added a test on updates

tests/test_update.py

+import torch 
+torch.manual_seed(42)
+
+dtype = torch.float64 
+device = 'cuda:0'
+N = 100
+chi = 20
+
+A = torch.randn(N, N, dtype=dtype, device=device)
+U, S, V = torch.svd(A)
+P = U[:, :chi]
+
+projected_trace = torch.trace(A@A.t() @ P @P.t())
+target = ((S[:chi])**2).sum()
+
+print (projected_trace.item(), target.item())
+
+w = torch.randn(N, chi, dtype=dtype, device=device)
+for step in range(20):
+    E = w.t()@A@A.t()
+    U, S, V = torch.svd(E)
+    w = V@U.t()
+
+    loss = torch.trace(A@A.t() @ w @ w.t())
+    print (step, ((loss-target)/target).item(), ((projected_trace-target)/target).item())
+