projection.py 文件源码

def projection(X, Y):

    rankX = rank(X)
    rankY = rank(Y)

    # rank, or dimension, or the original space
    rankO = rankX + rankY

    # check if two subspaces have the same shapes
    if X.shape != Y.shape:
        raise Exception('The two subspaces do not have the same shapes')

    # check if O is singular
    if la.det(np.hstack((X, Y))) == 0:
        raise Exception('X + Y is not the direct sum of the original space')

    # check whether each subspace is of full column/row rank
    if rankX < min(X.shape):
        raise Exception('subspace X is not of full rank')

    elif rankY < min(Y.shape):
        raise Exception('subspace Y is not of full rank')
    # X and Y are of full column rank
    elif rankX == X.shape[1] & rankY == Y.shape[1]:
        return np.hstack((X, np.zeros((X.shape[0], rankO - rankX)))).dot(la.inv(np.hstack((X, Y))))
    # X and Y are of full row rank
    elif rankX == X.shape[0] & rankY == Y.shape[0]:
        return np.vstack((X, np.zeros((rankO - rankX, X.shape[1])))).dot(la.inv(np.vstack(X, Y)))

# orthogonal projection matrix