def plot(self, res=1001):
"""
Plots the linear interpolation of the coordinate
lists provided. Resolution is optional and defaults
to 1001.
"""
LP.graph(self.xp, self.yp, resolution=res)
def test_p_L(self, f=np.sin, x=[0, np.pi], n=11):
"""
Tests the polynomial interpolation function on the given x values, which should return
exactly the given y values. The function uses the values on sin(x) default
"""
p_L = LagrangeInterpolation(f, x, n)
LP.test_p_l(p_L.xp, p_L.yp)
def plot(self, res = 1001):
"""
Plots the linear interpolation of the coordinate
lists provided. Resolution is optional and defaults
to 1001.
"""
LP.graph(self.xp, self.yp, resolution = res)
def test_p_L(self, f = np.sin, x = [0, np.pi], n = 11):
"""
Tests the polynomial interpolation function on the given x values, which should return
exactly the given y values. The function uses the values on sin(x) default
"""
p_L = LagrangeInterpolation(f, x, n)
LP.test_p_l(p_L.xp, p_L.yp)
def test_p_L(self,
xp=np.linspace(0, np.pi, 5),
yp=np.array([np.sin(y) for y in np.linspace(0, np.pi, 5)])):
"""
Tests the polynomial interpolation function on the given x values, which should return
exactly the given y values. The function uses the values on sin(x) default
"""
LP.test_p_l(xp, yp)
def multigrapher():
legender1 = ['F2', '2', 'F4', '4', 'F6', '6', 'F10', '10']
n_list = [2, 4, 6, 10]
figure(1)
p2.graph2(np.abs, n_list, -2, 2, legender1)
legender2 = ['F13', '13', 'F20', '20']
n_list2 = [13, 20]
figure(2)
p2.graph2(np.abs, n_list2, -2, 2, legender2)
def multigrapher():
legender1 = ['F2', '2', 'F4', '4', 'F6', '6', 'F10', '10']
n_list = [2, 4, 6, 10]
figure(1)
p2.graph2(np.abs, n_list, -2, 2, legender1)
legender2 = ['F13', '13', 'F20', '20']
n_list2 = [13, 20]
figure(2)
p2.graph2(np.abs, n_list2, -2, 2, legender2)
def __call__(self, x):
"""
Evaluates the interpolation model at point x
"""
return LP.p_L(x, self.xp, self.yp)
import Lagrange_poly2 as lp
import numpy as np
import matplotlib.pyplot as plt
nlist=(2,4,6,10)
plt.figure()
for n in nlist:
lp.graph(np.abs, n, -2, 2, resolution=1001)
plt.legend(["n=%d" %n for n in nlist ])
#plt.savefig("filename.pdf") if I wanted to save the figure
plt.figure()
nlist=(13,20)
for n in nlist:
lp.graph(np.abs, n, -2, 2, resolution=1001)
plt.legend(["n=%d" %n for n in nlist ])
plt.show()
#!/usr/bin/python """ File: Lagrange_poly2b.py Copyright (c) 2016 Michael Seaman License: MIT Implements the past Lagrange poly modules and tests them out with f(x) = abs(x) """ import Lagrange_poly2 as poly2 import math poly2.graph(math.fabs, 2, -2, 2) poly2.graph(math.fabs, 4, -2, 2) poly2.graph(math.fabs, 6, -2, 2) poly2.graph(math.fabs, 10, -2, 2) poly2.graph(math.fabs, 13, -2, 2) poly2.graph(math.fabs, 20, -2, 2)
def __call__(self, x):
"""
Evaluates the interpolation model at point x
"""
return LP.p_L(x, self.xp, self.yp)
def plot(self):
LP2.graph(np.sin, 5, 0, np.pi)
"""
Exercise 5.25: Investigate the behaviour of Langrange's interpolating polynomials
Author: Weiyun Lu
"""
import Lagrange_poly2
from scitools.std import hold, figure
figure()
for n in [2,4,6,10]:
Lagrange_poly2.graph(abs, n, -2, 2)
hold('on')
hold('off')
figure()
for n in [13,20]:
Lagrange_poly2.graph(abs, n, -2, 2)
hold('on')
hold('off')
def graph2():
n = [13, 20]
p1.graph2(np.abs, n, -2, 2)
plt.title('f(x) = |x| and Interpolation Points')
plt.xlim(-2.0, 2.0)
plt.ylim(-4.5, 5.5)
def graph1():
n = [2, 4, 6, 10]
p1.graph2(np.abs, n, -2, 2)
plt.title('f(x) = |x| and Interpolation Points')
plt.xlim(-2.0, 2.0)
plt.ylim(0.0, 2.1)
def problem_5_25():
L2.graph(absolute, 2, -2, 2, [-3,3,0,1])
L2.graph(absolute, 4, -2, 2, [-3,3,0,1])
L2.graph(absolute, 6, -2, 2, [-3,3,0,1])
L2.graph(absolute, 10, -2, 2, [-3,3,0,1])
L2.graph(absolute, 13, -2, 2, [-3,3,0,1])
L2.graph(absolute, 20, -2, 2, [-3,3,0,1])
def test_p_L(self, xp = np.linspace(0,np.pi, 5), yp = np.array([np.sin(y) for y in np.linspace(0,np.pi, 5)]) ):
"""
Tests the polynomial interpolation function on the given x values, which should return
exactly the given y values. The function uses the values on sin(x) default
"""
LP.test_p_l(xp, yp)
def problem_5_25():
L2.graph(absolute, 2, -2, 2, [-3, 3, 0, 1])
L2.graph(absolute, 4, -2, 2, [-3, 3, 0, 1])
L2.graph(absolute, 6, -2, 2, [-3, 3, 0, 1])
L2.graph(absolute, 10, -2, 2, [-3, 3, 0, 1])
L2.graph(absolute, 13, -2, 2, [-3, 3, 0, 1])
L2.graph(absolute, 20, -2, 2, [-3, 3, 0, 1])
