def approxUpdateEig(self, subW, ABBA, omega, Q):
        """
        Update the eigenvalue decomposition of ABBA
        """
        # --- remove rows/columns ---
        if self.n > ABBA.shape[0]:
            omega, Q = EigenUpdater.eigenRemove(omega, Q, ABBA.shape[0],
                                                min(self.k2, ABBA.shape[0]))

        # --- update existing nodes ---
        currentN = min(self.n, ABBA.shape[0])
        deltaDegrees = numpy.array(
            subW.sum(0)).ravel()[0:currentN] - self.degrees[:currentN]
        inds = numpy.arange(currentN)[deltaDegrees != 0]
        if len(inds) > 0:
            Y1 = ABBA[:currentN, inds] - self.ABBALast[:currentN, inds]
            Y1 = numpy.array(Y1.todense())
            Y1[inds, :] = Y1[inds, :] / 2
            Y2 = numpy.zeros((currentN, inds.shape[0]))
            Y2[(inds, numpy.arange(inds.shape[0]))] = 1
            omega, Q = EigenUpdater.eigenAdd2(omega, Q, Y1, Y2,
                                              min(self.k2, currentN))

        # --- add rows/columns ---
        if self.n < ABBA.shape[0]:
            AB = numpy.array(ABBA[0:self.n, self.n:].todense())
            BB = numpy.array(ABBA[self.n:, self.n:].todense())
            omega, Q = EigenUpdater.lazyEigenConcatAsUpdate(
                omega, Q, AB, BB, min(self.k2, ABBA.shape[0]))

        return omega, Q
    def approxUpdateEig(self, subW, ABBA, omega, Q):
        """
        Update the eigenvalue decomposition of ABBA
        """
        # --- remove rows/columns ---
        if self.n > ABBA.shape[0]:
            omega, Q = EigenUpdater.eigenRemove(omega, Q, ABBA.shape[0], min(self.k2, ABBA.shape[0]))

        # --- update existing nodes ---
        currentN = min(self.n, ABBA.shape[0])
        deltaDegrees = numpy.array(subW.sum(0)).ravel()[0:currentN]- self.degrees[:currentN]
        inds = numpy.arange(currentN)[deltaDegrees!=0]
        if len(inds) > 0:
            Y1 = ABBA[:currentN, inds] - self.ABBALast[:currentN, inds]
            Y1 = numpy.array(Y1.todense())
            Y1[inds, :] = Y1[inds, :]/2
            Y2 = numpy.zeros((currentN, inds.shape[0]))
            Y2[(inds, numpy.arange(inds.shape[0]))] = 1
            omega, Q = EigenUpdater.eigenAdd2(omega, Q, Y1, Y2, min(self.k2, currentN))

        # --- add rows/columns ---
        if self.n < ABBA.shape[0]:
            AB = numpy.array(ABBA[0:self.n, self.n:].todense())
            BB = numpy.array(ABBA[self.n:, self.n:].todense())
            omega, Q = EigenUpdater.lazyEigenConcatAsUpdate(omega, Q, AB, BB, min(self.k2, ABBA.shape[0]))
        
        return omega, Q
Пример #3
0
    def testEigenAdd2(self):
        tol = 10**-6

        for i in range(10):
            m = numpy.random.randint(5, 10)
            n = numpy.random.randint(5, 10)
            p = numpy.random.randint(5, 10)
            A = numpy.random.randn(m, n)
            Y1 = numpy.random.randn(n, p)
            Y2 = numpy.random.randn(n, p)

            AA = A.conj().T.dot(A)
            Y1Y2 = Y1.dot(Y2.conj().T)
            lastError = 100

            omega, Q = numpy.linalg.eigh(AA)
            self.assertTrue(
                numpy.linalg.norm(AA - (Q * omega).dot(Q.conj().T)) < tol)
            C = AA + Y1Y2 + Y1Y2.conj().T
            for k in range(1, 9):
                pi, V, D, DUD = EigenUpdater.eigenAdd2(omega,
                                                       Q,
                                                       Y1,
                                                       Y2,
                                                       k,
                                                       debug=True)
                # V is "orthogonal"
                self.assertTrue(
                    numpy.linalg.norm(V.conj().T.dot(V) -
                                      numpy.eye(V.shape[1])) < tol)

                # The approximation converges to the exact decomposition
                C_k = (V * pi).dot(V.conj().T)
                error = numpy.linalg.norm(C - C_k)
                if Util.rank(C) == k:
                    self.assertTrue(error <= tol)
                lastError = error

                # DomegaD corresponds to AA_k
                omega_k, Q_k = Util.indEig(
                    omega, Q,
                    numpy.flipud(numpy.argsort(omega))[0:k])
                DomegakD = (D *
                            numpy.c_[omega_k[numpy.newaxis, :],
                                     numpy.zeros(
                                         (1, max(D.shape[1] - k, 0)))]).dot(
                                             D.conj().T)
                self.assertTrue(
                    numpy.linalg.norm((Q_k * omega_k).dot(Q_k.conj().T) -
                                      DomegakD) < tol)

                # DUD is exactly decomposed
                self.assertTrue(
                    numpy.linalg.norm(Y1Y2 + Y1Y2.conj().T -
                                      D.dot(DUD).dot(D.conj().T)) < tol)
Пример #4
0
def eigenUpdate(L1, L2, omega, Q, k): 
    """
    Find the eigen-update between two matrices L1 (with eigenvalues omega, and 
    eigenvectors Q), and L2.  
    """
    deltaL = L2 - L1 
    deltaL.prune()
    inds = numpy.unique(deltaL.nonzero()[0]) 
    
    if len(inds) > 0:
        Y1 = deltaL[:, inds]
        Y1 = numpy.array(Y1.todense())
        Y1[inds, :] = Y1[inds, :]/2
        
        logging.debug("rank(deltaL)=" + str(Y1.shape[1]))
        
        Y2 = numpy.zeros((L1.shape[0], inds.shape[0]))
        Y2[(inds, numpy.arange(inds.shape[0]))] = 1
        
        omega, Q = EigenUpdater.eigenAdd2(omega, Q, Y1, Y2, min(k, L1.shape[0]))
    
    return omega, Q
Пример #5
0
    def testEigenAdd2(self):
        tol = 10**-6

        for i in range(10):
            m = numpy.random.randint(5, 10)
            n = numpy.random.randint(5, 10)
            p = numpy.random.randint(5, 10)
            A = numpy.random.randn(m, n)
            Y1 = numpy.random.randn(n, p)
            Y2 = numpy.random.randn(n, p)

            AA = A.conj().T.dot(A)
            Y1Y2 = Y1.dot(Y2.conj().T)
            lastError = 100

            omega, Q = numpy.linalg.eigh(AA)
            self.assertTrue(numpy.linalg.norm(AA-(Q*omega).dot(Q.conj().T)) < tol )
            C = AA + Y1Y2 + Y1Y2.conj().T
            for k in range(1,9):
                pi, V, D, DUD = EigenUpdater.eigenAdd2(omega, Q, Y1, Y2, k, debug = True)
                # V is "orthogonal"
                self.assertTrue(numpy.linalg.norm(V.conj().T.dot(V) - numpy.eye(V.shape[1])) < tol  )

                # The approximation converges to the exact decomposition 
                C_k = (V*pi).dot(V.conj().T)
                error = numpy.linalg.norm(C-C_k)
                if Util.rank(C)==k:
                    self.assertTrue(error <= tol)
                lastError = error
                
                # DomegaD corresponds to AA_k
                omega_k, Q_k = Util.indEig(omega, Q, numpy.flipud(numpy.argsort(omega))[0:k])
                DomegakD = (D*numpy.c_[omega_k[numpy.newaxis,:],numpy.zeros((1,max(D.shape[1]-k,0)))]).dot(D.conj().T)
                self.assertTrue(numpy.linalg.norm((Q_k*omega_k).dot(Q_k.conj().T)-DomegakD) < tol )
                
                # DUD is exactly decomposed
                self.assertTrue(numpy.linalg.norm(Y1Y2 + Y1Y2.conj().T - D.dot(DUD).dot(D.conj().T)) < tol )