mhjensen
69 lines
1.8 KiB
Python
69 lines
1.8 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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from mpl_toolkits.mplot3d import Axes3D
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from matplotlib import cm
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from sklearn.preprocessing import PolynomialFeatures
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from sklearn.linear_model import Ridge, LinearRegression, Lasso, Ridge
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from sklearn.model_selection import cross_validate
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np.random.seed(4155)
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### a)
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def FrankeFunction(x,y):
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term1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2))
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term2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1))
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term3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2))
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term4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2)
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return term1 + term2 + term3 + term4
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# Generate the data
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nrow = 100
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ncol = 200
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ax_row = np.random.uniform(0, 1, size=nrow)
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ax_col = np.random.uniform(0, 1, size=ncol)
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ind_sort_row = np.argsort(ax_row)
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ind_sort_col = np.argsort(ax_col)
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ax_row_sorted = ax_row[ind_sort_row]
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ax_col_sorted = ax_col[ind_sort_col]
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colmat, rowmat = np.meshgrid(ax_col_sorted, ax_row_sorted)
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noise_str = .0
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noise = np.random.randn(nrow, ncol)
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z = FrankeFunction(rowmat, colmat) + noise_str * noise
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row_arr = rowmat.ravel()
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col_arr = colmat.ravel()
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z_arr = z.ravel()
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# Generate the design matrix
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p = 10
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poly = PolynomialFeatures(degree = p)
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X = poly.fit_transform(np.c_[row_arr, col_arr])
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## Perform OLS
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linreg = LinearRegression()
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linreg.fit(X, z_arr)
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zpred = linreg.predict(X)
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zplot = zpred.reshape(nrow, ncol)
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# Plot the reuslting fit beside the original surface
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fig = plt.figure()
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ax = fig.add_subplot(1, 2, 1, projection='3d')
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surf = ax.plot_surface(colmat, rowmat, z, cmap=cm.viridis, linewidth=0, antialiased=False)
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fig.colorbar(surf, shrink=0.5, aspect=5)
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plt.title('Franke')
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ax = fig.add_subplot(1, 2, 2, projection='3d')
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surf = ax.plot_surface(colmat, rowmat, zplot, cmap=cm.viridis, linewidth=0, antialiased=False)
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fig.colorbar(surf, shrink=0.5, aspect=5)
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plt.title('Fitted Franke')
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plt.show()
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