def get_points(n, a, b):
points = []
r = b - a
step = r / n
for i in arange(-2 * pi, 2 * pi, step):
points.append((i, calculate_f_x(i)))
points.append((b, calculate_f_x(b)))
return points
def get_points(n):
points = []
r = end - start
step = r / n
for i in arange(-2 * pi, 2 * pi, step):
points.append((i, calculate_f_x(i)))
points.append((end, calculate_f_x(end)))
return points
def get_points(n):
points = []
r = end - start
step = r / n
for i in arange(-2 * pi, 2 * pi, step):
points.append((i, calculate_f_x(i)))
points.append((end, calculate_f_x(end)))
return points
def get_points(n, a, b):
points = []
r = b - a
step = r / n
for i in arange(-2 * pi, 2 * pi, step):
points.append((i, calculate_f_x(i)))
points.append((b, calculate_f_x(b)))
return points
def interpolate(n):
points = get_points(n - 1)
points = map(list, zip(*points))
a, b = points
t = points[0]
y = points[1]
cubic_spline_natural = create_spline_function(t, y, calculate_cubic_value)
cubic_spline_not_a_knot = create_spline_function(t, y, calculate_cubic_value_not_a_knot)
quadratic_spline_natural = create_quadratic_function(t, y, calculate_quadratic_value)
quadratic_spline_not_a_knot = create_quadratic_function(t, y, calculate_quadratic_value_not_a_knot)
x = arange(-2 * pi, 2 * pi, 0.05)
w = map(cubic_spline_natural, x)
w1 = map(quadratic_spline_natural, x)
w2 = map(cubic_spline_not_a_knot, x)
w3 = map(quadratic_spline_not_a_knot, x)
plt.plot(x, calculate_f_x(x), 'b', linewidth=2.5, label="given f")
plt.plot(x, w, 'r--', linewidth=2.5, label="interpolated cubic")
# plt.plot(x + 0.2, w2, 'g--', linewidth=2.5, label="interpolated cubic")
plt.plot(a, b, 'yo')
# plt.plot(x, [cubicSpline(a) for a in x], 'r--', linewidth=2.5, label="interpolated cubic")
plt.plot(x, w1, 'c--', linewidth=2.5, label="interpolated quadratic")
plt.plot(x, w3, 'm--', linewidth=2.5, label="interpolated quadratic")
# f = sci.interp1d(a, b, kind="cubic")
# plt.plot(x, f(x), '--', label='interpolated test')
plt.legend(loc='upper left')
plt.grid(True)
plt.show()
def interpolate(n):
points = get_points(n - 1)
points = map(list, zip(*points))
a, b = points
t = points[0]
y = points[1]
cubic_spline_natural = create_spline_function(t, y, calculate_cubic_value)
cubic_spline_not_a_knot = create_spline_function(
t, y, calculate_cubic_value_not_a_knot)
quadratic_spline_natural = create_quadratic_function(
t, y, calculate_quadratic_value)
quadratic_spline_not_a_knot = create_quadratic_function(
t, y, calculate_quadratic_value_not_a_knot)
x = arange(-2 * pi, 2 * pi, 0.05)
w = map(cubic_spline_natural, x)
w1 = map(quadratic_spline_natural, x)
w2 = map(cubic_spline_not_a_knot, x)
w3 = map(quadratic_spline_not_a_knot, x)
plt.plot(x, calculate_f_x(x), 'b', linewidth=2.5, label="given f")
plt.plot(x, w, 'r--', linewidth=2.5, label="interpolated cubic")
# plt.plot(x + 0.2, w2, 'g--', linewidth=2.5, label="interpolated cubic")
plt.plot(a, b, 'yo')
# plt.plot(x, [cubicSpline(a) for a in x], 'r--', linewidth=2.5, label="interpolated cubic")
plt.plot(x, w1, 'c--', linewidth=2.5, label="interpolated quadratic")
plt.plot(x, w3, 'm--', linewidth=2.5, label="interpolated quadratic")
# f = sci.interp1d(a, b, kind="cubic")
# plt.plot(x, f(x), '--', label='interpolated test')
plt.legend(loc='upper left')
plt.grid(True)
plt.show()
def gauss_legendre_integrate(n, a, b):
[Ws, xs, err] = GaussLegendreWeights(n)
half_lenght = (b - a) / 2.
# print half_lenght
if err == 0:
ans = half_lenght * sum(Ws * calculate_f_x(half_lenght * xs + (b + a) * 0.5))
else:
err = 1
ans = None
return [ans, err]
def gauss_legendre_integrate(n, a, b):
[Ws, xs, err] = GaussLegendreWeights(n)
half_lenght = (b - a) / 2.
# print half_lenght
if err == 0:
ans = half_lenght * sum(Ws * calculate_f_x(half_lenght * xs +
(b + a) * 0.5))
else:
err = 1
ans = None
return [ans, err]
def interpolate2(n, spline_creator, boundary_conditions, label=0, caption=0):
points = get_points(n - 1)
points = map(list, zip(*points))
t = points[0]
y = points[1]
spline = spline_creator(t, y, boundary_conditions)
x = arange(-2 * pi, 2 * pi, 0.05)
f_i = map(spline, x)
f_y = map(calculate_f_x, x)
if caption != 0:
plt.figure(num=1, figsize=(10, 6), dpi = 150)
plt.plot(x, calculate_f_x(x), 'b--', linewidth=1, label="given f")
plt.plot(x, f_i, 'r--', linewidth=1, label=label)
plt.plot(t, y, 'yo', label="Nodes: " + str(n))
plt.legend(loc='upper left', prop={'size':8})
plt.grid(True)
# plt.savefig(str(n) + "_" + caption + ".png", dpi=150)
# plt.show()
plt.close()
print ";" + str("{:1.7f}".format(calculate_mean_square_error(x, f_y, f_i))),
def interpolate2(n, spline_creator, boundary_conditions, label=0, caption=0):
points = get_points(n - 1)
points = map(list, zip(*points))
t = points[0]
y = points[1]
spline = spline_creator(t, y, boundary_conditions)
x = arange(-2 * pi, 2 * pi, 0.05)
f_i = map(spline, x)
f_y = map(calculate_f_x, x)
if caption != 0:
plt.figure(num=1, figsize=(10, 6), dpi=150)
plt.plot(x, calculate_f_x(x), 'b--', linewidth=1, label="given f")
plt.plot(x, f_i, 'r--', linewidth=1, label=label)
plt.plot(t, y, 'yo', label="Nodes: " + str(n))
plt.legend(loc='upper left', prop={'size': 8})
plt.grid(True)
# plt.savefig(str(n) + "_" + caption + ".png", dpi=150)
# plt.show()
plt.close()
print ";" + str("{:1.7f}".format(calculate_mean_square_error(x, f_y,
f_i))),
