renaming codes

doc/Programs/Regression/project1.py

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