def unifvscheb(n):
"""\
unifvscheb(n):
graphs the function (x-x0)...(x-x_{n-1}) for unif and cheb
point in [0,1].
n must be even.
functions nmlzed to be 1 at 0.
"""
import gridpts as gr
import numpy as np
from matplotlib import pyplot as plt
assert n%2 == 0
x = gr.unif(n)
xx = np.linspace(-1,1,200)*0.99+1e-6
yy = gr.evalprod(x, xx)
zero = np.array([0]) #nmlz
yy = yy/gr.evalprod(x, zero)
plt.subplot(211)
plt.plot(xx, yy)
plt.title('nmlz prod poly with ' + str(n) + ' unif points')
x = gr.cheb(n)
yy = gr.evalprod(x, xx)
yy = yy/gr.evalprod(x, zero) #nmlz
plt.subplot(212)
plt.plot(xx, yy)
plt.title('nmlz prod poly with ' + str(n) + ' cheb points')
import numpy as np
from matplotlib import pyplot as plt
import sys, os
sys.path.append(os.getcwd() + "/..")
import gridpts
import lgrng
x = gridpts.cheb(20)
y = np.sin(np.sin(x))
plt.plot(x, y, "ro")
xx = gridpts.unif(200)
xx = xx * 0.999 + 1e-6
yy = lgrng.interp(x, y, xx)
plt.plot(xx, yy, "k")
plt.axis("tight")
plt.show()