def suboptimalSysID(self, Y):
"""System identification using KPCA.
Updates the NLDS parameters.
Parameters:
-----------
Y : numpy array, shape = (N, D)
Input data.
"""
nStates = self._nStates
# call KPCA to get state estimate
if self._verbose:
with Timer('kpca'):
Xhat = kpca(Y, nStates, self._kpcaParams)
else:
Xhat = kpca(Y, nStates, self._kpcaParams)
# estimate rest of parameters
_, tau = Y.shape
Ahat = Xhat[:,1:tau]*np.linalg.pinv(Xhat[:,0:tau-1])
Vhat = Xhat[:,1:tau]-Ahat*Xhat[:,0:tau-1]
Qhat = (Vhat*Vhat.T)/(tau-1)
initX0 = Xhat[:,0]
initM0 = np.mean(Xhat, axis=1)
initS0 = np.diag(np.cov(Xhat))
self._Rhat = 0
self._Ahat = Ahat
self._Xhat = Xhat
self._Vhat = Vhat
self._Qhat = Qhat
self._initX0 = initX0
self._initM0 = initM0
self._initS0 = initS0
def suboptimalSysID(self, Y):
"""System identification using KPCA.
Updates the NLDS parameters.
Parameters:
-----------
Y : numpy array, shape = (N, D)
Input data.
"""
nStates = self._nStates
# call KPCA to get state estimate
if self._verbose:
with Timer('kpca'):
Xhat = kpca(Y, nStates, self._kpcaParams)
else:
Xhat = kpca(Y, nStates, self._kpcaParams)
# estimate rest of parameters
_, tau = Y.shape
Ahat = Xhat[:, 1:tau] * np.linalg.pinv(Xhat[:, 0:tau - 1])
Vhat = Xhat[:, 1:tau] - Ahat * Xhat[:, 0:tau - 1]
Qhat = (Vhat * Vhat.T) / (tau - 1)
initX0 = Xhat[:, 0]
initM0 = np.mean(Xhat, axis=1)
initS0 = np.diag(np.cov(Xhat))
self._Rhat = 0
self._Ahat = Ahat
self._Xhat = Xhat
self._Vhat = Vhat
self._Qhat = Qhat
self._initX0 = initX0
self._initM0 = initM0
self._initS0 = initS0
def test_kpca():
dataFile = os.path.join(TESTBASE, "data/data1.txt")
data, _ = loadDataFromASCIIFile(dataFile)
kpcaP = KPCAParam()
kpcaP._kPar = RBFParam()
kpcaP._kPar._kCen = True
kpcaP._kFun = rbfK
X = kpca(data, 5, kpcaP)
baseKPCACoeffFile = os.path.join(TESTBASE, "data/data1-rbf-kpca-5c-center.txt")
baseKPCACoeff = np.genfromtxt(baseKPCACoeffFile, dtype=np.double)
# don't care about the sign
err = np.linalg.norm(np.abs(baseKPCACoeff) - np.abs(X), "fro")
np.testing.assert_almost_equal(err, 0, 2)
def test_kpca():
dataFile = os.path.join(TESTBASE, "data/data1.txt")
data, _ = loadDataFromASCIIFile(dataFile)
kpcaP = KPCAParam()
kpcaP._kPar = RBFParam()
kpcaP._kPar._kCen = True
kpcaP._kFun = rbfK
X = kpca(data, 5, kpcaP)
baseKPCACoeffFile = os.path.join(TESTBASE,
"data/data1-rbf-kpca-5c-center.txt")
baseKPCACoeff = np.genfromtxt(baseKPCACoeffFile, dtype=np.double)
# don't care about the sign
err = np.linalg.norm(np.abs(baseKPCACoeff) - np.abs(X), 'fro')
np.testing.assert_almost_equal(err, 0, 2)