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 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
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)
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)
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