#!/usr/bin/env python
# coding: utf-8

# # Vandermonde Conditioning

# In[20]:


import numpy as np
import numpy.linalg as la
import scipy.special as sp
import matplotlib.pyplot as pt


# In[21]:


n = 5

nodes = np.linspace(-1, 1, n)
#nodes = sp.legendre(n).weights[:, 0]

pt.plot(nodes, 0*nodes, "o")


# ### Monomials

# In[22]:


exponents = np.arange(n)
exponents


# In[23]:


exponents[:, np.newaxis]


# In[24]:


vdm = nodes ** exponents[:, np. newaxis]

if n < 5:
    print(vdm)


# In[29]:


print(la.cond(vdm))


# ### Legendre polynomials

# In[30]:


vdm = np.array([sp.eval_legendre(i, nodes) for i in range(n)]).T

print(la.cond(vdm))