def part8a(plotA=True, printA=False, saveA=False, fs=20, size=(15, 7.5)):
tau = np.arange(12, 25) # ms
tau = np.log(tau)
amp = np.array([
2.98, 2.56, 2.14, 1.78, 1.42, 1.09, .62, .59, .82, 1.07, 1.29, 1.59,
1.90
]) # V
T = np.linspace(10, 25, 1000)
T = np.log(T)
par_m = [10, np.log(19), 0, .8]
A_m = quadfit(par_m, T)
par_f = df.least_square(quadfit, par_m, tau, amp)
# testfit(1,0,par_f) # alpha
# testfit(.7,2,par_f) # beta
# testfit(.05,3,par_f) # A_0
# testfit(.05,1,par_f) # t_0
A_f = quadfit(par_f, T)
alpha = dg.var(par_f[0], 1, 'V/s^2')
beta = dg.var(par_f[2], .7, 'V/s')
t_1 = dg.var(par_f[1], .05, 'ms')
A_0 = dg.var(par_f[3], .05, 'V')
tau_1 = err.err8a(t_1)
# tau1 = err.quad_err('part8a',alpha,beta,A_0,T,A_f)
if plotA == True:
fig = plt.figure(figsize=size)
plt.title('$\\tau_1$ Two Pulse, Zero Crossing : Glycerin',
fontsize=fs + 2)
plt.xlabel('ln(delay time/ms)', fontsize=fs)
plt.ylabel('amplitude [V]', fontsize=fs)
plt.plot(tau, amp, 's', color='b', label='data')
# plt.plot(T,A_m,'-', color='m', lw=2, label='manual fit')
plt.plot(T, A_f, '-', color='r', lw=2, label='least square fit')
note = '$A = \\alpha (t_q-t_1)^2 + \\beta (t_q-t_1) + \gamma$\n$\\alpha = %s \pm %s\ [V/s^2]$\n$\\beta = %s \pm %s\ [V/s]$\n$\\gamma = %s \pm %s\ [V]$\n$ln(t_1/ms) = %s \pm %s$\n$\\tau_1 = %s \pm %s\ [ms]$' % (
alpha.pval, alpha.perr, beta.pval, beta.perr, A_0.pval, A_0.perr,
t_1.pval, t_1.perr, tau_1.pval, tau_1.perr)
plt.annotate(note, xy=(2.8, 1.5), color='r', fontsize=fs)
plt.xlim([min(T), max(T)])
plt.legend(loc='best', numpoints=1)
plt.tight_layout()
if saveA == True:
fig.savefig('../graphs/fig05.png')
plt.close(fig)
else:
plt.show()
if printA == True:
print("tau_1_g = %s +- %s" % (tau_1.pval, tau_1.perr))
# print("tau1_g = %s +- %s" % (tau1.pval,tau1.perr))
return tau_1
def part7(plotA=True, printA=False, saveA=False, fs=20, size=(15, 7.5)):
# tau = np.arange(20,124,20) # ms
# amp = np.array([4.20, 2.39, 1.37, 1.00, .65, .35]) # V
tau = np.arange(2, 32, 2)
amp = np.array([
9.84, 8.86, 7.92, 7.06, 6.58, 6.06, 5.50, 5.12, 4.74, 4.50, 4.14, 3.96,
3.70, 3.50, 3.30
])
T = np.linspace(0, 60, 1000)
par_m = [12, 20, 1]
A_m = expfit(par_m, T)
par_f = df.least_square(expfit, par_m, tau, amp)
# testfit(.3,0,par_f) # A_0
# testfit(.3,1,par_f) # t_2
# testfit(.1,2,par_f) # C
A_f = expfit(par_f, T)
A_0 = dg.var(par_f[0], .3, 'V')
t_2 = dg.var(par_f[1], .3, 'ms')
C = dg.var(par_f[2], .1, 'V')
tau_2 = t_2
# tau_2 = err.err7(t_2)
# tau2 = err.exp_err(tau_2,A_0,T[1:],A_f[1:],double='yes')
if plotA == True:
fig = plt.figure(figsize=size)
plt.title('$\\tau_2$ Meiboom-Gill : Mineral Oil', fontsize=fs + 2)
plt.xlabel('delay time [ms]', fontsize=fs)
plt.ylabel('amplitude [V]', fontsize=fs)
plt.plot(tau, amp, 's', color='b', label='data')
# plt.plot(T,A_m,'-', color='m', lw=2, label='manual fit')
plt.plot(T, A_f, '-', color='r', lw=2, label='least square fit')
note = '$A = A_0 e^{-t/\\tau_2} + C$\n$A_0 = %s \pm %s\ [V]$\n$\\tau_2 = %s \pm %s\ [ms]$\n$C = %s \pm %s\ [V]$' % (
A_0.pval, A_0.perr, tau_2.pval, tau_2.perr, C.pval, C.perr)
plt.annotate(note, xy=(30, 4), color='r', fontsize=fs)
plt.xlim([min(T), max(T)])
plt.legend(loc='best', numpoints=1)
plt.tight_layout()
if saveA == True:
fig.savefig('../graphs/fig04.png')
plt.close(fig)
else:
plt.show()
if printA == True:
print("tau2 = %s +- %s" % (tau_2.pval, tau_2.perr))
# print("tau2 = %s +- %s" % (tau2.pval,tau2.perr))
return tau_2
def part6(plotA=True, printA=False, saveA=False, fs=20, size=(15, 7.5)):
# tau = np.arange(20,120,20) # ms
# amp = np.array([4.2, 2.10, 1.09, .62, .34]) # V
tau = np.arange(2, 18, 2) # ms
amp = np.array([9.52, 8.02, 6.5, 5.3, 3.96, 3.06, 2.36, 1.70])
T = np.linspace(0, 40, 1000)
par_m = [12, 10, -1]
A_m = expfit(par_m, T)
par_f = df.least_square(expfit, par_m, tau, amp)
# testfit(.5,0,par_f) # A_0
# testfit(.3,1,par_f) # t_2
# testfit(.2,2,par_f) # C
A_f = expfit(par_f, T)
A_0 = dg.var(par_f[0], .5, 'V')
t_2 = dg.var(par_f[1], .3, 'ms')
C = dg.var(par_f[2], .2, 'V')
tau_2 = t_2
# tau_2 = err.err6(t_2)
# tau2 = err.exp_err(A_0,T[1:],A_f[1:],double='yes')
if plotA == True:
fig = plt.figure(figsize=size)
plt.title('$\\tau_2$ Carr-Purcell : Mineral Oil', fontsize=fs + 2)
plt.xlabel('delay time [ms]', fontsize=fs)
plt.ylabel('amplitude [V]', fontsize=fs)
plt.plot(tau, amp, 's', color='b', label='data')
# plt.plot(T,A_m,'-', color='m', lw=2, label='manual fit')
plt.plot(T, A_f, '-', color='r', lw=2, label='least square fit')
note = '$A = A_0 e^{-t/\\tau_2} + C$\n$A_0 = %s \pm %s\ [V]$\n$\\tau_2 = %s \pm %s\ [ms]$\n$C = %s \pm %s\ [V]$' % (
A_0.pval, A_0.err, tau_2.pval, tau_2.perr, C.pval, C.perr)
plt.annotate(note, xy=(20, 3), color='r', fontsize=fs)
plt.xlim([min(T), max(T)])
plt.legend(loc='best', numpoints=1)
plt.tight_layout()
if saveA == True:
fig.savefig('../graphs/fig03.png')
plt.close(fig)
else:
plt.show()
if printA == True:
print("tau2 = %s +- %s" % (tau_2.pval, tau_2.perr))
# print("tau2 = %s +- %s" % (tau2.pval,tau2.perr))
return tau_2
def part5(plotA=True, printA=False, saveA=False, fs=20, size=(15, 7.5)):
tau = np.arange(1, 17) # ms
tau *= 2
amp = np.array([
7.5, 6.8, 6.0, 5.3, 4.9, 4.2, 4.0, 3.6, 3.4, 3.0, 2.8, 2.6, 2.4, 2.2,
2.0, 1.8
]) # V
T = np.linspace(0, 30, 1000)
par_m = [8, 10, .01]
A_m = expfit(par_m, T)
par_f = df.least_square(expfit, par_m, tau, amp)
# testfit(.2,0,par_f) # A_0
# testfit(.3,1,par_f) # tau_2
# testfit(.2,2,par_f) # C
A_f = expfit(par_f, T)
A_0 = dg.var(par_f[0], .2, 'V')
tau_2 = dg.var(par_f[1], .3, 'ms')
# tau2 = err.exp_err(A_0,T[1:],A_f[1:],double='yes')
C = dg.var(par_f[2], .2, 'V')
if plotA == True:
fig = plt.figure(figsize=size)
plt.title('$\\tau_2$ Two-Pulse Spin Echo : Mineral Oil',
fontsize=fs + 2)
plt.xlabel('delay time [ms]', fontsize=fs)
plt.ylabel('amplitude [V]', fontsize=fs)
plt.plot(tau, amp, 's', color='b', label='data')
# plt.plot(T,A_m,'-', color='m', lw=2, label='manual fit')
plt.plot(T, A_f, '-', color='r', lw=2, label='least square fit')
note = '$A = A_0 e^{-t/\\tau_2} + C$\n$A_0 = %s \pm %s\ [V]$\n$\\tau_2 = %s \pm %s\ [ms]$\n$C = %s \pm %s\ [V]$' % (
A_0.pval, A_0.perr, tau_2.pval, tau_2.perr, C.pval, C.perr)
plt.annotate(note, xy=(15, 4), color='r', fontsize=fs)
plt.xlim([min(T), max(T)])
plt.legend(loc='best', numpoints=1)
plt.tight_layout()
if saveA == True:
fig.savefig('../graphs/fig02.png')
plt.close(fig)
else:
plt.show()
if printA == True:
print("tau_2 = %s +- %s" % (tau_2.pval, tau_2.perr))
# print("tau2 = %s +- %s" % (tau2.pval,tau2.perr))
return tau_2
def part8b(plotA=True, printA=False, saveA=False, fs=20, size=(15, 7.5)):
tau = np.arange(20, 100, 20) # ms
amp = np.array([4, 1.71, .76, .43]) # V
T = np.linspace(0, 120, 1000)
par_m = [7, 30, 0]
A_m = expfit(par_m, T)
par_f = df.least_square(expfit, par_m, tau, amp)
# testfit(.3,0,par_f) # A_0
# testfit(.9,1,par_f) # t_2
# testfit(.1,2,par_f) # C
A_f = expfit(par_f, T)
A_0 = dg.var(par_f[0], .3, 'V')
t_2 = dg.var(par_f[1], .9, 'ms')
C = dg.var(par_f[2], .1, 'V')
tau_2 = t_2
# tau_2 = err.err8b(t_2)
# tau2 = err.exp_err(A_0,T[1:],A_f[1:],double='yes')
if plotA == True:
fig = plt.figure(figsize=size)
plt.title('$\\tau_2$ Meiboom-Gill : Glycerin', fontsize=fs + 2)
plt.xlabel('delay time [ms]', fontsize=fs)
plt.ylabel('amplitude [V]', fontsize=fs)
plt.plot(tau, amp, 's', color='b', label='data')
# plt.plot(T,A_m,'-', color='m', lw=2, label='manual fit')
plt.plot(T, A_f, '-', color='r', lw=2, label='least square fit')
note = '$A = A_0 e^{-t/\\tau_2} + C$\n$A_0 = %s \pm %s\ [V]$\n$\\tau_2 = %s \pm %s\ [ms]$\n$C = %s \pm %s\ [V]$' % (
A_0.pval, A_0.perr, tau_2.pval, tau_2.perr, C.pval, C.perr)
plt.annotate(note, xy=(60, 1.5), color='r', fontsize=fs)
plt.xlim([min(T), max(T)])
plt.legend(loc='best', numpoints=1)
plt.tight_layout()
if saveA == True:
fig.savefig('../graphs/fig06.png')
plt.close(fig)
else:
plt.show()
if printA == True:
print("tau_2_g = %s +- %s" % (tau_2.pval, tau_2.perr))
# print("tau2_g = %s +- %s" % (tau2.pval,tau2.perr))
return tau_2
def dampedWave(X, Y, par_m):
# par = [theta_0, A, gamma, omega]
def envelope(x):
t = x - X[0]
return par_m[1] * np.exp(-par_m[2] * t)
def fitfunc(p, x):
t = x - X[0]
return p[0] + p[1] * np.exp(-p[2] * t) * np.cos(p[3] * t)
par_f = df.least_square(fitfunc, par_m, X, Y)
#par_f[3] += .2
Y_env = envelope(X)
Y_man = fitfunc(par_m, X)
Y_fit = fitfunc(par_f, X)
return Y_env, Y_man, Y_fit, par_f
def part4(plotA=True, printA=False, saveA=False, fs=20, size=(15, 7.5)):
#plt.xscale('log')
tau = np.arange(7, 26) # ms
tau = np.log(tau)
amp = np.array([
3.8, 3.4, 2.9, 2.4, 2, 1.7, 1.2, .9, .5, .3, .4, .7, .9, 1.2, 1.5, 1.8,
2.0, 2.3, 2.6
]) # V
amp = amp[2:]
tau = tau[2:]
T = np.linspace(5, 30, 1000)
T = np.log(T)
par_m = [12.5, 2.8, 0, .5]
A_m = quadfit(par_m, T)
par_f = df.least_square(quadfit, par_m, tau, amp)
# testfit(2,0,par_f) # alpha
# testfit(.7,2,par_f) # beta
# testfit(.2,3,par_f) # A_0
# testfit(.05,1,par_f) # t_0
A_f = quadfit(par_f, T)
alpha = dg.var(par_f[0], 2, 'V/s^2')
beta = dg.var(par_f[2], .7, 'V/s')
t_1 = dg.var(par_f[1], .05, 'ms')
A_0 = dg.var(par_f[3], .2, 'V')
# tau_1 = t_1
tau_1 = err.err4(t_1)
# tau1 = err.quad_err(alpha,beta,A_0,T,A_f)
if plotA == True:
fig = plt.figure(figsize=size)
plt.title('$\\tau_1$ Two Pulse, Zero Crossing : Mineral Oil',
fontsize=fs + 2)
plt.xlabel('ln(delay time/ms)', fontsize=fs)
plt.ylabel('amplitude [V]', fontsize=fs)
plt.plot(tau, amp, 's', color='b', label='data')
# plt.plot(T,A_m,'-', color='m', lw=2, label='manual fit')
plt.plot(T, A_f, '-', color='r', lw=2, label='least square fit')
note = '$A = \\alpha (t_q-t_1)^2 + \\beta (t_q-t_1) + \gamma$\n$\\alpha = %s \pm %s\ [V/s^2]$\n$\\beta = %s \pm %s\ [V/s]$\n$\\gamma = %s \pm %s\ [V]$\n$ln(t_1/ms) = %s \pm %s$\n$\\tau_1 = %s \pm %s\ [ms]$' % (
alpha.pval, alpha.perr, beta.pval, beta.perr, A_0.pval, A_0.perr,
t_1.pval, t_1.perr, tau_1.pval, tau_1.perr)
plt.annotate(note, xy=(2.5, 4), color='r', fontsize=fs)
plt.xlim([min(T), max(T)])
plt.legend(loc='best', numpoints=1)
plt.tight_layout()
if saveA == True:
fig.savefig('../graphs/fig01.png')
plt.close(fig)
else:
plt.show()
if printA == True:
print("tau_1 = %s +- %s" % (tau_1.pval, tau_1.perr))
# print("tau1 = %s +- %s" % (tau1.pval,tau1.perr))
return tau_1