added codes

doc/Programs/VariousCodes/functions.py

@@ -0,0 +1,188 @@
+import sys
+import numpy as np
+from matplotlib import cm
+"""
+A file for all common functions used in project 1
+"""
+
+
+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
+
+def MSE(y, y_tilde):
+	"""
+	Function for computing mean squared error.
+	Input is y: analytical solution, y_tilde: computed solution.
+	"""
+	return np.sum((y-y_tilde)**2)/y.size
+
+def R2_Score(y, y_tilde):
+	"""
+	Function for computing the R2 score.
+	Input is y: analytical solution, y_tilde: computed solution.
+	"""
+
+	return 1 - np.sum((y[:-2]-y_tilde[:-2])**2)/np.sum((y[:-2]-np.average(y))**2)
+
+def create_X(x, y, n = 5):
+	"""
+	Function for creating a X-matrix with rows [1, x, y, x^2, xy, xy^2 , etc.]
+	Input is x and y mesh or raveled mesh, keyword agruments n is the degree of the polinomial you want to fit.
+	"""
+	if len(x.shape) > 1:
+		x = np.ravel(x)
+		y = np.ravel(y)
+
+	N = len(x)
+	l = int((n+1)*(n+2)/2)		# Number of elements in beta
+	X = np.ones((N,l))
+
+	for i in range(1,n+1):
+		q = int((i)*(i+1)/2)
+		for k in range(i+1):
+			X[:,q+k] = (x**(i-k))*(y**k)
+
+	return X
+
+
+def plot_surface(x, y, z, title = "", show = False, cmap=cm.coolwarm, figsize = None):
+	"""
+	Function to plot surfaces of z, given an x and y.
+	Input: x, y, z (NxN'Modeler' matrices), and a title (string)
+	"""
+
+	from mpl_toolkits.mplot3d import Axes3D
+	import matplotlib.pyplot as plt
+	from matplotlib.ticker import LinearLocator, FormatStrFormatter
+
+	if figsize:
+		fig = plt.figure(figsize = figsize)
+	else:
+		fig = plt.figure()
+	
+	ax = fig.gca(projection='3d')
+
+	# Plot the surface.of the best fit
+
+	surf = ax.plot_surface(x, y, z, cmap=cmap,
+				   linewidth=0, antialiased=False)
+
+
+	# Customize the z axis automatically
+	z_min = np.min(z)
+	z_min = z_min*1.01 if z_min < 0 else z_min*.99
+	z_max = np.max(z)
+	z_max = z_max*1.01 if z_max > 0 else z_max*.99
+
+	ax.set_zlim(z_min, z_max)
+	ax.zaxis.set_major_locator(LinearLocator(10))
+	ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
+	ax.view_init(azim=20,elev=45)
+	# Add a color bar which maps values to colors.
+	fig.colorbar(surf, shrink=0.5, aspect=5)
+	ax.set_title(title)
+
+	if show:
+		plt.show()
+
+	return fig, ax ,surf
+
+def train_test_data(x_,y_,z_,i):
+	"""
+	Takes in x,y and z arrays, and a array with random indesies iself.
+	returns learning arrays for x, y and z with (N-len(i)) dimetions
+	and test data with length (len(i))
+	"""
+	x_learn=np.delete(x_,i)
+	y_learn=np.delete(y_,i)
+	z_learn=np.delete(z_,i)
+	x_test=np.take(x_,i)
+	y_test=np.take(y_,i)
+	z_test=np.take(z_,i)
+
+	return x_learn,y_learn,z_learn,x_test,y_test,z_test
+
+
+def K_fold(x,y,z,k,alpha,model,m=5, ret_std = False):
+	"""Function to who calculate the average MSE and R2 using k-fold.
+	Takes in x,y and z varibles for a dataset, k number of folds, alpha and which method beta shall use. (OLS,Ridge or Lasso)
+	Returns average MSE and average R2"""
+	print(m)
+	if len(x.shape) > 1:
+		x = np.ravel(x)
+		y = np.ravel(y)
+		z = np.ravel(z)
+	n=len(x)
+	n_k=int(n/k)
+	if n_k*k!=n:
+		print("k needs to be a multiple of ", n,k)
+	i=np.arange(n)
+	np.random.shuffle(i)
+
+	MSE_=0
+	R2_=0
+	Variance_=0
+	Bias_=0
+	betas = np.zeros((k,int((m+1)*(m+2)/2)))
+	for t in range(k):
+		x_,y_,z_,x_test,y_test,z_test=train_test_data(x,y,z,i[t*n_k:(t+1)*n_k])
+		X= create_X(x_,y_,n=m)
+		X_test= create_X(x_test,y_test,n=m)
+
+
+		model.fit(X,z_)
+		betas[t] = model.beta
+		z_predict=model.predict(X_test)
+
+		MSE_+=MSE(z_test,z_predict)
+		R2_+=R2_Score(z_test,z_predict)
+		Bias_+=bias(z_test,z_predict)
+		Variance_+=variance(z_predict)
+
+	return (MSE_/k, R2_/k, Bias_/k, Variance_/k, np.std(betas, axis = 0), np.mean(betas, axis = 0))
+
+
+def variance(y_tilde):
+	"""
+	Calculates the variance of the predicted values y_tilde.
+	"""
+	return np.sum((y_tilde - np.mean(y_tilde))**2)/np.size(y_tilde)
+
+def bias(y, y_tilde):
+	"""
+	Calculates the bias of the predicted values y_tilde compared to
+	the actual data y.
+	"""
+	return np.sum((y - np.mean(y_tilde))**2)/np.size(y_tilde)
+
+
+def update_progress(job_title, progress):
+	"""
+	Shows the progress of an for-loop.
+	"""
+	length = 20 # modify this to change the length
+	block = int(round(length*progress))
+	msg = "\r{0}: [{1}] {2}%".format(job_title, "#"*block + "-"*(length-block), round(progress*100, 2))
+	if progress >= 1: msg += " DONE\r\n"
+	sys.stdout.write(msg)
+	sys.stdout.flush()
+
+
+def savefigure(name, figure = "gcf"):
+	"""
+	Function for saving figures as a .tex-file for easier integration with latex.
+	"""
+	try:
+		from matplotlib2tikz import save as tikz_save
+		tikz_save(name.replace(" ", "_") + ".tex", figure = figure, figureheight='\\figureheight', figurewidth='\\figurewidth')
+	except ImportError:
+		print("Please install matplotlib2tikz to save figure as a .tex-file.")
+		import matplotlib.pyplot as plt
+		if figure == "gcf":
+			plt.savefig(name+".pdf")
+		else:
+			fig.savefig(name+".pdf")