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

# # PN vs QN
# 
# Copyright (C) 2026 Andreas Kloeckner
# 
# <details>
# <summary>MIT License</summary>
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
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# The above copyright notice and this permission notice shall be included in
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# 
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# THE SOFTWARE.
# </details>
# 
# ---
# 
# Based on [Cubature, Approximation, and Isotropy in the Hypercube](https://10.1137/16M1066312). (Trefethen)

# In[19]:


import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as plt

import modepy as mp
import modepy.tools as mp_tools


# In[32]:


shape = mp.Hypercube(2)
space = mp.QN(2, 60)

nodes = mp.edge_clustered_nodes_for_space(space, shape)
basis = mp.basis_for_space(space, shape)

plt.plot(nodes[0], nodes[1], "o")


# In[52]:


vdm = mp.vandermonde(basis.functions, nodes)

r = la.norm(nodes, 2, axis=0)
gauss_coeffs = la.solve(vdm, np.exp(-(r/0.2)**2))


# In[53]:


coeffs_reshaped = mp_tools.reshape_array_for_tensor_product_space(space, gauss_coeffs, axis=0)


# In[54]:


plt.imshow(np.log10(1e-15+np.abs(coeffs_reshaped)))
plt.colorbar()


# In[55]:


plt.imshow(np.log10(1e-15+np.abs(coeffs_reshaped[::2, ::2])))
plt.colorbar()


# In[ ]: