def plot_fit(min_x, max_x, mu, sigma, theta, p):
x = np.arange(min_x - 15, max_x + 25, 0.05)
x_poly = poly_features(x, p)
for i in range(np.shape(x_poly)[0]):
x_poly[i] = (x_poly[i] - mu) / sigma
x_poly = np.append(np.ones((x_poly.shape[0], 1)), x_poly, axis=1)
plt.plot(x, np.dot(x_poly, theta), '--')
def plot_fit(min_x, max_x, mu, sigma, theta, p):
"""
plot a polynomial fit
"""
x = np.arange(min_x - 15, max_x + 25, 0.05)
X_poly = poly_features(x, p)
X_poly -= mu
X_poly /= sigma
X_poly = np.c_[np.ones(x.size), X_poly]
plt.plot(x, np.dot(X_poly, theta))
def plot_fit(min_x, max_x, mu, sigma, theta, p):
# We plot a range slightly bigger than the min and max values to get
# an idea of how the fit will vary outside the range of the data points
x = np.arange(min_x - 15, max_x + 25, 0.05).T
# Map the X values
X_poly = poly_features(x, p)
X_poly = X_poly - mu
X_poly = X_poly / sigma
# Add ones
X_poly = np.column_stack((np.ones(x.shape[0]), X_poly))
# Plot
plt.plot(x, X_poly.dot(theta), '--', lw=2)
def plot_fit(min_x, max_x, mu, sigma, theta, p, lmd):
x = np.arange(min_x - 15, max_x + 15, 0.1)
x = x.reshape((len(x), 1))
X_poly = pf.poly_features(x, p)
X_poly -= mu
X_poly /= sigma
X_poly = np.c_[np.ones(x.size), X_poly]
plt.plot(x, np.dot(X_poly, theta))
plt.xlabel('Change in water level (x)')
plt.ylabel('Water folowing out of the dam (y)')
plt.ylim([-20, 60])
plt.title('Polynomial Regression Fit (lambda = {})'.format(lmd))
plt.show()
plt.ylabel('Error')
plt.axis([0, 13, 0, 150])
#plt.xticks(list(range(0,13,2)))
#plt.yticks(list(range(0,200,50)))
input('Program paused. Press ENTER to continue')
# ===================== Part 6 : Feature Mapping for Polynomial Regression =====================
# One solution to this is to use polynomial regression. You should now
# complete polyFeatures to map each example into its powers
#
p = 8
# Map X onto Polynomial Features and Normalize
X_poly = pf.poly_features(X, p)
X_poly, mu, sigma = fn.feature_normalize(X_poly)
X_poly = np.c_[np.ones(m), X_poly]
# Map X_poly_test and normalize (using mu and sigma)
X_poly_test = pf.poly_features(Xtest, p)
X_poly_test -= mu
X_poly_test /= sigma
X_poly_test = np.c_[np.ones(X_poly_test.shape[0]), X_poly_test]
# Map X_poly_val and normalize (using mu and sigma)
X_poly_val = pf.poly_features(Xval, p)
X_poly_val -= mu
X_poly_val /= sigma
X_poly_val = np.c_[np.ones(X_poly_val.shape[0]), X_poly_val]
