def rank_correction(measure, N, rank=1, dtype=torch.float):
    """Return low-rank matrix L such that A + L is normal."""

    if measure == 'legs':
        assert rank >= 1
        P = torch.sqrt(.5+torch.arange(N, dtype=dtype)).unsqueeze(0) # (1 N)
    elif measure == 'legt':
        assert rank >= 2
        P = torch.sqrt(1+2*torch.arange(N, dtype=dtype)) # (N)
        P0 = P.clone()
        P0[0::2] = 0.
        P1 = P.clone()
        P1[1::2] = 0.
        P = torch.stack([P0, P1], dim=0) # (2 N)
        P *= 2**(-0.5) # Halve the rank correct just like the original matrix was halved
    elif measure == 'lagt':
        assert rank >= 1
        P = .5**.5 * torch.ones(1, N, dtype=dtype)
    elif measure in ['fourier', 'fout']:
        P = torch.zeros(N)
        P[0::2] = 2**.5
        P[0] = 1
        P = P.unsqueeze(0)
    elif measure == 'fourier_decay':
        P = torch.zeros(N)
        P[0::2] = 2**.5
        P[0] = 1
        P = P.unsqueeze(0)
        P = P / 2**.5
    elif measure == 'fourier2':
        P = torch.zeros(N)
        P[0::2] = 2**.5
        P[0] = 1
        P = 2**.5 * P.unsqueeze(0)
    elif measure in ['fourier_diag', 'foud', 'legsd']:
        P = torch.zeros(1, N, dtype=dtype)
    else: raise NotImplementedError

    d = P.size(0)
    if rank > d:
        P = torch.cat([P, torch.zeros(rank-d, N, dtype=dtype)], dim=0)  # (R N)
    return P
Return low-rank matrix L such that A + L is normal.
analyze/convnexts4nd/src/models/hippo/hippo.py