def bootstrap_N(n,BaryonMass,dBM,W,costheta,s_fit_range,ds_dcos,ds_dcos_ran,ds_dcos_sys):
s = np.power(W,2)
cosThetaMatrix = []
for i in range(len(s)):
cosThetaMatrix.append(0)
cosThetaMatrix[i] = costheta
cosThetaMatrix = np.array(cosThetaMatrix)
mt,dfc,dfc_err = D.Theta_to_t(s,BaryonMass,dBM,cosThetaMatrix,ds_dcos,ds_dcos_ran,ds_dcos_sys)
N_list = []
A_list = []
j = 0
while s[j] < s_fit_range:
j += 1
for i in range(n):
dfc_err_b = resample(dfc_err)
mt_fit = mt[j:]
s_fit = s[j:]
dfc_fit = dfc[j:]
dfc_err_fit = dfc_err_b[j:]
print(i)
def f(s,A,N):
return(A*s**(-N))
popt, pcov = curve_fit(f, s_fit, dfc_fit, sigma = dfc_err_fit, maxfev=10000)
A,N = popt
N_list.append(N)
A_list.append(A)
B_err = np.sqrt(pcov[1][1])
print("N = %s" % N)
print("N_err = %s" % B_err )
bins = np.linspace(min(N_list),max(N_list), 150)
binscenters = np.array([0.5 * (bins[i] + bins[i+1]) for i in range(len(bins)-1)])
#fig1 = plt.figure()
hist = plt.hist(N_list, bins = bins)
#binscenters = np.array([0.5 * (hist[1][k] + hist[1][k+1]) for k in range(len(hist[1])-1)])
def gaussian(x,a,b,c):
return(a*np.exp(-((x-b)**2)/(2*c**2)) )
param, param_cov = curve_fit(gaussian,binscenters,hist[0], maxfev=10000)
print("Height = %s , location = %s , standard deviation = %s " % (param[0],param[1],param[2]))
smooth = np.linspace(min(N_list),max(N_list),10000)
loc_ord = sorted(N_list)
#print("The expected 95% confidence interval is [%f,%f]" % (loc_ord[249],loc_ord[9749]))
print(loc_ord[249])
print(loc_ord[9749])
plt.plot(smooth, gaussian(smooth,*param), label = 'mean = %s, SD = %s, 95 percent CI = [%s,%s]' % ( round(param[1],3),round(param[2],3),round(loc_ord[249],3),round(loc_ord[9749],3) ))
#plt.plot(location_mean,gaussian(location_mean,*param))
plt.xlabel(r'$N$')
plt.ylabel(r'Frequency')
plt.legend()
plt.title(r'N Histogram $[ As^{-N} ]$ for 10,000 samples fitted from %s $GeV^2$ ' % s_fit_range)
'''
def bootstrap_N3(n,BaryonMass,dBM,W,costheta,s_fit_range,ds_dcos,ds_dcos_ran,ds_dcos_sys):
s = np.power(W,2)
cosThetaMatrix = []
for i in range(len(s)):
cosThetaMatrix.append(0)
cosThetaMatrix[i] = costheta
cosThetaMatrix = np.array(cosThetaMatrix)
mt,dfc,dfc_err = D.Theta_to_t(s,BaryonMass,dBM,cosThetaMatrix,ds_dcos,ds_dcos_ran,ds_dcos_sys)
N_list = []
j = 0
while s[j] < s_fit_range:
j += 1
mt_fit = mt[j:]
s_fit = s[j:]
dfc_fit = dfc[j:]
dfc_err_fit = dfc_err[j:]
def f(s,A,N):
return(A*s**(-N))
popt, pcov = curve_fit(f, s_fit, dfc_fit, sigma = dfc_err_fit)
A_est,N_est = popt
res = dfc_fit - f(s_fit,*popt)
mean_res = np.mean(res)
adj_res = res - mean_res
for i in range(n):
adj_res_b = resample(adj_res)
popt, pcov = curve_fit(f, s_fit, dfc_fit, sigma = adj_res_b, maxfev = 1000000)
A,N = popt
N_list.append(N)
print(i)
hist = plt.hist(N_list, bins = 'auto')
binscenters = np.array([0.5 * (hist[1][k] + hist[1][k+1]) for k in range(len(hist[1])-1)])
def pdf(x,a,b,c): # gaussian pdf
return(a*np.exp(-((x-b)**2)/(2*c**2)) )
param, param_cov = curve_fit(pdf,binscenters,hist[0], maxfev=1000000)
a,b,c = param
smooth = np.linspace(min(N_list),max(N_list),10000)
ordered_list = sorted(N_list)
BEG,END = D.BCa('sp',n,0.16,N_est,s_fit,dfc_fit,adj_res,ordered_list)
plt.plot(smooth,pdf(smooth,*param), label = "mean = %s, SD = %s"
"\n"
r"68 percent CI: [%s,%s]" % (round(b,3),round(c,3),round(BEG,3),round(END,3) ))
plt.xlabel(r'N')
plt.ylabel(r'Frequency')
plt.legend()
plt.show()
print("The mean is: %s, and the standard deviation is: %s" % (b,c))
def interp(Baryon_name, BaryonMass, dBM, costheta, W, ds_dcos, ds_dcos_ran_err,
ds_dcos_sys_err):
s = np.power(W, 2)
cosThetaMatrix = []
for i in range(len(s)):
cosThetaMatrix.append(0)
cosThetaMatrix[i] = costheta
cosThetaMatrix = np.array(cosThetaMatrix)
mt1, dfc1, dfc_err1 = D.Theta_to_t(s, BaryonMass, dBM, cosThetaMatrix,
ds_dcos, ds_dcos_ran_err,
ds_dcos_sys_err)
# interpolating the cross section values
spl1 = splrep(s, dfc1, w=1 / dfc_err1,
k=3) #, full_output = 1) #, task = -1, t = s[1:-1])
s1 = np.linspace(min(s), max(s), 100)
y1 = splev(s1, spl1)
#interpolating the cross section errors
spl2 = splrep(s, dfc_err1, k=3)
s2 = s1
y2 = splev(s2, spl2)
# normal distribution from which to choose cross section errors
#err = np.random.normal(y1,y2)
err = y2
#fig1 = plt.figure()
#####plt.errorbar(s, dfc1, yerr = dfc_err1, fmt = 'go', ecolor = 'r', label = r'Experimental values')######
#plt.plot(s1,y1,'o')
######plt.errorbar(s1,y1, yerr = err, fmt = 'b.', ecolor = 'black', label = r'Interpolated values')######
#plt.plot(s,dfc_err1, 'bo')
#plt.show()
#CCR fit
s_beg = s[2]
i = 0
while s1[i] < s_beg:
i += 1
s_fit = s1[i:]
dfc_fit = y1[i:]
dfc_err_fit = err[i:]
#fig2 = plt.figure()
fit(s_fit, dfc_fit, dfc_err_fit)
######plt.legend()######
#plt.show()
return (s_fit, dfc_fit, dfc_err_fit)
def Best_s_range(Baryon_name,BaryonMass,dBM,costheta,W,ds_dcos,ds_dcos_ran_err,ds_dcos_sys_err):
# BaryonMass is to indicate the particle mass
# s_fit_range indicates that you only want to consider s_fit_range <= s <= max {s} for the fit
# mt = momentum_transfer(t), dfc = differential cross section (dsig/dt), dfc_err is the error in dfc
s = np.power(W,2)
cosThetaMatrix = []
for i in range(len(s)):
cosThetaMatrix.append(0)
cosThetaMatrix[i] = costheta
cosThetaMatrix = np.array(cosThetaMatrix)
mt,dfc,dfc_err = D.Theta_to_t(s,BaryonMass,dBM,cosThetaMatrix,ds_dcos,ds_dcos_ran_err,ds_dcos_sys_err)
red_chisq = []
for i in range(len(s)-1): # the last 4 data points are giving trouble for some reason
def f(s,A,N):
return(A*s**(-N))
popt, pcov = curve_fit(f, s[i:], dfc[i:], sigma = dfc_err[i:], maxfev = 1000000)
A,N = popt
res = dfc[i:] - f(s[i:],A,N)
#return(res)
chisq = sum((res/dfc_err[i:])**2)
red_chisq.append(chisq/(len(dfc[i:])-len(popt)))
ideal_chisq = []
for i in range(len(red_chisq)):
ideal_chisq.append(1)
plt.plot(s[:-1], red_chisq, 'go')#,label = r'Optimal $s \approx %s$' % round(5.1,2) + ' \n ' + r'$\frac{d\sigma}{dt} = A*s^{2-n}$' )
plt.plot(s[:-1],ideal_chisq, 'b-')#,label = '')
plt.xlabel(r'$\ s (GeV^2)$')
plt.ylabel(r'$\chi^2/\nu $')
#plt.legend()
#plt.title(r'$\gamma + P \rightarrow K^+ + \%s$' % Baryon_name + " Statistical Analysis " + r'for $\cos \theta _{c.m.} = %s $' % costheta )
plt.show()
# shifted the graph down by one to find roots, i.e. points that would normally be at red_chisq = 1
red_chisq2 = np.array(red_chisq) - 1
# Method (Bisection)
delta = 0.1
a = 0
b = len(red_chisq2)
q = []
q.append((a+b)/2)
COUNTER = 0
while abs(red_chisq2[int(q[COUNTER])]) > delta:
if red_chisq2[int(q[COUNTER])]*red_chisq2[int(a)] > 0:
a = q[COUNTER]
else:
b = q[COUNTER]
q.append((a+b)/2)
#print(COUNTER)
COUNTER += 1
if COUNTER > 100:
break
if s[int(q[-2])] > s[int(q[-1])]:
s1 = s[int(q[-1])]
s2 = s[int(q[-2])]
else:
s1 = s[int(q[-2])]
s2 = s[int(q[-1])]
s_bi = s[int(q[-1])]
#print(len(s))
#print(len(red_chisq))
plt.plot(s[:-1], red_chisq, 'go' , label = 'green = Lambda')#,label = r'Optimal $s \approx %s$' % round(s_bi,2) + ' \n ' + r'$\frac{d\sigma}{dt} = A*s^{2-n}$' )
plt.plot(s[:-1],ideal_chisq, 'b-')#,label = '')
plt.xlabel(r'$\ s (GeV^2)$')
plt.ylabel(r'$\chi^2/\nu $')
plt.legend()
#plt.title(r'$\gamma + P \rightarrow K^+ + \%s$' % Baryon_name + " Statistical Analysis " + r'for $\cos \theta _{c.m.} = %s $' % costheta )
'''
plt.annotate("", xy=(4.3, 1.17), xytext=(5.29,14.48), arrowprops=dict(arrowstyle="->"))
a = plt.axes([0.45, 0.6, .2, .2])
plt.plot(s[8:],red_chisq[:], 'go')
plt.plot(s[8:],ideal_chisq[:],'b-')
#plt.title('Impulse response')
plt.xlim(3.2, 5.7)
plt.ylim(0.5,1.5)
plt.xticks([])
plt.yticks([])
'''
plt.show()
print("Bisection: Best range %s < s < %s " % (s1,s2))
print("Bisection: Reduced Chi Square = %s" % (red_chisq2[int(q[-1])]+1))
return(s_bi)
def bootstrap_unc(n,num_bins,BaryonMass,dBM,W,costheta,ds_dcos,ds_dcos_ran,ds_dcos_sys): # n stands for number of bootstrap samples
location_mean = []
arithmetic_mean = []
median = []
p0 = [1,1,1]
s = np.power(W,2)
cosThetaMatrix = []
for i in range(len(s)):
cosThetaMatrix.append(0)
cosThetaMatrix[i] = costheta
cosThetaMatrix = np.array(cosThetaMatrix)
mt,dfc,dfc_err = D.Theta_to_t(s,BaryonMass,dBM,cosThetaMatrix,ds_dcos,ds_dcos_ran,ds_dcos_sys)
def phi(x,A,B,C):
return((1/A)*np.exp(-(x-B)/A) + C)
for i in range(n):
dfc_err_b = resample(dfc_err)
bins = np.linspace(min(dfc_err_b),max(dfc_err_b),num_bins)
binscenters = np.array([0.5 * (bins[i] + bins[i+1]) for i in range(len(bins)-1)])
hist = np.histogram(dfc_err_b, bins= bins)
popt, pcov = curve_fit(phi,binscenters,hist[0], p0 = p0, maxfev=10000)
p0 = [popt[0],popt[1],popt[2]]
location_mean.append(popt[0])
arithmetic_mean.append(np.mean(dfc_err_b))
median.append(np.median(dfc_err_b))
print(i)
print("A = %f, B = %f, C = %f " % (popt[0],popt[1],popt[2]) )
smooth_x = np.linspace(min(dfc_err_b),max(dfc_err_b),10000)
plt.subplot(2,1,2)
plt.hist(dfc_err_b, bins = bins)
plt.plot(smooth_x,phi(smooth_x,*popt) , label = ("A = %f, B = %f, C = %f " % (popt[0],popt[1],popt[2])) )
plt.xlabel(r'$\sigma_{d\sigma/dt}$')
plt.ylabel(r'Frequency')
plt.legend()
plt.show()
location_mean = arithmetic_mean
binss = np.linspace(min(location_mean),max(location_mean), 60)
bin_cent = np.array([0.5 * (binss[place_holder] + binss[place_holder+1]) for place_holder in range(len(binss)-1)])
histo_info = np.histogram(location_mean,bins= binss)
#return("The length of the bin center array is %s and the length of the frequency array is %s " % (len(histo_info[1]), len(histo_info[0])))
def gaussian(x,a,b,c):
return( a*np.exp(-((x-b)**2)/(2*c**2) ) )
param, param_cov = curve_fit(gaussian,bin_cent,histo_info[0], p0 = [500,0.0565,0.0482], maxfev=10000)
print("Height = %s , location = %s , standard deviation = %s " % (param[0],param[1],param[2]))
print("The length of the location_mean array is %s " % len(location_mean))
smooth = np.linspace(min(location_mean),max(location_mean),10000)
loc_ord = sorted(location_mean)
#print("The expected 95% confidence interval is [%f,%f]" % (loc_ord[249],loc_ord[9749]))
print(loc_ord[249])
print(loc_ord[9749])
plt.subplot(2,1,1)
plt.hist(location_mean,bins= binss)
plt.plot(smooth, gaussian(smooth,*param), label = "Mean = %s, SD = %s, 95 percent CI = [%s,%s] " % (round(param[1],3),round(param[2],3),round(loc_ord[249],3) ,round(loc_ord[9749],3)))
plt.xlabel(r'Mean $\sigma_{d\sigma/dt}$')
plt.ylabel(r'Frequency')
plt.legend()
plt.title(r'$\sigma_{d\sigma/dt}$ Histograms fitted to $ae^{-({x-b})^2/{2c^2}}$ and $(1/A)e^{-({x-B})/{A}} + C$ for 10,000 samples')
plt.show()
def bootstrap_N2(n,BaryonMass,dBM,W,costheta,s_fit_range,ds_dcos,ds_dcos_ran,ds_dcos_sys):
s = np.power(W,2)
cosThetaMatrix = []
for i in range(len(s)):
cosThetaMatrix.append(0)
cosThetaMatrix[i] = costheta
cosThetaMatrix = np.array(cosThetaMatrix)
mt,dfc,dfc_err = D.Theta_to_t(s,BaryonMass,dBM,cosThetaMatrix,ds_dcos,ds_dcos_ran,ds_dcos_sys)
s = np.delete(s,0)
mt = np.delete(mt,0)
dfc = np.delete(dfc,0)
dfc_err = np.delete(dfc_err,0)
neg_dfc_err = -dfc_err
tot_dfc_err = np.append(dfc_err, neg_dfc_err)
#neg_dfc_err = -dfc_err
#tot_dfc_err = np.append(dfc_err, neg_dfc_err)
N_list = []
A_list = []
#bins = np.linspace(min(tot_dfc_err),max(tot_dfc_err),30)
#binscenters = np.array([0.5 * (bins[i] + bins[i+1]) for i in range(len(bins)-1)])
fig1 = plt.figure()
hist = plt.hist(tot_dfc_err, bins = 'auto')
binscenters = np.array([0.5 * (hist[1][k] + hist[1][k+1]) for k in range(len(hist[1])-1)])
#print(len(binscenters))
def gaussian(x,a,b,c):
return(a*np.exp(-((x-b)**2)/(2*c**2)) )
param, param_cov = curve_fit(gaussian,binscenters,hist[0], maxfev=10000)
mean = round(param[1],5)
#SD = 3*round(abs(param[2]),5)
SD = 1000
print("Height = %s , location = %s , standard deviation = %s " % (param[0],param[1],param[2]))
smooth = np.linspace(min(tot_dfc_err),max(tot_dfc_err),10000)
plt.plot(smooth,gaussian(smooth,*param))
plt.show()
j = 0
while s[j] < s_fit_range:
j += 1
for i in range(n):
normal_boot_err = np.random.normal(mean,SD,len(dfc_err))
s_fit = s[j:]
dfc_fit = dfc[j:]
dfc_err_fit = normal_boot_err[j:]
def f(s,A,N):
return(A*s**(-N))
popt, pcov = curve_fit(f, s_fit, dfc_fit, sigma = dfc_err_fit, maxfev=1000000)
A,N = popt
N_list.append(N)
A_list.append(A)
print(i)
print(mean)
print(SD)
fig2 = plt.figure()
hist = plt.hist(N_list, bins = 'auto')
binscenters = np.array([0.5 * (hist[1][k] + hist[1][k+1]) for k in range(len(hist[1])-1)])
print("Hello")
param, param_cov = curve_fit(gaussian,binscenters,hist[0], maxfev=10000)
print("Height = %s , location = %s , standard deviation = %s " % (param[0],param[1],param[2]))
smooth = np.linspace(min(N_list),max(N_list),10000)
loc_ord = sorted(N_list)
#print("The expected 95% confidence interval is [%f,%f]" % (loc_ord[249],loc_ord[9749]))
print(loc_ord[249])
print(loc_ord[9749])
plt.plot(smooth, gaussian(smooth,*param), label = ' ') #label = 'mean = %s, SD = %s, 95 percent CI = [%s,%s]' % ( round(param[1],3),round(param[2],3),round(loc_ord[249],3),round(loc_ord[9749],3) ))
plt.xlabel(r'$N$')
plt.ylabel(r'Frequency')
plt.legend()
plt.title(r'N Histogram $[ As^{-N} ]$ for 10,000 samples fitted from %s $GeV^2$ ' % s_fit_range)
plt.show()
def s_range(Baryon_name, BaryonMass, dBM, costheta, W, ds_dcos,
ds_dcos_ran_err, ds_dcos_sys_err):
# BaryonMass is to indicate the particle mass
# s_fit_range indicates that you only want to consider s_fit_range <= s <= max {s} for the fit
# mt = momentum_transfer(t), dfc = differential cross section (dsig/dt), dfc_err is the error in dfc
s = np.power(W, 2)
cosThetaMatrix = []
for i in range(len(s)):
cosThetaMatrix.append(0)
cosThetaMatrix[i] = costheta
cosThetaMatrix = np.array(cosThetaMatrix)
mt1, dfc1, dfc_err1 = D.Theta_to_t(s, BaryonMass, dBM, cosThetaMatrix,
ds_dcos, ds_dcos_ran_err,
ds_dcos_sys_err)
mt2, dfc2, dfc_err2 = D.Theta_to_t(s, BaryonMass, dBM, cosThetaMatrix,
D.ds_dcos_1405NPN,
D.ds_dcos_ran_1405NPN,
D.ds_dcos_sys_1405NPN)
mt3, dfc3, dfc_err3 = D.Theta_to_t(s, BaryonMass, dBM, cosThetaMatrix,
D.ds_dcos_1405P00,
D.ds_dcos_ran_1405P00,
D.ds_dcos_sys_1405P00)
mt4, dfc4, dfc_err4 = D.Theta_to_t(s, BaryonMass, dBM, cosThetaMatrix,
D.ds_dcos_1405N00,
D.ds_dcos_ran_1405N00,
D.ds_dcos_sys_1405N00)
mt5, dfc5, dfc_err5 = D.Theta_to_t(s, BaryonMass, dBM, cosThetaMatrix,
D.ds_dcos_1405PNP,
D.ds_dcos_ran_1405PNP,
D.ds_dcos_sys_1405PNP)
mt6, dfc6, dfc_err6 = D.Theta_to_t(s, BaryonMass, dBM, cosThetaMatrix,
D.ds_dcos_1405NNP,
D.ds_dcos_ran_1405NNP,
D.ds_dcos_sys_1405NNP)
print(dfc5 / dfc6)
print
plt.subplot(2, 3, 1)
fit(s, dfc1, dfc_err1)
plt.title(r'$cos \theta = 0.05$, $\Lambda(1405) < \Sigma^+ \pi^-$ ')
plt.ylabel(r'$\frac{d\sigma}{dt}$')
plt.subplot(2, 3, 2)
fit(s, dfc3, dfc_err3)
plt.title(r'$cos \theta = 0.05$, $\Lambda(1405) < \Sigma^0 \pi^0$ ')
plt.subplot(2, 3, 3)
fit(s, dfc5, dfc_err5)
plt.title(r'$cos \theta = 0.05$, $\Lambda(1405) < \Sigma^- \pi^+$ ')
plt.subplot(2, 3, 4)
fit(s, dfc2, dfc_err2)
plt.title(r'$cos \theta = -0.05$') #, $\Lambda(1405) < \Sigma^+ \pi^-$ ')
plt.ylabel(r'$\frac{d\sigma}{dt}$')
plt.xlabel(r'$s$')
plt.subplot(2, 3, 5)
fit(s, dfc4, dfc_err4)
plt.title(r'$cos \theta = -0.05$') #, $\Lambda(1405) < \Sigma^0 \pi^0$ ')
plt.xlabel(r'$s$')
plt.subplot(2, 3, 6)
fit(s, dfc6, dfc_err6)
plt.title(r'$cos \theta = -0.05$') # , $\Lambda(1405) < \Sigma^- \pi^+$ ')
plt.xlabel(r'$s$')
plt.show()
plt.subplot(2, 3, 6)
SP_boot(n, D.Lambda1405PN, D.Lambda1405Mass, D.d1405, 0, D.W_1405PPN,
D.ds_dcos_1405NNP, D.ds_dcos_ran_1405NNP, D.ds_dcos_sys_1405NNP)
plt.title(r'$cos \theta = -0.05$') # , $\Lambda(1405) < \Sigma^- \pi^+$ ')
plt.xlabel(r'$N$')
plt.show()
##################################################### FINAL RESULTS #####################################################
# cos(theta) expansion and 2d fit
_s = np.power(D.W_1405PPN, 2)
costheta = np.array([-0.15, -0.05, 0.05, 0.15])
# for SIGMA+ PI-
mt1, dfc1, dfc_err1 = D.Theta_to_t(_s, D.Lambda1405Mass, D.d1405, costheta[3],
D.Pds_dcos_1405PPN, D.Pds_dcos_ran_1405PPN,
D.Pds_dcos_sys_1405PPN)
mt2, dfc2, dfc_err2 = D.Theta_to_t(_s, D.Lambda1405Mass, D.d1405, costheta[2],
D.ds_dcos_1405PPN, D.ds_dcos_ran_1405PPN,
D.ds_dcos_sys_1405PPN)
mt3, dfc3, dfc_err3 = D.Theta_to_t(_s, D.Lambda1405Mass, D.d1405, costheta[1],
D.ds_dcos_1405NPN, D.ds_dcos_ran_1405NPN,
D.ds_dcos_sys_1405NPN)
mt4, dfc4, dfc_err4 = D.Theta_to_t(_s, D.Lambda1405Mass, D.d1405, costheta[0],
D.Nds_dcos_1405NPN, D.Nds_dcos_ran_1405NPN,
D.Nds_dcos_sys_1405NPN)
# for SIGMA0 PI0
mt5, dfc5, dfc_err5 = D.Theta_to_t(_s, D.Lambda1405Mass, D.d1405, costheta[3],
D.Pds_dcos_1405P00, D.Pds_dcos_ran_1405P00,
D.Pds_dcos_sys_1405P00)