human
I wrote the below code

    (p, _) = corr.shape
    (u, s, vt) = svds(corr, rank)
    X = (u * np.sqrt(s))
    nm = np.sqrt((X ** 2).sum(1))
    ii = np.flatnonzero((nm > 1e-05))
    X[ii, :] /= nm[ii][:, None]
    corr1 = corr.copy()
    if (type(corr1) == np.ndarray):
        np.fill_diagonal(corr1, 0)
    elif sparse.issparse(corr1):
        corr1.setdiag(np.zeros(corr1.shape[0]))
        corr1.eliminate_zeros()
        corr1.sort_indices()
    else:
        raise ValueError('Matrix    type    not    supported')
    def grad(X):
        gr = np.dot(X, np.dot(X.T, X))
        if (type(corr1) == np.ndarray):
            gr -= np.dot(corr1, X)
        else:
            gr -= corr1.dot(X)
        gr -= ((X * X).sum(1)[:, None] * X)
        return (4 * gr)
    def func(X):
        if (type(corr1) == np.ndarray):
            M = np.dot(X, X.T)
            np.fill_diagonal(M, 0)
            M -= corr1
            fval = (M * M).sum()
            return fval
        else:
            fval = 0.0
            max_ws = 1000000.0
            bs = int((max_ws / X.shape[0]))
            ir = 0
            while (ir < X.shape[0]):
                ir2 = min((ir + bs), X.shape[0])
                u = np.dot(X[ir:ir2, :], X.T)
                ii = np.arange(u.shape[0])
                u[(ii, (ir + ii))] = 0
                u -= np.asarray(corr1[ir:ir2, :].todense())
                fval += (u * u).sum()
                ir += bs
            return fval
    rslt = _spg_optim(func, grad, X, _project_correlation_factors)
    root = rslt.params
    diag = (1 - (root ** 2).sum(1))
    soln = FactoredPSDMatrix(diag, root)
    rslt.corr = soln
    del rslt.params
    return rslt

What's a good function header?
assistant
#Here's a good function header.

def corr_nearest_factor(corr, rank, ctol=1e-06, lam_min=1e-30, lam_max=1e+30, maxiter=1000):