lowRankOperator.py 文件源码

def trace2(self,W=None):
        """
        Compute the trace of A*A (Note this is the square of Frob norm, since A is symmetic).
        If the weight W is provided, it will compute the trace of (AW)^2.

        This is equivalent to 
        tr_W(A) = \sum_i lambda_i^2,
        where lambda_i are the generalized eigenvalues of
        A x = lambda W^-1 x.

        Note if U is a W-orthogonal matrix then
        tr_W(A) = \sum_i D(i,i)^2. 
        """
        if W is None:
            UtU = np.dot(self.U.T, self.U)
            dUtU = self.d[:,None] * UtU #diag(d)*UtU.
            tr2 = np.sum(dUtU*dUtU)
        else:
            WU = np.zeros(self.U.shape, dtype=self.U.dtype)
            u, wu = Vector(), Vector()
            W.init_vector(u,1)
            W.init_vector(wu,0)
            for i in range(self.U.shape[1]):
                u.set_local(self.U[:,i])
                W.mult(u,wu)
                WU[:,i] = wu.get_local()
            UtWU = np.dot(self.U.T, WU)
            dUtWU = self.d[:,None] * UtWU #diag(d)*UtU.
            tr2 = np.power(np.linalg.norm(dUtWU),2)

        return tr2