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# bnewbold_stats.py
# helper functions!
# @author: bryan newbold
# @email: bnewbold@mit.edu
# @date: oct 2006
import scipy, pylab
def floored_val(x,min=1.):
if pylab.size(x) > 1:
ret = scipy.array(pylab.copy.copy(x));
for i in range(0,pylab.size(x)):
ret[i] = floored_val(x[i],min=min);
return ret;
if(abs(x) < min):
return min;
else:
return abs(x);
def floored_root(x,min=1.):
return scipy.sqrt(floored_val(x,min=min));
def rchisqr(tp,ffunc,tx,ty,terr):
"""finds reduced chi squared for a function compared to data"""
if not (pylab.size(tx) == pylab.size(ty) == pylab.size(terr)):
print "ERROR: input matrix mismatch... (rchisqr)";
return;
try:
ffunc(tp,tx[-1]);
except:
print "problem with passed function and/or parameters!";
try:
eta_err = (ty - ffunc(tp,tx))**2 / (terr**2)
except:
print "i think you have a zero error in there...";
eta_err = (ty - ffunc(tp,tx))**2 / (terr**2)
return sum(eta_err)/(pylab.size(tx)-pylab.size(tp));
def rchisqr_poisson(tp,ffunc,tx,ty,floor=1.):
"""finds reduced chi squared for a function compared to data,
assuming each data point has a poisson distribution and thus
an error of sqrt(val). The error value is floored at 1.0 to
prevent stupid val=0 cases..."""
if not (pylab.size(tx) == pylab.size(ty)):
print "ERROR: input matrix mismatch... (rchisqr_poisson)";
return;
terr = floored_root(tx,min=floor);
return rchisqr(tp,ffunc,tx,ty,terr);
def fittodata(tx,ty,p0,ffunc,err=None,floor=1.,ret_all=False):
"""does a fit and returns a dict of shit.
ret_all=True gives more shit."""
if err == None:
err = floored_root(ty,min=floor);
if not (pylab.size(tx) == pylab.size(ty) == pylab.size(err)):
print "ERROR: input matrix mismatch... (fittodata)";
return;
errfunc = lambda n,m,w: ffunc(n,m) - w;
tx = scipy.array(tx);
#tx = tx.tolist(); tx = scipy.array(tx);
ty = scipy.array(ty);
#ty = ty.tolist(); ty = scipy.array(ty);
err = err.tolist(); err = scipy.array(err);
p0 = scipy.array(p0).tolist(); p0 = scipy.array(p0);
p1,cov_x,extra1,extra2,success = scipy.optimize.leastsq(errfunc,
p0.copy(), args=(tx,ty), full_output=1)
if size(p1) == 1:
p1 = [p1,]
print "DEBUG: done with fit"
print "p1: " + str(p1)
rcs = rchisqr(p1,ffunc,tx,ty,err);
try:
p1_err = p1.copy()
except:
p1_err = [0,]
for i in range(scipy.size(p1)):
try:
scipy.size(cov_x);
except:
p1_err = array([0.0,])
p1 = array([p1,])
break;
if scipy.size(cov_x) == 1:
p1_err = array([scipy.sqrt(cov_x),]);
p1 = array([p1,]);
else:
p1_err[i] = scipy.sqrt(cov_x[i,i]);
if ret_all:
return {"params":p1,
"param_error":p1_err,
"rchisqr":rcs,
"ffunc":ffunc,
"err":err,
"x":tx,
"y":ty,
"success":success};
else:
return {"params":p1,
"param_error":p1_err,
"rchisqr":rcs}
def fittodata_gaussian(tx,ty,p0,err=None,floor=1.,ret_all=False):
"""runs fittodata for a gaussian (first parameter is mean,
second is stddev, third is amplitude)"""
#gauss_func = lambda a,b: a[2]/(a[1] * sqrt(2*pi)) * exp(-.5 * ((b - a[0])/a[1])**2)
#thing = std(ty);
bigsum = scipy.integrate.simps(ty,x=tx)
gauss_func = lambda a,b: bigsum/(a[1] * scipy.sqrt(2*pi)) * scipy.exp(-.5 * ((b - a[0])/a[1])**2)
return fittodata(tx,ty,p0,gauss_func,err=err,floor=floor,ret_all=ret_all);
def fittodata_linear(tx,ty,p0,err=None,floor=1.,ret_all=False):
"""runs fittodata for a linear curve (first param is slope,
second is vertical offset)"""
lin_func = lambda a,b: a[0] * b + a[1]
return fittodata(tx,ty,p0,lin_func,err=err,floor=floor,ret_all=ret_all);
def fittodata_poisson(tx,ty,p0,err=None,floor=.5,ret_all=False):
"""runs fittodata for a poisson (first param is the mean"""
bigsum = scipy.integrate.simps(ty,x=tx)
if type(p0) == type(0.1):
p0 = [p0,]
poissfunc = lambda a,b: bigsum * scipy.power(a[0],b) / scipy.factorial(b) * scipy.exp(-1 * a[0])
#def poissfunc(a,b):
# print "--------"
# print a
# print b
# print bigsum
# print scipy.power(a[0],b)
# print scipy.exp(a[0])
# print bigsum * scipy.power(a[0],b) / scipy.factorial(b) * scipy.exp(-1 * a[0])
# return bigsum * scipy.power(a[0],b) / scipy.factorial(b) * scipy.exp(-1 * a[0])
return fittodata(tx,ty,p0,poissfunc,err=err,floor=floor,ret_all=ret_all);
def fittodata_exp(tx,ty,p0,err=None,floor=1.,ret_all=False):
"""runs fittodata for an exponential (first param is x0,
second param is tau, third param is vertical offset)"""
#exp_func = lambda a,b: a[0] * scipy.exp(- b/a[1]) + a[2]
exp_func = lambda a,b: a[0] * e ** (- b/a[1]) + a[2]
return fittodata(tx,ty,p0,exp_func,err=err,floor=floor,ret_all=ret_all);
def fittodata_lorentz(tx,ty,p0,err=None,floor=1.,ret_all=False):
"""runs fittodata for a lorentzian (first param is gamma,
second param is mean)"""
bigsum = scipy.integrate.simps(ty,x=tx)
if type(p0) == type(0.1):
p0 = [p0,]
lorentz_func = lambda a,b: bigsum * a[0]/(2.*pi*((a[1]-b)**2+(a[0]/2.)**2. ))
return fittodata(tx,ty,p0,lorentz_func,err=err,floor=floor,ret_all=ret_all);
def plotfit(indict,newfig=True):
if not indict.has_key('x'):
print "forgot to use ret_all on the fittodata?";
return;
p1 = indict['params'];
x = indict['x']
y = indict['y']
err = indict['err']
ffunc = indict['ffunc']
if newfig: pylab.figure();
pylab.errorbar(x,y,fmt='b.',yerr=err)
d=pylab.plot(x,y,'k.')
fx = x
if pylab.size(fx) < 100:
fx = r_[min(x):max(x):(max(x)-min(x))/150.]
f=pylab.plot(fx,ffunc(p1,fx),'r-')
#fy = indict['ffunc'](indict['params'],indict['x'])
pylab.title("Rough Fit of Data")
pylab.xlabel("X")
pylab.ylabel("Y")
p1 = indict['params']
p1_err = indict['param_error']
ax = pylab.gca()
extra_txt = 'reduced chi squared: %g'\
% (indict['rchisqr'])
for i in range(scipy.size(p1)):
extra_txt += '\np[%i]: %g +/- %g' \
% (i,p1[i],p1_err[i]);
# if(pylab.size(p1) == 2):
# extra_txt = 'reduced chi squared: %g\np[0]: %g\np[1]: %g' \
# % (indict['rchisqr'],p1[0],p1[1])
# else:
# extra_txt= 'reduced chi squared:%g\np[0]:%g, +/- %g\n p[1]:%g\np[2]:%g' \
# % (indict['rchisqr'],p1[0],p1[1],p1[2])
t = pylab.text(.77, .75, extra_txt,
horizontalalignment='center',
verticalalignment='center',
transform = ax.transAxes)
pylab.legend((d,f),('Data', 'Fit'))
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