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
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 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)
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
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
def testEigenAdd(self):
for i in range(3):
numCols = numpy.random.randint(5, 10)
numXRows = numpy.random.randint(5, 10)
numYRows = numpy.random.randint(5, 10)
A = numpy.random.rand(numXRows, numCols)
Y = numpy.random.rand(numYRows, numCols)
AA = A.conj().T.dot(A)
AA = (AA + AA.conj().T) / 2
YY = Y.conj().T.dot(Y)
lastError = 1000
for k in range(1, min((numXRows, numCols))):
#Note using eigh since AA is hermatian
omega, Q = numpy.linalg.eigh(AA)
pi, V = EigenUpdater.eigenAdd(omega, Q, Y, k)
Pi = numpy.diag(pi)
tol = 10**-3
t = min(k, Util.rank(AA + YY))
self.assertTrue(pi.shape[0] == t)
self.assertTrue(
numpy.linalg.norm(V.conj().T.dot(V) - numpy.eye(t)) < tol)
inds2 = numpy.flipud(numpy.argsort(numpy.abs(omega)))
Q = Q[:, inds2[0:k]]
omega = omega[inds2[0:k]]
AAk = Q.dot(numpy.diag(omega)).dot(Q.conj().T)
AAkpYY = AAk + YY
AApYYEst = V.dot(Pi.dot(V.conj().T))
error = numpy.linalg.norm(AApYYEst - (AA + YY))
self.assertTrue(lastError - error >= -tol)
lastError = error
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 )
def testEigenAdd(self):
for i in range(3):
numCols = numpy.random.randint(5, 10)
numXRows = numpy.random.randint(5, 10)
numYRows = numpy.random.randint(5, 10)
A = numpy.random.rand(numXRows, numCols)
Y = numpy.random.rand(numYRows, numCols)
AA = A.conj().T.dot(A)
AA = (AA + AA.conj().T)/2
YY = Y.conj().T.dot(Y)
lastError = 1000
for k in range(1, min((numXRows, numCols))):
#Note using eigh since AA is hermatian
omega, Q = numpy.linalg.eigh(AA)
pi, V = EigenUpdater.eigenAdd(omega, Q, Y, k)
Pi = numpy.diag(pi)
tol = 10**-3
t = min(k, Util.rank(AA+YY))
self.assertTrue(pi.shape[0] == t)
self.assertTrue(numpy.linalg.norm(V.conj().T.dot(V) - numpy.eye(t)) < tol)
inds2 = numpy.flipud(numpy.argsort(numpy.abs(omega)))
Q = Q[:, inds2[0:k]]
omega = omega[inds2[0:k]]
AAk = Q.dot(numpy.diag(omega)).dot(Q.conj().T)
AAkpYY = AAk + YY
AApYYEst = V.dot(Pi.dot(V.conj().T))
error = numpy.linalg.norm(AApYYEst - (AA+YY))
self.assertTrue(lastError - error >= -tol)
lastError = error
def testEigenConcat(self):
tol = 10**-6
for i in range(3):
m = numpy.random.randint(10, 20)
n = numpy.random.randint(5, 10)
p = numpy.random.randint(5, 10)
# A = numpy.zeros((m, n), numpy.complex)
# B = numpy.zeros((m, p), numpy.complex)
# A.real = numpy.random.randn(m, n)
# A.imag = numpy.random.randn(m, n)
# B.real = numpy.random.randn(m, p)
# B.imag = numpy.random.randn(m, p)
A = numpy.random.randn(m, n)
B = numpy.random.randn(m, p)
#logging.debug("m="+str(m)+" n="+str(n)+" p="+str(p))
AcB = numpy.c_[A, B]
ABBA = AcB.conj().T.dot(AcB)
AA = ABBA[0:n, 0:n]
AB = ABBA[0:n, n:]
BB = ABBA[n:, n:]
lastError = 1000
lastError2 = 1000
for k in range(1, n):
#logging.debug("k="+str(k))
#First compute eigen update estimate
omega, Q = numpy.linalg.eig(AA)
pi, V = EigenUpdater.eigenConcat(omega, Q, AB, BB, k)
ABBAEst = V.dot(numpy.diag(pi)).dot(V.conj().T)
t = min(k, Util.rank(ABBA))
self.assertTrue(pi.shape[0] == t)
self.assertTrue(
numpy.linalg.norm(V.conj().T.dot(V) - numpy.eye(t)) < tol)
#Second compute another eigen update estimate
omega, Q = numpy.linalg.eig(AA)
pi2, V2, D2, D2UD2 = EigenUpdater.lazyEigenConcatAsUpdate(
omega, Q, AB, BB, k, debug=True)
ABBAEst2 = V2.dot(numpy.diag(pi2)).dot(V2.conj().T)
U = ABBA.copy()
U[0:n, 0:n] = 0
self.assertTrue(
numpy.linalg.norm(U -
D2.dot(D2UD2).dot(D2.conj().T)) < tol)
t = min(k, Util.rank(ABBA))
self.assertTrue(
numpy.linalg.norm(V2.conj().T.dot(V2) -
numpy.eye(pi2.shape[0])) < tol)
#Compute estimate using eigendecomposition of full matrix
sfull, Vfull = numpy.linalg.eig(ABBA)
indsfull = numpy.flipud(numpy.argsort(numpy.abs(sfull)))
Vfull = Vfull[:, indsfull[0:k]]
sfull = sfull[indsfull[0:k]]
ABBAEstfull = Vfull.dot(numpy.diag(sfull)).dot(Vfull.conj().T)
#The errors should reduce
error = numpy.linalg.norm(ABBAEst - ABBA)
if Util.rank(ABBA) == k:
self.assertTrue(error <= tol)
lastError = error
error = numpy.linalg.norm(ABBAEst2 - ABBA)
self.assertTrue(error <= lastError2 + tol)
lastError2 = error
def testEigenConcat(self):
tol = 10**-6
for i in range(3):
m = numpy.random.randint(10, 20)
n = numpy.random.randint(5, 10)
p = numpy.random.randint(5, 10)
# A = numpy.zeros((m, n), numpy.complex)
# B = numpy.zeros((m, p), numpy.complex)
# A.real = numpy.random.randn(m, n)
# A.imag = numpy.random.randn(m, n)
# B.real = numpy.random.randn(m, p)
# B.imag = numpy.random.randn(m, p)
A = numpy.random.randn(m, n)
B = numpy.random.randn(m, p)
#logging.debug("m="+str(m)+" n="+str(n)+" p="+str(p))
AcB = numpy.c_[A, B]
ABBA = AcB.conj().T.dot(AcB)
AA = ABBA[0:n, 0:n]
AB = ABBA[0:n, n:]
BB = ABBA[n:, n:]
lastError = 1000
lastError2 = 1000
for k in range(1,n):
#logging.debug("k="+str(k))
#First compute eigen update estimate
omega, Q = numpy.linalg.eig(AA)
pi, V = EigenUpdater.eigenConcat(omega, Q, AB, BB, k)
ABBAEst = V.dot(numpy.diag(pi)).dot(V.conj().T)
t = min(k, Util.rank(ABBA))
self.assertTrue(pi.shape[0] == t)
self.assertTrue(numpy.linalg.norm(V.conj().T.dot(V) - numpy.eye(t)) < tol)
#Second compute another eigen update estimate
omega, Q = numpy.linalg.eig(AA)
pi2, V2, D2, D2UD2 = EigenUpdater.lazyEigenConcatAsUpdate(omega, Q, AB, BB, k, debug=True)
ABBAEst2 = V2.dot(numpy.diag(pi2)).dot(V2.conj().T)
U = ABBA.copy()
U[0:n, 0:n] = 0
self.assertTrue(numpy.linalg.norm(U - D2.dot(D2UD2).dot(D2.conj().T)) < tol )
t = min(k, Util.rank(ABBA))
self.assertTrue(numpy.linalg.norm(V2.conj().T.dot(V2) - numpy.eye(pi2.shape[0])) < tol)
#Compute estimate using eigendecomposition of full matrix
sfull, Vfull = numpy.linalg.eig(ABBA)
indsfull = numpy.flipud(numpy.argsort(numpy.abs(sfull)))
Vfull = Vfull[:, indsfull[0:k]]
sfull = sfull[indsfull[0:k]]
ABBAEstfull = Vfull.dot(numpy.diag(sfull)).dot(Vfull.conj().T)
#The errors should reduce
error = numpy.linalg.norm(ABBAEst - ABBA)
if Util.rank(ABBA)==k:
self.assertTrue(error <= tol)
lastError = error
error = numpy.linalg.norm(ABBAEst2 - ABBA)
self.assertTrue(error <= lastError2+tol)
lastError2 = error