def shade_under_curve(self, fig, f):
"""
shade_under_curve draws a plot of f from a to b and adds a
lagrange fit that shows a pictorial representation of
Gaussian-Legendre Quadrature.
Parameters
----------
fig : The figure in which to add the plots
f : The function to be plotted.
"""
# Add a subplot to the supplied figure.
ax = fig.add_subplot(111)
# Create the Lagrange Interpolation fit.
x_points = self.evaluation_pts
y_points = f(x_points)
poly_fit = scibary(x_points, y_points)
# Create the points to be graphed.
xL = np.linspace(self.a, self.b, 150)
yL = poly_fit(xL)
# Draw yellow lines going from the x-axis to the evaluation
# points.
for x, y in zip(x_points, y_points):
ax.plot([x, x], [0, y], 'y-')
# Plot the Lagrange fit and shade underneath.
ax.plot(xL, yL, 'y-')
ax.fill_between(xL, yL, color='y', alpha='0.25')
# Plot the actual function and set appropriate x-axis limits.
ax.plot(xL, f(xL))
ax.set_xlim([self.a, self.b])
def shade_under_curve(self, fig, f):
"""
Adds floor(n/2) quadratic lagrange interpolants using 3
adjacent points to fig and shades them underneath. Also draws
a plot of f.
Parameters
----------
fig : The figure in which to add the trapezoids or rectangles.
f : The function to be plotted.
"""
# Add a sub plot to the supplied figure.
ax = fig.add_subplot(111)
# Create the points to make the Quadratic fits.
x_points = self.evaluation_pts
y_points = f(x_points)
points = zip(x_points, y_points)
pts1 = points[0:-1:2]
pts2 = points[1::2]
pts3 = points[2::2]
plotPts = zip(pts1, pts2, pts3)
# Plot the Quadratic fits and shade them in.
for pts in plotPts:
x_pts = [p[0] for p in pts]
y_pts = [p[1] for p in pts]
poly_fit = scibary(x_pts, y_pts)
x1 = x_pts[0]
x2 = x_pts[-1]
if self.n > 150:
xL = np.linspace(x1, x2, 1)
else:
xL = np.linspace(x1, x2, 150 / self.n)
yL = poly_fit(xL)
for x, y in pts:
ax.plot([x, x], [0, y], 'y-')
ax.plot(xL, yL, 'y-')
ax.fill_between(xL, yL, color='y', alpha='0.25')
# Plot the actual function.
xL2 = np.linspace(self.a, self.b, 150)
ax.plot(xL2, f(xL2))
ax.set_xlim([self.a, self.b])
