def AND(C, B):
# Local Variables: UB0, varargout, numRankSigma, nout, k, Ux, UC0, Wt, tol, C, B, numRankB, numRankC, UtC, Vx, Wgk, W, Sigma, UtB, dim, Sx, CandB, SC, SB, dSB, dSC, UC, UB
# Function calls: AND, eye, diag, svd, nargout, inv, pinv, max, sum, size
dim = matcompat.size(C, 1.0)
tol = 1e-14
[UC, SC, UtC] = plt.svd(C)
[UB, SB, UtB] = plt.svd(B)
dSC = np.diag(SC)
dSB = np.diag(SB)
numRankC = np.sum(np.dot(1.0, dSC > tol))
numRankB = np.sum(np.dot(1.0, dSB > tol))
UC0 = UC[:, int(numRankC + 1.0) - 1 :]
UB0 = UB[:, int(numRankB + 1.0) - 1 :]
[W, Sigma, Wt] = plt.svd((np.dot(UC0, UC0.conj().T) + np.dot(UB0, UB0.conj().T)))
numRankSigma = np.sum(np.dot(1.0, np.diag(Sigma) > tol))
Wgk = W[:, int(numRankSigma + 1.0) - 1 :]
CandB = np.dot(
np.dot(
Wgk, linalg.inv(np.dot(np.dot(Wgk.conj().T, linalg.pinv(C, tol) + linalg.pinv(B, tol) - np.eye(dim)), Wgk))
),
Wgk.conj().T,
)
nout = matcompat.max(nargout, 1.0) - 1.0
if nout > 0.0:
[Ux, Sx, Vx] = plt.svd(CandB)
for k in np.arange(1.0, (nout) + 1):
if k == 1.0:
varargout[int(k) - 1] = cellarray(np.hstack((Ux)))
elif k == 2.0:
varargout[int(k) - 1] = cellarray(np.hstack((Sx)))
return [CandB, varargout]
def AND(C, B):
# Local Variables: UB0, varargout, numRankSigma, nout, k, Ux, UC0, Wt, tol, C, B, numRankB, numRankC, UtC, Vx, Wgk, W, Sigma, UtB, dim, Sx, CandB, SC, SB, dSB, dSC, UC, UB
# Function calls: AND, eye, diag, svd, nargout, inv, pinv, max, sum, size
dim = matcompat.size(C, 1.)
tol = 1e-14
[UC, SC, UtC] = plt.svd(C)
[UB, SB, UtB] = plt.svd(B)
dSC = np.diag(SC)
dSB = np.diag(SB)
numRankC = np.sum(np.dot(1.0, dSC > tol))
numRankB = np.sum(np.dot(1.0, dSB > tol))
UC0 = UC[:, int(numRankC + 1.) - 1:]
UB0 = UB[:, int(numRankB + 1.) - 1:]
[W, Sigma, Wt] = plt.svd((np.dot(UC0,
UC0.conj().T) + np.dot(UB0,
UB0.conj().T)))
numRankSigma = np.sum(np.dot(1.0, np.diag(Sigma) > tol))
Wgk = W[:, int(numRankSigma + 1.) - 1:]
CandB = np.dot(
np.dot(
Wgk,
linalg.inv(
np.dot(
np.dot(
Wgk.conj().T,
linalg.pinv(C, tol) + linalg.pinv(B, tol) -
np.eye(dim)), Wgk))),
Wgk.conj().T)
nout = matcompat.max(nargout, 1.) - 1.
if nout > 0.:
[Ux, Sx, Vx] = plt.svd(CandB)
for k in np.arange(1., (nout) + 1):
if k == 1.:
varargout[int(k) - 1] = cellarray(np.hstack((Ux)))
elif k == 2.:
varargout[int(k) - 1] = cellarray(np.hstack((Sx)))
return [CandB, varargout]
pPL.cell[0,int(p)-1] = pCollector[0,0:signalPlotLength]
R = matdiv(np.dot(xOldCollector, xOldCollector.conj().T), learnLength+1.)
Cnative = np.dot(R, linalg.inv((R+I)))
nativeCs.cell[0,int(p)-1] = Cnative
startxs[:,int(p)-1] = x
#% compute D increment
Dtargs = np.dot(Win, pCollector)
F = NOT(Call)
Dargs = xOldCollector
Dinc = matdiv(np.dot(np.dot(linalg.pinv((matdiv(np.dot(Dargs, Dargs.conj().T), learnLength)+np.dot(matixpower(aperture, -2.), I))), Dargs), Dtargs.conj().T), learnLength).conj().T
#% update D and Call
D = D+Dinc
Cap = PHI(Cnative, aperture)
Call = OR(Call, Cap)
Calls.cell[0,int(p)-1] = Call
[Ux, Sx, Vx] = plt.svd(Call)
sizesCall[0,int(p)-1] = np.mean(np.diag(Sx))
[Ux, Sx, Vx] = plt.svd(Cap)
sizesCap[0,int(p)-1] = np.mean(np.diag(Sx))
elif learnType == 2.:
#% extension exploiting redundancies
patternCollectors = cell(1., Np)
pPL = cell(1., Np)
sizesCall = np.zeros(1., Np)
sizesCap = np.zeros(1., Np)
Calls = cell(1., Np)
startxs = np.zeros(Netsize, Np)
Call = np.zeros(Netsize, Netsize)
D = np.zeros(Netsize, Netsize)
nativeCs = cell(1., Np)
for n in np.arange(1., (washoutLength + learnLength) + 1):
u = patt[int(n) - 1]
#% pattern input
xOld = x
x = np.tanh((np.dot(Wstar, x) + np.dot(Win, u) + Wbias))
if n > washoutLength:
xCollector[:, int((n - washoutLength)) - 1] = x
xOldCollector[:, int((n - washoutLength)) - 1] = xOld
pCollector[0, int((n - washoutLength)) - 1] = u
xCollectorCentered = xCollector - matcompat.repmat(np.mean(xCollector, 2.),
1., learnLength)
xCollectorsCentered.cell[0, int(p) - 1] = xCollectorCentered
xCollectors.cell[0, int(p) - 1] = xCollector
R = matdiv(np.dot(xCollector, xCollector.conj().T), learnLength)
[Ux, Sx, Vx] = plt.svd(R)
SRCollectors.cell[0, int(p) - 1] = Sx
URCollectors.cell[0, int(p) - 1] = Ux
patternRs.cell[int(p) - 1] = R
startXs[:, int(p) - 1] = x
train_xPL.cell[0, int(p) - 1] = xCollector[0:5., 0:signalPlotLength]
train_pPL.cell[0, int(p) - 1] = pCollector[0, 0:signalPlotLength]
patternCollectors.cell[0, int(p) - 1] = pCollector
allTrainArgs[:,
int(np.dot(p - 1., learnLength) + 1.) -
1:np.dot(p, learnLength)] = xCollector
allTrainOldArgs[:,
int(np.dot(p - 1., learnLength) + 1.) -
1:np.dot(p, learnLength)] = xOldCollector
allTrainOuts[0,
int(np.dot(p - 1., learnLength) + 1.) -
u = patt[int(n)-1]
#% pattern input
xOld = x
x = np.tanh((np.dot(Wstar, x)+np.dot(Win, u)+Wbias))
if n > washoutLength:
xCollector[:,int((n-washoutLength))-1] = x
xOldCollector[:,int((n-washoutLength))-1] = xOld
pCollector[0,int((n-washoutLength))-1] = u
xCollectorCentered = xCollector-matcompat.repmat(np.mean(xCollector, 2.), 1., learnLength)
xCollectorsCentered.cell[0,int(p)-1] = xCollectorCentered
xCollectors.cell[0,int(p)-1] = xCollector
R = matdiv(np.dot(xCollector, xCollector.conj().T), learnLength)
[Ux, Sx, Vx] = plt.svd(R)
SRCollectors.cell[0,int(p)-1] = Sx
URCollectors.cell[0,int(p)-1] = Ux
patternRs.cell[int(p)-1] = R
startXs[:,int(p)-1] = x
train_xPL.cell[0,int(p)-1] = xCollector[:,0:signalPlotLength]
train_pPL.cell[0,int(p)-1] = pCollector[0,0:signalPlotLength]
patternCollectors.cell[0,int(p)-1] = pCollector
allTrainArgs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = xCollector
allTrainOldArgs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = xOldCollector
allTrainOuts[0,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = pCollector
allTrainTargs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = np.dot(Win, pCollector)
#%%% compute readout
Wout = np.dot(np.dot(linalg.inv((np.dot(allTrainArgs, allTrainArgs.conj().T)+np.dot(TychonovAlphaReadout, np.eye(Netsize)))), allTrainArgs), allTrainOuts.conj().T).conj().T
#% training error
u = patt[int(n)-1]
#% pattern input
xOld = x
x = np.tanh((np.dot(Wstar, x)+np.dot(Win, u)+Wbias))
if n > washoutLength:
xCollector[:,int((n-washoutLength))-1] = x
xOldCollector[:,int((n-washoutLength))-1] = xOld
pCollector[0,int((n-washoutLength))-1] = u
xCollectorCentered = xCollector-matcompat.repmat(np.mean(xCollector, 2.), 1., learnLength)
xCollectorsCentered.cell[0,int(p)-1] = xCollectorCentered
xCollectors.cell[0,int(p)-1] = xCollector
R = matdiv(np.dot(xCollector, xCollector.conj().T), learnLength)
[Ux, Sx, Vx] = plt.svd(R)
SRCollectors.cell[0,int(p)-1] = Sx
URCollectors.cell[0,int(p)-1] = Ux
patternRs.cell[int(p)-1] = R
startXs[:,int(p)-1] = x
train_xPL.cell[0,int(p)-1] = xCollector[:,0:signalPlotLength]
train_pPL.cell[0,int(p)-1] = pCollector[0,0:signalPlotLength]
patternCollectors.cell[0,int(p)-1] = pCollector
allTrainArgs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = xCollector
allTrainOldArgs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = xOldCollector
allTrainOuts[0,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = pCollector
allTrainTargs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = np.dot(Win, pCollector)
#%%% compute readout
Wout = np.dot(np.dot(linalg.inv((np.dot(allTrainArgs, allTrainArgs.conj().T)+np.dot(TychonovAlphaReadout, np.eye(Netsize)))), allTrainArgs), allTrainOuts.conj().T).conj().T
#% training error
for n in np.arange(1., (washoutLength + learnLength) + 1):
u = patt[int(n) - 1]
#% pattern input
xOld = x
x = np.tanh((np.dot(Wstar, x) + np.dot(Win, u) + Wbias))
if n > washoutLength:
xCollector[:, int((n - washoutLength)) - 1] = x
xOldCollector[:, int((n - washoutLength)) - 1] = xOld
pCollector[0, int((n - washoutLength)) - 1] = u
xCollectorCentered = xCollector - matcompat.repmat(np.mean(xCollector, 2.),
1., learnLength)
xCollectorsCentered.cell[0, int(p) - 1] = xCollectorCentered
xCollectors.cell[0, int(p) - 1] = xCollector
R = matdiv(np.dot(xCollector, xCollector.conj().T), learnLength)
[Ux, Sx, Vx] = plt.svd(R)
SRCollectors.cell[0, int(p) - 1] = Sx
URCollectors.cell[0, int(p) - 1] = Ux
patternRs.cell[int(p) - 1] = R
startXs[:, int(p) - 1] = x
train_xPL.cell[0, int(p) - 1] = xCollector[0:5., 0:signalPlotLength]
train_pPL.cell[0, int(p) - 1] = pCollector[0, 0:signalPlotLength]
patternCollectors.cell[0, int(p) - 1] = pCollector
allTrainArgs[:,
int(np.dot(p - 1., learnLength) + 1.) -
1:np.dot(p, learnLength)] = xCollector
allTrainOldArgs[:,
int(np.dot(p - 1., learnLength) + 1.) -
1:np.dot(p, learnLength)] = xOldCollector
allTrainOuts[0,
int(np.dot(p - 1., learnLength) + 1.) -
xOldCollector[:,int((n-washoutLength))-1] = xOld
if p == 2. or p == 3.:
#% the Lorenz and MG observers are rescaled to [0 1]
#% the other two are already in that range
pCollector[0,int((n-washoutLength))-1] = np.dot(0.5, u[0]+1.)
else:
pCollector[0,int((n-washoutLength))-1] = u[0]
xCollectorCentered = xCollector-matcompat.repmat(np.mean(xCollector, 2.), 1., learnLength)
xCollectorsCentered.cell[0,int(p)-1] = xCollectorCentered
xCollectors.cell[0,int(p)-1] = xCollector
[Ux, Sx, Vx] = plt.svd(matdiv(np.dot(xCollector, xCollector.conj().T), learnLength))
startXs[:,int(p)-1] = x
diagSx = np.diag(Sx)
#%diagSx(diagSx < 1e-6,1) = zeros(sum(diagSx < 1e-6),1);
R = np.dot(np.dot(Ux, np.diag(diagSx)), Ux.conj().T)
patternRs.cell[int(p)-1] = R
patternCollectors.cell[0,int(p)-1] = pCollector
allTrainArgs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = xCollector
allTrainOldArgs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = xOldCollector
allTrainOuts[0,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = pCollector
#%%% compute readout
Wout = np.dot(np.dot(linalg.inv((np.dot(allTrainArgs, allTrainArgs.conj().T)+np.dot(TychonovAlphaReadout, np.eye(Netsize)))), allTrainArgs), allTrainOuts.conj().T).conj().T
#% training error
NRMSE_readout = nrmse(np.dot(Wout, allTrainArgs), allTrainOuts)
np.disp(sprintf('NRMSE readout: %g', NRMSE_readout))
u = patt[int(n)-1]
#% pattern input
xOld = x
x = np.tanh((np.dot(Wstar, x)+np.dot(Win, u)+Wbias))
if n > washoutLength:
xCollector[:,int((n-washoutLength))-1] = x
xOldCollector[:,int((n-washoutLength))-1] = xOld
pCollector[0,int((n-washoutLength))-1] = u
xCollectorCentered = xCollector-matcompat.repmat(np.mean(xCollector, 2.), 1., learnLength)
xCollectorsCentered.cell[0,int(p)-1] = xCollectorCentered
xCollectors.cell[0,int(p)-1] = xCollector
R = matdiv(np.dot(xCollector, xCollector.conj().T), learnLength)
[Ux, Sx, Vx] = plt.svd(R)
SRCollectors.cell[0,int(p)-1] = Sx
URCollectors.cell[0,int(p)-1] = Ux
patternRs.cell[int(p)-1] = R
startXs[:,int(p)-1] = x
train_xPL.cell[0,int(p)-1] = xCollector[0:5.,0:signalPlotLength]
train_pPL.cell[0,int(p)-1] = pCollector[0,0:signalPlotLength]
patternCollectors.cell[0,int(p)-1] = pCollector
allTrainArgs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = xCollector
allTrainOldArgs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = xOldCollector
allTrainOuts[0,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = pCollector
allTrainTargs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = np.dot(Win, pCollector)
#%%% compute readout
Wout = np.dot(np.dot(linalg.inv((np.dot(allTrainArgs, allTrainArgs.conj().T)+np.dot(TychonovAlphaReadout, np.eye(Netsize)))), allTrainArgs), allTrainOuts.conj().T).conj().T
#% training error
u = patt[int(n)-1]
#% pattern input
xOld = x
x = np.tanh((np.dot(Wstar, x)+np.dot(Win, u)+Wbias))
if n > washoutLength:
xCollector[:,int((n-washoutLength))-1] = x
xOldCollector[:,int((n-washoutLength))-1] = xOld
pCollector[0,int((n-washoutLength))-1] = u
xCollectorCentered = xCollector-matcompat.repmat(np.mean(xCollector, 2.), 1., learnLength)
xCollectorsCentered.cell[0,int(p)-1] = xCollectorCentered
xCollectors.cell[0,int(p)-1] = xCollector
R = matdiv(np.dot(xCollector, xCollector.conj().T), learnLength)
[Ux, Sx, Vx] = plt.svd(R)
SRCollectors.cell[0,int(p)-1] = Sx
URCollectors.cell[0,int(p)-1] = Ux
patternRs.cell[int(p)-1] = R
startXs[:,int(p)-1] = x
train_xPL.cell[0,int(p)-1] = xCollector[0:5.,0:signalPlotLength]
train_pPL.cell[0,int(p)-1] = pCollector[0,0:signalPlotLength]
patternCollectors.cell[0,int(p)-1] = pCollector
allTrainArgs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = xCollector
allTrainOldArgs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = xOldCollector
allTrainOuts[0,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = pCollector
allTrainTargs[:,int(np.dot(p-1., learnLength)+1.)-1:np.dot(p, learnLength)] = np.dot(Win, pCollector)
#%%% compute readout
Wout = np.dot(np.dot(linalg.inv((np.dot(allTrainArgs, allTrainArgs.conj().T)+np.dot(TychonovAlphaReadout, np.eye(Netsize)))), allTrainArgs), allTrainOuts.conj().T).conj().T
#% training error