fitting exponential decay with no initial guessing

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Does anyone know a scipy/numpy module which will allow to fit exponential decay to data?

Google search returned a few blog posts, for example - http://exnumerus.blogspot.com/2010/04/how-to-fit-exponential-decay-example-in.html , but that solution requires y-offset to be pre-specified, which is not always possible

EDIT:

curve_fit works, but it can fail quite miserably with no initial guess for parameters, and that is sometimes needed. The code I'm working with is

#!/usr/bin/env python
import numpy as np
import scipy as sp
import pylab as pl
from scipy.optimize.minpack import curve_fit

x = np.array([  50.,  110.,  170.,  230.,  290.,  350.,  410.,  470.,  
530.,  590.])
y = np.array([ 3173.,  2391.,  1726.,  1388.,  1057.,   786.,   598.,   
443.,   339.,   263.])

smoothx = np.linspace(x[0], x[-1], 20)

guess_a, guess_b, guess_c = 4000, -0.005, 100
guess = [guess_a, guess_b, guess_c]

exp_decay = lambda x, A, t, y0: A * np.exp(x * t) + y0

params, cov = curve_fit(exp_decay, x, y, p0=guess)

A, t, y0 = params

print "A = %s\nt = %s\ny0 = %s\n" % (A, t, y0)

pl.clf()
best_fit = lambda x: A * np.exp(t * x) + y0

pl.plot(x, y, 'b.')
pl.plot(smoothx, best_fit(smoothx), 'r-')
pl.show()

which works, but if we remove "p0=guess", it fails miserably.

scipy numpy python
8 Answers

Python implementation of @JJacquelin's solution. I needed an approximate non-solve based solution with no initial guesses so @JJacquelin's answer was really helpful. The original question was posed as a python numpy/scipy request. I took @johanvdw's nice clean R code and refactored it as python/numpy. Hopefully useful to someone: https://gist.github.com/friendtogeoff/00b89fa8d9acc1b2bdf3bdb675178a29

import numpy as np

"""
compute an exponential decay fit to two vectors of x and y data
result is in form y = a + b * exp(c*x).
ref. https://gist.github.com/johanvdw/443a820a7f4ffa7e9f8997481d7ca8b3
"""
def exp_est(x,y):
    n = np.size(x)
    # sort the data into ascending x order
    y = y[np.argsort(x)]
    x = x[np.argsort(x)]

    Sk = np.zeros(n)

    for n in range(1,n):
        Sk[n] = Sk[n-1] + (y[n] + y[n-1])*(x[n]-x[n-1])/2
    dx = x - x[0]
    dy = y - y[0]

    m1 = np.matrix([[np.sum(dx**2), np.sum(dx*Sk)],
                    [np.sum(dx*Sk), np.sum(Sk**2)]])
    m2 = np.matrix([np.sum(dx*dy), np.sum(dy*Sk)])

    [d, c] = (m1.I * m2.T).flat

    m3 = np.matrix([[n,                  np.sum(np.exp(  c*x))],
                    [np.sum(np.exp(c*x)),np.sum(np.exp(2*c*x))]])

    m4 = np.matrix([np.sum(y), np.sum(y*np.exp(c*x).T)])

    [a, b] = (m3.I * m4.T).flat

    return [a,b,c]
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