Unsymmetric equations - solve A * x = b 2. Statistical functions for masked arrays (ġ.
K-means clustering and vector quantization ( contour ( X, Y, fit, colors = 'w' ) plt. imshow ( Z, origin = 'bottom', cmap = 'plasma', extent = ( x. show () # Plot the test data as a 2D image and the fit as overlaid contours. contourf ( X, Y, Z - fit, zdir = 'z', offset =- 4, cmap = 'plasma' ) ax. plot_surface ( X, Y, fit, cmap = 'plasma' ) cset = ax. mean (( Z - fit ) ** 2 )) print ( 'RMS residual =', rms ) # Plot the 3D figure of the fitted function and the residuals. shape ) for i in range ( len ( popt ) // 5 ): fit += gaussian ( X, Y, * popt ) print ( 'Fitted parameters:' ) print ( popt ) rms = np. popt, pcov = curve_fit ( _gaussian, xdata, Z. ravel ())) # Do the fit, using our custom _gaussian function which understands our # flattened (ravelled) ordering of the data points. p0 = # We need to ravel the meshgrids of X, Y points to a pair of 1-D arrays. guess_prms = # Flatten the initial guess parameter list. shape ) for i in range ( len ( args ) // 5 ): arr += gaussian ( x, y, * args ) return arr # Initial guesses to the fit parameters. def _gaussian ( M, * args ): x, y = M arr = np. M is a (2,N) array # where N is the total number of data points in Z, which will be ravelled # to one dimension. show () # This is the callable that is passed to curve_fit. plot_surface ( X, Y, Z, cmap = 'plasma' ) ax. shape ) # Plot the 3D figure of the fitted function and the residuals. shape ) for p in gprms : Z += gaussian ( X, Y, * p ) Z += noise_sigma * np. noise_sigma = 0.1 # The function to be fit is Z. exp ( - (( x - x0 ) / xalpha ) ** 2 - (( y - y0 ) / yalpha ) ** 2 ) # A list of the Gaussian parameters: x0, y0, xalpha, yalpha, A gprms = # Standard deviation of normally-distributed noise to add in generating # our test function to fit.
meshgrid ( x, y ) # Our function to fit is going to be a sum of two-dimensional Gaussians def gaussian ( x, y, x0, y0, xalpha, yalpha, A ): return A * np. linspace ( ymin, ymax, ny ) X, Y = np.
Import numpy as np from scipy.optimize import curve_fit import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D # The two-dimensional domain of the fit.
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