize=5,
sumsq = 0
i = 0
while i < N:
sumsq = sumsq + (x[i] - mu)**2
i += 1
return np.sqrt((1 / (N - 1)) * sumsq)
##Test against H0
lowZdeviation = []
midZdeviation = []
highZdeviation = []
i = 0
while i < len(lowZ):
lowZdeviation.append((fun.D(fun.HubbleIntegrate(fun.extract(lowZ, 4)[i])) -
fun.extract(lowZ, 5)[i]) /
fun.D(fun.HubbleIntegrate(fun.extract(lowZ, 4)[i])))
i += 1
i = 0
while i < len(midZ):
midZdeviation.append((fun.D(fun.HubbleIntegrate(fun.extract(midZ, 4)[i])) -
fun.extract(midZ, 5)[i]) /
fun.D(fun.HubbleIntegrate(fun.extract(midZ, 4)[i])))
i += 1 ##(D_L(z) - D_L) / D_L(z)
i = 0
while i < len(highZ):
highZdeviation.append(
(fun.D(fun.HubbleIntegrate(fun.extract(highZ, 4)[i])) -
