def graph(f, n, xmin, xmax, axis, resolution = 1001):
"""
Plots p_L based on points taken from f(x)
"""
x = []
y = []
y_p = []
x_f = []
y_f = []
step = (xmax - xmin) / float(n)
step_res = (xmax - xmin) / float(resolution)
for i in xrange(n):
x.append(xmin + i * step)
for elem_x in x:
y.append(f(elem_x))
for i in xrange(resolution):
x_f.append(xmin + i * step_res)
for elem in x_f:
y_f.append(f(elem))
for elem_x in x:
y_p.append(L1.p_L(elem_x, x, y))
plt.plot(x, y_p, 'ro')
plt.plot(x_f, y_f, '.')
plt.axis(axis)
plt.show()
def graph(f, n, xmin, xmax, axis, resolution=1001):
"""
Plots p_L based on points taken from f(x)
"""
x = []
y = []
y_p = []
x_f = []
y_f = []
step = (xmax - xmin) / float(n)
step_res = (xmax - xmin) / float(resolution)
for i in xrange(n):
x.append(xmin + i * step)
for elem_x in x:
y.append(f(elem_x))
for i in xrange(resolution):
x_f.append(xmin + i * step_res)
for elem in x_f:
y_f.append(f(elem))
for elem_x in x:
y_p.append(L1.p_L(elem_x, x, y))
plt.plot(x, y_p, 'ro')
plt.plot(x_f, y_f, '.')
plt.axis(axis)
plt.show()
def graph2(f, n, xmin, xmax, legend_list, resolution=1001):
for element in n:
x_actual = np.linspace(xmin, xmax, element)
y_actual = f(x_actual)
x_array = np.linspace(xmin, xmax, resolution)
y_array = np.array([p1.p_L(x, x_actual, y_actual) for x in x_array])
plot(x_actual, y_actual, 'o')
plot(x_array, y_array, '-')
legend(legend_list, loc=9)
title('Sin and Interpolating Functions from 0 to Pi')
xlabel('x')
ylabel('y')
def graph2(f, n, xmin, xmax, legend_list, resolution=1001):
for element in n:
x_actual = np.linspace(xmin, xmax, element)
y_actual = f(x_actual)
x_array = np.linspace(xmin, xmax, resolution)
y_array = np.array([p1.p_L(x, x_actual, y_actual) for x in x_array])
plot(x_actual, y_actual, 'o')
plot(x_array, y_array, '-')
legend(legend_list, loc=9)
title('Sin and Interpolating Functions from 0 to Pi')
xlabel('x')
ylabel('y')
def graph(f, n, xmin, xmax, resolution=1001):
x_values = np.linspace(xmin, xmax, n)
y_values = f(x_values)
x_arr = np.linspace(xmin, xmax, resolution)
y_arr = []
for x in x_arr:
y_arr.append(p1.p_L(x, x_values, y_values))
plt.plot(x_values, y_values, 'ko')
plt.plot(x_arr, y_arr)
plt.title('Interpolation Polynomial and sin(x) from 0 to pi')
plt.xlabel('x')
plt.ylabel('y')
plt.xlim(-0.1, 3.2)
plt.ylim(-0.1, 1.1)
def graph(f, n, xmin, xmax, resolution=1001):
"""Creates a graph of a given function f by both plotting n evenly spaced
points of the function on the given interval as black circles, and by plotting
a blue line of the given resolution by the interpolating function p_L and its
property L_k of the module Lagrange_poly1"""
x_actual = np.linspace(xmin, xmax, n)
y_actual = f(x_actual)
x_array = np.linspace(xmin, xmax, resolution)
y_array = np.array([p1.p_L(x, x_actual, y_actual) for x in x_array])
plot(x_actual, y_actual, 'ko')
plot(x_array, y_array, 'b-')
xlim([-0.01, math.pi + 0.01])
ylim([0, 1.1])
title('Sin and Interpolating Function from 0 to Pi')
xlabel('x')
ylabel('y')
def graph(f, n, xmin, xmax, resolution=1001):
"""Creates a graph of a given function f by both plotting n evenly spaced
points of the function on the given interval as black circles, and by plotting
a blue line of the given resolution by the interpolating function p_L and its
property L_k of the module Lagrange_poly1"""
x_actual = np.linspace(xmin, xmax, n)
y_actual = f(x_actual)
x_array = np.linspace(xmin, xmax, resolution)
y_array = np.array([p1.p_L(x, x_actual, y_actual) for x in x_array])
plot(x_actual, y_actual, 'ko')
plot(x_array, y_array, 'b-')
xlim([-0.01, math.pi + 0.01])
ylim([0, 1.1])
title('Sin and Interpolating Function from 0 to Pi')
xlabel('x')
ylabel('y')
def test_p_l(xp = np.linspace(0,math.pi, 5), yp = np.array([math.sin(y) for y in np.linspace(0,math.pi, 5)]) ):
plt.plot(xp, yp)
Lagrange_poly1.test_p_l(xp, yp)
def p_L(x, xp, yp):
return Lagrange_poly1.p_L(x, xp, yp)
def test_p_l(xp=np.linspace(0, math.pi, 5),
yp=np.array([math.sin(y) for y in np.linspace(0, math.pi, 5)])):
Lagrange_poly1.test_p_l(xp, yp)
def L_k(x, k, xp):
return Lagrange_poly1.L_k(x, k, xp)
def p_L(x, xp, yp):
return Lagrange_poly1.p_L(x, xp, yp)
