__init__.py 文件源码

def principal_coordinates(D, nd=None):
    """
    Reconstruction of a multidimensional configuration that
    optimally reproduces the input distance matrix.

    See: Gower, J (1966)
    """
    from numpy import clip, sqrt, take, argsort, sort
    from csb.numeric import reverse
    from scipy.linalg import eigh

    ## calculate centered similarity matrix

    B = -clip(D, 1e-150, 1e150) ** 2 / 2.

    b = B.mean(0)

    B = B - b
    B = (B.T - b).T
    B += b.mean()

    ## calculate spectral decomposition

    v, U = eigh(B)
    v = v.real
    U = U.real

    U = take(U, argsort(v), 1)
    v = sort(v)

    U = reverse(U, 1)
    v = reverse(v)

    if nd is None: nd = len(v)

    X = U[:, :nd] * sqrt(clip(v[:nd], 0., 1e300))

    return X