def node_project():
resolution = 513
num_of_nodes = 12
X = nodes(-1, 1, resolution-1)
Y = lambda x: np.sqrt(1 - x**2)
Xpts = nodes(-1, 1, num_of_nodes-1)
Ypts = Y(Xpts)
plt.plot(X, Y(X), zorder=-1)
plt.plot(X, np.zeros_like(X), zorder=-1)
for x, y in zip(Xpts, Ypts):
plt.plot([x, x], [y, 0], 'r', zorder=-1)
plt.scatter(Xpts, Ypts, color='b')
plt.scatter(Xpts, np.zeros_like(Xpts), color='b')
plt.xlim((-1.05, 1.05))
plt.ylim((-.25, 1.25))
plt.savefig("node_project.pdf")
plt.clf()
def node_project():
resolution = 513
num_of_nodes = 12
X = nodes(-1, 1, resolution - 1)
Y = lambda x: np.sqrt(1 - x**2)
Xpts = nodes(-1, 1, num_of_nodes - 1)
Ypts = Y(Xpts)
plt.plot(X, Y(X), zorder=-1)
plt.plot(X, np.zeros_like(X), zorder=-1)
for x, y in zip(Xpts, Ypts):
plt.plot([x, x], [y, 0], 'r', zorder=-1)
plt.scatter(Xpts, Ypts, color='b')
plt.scatter(Xpts, np.zeros_like(Xpts), color='b')
plt.xlim((-1.05, 1.05))
plt.ylim((-.25, 1.25))
plt.savefig("node_project.pdf")
plt.clf()
def runge_plot():
a, b = -1, 1
resolution = 513
runge = lambda x: 1 / (1 + 25 * x**2)
X2 = np.linspace(a, b, resolution)
ax = plt.subplot(1, 1, 1)
plt.plot(X2, runge(X2), label="$\\frac{1}{1+25x^2}$")
for order in [5, 10, 15, 25]:
X = nodes(a, b, order)
Y = runge(X)
C = get_coefs(Y)
f = Chebyshev(C)
plt.plot(X2, f(X2), label="Order " + str(order))
handles, labels = ax.get_legend_handles_labels()
ax.legend(handles, labels, loc="upper right")
plt.savefig("runge_chebyshev.pdf")
plt.clf()
def runge_plot():
a, b = -1, 1
resolution = 513
runge = lambda x: 1 / (1 + 25 * x**2)
X2 = np.linspace(a, b, resolution)
ax = plt.subplot(1, 1, 1)
plt.plot(X2, runge(X2), label="$\\frac{1}{1+25x^2}$")
for order in [5, 10, 15, 25]:
X = nodes(a, b, order)
Y = runge(X)
C = get_coefs(Y)
f = Chebyshev(C)
plt.plot(X2, f(X2), label="Order " + str(order))
handles, labels = ax.get_legend_handles_labels()
ax.legend(handles, labels, loc="upper right")
plt.savefig("runge_chebyshev.pdf")
plt.clf()
