Python Error Function Fit
If you are trying to fit a power-law distribution, this solution is more appropriate. 1 ########## 2 # Fitting the data -- Least Squares Method 3 ########## 4 5 # Power-law Numpy's polyfit doesn't compute them. Created using Sphinx 1.2.2. [Tutor] Fitting data to error function Colin Ross colin.ross.dal at gmail.com Sun Mar 15 16:27:50 CET 2015 Previous message (by thread): [Tutor] Fitting data to error function check_finite : bool, optional If True, check that the input arrays do not contain nans of infs, and raise a ValueError if they do. http://vealcine.com/python-error/python-error-function-2-6.php
erf(1e-9) calculated in this approximation has no correct decimal digits. Thanks Allen Downey 6 May 2010 at 08:50 Thanks for this -- I would like to distribute a modified version of this code -- can you tell me what license you It must take the independent variable as the first argument and the parameters to fit as separate remaining arguments. This week, we will take a look at how to fit models to data. http://stackoverflow.com/questions/33187433/python-fit-error-function-erf-or-similar-to-data
Python Curve Fit
Join them; it only takes a minute: Sign up Python: Fit error function (erf) or similar to data up vote 3 down vote favorite I need to fit a special distribution A more complicated to use but more complete option is to use scipy's odrpack (Orthogonal Distance Regression). Contact GitHub API Training Shop Blog About © 2016 GitHub, Inc. We'll start by importing the needed libraries and defining a fitting function: import numpy as np import matplotlib.pyplot as plt from scipy.optimize import curve_fit def fitFunc(t, a, b, c): return a*np.exp(-b*t)
- For now I have settled fitting a sigmoid function: en.wikipedia.org/wiki/Sigmoid_function with scope's curve_fit.
- Setting this parameter to False may silently produce nonsensical results if the input arrays do contain nans.
- The coefficients are stored in fit.beta, and the errors in the coefficients in fit.sd_beta.
- If you're sure the function is monotonic, you can simply to a spline of x(y) --- i.e.
- def G(y): return quad(integrand, -np.infty, np.infty, args=(y)) G_plot =  for tau in t_d: integral,error = G(tau) G_plot.append(integral) #fit data params = curve_fit(fit,pos[174-100:174+100],amp[174-100:174+100],p0=[0.003, 8550,350]) #function, xdata, ydata, initial guess (from plot)
- I know the distribution closely resembles an error function, but I did not manage to fit such a function with scipy...
- The first item are the results, and the second is 1 if the fit converged (other numbers for other scenarios).
- I have problems with getting a robust fit.
- Gene 20 January 2009 at 08:48 I re-factored a sixth order polynomial using Horner’s method.
- erf(-x) = -erf(x).
Just calculating the moments of the distribution is enough, and this is much faster. Plotting the results: import matplotlib.pyplot as plt plt.scatter(xb,yb) plt.plot(x,f(x)) plt.plot(x,fitpoly(x)) plt.plot(x,fitfunc(x,p,p)) plt.show() Using the least-square function directly The basic syntax is the following: #!/usr/bin/python from scipy import optimize from numpy import ydata : M-length sequence The dependent data -- nominally f(xdata, ...) p0 : None, scalar, or N-length sequence, optional Initial guess for the parameters. Scipy.optimize.leastsq Example If the Jacobian matrix at the solution doesn't have a full rank, then ‘lm' method returns a matrix filled with np.inf, on the other hand ‘trf' and ‘dogbox' methods use Moore-Penrose
Setting this parameter to False may silently produce nonsensical results if the input arrays do contain nans. Scipy Optimize Leastsq What is the overall average temperature in Munich, and what are the typical daily average values predicted by the model for the coldest and hottest time of year? Thus the leastsq routine is optimizing both data sets at the same time. 1 # Target function 2 fitfunc = lambda T, p, x: p*cos(2*pi/T*x+p) + p*x 3 # Initial guess The idea is that you return, as a "cost" array, the concatenation of the costs of your two data sets for one choice of parameters.
In my case I only needed the errors on the fitting parameters, so numpy's polyfit was not an option. Scipy Odr Only the relative magnitudes of the sigma values matter. When you do define an odr.Model(), it's useful to add the derivatives of the function in respect to the parameters and to the data (in this case, x). Odrpack has a lot of functions and manipulations before a fit can be done, so I have a small program to do that for me and extract only what I need
Scipy Optimize Leastsq
Scipy is basically a very large library of functions that you can use for scientific analysis. http://scipy.github.io/old-wiki/pages/Cookbook/FittingData gamma = 200.*10**(-15) # sec dt = (t-t)*(1*10**(-12)) def phi(x): return alpha*np.cos(gamma*(x - omega_o) - delta) def M(x): return np.exp(1j*phi(x)) def E_out(x): E_in_w = fft(E_(x)) omega = fftfreq(len(x),dt)*2*np.pi E_out_w = E_in_w*M(omega) Python Curve Fit We can now call curve_fit to find the best-fit parameters using a least-squares fit: In: popt, pcov = curve_fit(line, x, y) The curve_fit function returns two items, which we can popt Python Lmfit Examples >>> import numpy as np >>> from scipy.optimize import curve_fit >>> def func(x, a, b, c): ...
Not the answer you're looking for? his comment is here We start off by definining a function representing the model: In: def line(x, a, b): return a * x + b The arguments to the function should be x, followed by I guess there is no other way to easily fit that function in a more robust way. The distribution does not really follow a specific theoretical prediction, so I just want to fit any given function without great meaning. Numpy Exponential Fit
A clever use of the cost function can allow you to fit both set of data in one fit, using the same frequency. So there's > definitely a problem there. > > > See messages such as: > > https://groups.google.com/forum/#!topic/comp.lang.python/9E4HX4AES-M > > which suggest that trying to use the standard library math functions > If None, then the initial values will all be 1 (if the number of parameters for the function can be determined using introspection, otherwise a ValueError is raised). this contact form Uses scipy odrpack, but for least squares.
the x value at y position 90 and then an interpolation does not work since the answer is ambiguous. Python Linear Fit For example, if you just want to be able interpolate/extrapolate your data --- then using something like a 'spline' would be fine. Let's now try and fit the data assuming each point has a vertical error (standard deviation) of +/-10: In: e = np.repeat(10., 100) plt.errorbar(x, y, yerr=e, fmt=None) Out:
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To compute one standard deviation errors on the parameters use perr = np.sqrt(np.diag(pcov)). To compute one standard deviation errors on the parameters use perr = np.sqrt(np.diag(pcov)). What are the best-fit values of the parameters? navigate here You don't always have to define an odr.Model().
I truly appreciate it. Returns:popt : array Optimal values for the parameters so that the sum of the squared error of f(xdata, *popt) - ydata is minimized pcov : 2d array The estimated covariance of Do not try to be smart and return the squared difference, it will not work! This (you guessed) is a wrapper around the MINPACK FORTRAN library.
Pingback: Numerical computing in IronPython with IroncladLeave a Reply Cancel replyYour email address will not be published. isomorphismes 15 June 2015 at 19:40 re: Horner's method. kwargs Keyword arguments passed to leastsq for method='lm' or least_squares otherwise. Below is a copy of my program and the stack trace, showing a new error.
In this case we will use mode 2 of odrpack, which is least-squares. For a more complete gaussian, one with an optional additive constant and rotation, see http://code.google.com/p/agpy/source/browse/trunk/agpy/gaussfitter.py. Once you have the function y ou want to fit, you create a model object based on that function, a data object based on the data you want to fit, and absolute_sigma : bool, optional If False, sigma denotes relative weights of the data points.
You can visualize the results by using polyval: y_new = N.polyval(fit,x) plot(x,y,'b-') plot(x,y_new,'r-') odrpack If the above is not enough for you and you need something more serious, then ODRPACK is Why would breathing pure oxygen be a bad idea? First, define a generic gaussian function: import numpy as N def gaussian(B,x): ''' Returns the gaussian function for B=m,stdev,max,offset ''' return B+B/(B*N.sqrt(2*N.pi))*N.exp(-((x-B)**2/(2*B**2))) Now, to use scipy's least squares you need to python scipy share|improve this question asked Oct 17 '15 at 13:54 HansSnah 31929 The starting point is: what is the purpose of the fit?
Examples of the functionality include: Integration (scipy.integrate) Optimization/Fitting (scipy.optimize) Interpolation (scipy.interpolate) Fourier Transforms (scipy.fftpack) Signal Processing (scipy.signal) Linear Algebra (scipy.linalg) Spatial data structures and algorithms (scipy.spatial) Statistics (scipy.stats) Multi-dimensional image processing That's why providing a good stack > trace is so important in bug reports: there can be multiple causes for > something to go wrong. Note that there is a way to simplify the call to the function with the best-fit parameters, which is: line(x, *popt) The * notation will expand a list of values into The reason the values are not exact is because there are only a limited number of random samples, so the best-fit slope is not going to be exactly those used in
The problem with this is that it needs quite accurate initial guesses on the parameters... –HansSnah Oct 17 '15 at 17:14 It might be more well behaved in log-space. General least-squares Real life is not only made of polynomials, so you will eventually want to fit other functions. Make a plot of the data and the best-fit model in the range 2008 to 2012.