I am tying to find out the best fit for data given. What I did is I loop through various values of n and calculate the residual at each p using the formula ((y_fit - y_actual) / y_actual) x 100. Then I calculate the average of this for each n and then find the minimum residual mean and the corresponding n value and fit using this value. A reproducible code included: Show
Plotting residual mean with n, this is what I get: I need to know if this method is correct to determine the best fit. And if it can be done with some other functions in SciPy or any other packages. In essence what I want is to quantitatively know which is the best fit. I already went through Goodness of fit tests in SciPy but it didn't help me much. Use non-linear least squares to fit a function, f, to data. Assumes
The model function, f(x, …). It must take the independent variable as the first argument and the parameters to fit as separate remaining arguments. xdataarray_like or objectThe independent variable where the data is measured. Should usually be an M-length sequence or an (k,M)-shaped array for functions with k predictors, but can actually be any object. ydataarray_likeThe dependent data, a length M array - nominally Initial guess for the parameters (length N). 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). sigmaNone or M-length sequence or MxM array, optionalDetermines the uncertainty in ydata. If we define residuals as
None (default) is equivalent of 1-D sigma filled with ones. absolute_sigmabool, optionalIf True, sigma is used in an absolute sense and the estimated parameter covariance pcov reflects these absolute values. If False (default), only the relative magnitudes of the sigma values matter. The returned parameter covariance matrix pcov is based on scaling sigma by a constant factor. This constant is set by demanding that the reduced chisq for the optimal parameters popt when using the scaled sigma equals unity. In other words, sigma is scaled to match the sample variance of the residuals after the fit. Default is
False. Mathematically, If True, check that the input arrays do not contain nans of infs, and raise a ValueError if they do. Setting this parameter to False may silently produce nonsensical results if the input arrays do contain nans. Default is True. bounds2-tuple of array_like, optionalLower and upper bounds on parameters. Defaults to no bounds. Each
element of the tuple must be either an array with the length equal to the number of parameters, or a scalar (in which case the bound is taken to be the same for all parameters). Use New in version 0.17. method{‘lm’, ‘trf’, ‘dogbox’}, optionalMethod to use for optimization. See
New in version 0.17. jaccallable, string or None, optionalFunction with signature New in version 0.18. full_outputboolean, optionalIf True, this function returns additioal information: infodict, mesg, and ier. New in version 1.9. **kwargsKeyword arguments passed to Optimal values for the parameters so that the sum of the squared residuals of The estimated covariance of popt. The diagonals provide the variance of the parameter estimate. To compute one standard deviation errors on the parameters use How the sigma parameter affects the estimated covariance depends on absolute_sigma argument, as described above. If the
Jacobian matrix at the solution doesn’t have a full rank, then ‘lm’ method returns a matrix filled with a dictionary of optional outputs with the keys: nfev The number of function calls. Methods ‘trf’ and ‘dogbox’ do not count function calls for numerical Jacobian approximation, as opposed to ‘lm’ method. fvec The function values evaluated at the solution. fjac A permutation of the R matrix of a QR factorization of the final approximate Jacobian matrix, stored column wise. Together with ipvt, the covariance of the estimate can be approximated. Method ‘lm’ only provides this information. ipvt An integer array of length N which defines a permutation matrix, p, such that fjac*p = q*r, where r is upper triangular with diagonal elements of nonincreasing magnitude. Column j of p is column ipvt(j) of the identity matrix. Method ‘lm’ only provides this information. qtf The vector (transpose(q) * fvec). Method ‘lm’ only provides this information. New in version 1.9. mesgstr (returned only if full_output is True)A string message giving information about the solution. New in version 1.9. ierint (returnned only if full_output is True)An integer flag. If it is equal to 1, 2, 3 or 4, the solution was found. Otherwise, the solution was not found. In either case, the optional output variable mesg gives more information. New in version 1.9. RaisesValueErrorif either ydata or xdata contain NaNs, or if incompatible options are used. RuntimeErrorif the least-squares minimization fails. OptimizeWarningif covariance of the parameters can not be estimated. Notes Users should ensure that inputs xdata, ydata, and the output of f are With Box constraints can be handled by methods ‘trf’ and ‘dogbox’. Refer to the docstring of
Examples >>> import matplotlib.pyplot as plt >>> from scipy.optimize import curve_fit >>> def func(x, a, b, c): ... return a * np.exp(-b * x) + c Define the data to be fit with some noise: >>> xdata = np.linspace(0, 4, 50) >>> y = func(xdata, 2.5, 1.3, 0.5) >>> rng = np.random.default_rng() >>> y_noise = 0.2 * rng.normal(size=xdata.size) >>> ydata = y + y_noise >>> plt.plot(xdata, ydata, 'b-', label='data') Fit for the parameters a, b, c of the function func: >>> popt, pcov = curve_fit(func, xdata, ydata) >>> popt array([2.56274217, 1.37268521, 0.47427475]) >>> plt.plot(xdata, func(xdata, *popt), 'r-', ... label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt)) Constrain the optimization to the region of >>> popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [3., 1., 0.5])) >>> popt array([2.43736712, 1. , 0.34463856]) >>> plt.plot(xdata, func(xdata, *popt), 'g--', ... label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt)) >>> plt.xlabel('x') >>> plt.ylabel('y') >>> plt.legend() >>> plt.show() How do you evaluate goodness of fit in Python?If you want to know the "goodness of fit", use the R squared stat. R squared tells you how much of the observed variance in the outcome is explained by the input. Here is an example in python. This returns 0.801 , so 80.1% percent of the variance in y seems to be explained by x.
What is curve_fit in Python?Curve fitting is a type of optimization that finds an optimal set of parameters for a defined function that best fits a given set of observations. Unlike supervised learning, curve fitting requires that you define the function that maps examples of inputs to outputs.
What does curve_fit return?The curve_fit() function returns an optimal parameters and estimated covariance values as an output. Now, we'll start fitting the data by setting the target function, and x, y data into the curve_fit() function and get the output data which contains a, b, and c parameter values.
How do you fit data points in Python?The basic steps to fitting data are:. Import the curve_fit function from scipy.. Create a list or numpy array of your independent variable (your x values). ... . Create a list of numpy array of your depedent variables (your y values). ... . Create a function for the equation you want to fit.. |