def fit_powerlaw_covariance(xdata, ydata, yerr = None, should_plot=True, debug=False):
'''
Implements http://www.scipy.org/Cookbook/FittingData
We actually compute the standard deviation for each x-value, and use this
when computing the fit.
'''
assert not (ydata.ndim == 1 and yerr is None), 'Use another function or provide yerr, this function requires the standard deviation'
if ydata.ndim == 2:
# Y data 2-dim, compute the standard errors, along the second dimension
yerr = np.std(ydata, axis=1)
ydata = np.mean(ydata, axis=1)
logx = np.log(xdata.astype('float'))
logy = np.log(ydata)
logyerr = yerr/ydata
# define our (line) fitting function
fitfunc = lambda p, x: p[0] + p[1] * x
errfunc = lambda p, x, y, err: (y - fitfunc(p, x)) / err
# Initial parameters
pinit = np.array([1.0, -1.0])
out = spopt.leastsq(errfunc, pinit, args=(logx, logy, logyerr), full_output=1)
pfinal = out[0]
covar = out[1]
index = pfinal[1]
amp = np.exp(pfinal[0])
if debug:
indexErr = np.sqrt( covar[0][0] )
ampErr = np.sqrt( covar[1][1] ) * amp
print pfinal
print 'Ampli = %5.2f +/- %5.2f' % (amp, ampErr)
print 'Index = %5.2f +/- %5.2f' % (index, indexErr)
##########
# Plotting data
##########
if should_plot:
plot_powerlaw_fit(xdata, ydata, amp, index, yerr=yerr)
return np.array([index, amp])
def fit_powerlaw(xdata, ydata, should_plot=False, debug=False):
'''
Fit a power law to the provided data.
y = a x**p
Actually fit to the mean of the provided data, if multiple columns given (axis 1)
Look for next function in order to fit a powerlaw while taking std dev into account.
returns (power p, amplitude a)
'''
##########
# Fitting the data -- Least Squares Method
##########
# Power-law fitting is best done by first converting
# to a linear equation and then fitting to a straight line.
#
# y = a * x^b
# log(y) = log(a) + b*log(x)
#
if ydata.ndim == 1:
# We have a 1D array, need a flat 2D array...
ydata = ydata[:, np.newaxis]
if xdata.ndim == 1:
# We need to tile the x values appropriately, to fit the size of y
# (just because leastsq is not funny)
xdata = np.tile(xdata, (ydata.shape[1], 1)).T
logx = np.log(xdata.astype('float'))
logy = np.log(ydata)
if np.any(np.isnan(logy)):
# Something went wrong, just stop here...
return np.array([np.nan, np.nan])
# define our (line) fitting function
fitfunc = lambda p, x: p[0] + p[1] * x
errfunc = lambda p, x, y: np.mean(y - fitfunc(p, x), axis=1)
# Initial parameters
pinit = np.array([1.0, -1.0])
out = spopt.leastsq(errfunc, pinit, args=(logx, logy), full_output=1)
# out = spopt.fmin(errfunc_mse, pinit, args=(logx, logy))
pfinal = out[0]
index = pfinal[1]
amp = np.exp(pfinal[0])
if debug:
print pfinal
print 'Ampli = %5.2f' % amp
print 'Index = %5.2f' % index
##########
# Plotting data
##########
if should_plot:
plot_powerlaw_fit(xdata, ydata, amp, index)
return np.array([index, amp])
