def electron_spin(plot=False, genTex=False):
a = np.loadtxt('electron_flip')
freqs = a[:,0]
dfreqs = 0.01*np.ones(freqs.shape)
currs = np.mean(a[:,1:],axis=1)
sdcurrs = np.std(a[:,1:],axis=1)
dcurrs = 0.04*np.ones(currs.shape)
print sdcurrs
bfield = currs*4.8 #gauss
dbfield = 4.8*dcurrs
ang_freqs = freqs*1000000*2*sp.constants.pi
dang_freqs = dfreqs*1000000*2*sp.constants.pi
gmr_inv = Parameter(1.,'gmr')
yint = Parameter(1.,'yint')
#ps = [gmr_inv,yint]
ps = [gmr_inv]
p1,cov,info,msg,success = fit((lambda x:x*gmr_inv()),ps,ang_freqs,bfield,dang_freqs,dbfield)
chisq = sum(info['fvec']*info['fvec'])
dof = len(bfield)-len(ps)
#dyint = np.sqrt(cov[1,1])*np.sqrt(chisq/dof)
gmr = 1/gmr_inv()
dgmr = np.sqrt(cov[0,0])*np.sqrt(chisq/dof)/gmr_inv()**2
print 'slope: %s'%sig_fig(gmr_inv(),np.sqrt(cov[0,0])*np.sqrt(chisq/dof))
print 'GMR: %s'%sig_fig(gmr,dgmr)
print gmr
#print 'y int: %s'%sig_fig(yint(),dyint)
print 'reduced chisq: %.3f'%(chisq/dof)
if genTex:
for i in range(len(freqs)):
print '$%.2f$ & '%freqs[i],
for volt in a[i,1:]:
print '$%.2f$, '%volt,
print '& $%.2f$\\\\'%currs[i]
if plot:
plt.figure()
plt.errorbar(ang_freqs,bfield,xerr=dang_freqs,yerr=dbfield,fmt='g.')
indep = np.arange(ang_freqs[0],ang_freqs[len(ang_freqs)-1:],1)
plt.plot(indep,indep*gmr_inv(),'k-')
plt.gca().set_xlabel('Resonance frequency(rad/s)')
plt.gca().set_ylabel('Magnetic field(Gauss)')
plt.savefig('elec-fit.png')
plt.show()
def clas_mom(plot=False, genTex = False):
m_pos_tmp, curr, dcurr_tmp = np.loadtxt('classical_moment',unpack=True)
dcurr = np.ones(curr.shape)*0.02 #correct the lazy entry of the data file
m_pos = m_pos_tmp*0.1
dm_pos = np.ones(m_pos.shape)*0.001
b_field = 13.6*curr #in Gauss
db_field = b_field*np.sqrt((0.3/13.6)**2+(dcurr/curr)**2)
rmg = m_pos*1.39*980.438 #value of g from wolfram alpha
drmg = rmg*np.sqrt((dm_pos/m_pos)**2+(0.01/1.39)**2)
mu_inv = Parameter(1.,'mu_inv')
yint = Parameter(1.,'yint')
ps = [mu_inv,yint]
p1,cov1,info1,msg1,success1 = fit((lambda x:x*mu_inv()+yint()),ps,rmg,b_field,drmg,db_field)
chisq1 = sum(info1['fvec']*info1['fvec'])
dof1 = len(b_field)-len(ps)
mu = 1./mu_inv()
dmu = mu*(np.sqrt(cov1[0,0])*np.sqrt(chisq1/dof1)/mu_inv())
print 'slope=%s, yint=%s'%(sig_fig(mu_inv(),np.sqrt(cov1[0,0])*np.sqrt(chisq1/dof1)),sig_fig(yint(),np.sqrt(cov1[1,1])*np.sqrt(chisq1/dof1)))
print 'mu = %s'%sig_fig(mu,dmu)
print 'reduced chisq : %.3f'%(chisq1/dof1)
if genTex:
for i in range(len(curr)):
print '$%.2f$ & $%s$\\\\'%(m_pos_tmp[i],sig_fig(curr[i],dcurr[i]))
if plot:
plt.figure()
plt.errorbar(rmg,b_field,xerr=drmg,yerr=db_field,fmt='r.')
indep1 = np.arange(rmg[0],rmg[len(rmg)-1:],300)
plt.plot(indep1,indep1*mu_inv()+yint(),'b-')
plt.gca().set_xlabel(r'rmg ($g\cdot\frac{\mathrm{cm}^2}{\mathrm{s}^2}$)')
plt.gca().set_ylabel(r'Magnetic field (Gauss)')
plt.savefig('grav-fit.png')
plt.show()
return [mu,dmu]
def clas_pre(exp_mu,plot=False,genTex=False):
curr, pd = np.loadtxt('classical_precession',unpack=True)
dpd = 0.1*np.ones(pd.shape)
dcurr = 0.02*np.ones(curr.shape)
b_field = 13.6*curr #in Gauss
db_field = b_field*np.sqrt((0.3/13.6)**2+(dcurr/curr)**2)
omega = 2*sp.constants.pi/pd
domega = omega*(dpd/pd)
mul = Parameter(1., 'mul')
yint = Parameter(1., 'yint')
ps = [mul,yint]
p1,cov,info,msg,success = fit((lambda x:x*mul()+yint()),ps,b_field,omega,db_field,domega)
chisq = sum(info['fvec']*info['fvec'])
dof = len(omega)-len(ps)
dyint = np.sqrt(cov[1,1])*np.sqrt(chisq/dof)
dmul = np.sqrt(cov[0,0])*np.sqrt(chisq/dof)
print 'slope: %s\nyint: %s'%(sig_fig(mul(),dmul),sig_fig(yint(),dyint))
mom_in = 2./5*137.5*(5.377/2)**2
dmom_in = mom_in*np.sqrt((.01/137.5)**2+(.04/5.377)**2)
print 'I=%s'%sig_fig(mom_in,dmom_in)
ang_mom = mom_in*2*sp.constants.pi*5.1
dang_mom = ang_mom*np.sqrt((dmom_in/mom_in)**2+(0.1/5.1)**2)
print 'L=%s'%sig_fig(ang_mom,dang_mom)
exp_coef = exp_mu[0]/ang_mom
dexp_coef = exp_coef*np.sqrt((exp_mu[1]/exp_mu[0])**2+(dang_mom/ang_mom)**2)
print 'Expected mu: %s'%sig_fig(exp_mu[0],exp_mu[1])
print 'Got : %s with reduced chisq %.3f'%(sig_fig(mul()*ang_mom,mul()*ang_mom*np.sqrt((dmul/mul())**2+(dang_mom/ang_mom)**2)),chisq/dof)
print 'y-int: %s'%sig_fig(yint(),dyint)
print 'Residuals:'
for i in range(len(pd)):
print '%.3f: residual of %.3f'%(curr[i],omega[i]-b_field[i]*mul()+yint())
print
if genTex:
for i in range(len(curr)):
print '$%s$ & $%s$\\\\'%(curr[i],pd[i])
if plot:
plt.figure()
plt.errorbar(b_field,omega,xerr=db_field, yerr=domega,fmt='g.')
indep = np.arange(b_field[0],b_field[len(b_field)-1]+9,1)
plt.plot(indep,indep*mul()+yint(),'k-')
plt.gca().set_xlabel(r'B-field (Gauss)')
plt.gca().set_ylabel(r'Precession frequency(rad/s)')
plt.savefig('prec-fit.png')
plt.show()
p2,cov,info,msg,success = fit(lin_fit,p0,np.arange(1,len(data[b][r])+1),np.array(data[b][r])**2,np.array(data[b][r+1])*np.sqrt(2)*np.array(data[b][r]))
chisq = sum(info['fvec']*info['fvec'])
dof = len(data[b][r])-len(p0)
epsilons[b][r]=B()/A()+1
a_err = np.sqrt(cov[0,0])*np.sqrt(chisq/dof)
b_err = np.sqrt(cov[1,1])*np.sqrt(chisq/dof)
frac_err = np.sqrt((b_err/B())**2+(a_err/A())**2)
epsilons[b][r+1]=frac_err*epsilons[b][r]
print "Magnetic field: %d, ring %d"%(b,r)
print "Converged with chi squared ",chisq
print "degrees of freedom, dof ", dof
print "RMS of residuals (i.e. sqrt(chisq/dof)) ", sqrt(chisq/dof)
print "Reduced chisq (i.e. variance of residuals) ", chisq/dof
print "a, da: ",A(), a_err
print "b, db: ",B(), b_err
print "epsilon: "+sig_fig(epsilons[b][r],epsilons[b][r+1])
print
#B-field calibration
volt, bmtr, dbmtr = loadtxt('calibrationvb',unpack=True)
bref,bmtr1,dbmtr1 = loadtxt('calibrationrm',unpack=True)
A=Parameter(1.,'A')
B=Parameter(1.,'B')
a=Parameter(1.,'a')
b=Parameter(1.,'b')
p0=[A,B]
p1=[a,b]
p00,cov0,info0,msg0,success0=fit((lambda x:A()*x+B()),p0,volt,bmtr,dbmtr)
p11,cov1,info1,msg1,success1=fit((lambda x:a()*x+b()),p1,bref,bmtr1,dbmtr1)
dof0=len(volt)-2