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

# # Reusing Decompressors
# 
# 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
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# THE SOFTWARE.
# </details>

# In[15]:


import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as pt
import scipy.linalg.interpolative as sli


# In[28]:


sources = np.random.rand(2, 800)
targets = np.random.rand(2, 800) + 3

all_distvecs = sources.reshape(2, 1, -1) - targets.reshape(2, -1, 1)
dists = np.sqrt(np.sum(all_distvecs**2, axis=0))
A = 1/dists


# In[31]:


k = 40
U, sigma, VT = la.svd(A)
pt.semilogy(sigma[:k])


# In[55]:


Q = U[:, :k]
Q.shape


# In[36]:


la.norm(Q@Q.T@A - A, 2)


# In[49]:


def interp_decomp(A, k):
    idx, proj = sli.interp_decomp(A, k)
    P = np.hstack([np.eye(k), proj])[:,np.argsort(idx)]
    return P, idx[:k]


# In[53]:


P, J = interp_decomp(Q.T, k)
print(P.T.shape)


# In[62]:


la.norm(Q.T[:, J]@P - Q.T, 2)


# Recast this as $\tilde P Q_J \approx Q$.

# In[66]:


la.norm(P.T@Q[J] - Q, 2)


# Now try the same thing on $A$:

# In[65]:


la.norm(P.T@A[J] - A, 2)


# In[ ]: