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4aa7bc6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | """Independent conforming P1 finite-element regressions (not proof certificates)."""
from __future__ import annotations
import numpy as np
from scipy.sparse import coo_matrix
from scipy.sparse.linalg import eigsh
def eigenvalues(edges, dirichlet=(), count=20, density=60):
vertices=sorted({e.u for e in edges}|{e.v for e in edges})
ids={v:i for i,v in enumerate(vertices)}; total=len(ids)
entries=[]
for e in edges:
length=float(e.length)
ne=max(8,int(np.ceil(density*length)))
nodes=[ids[e.u]]+list(range(total,total+ne-1))+[ids[e.v]]
total+=ne-1
h=length/ne
for a,b in zip(nodes[:-1],nodes[1:]):
for i,gi in enumerate((a,b)):
for j,gj in enumerate((a,b)):
entries.append((gi,gj,(1 if i==j else -1)/h,h*(2 if i==j else 1)/6))
rows,cols,kdata,mdata=map(np.array,zip(*entries))
K=coo_matrix((kdata,(rows.astype(int),cols.astype(int))),shape=(total,total)).tocsr()
M=coo_matrix((mdata,(rows.astype(int),cols.astype(int))),shape=(total,total)).tocsr()
excluded={ids[v] for v in dirichlet}
keep=[v for v in range(total) if v not in excluded]
K=K[keep,:][:,keep]; M=M[keep,:][:,keep]
if count>=len(keep):
raise ValueError('Too many requested eigenvalues for this mesh.')
vals=eigsh(K,k=count,M=M,sigma=-1e-5,which='LM',return_eigenvectors=False,tol=1e-10)
return np.sort(vals)
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