import torch, numpy as np
np.set_printoptions(precision=3, suppress=True, linewidth=200)
def standardise(M):
    M=np.asarray(M,dtype=np.float64); mask=~np.eye(len(M),dtype=bool); v=M[mask]
    out=(M-v.mean())/v.std(); np.fill_diagonal(out,0.0); return out
d=torch.load('artifacts/synth_v1/omit_size.pt',map_location='cpu')
V=standardise(d['visual_field']); T=standardise(d['text_field']); N=len(V)

wV,UV=np.linalg.eigh(V); wV=wV[::-1]; UV=UV[:,::-1]
wT,UT=np.linalg.eigh(T); wT=wT[::-1]; UT=UT[:,::-1]
K=24
X=np.abs(UV[:,:K].T@UT[:,:K])
print("|<u_k(V), u_l(T)>| top-16 block (rows=V index, cols=T index):")
print(X[:16,:16])
print("\ndiagonal |<u_k(V),u_k(T)>| k=0..23:", np.diag(X))
print("row-max of |overlap| (best T partner for each V eigvec):", X.max(1))
print("argmax:", X.argmax(1))
# subspace alignment: principal angles between top-r spaces
for r in (4,6,8,10,12,16,20,24,32,48):
    s=np.linalg.svd(UV[:,:r].T@UT[:,:r],compute_uv=False)
    print(f"r={r:3d}  mean cos principal angle {s.mean():.3f}  captured energy {np.sum(s**2)/r:.3f}  min {s.min():.3f}")