python – 如何计算非方矩阵的Cholesky分解,以便用’numpy’计算

def get_fitting_function(G):
    print(G.shape) #(14L,11L) --> 14 samples of dimension 11
    g_mu = G.mean(axis=0) 
    #Cholesky decomposition uses half of the operations as LU
    #and is numerically more stable.
    L = np.linalg.cholesky(G)

    def fitting_function(g):
        x = g - g_mu
        z = np.linalg.solve(L,x)
        #Mahalanobis Distance 
        MD = z.T*z
        return math.sqrt(MD)
    return fitting_function  


C:UsersMatthiasCVsrcfitting_function.py in get_fitting_function(G)
     22     #Cholesky decomposition uses half of the operations as LU
     23     #and is numerically more stable.
---> 24     L = np.linalg.cholesky(G)
     25 
     26     def fitting_function(g):

C:UsersMatthiasAppDataLocalEnthoughtCanopyUserlibsite-packagesnumpylinalglinalg.pyc in cholesky(a)
    598     a,wrap = _makearray(a)
    599     _assertRankAtLeast2(a)
--> 600     _assertNdSquareness(a)
    601     t,result_t = _commonType(a)
    602     signature = 'D->D' if isComplexType(t) else 'd->d'

C:UsersMatthiasAppDataLocalEnthoughtCanopyUserlibsite-packagesnumpylinalglinalg.pyc in _assertNdSquareness(*arrays)
    210     for a in arrays:
    211         if max(a.shape[-2:]) != min(a.shape[-2:]):
--> 212             raise LinAlgError('Last 2 dimensions of the array must be square')
    213 
    214 def _assertFinite(*arrays):

LinAlgError: Last 2 dimensions of the array must be square 


    LinAlgError: Last 2 dimensions of the array must be square

基于Matlab实现：Mahalanobis distance inverting the covariance matrix

编辑：chol(a)= linalg.cholesky(a).T
矩阵的cholesky分解(matlab中的chol(a)返回一个上三角矩阵,但linalg.cholesky(a)返回一个下三角矩阵)(来源：http://wiki.scipy.org/NumPy_for_Matlab_Users)

EDIT2：

G -= G.mean(axis=0)[None,:]
C = (np.dot(G,G.T) / float(G.shape[0]))
#Cholesky decomposition uses half of the operations as LU
#and is numerically more stable.
L = np.linalg.cholesky(C).T

所以如果D = x ^ t.S ^ -1.x = x ^ t.(L.L ^ t)^ – 1.x = x ^ t.L.L ^ t.x = z ^ t.z