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
Exemplo n.º 2
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    def testEigenRemove(self):
        tol = 10**-6

        for i in range(10):
            m = numpy.random.randint(5, 10)
            n = numpy.random.randint(5, 10)

            #How many rows/cols to remove 
            p = numpy.random.randint(1, 5)

            A = numpy.random.randn(m, n)
            C = A.conj().T.dot(A)

            lastError = 100

            omega, Q = numpy.linalg.eigh(C)
            self.assertTrue(numpy.linalg.norm(C-(Q*omega).dot(Q.conj().T)) < tol )
            #
            Cprime = C[0:n-p, 0:n-p]
            
            for k in range(1,9):
                pi, V, K, Y1, Y2, omega2 = EigenUpdater.eigenRemove(omega, Q, n-p, 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(Cprime-C_k)

                if Util.rank(C)<k:
                    self.assertTrue(error <= tol)
                lastError = error
    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
Exemplo n.º 4
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    def testEigenRemove2(self):
        tol = 10**-6
        m = 10
        n = 8
        A = numpy.random.randn(m, n)
        C = A.conj().T.dot(A)

        p = 5
        k = 8

        omega, Q = numpy.linalg.eig(C)
        Cprime = C[0:n - p, 0:n - p]

        pi, V = EigenUpdater.eigenRemove(omega, Q, n - p, k, debug=False)

        C_k = (V * pi).dot(V.conj().T)
        error = numpy.linalg.norm(Cprime - C_k)

        self.assertTrue(error <= tol)
Exemplo n.º 5
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    def testEigenRemove2(self):
        tol = 10**-6 
        m = 10
        n = 8
        A = numpy.random.randn(m, n)
        C = A.conj().T.dot(A)

        p = 5
        k = 8

        omega, Q = numpy.linalg.eig(C)
        Cprime = C[0:n-p, 0:n-p]

        pi, V = EigenUpdater.eigenRemove(omega, Q, n-p, k, debug=False)

        C_k = (V*pi).dot(V.conj().T)
        error = numpy.linalg.norm(Cprime-C_k)

        self.assertTrue(error <= tol)
Exemplo n.º 6
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    def testEigenRemove(self):
        tol = 10**-6

        for i in range(10):
            m = numpy.random.randint(5, 10)
            n = numpy.random.randint(5, 10)

            #How many rows/cols to remove
            p = numpy.random.randint(1, 5)

            A = numpy.random.randn(m, n)
            C = A.conj().T.dot(A)

            lastError = 100

            omega, Q = numpy.linalg.eigh(C)
            self.assertTrue(
                numpy.linalg.norm(C - (Q * omega).dot(Q.conj().T)) < tol)
            #
            Cprime = C[0:n - p, 0:n - p]

            for k in range(1, 9):
                pi, V, K, Y1, Y2, omega2 = EigenUpdater.eigenRemove(omega,
                                                                    Q,
                                                                    n - p,
                                                                    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(Cprime - C_k)

                if Util.rank(C) < k:
                    self.assertTrue(error <= tol)
                lastError = error