def matrix_multiply(a, b):
"""Takes two matrices and does a complicated matrix multiply. Yes that one.
NOTE: THIS APPEARS TO BE VERY BROKEN
"""
if len(a.shape) == 1:
nrows, = a.shape
a = np.zeros((nrows, 1))
if len(b.shape) == 1:
bc, = b.shape
if bc == a.shape[1]:
b = np.zeros((bc, 1))
else:
b = np.zeros((1, bc))
nrows,ac = a.shape
bc,ncols = b.shape
assert ac == bc
if ispypy():
n = np.zeros((nrows, ncols))
for i in xrange(nrows):
for j in xrange(ncols):
n[i,j] = np.sum(a[i] * b[:,j])
return n
else:
np.dot(a, b)
def partial_slda_recalculate_eta_sigma(eta, y, phi):
"""
Same as slda_recalculate_eta_sigma, but also
supports partial updates if len(eta) < phi.shape[1] .
Will only update based on first Ks topics of phi
"""
D = len(phi)
ensure(D >= 1)
N,K = phi[0].shape
Ks = len(eta)
print 'e_a...'
E_A = np.empty((D, Ks))
for d in xrange(D):
E_A[d,:] = calculate_EZ(phi[d][:,:Ks])
E_ATA_inverse = calculate_E_ATA_inverse([p[:,:Ks] for p in phi])
print 'new eta...'
new_eta = np.dot(np.dot(E_ATA_inverse, E_A.T), y)
eta[:] = new_eta
print 'new sigma squared...'
new_sigma_squared = (1.0 / D) * (np.dot(y, y) - np.dot(np.dot(y, E_A), eta))
return new_sigma_squared
def test_dot(self):
from numpypy import array, dot
a = array(range(5))
assert a.dot(a) == 30.0
a = array(range(5))
assert a.dot(range(5)) == 30
assert dot(range(5), range(5)) == 30
assert (dot(5, [1, 2, 3]) == [5, 10, 15]).all()
def test_dot(self):
from numpypy import array, dot, arange
a = array(range(5))
assert dot(a, a) == 30.0
a = array(range(5))
assert a.dot(range(5)) == 30
assert dot(range(5), range(5)) == 30
assert (dot(5, [1, 2, 3]) == [5, 10, 15]).all()
a = arange(12).reshape(3, 4)
b = arange(12).reshape(4, 3)
c = a.dot(b)
assert (c == [[ 42, 48, 54], [114, 136, 158], [186, 224, 262]]).all()
a = arange(24).reshape(2, 3, 4)
raises(ValueError, "a.dot(a)")
b = a[0, :, :].T
#Superfluous shape test makes the intention of the test clearer
assert a.shape == (2, 3, 4)
assert b.shape == (4, 3)
c = dot(a, b)
assert (c == [[[14, 38, 62], [38, 126, 214], [62, 214, 366]],
[[86, 302, 518], [110, 390, 670], [134, 478, 822]]]).all()
c = dot(a, b[:, 2])
assert (c == [[62, 214, 366], [518, 670, 822]]).all()
a = arange(3*2*6).reshape((3,2,6))
b = arange(3*2*6)[::-1].reshape((2,6,3))
assert dot(a, b)[2,0,1,2] == 1140
assert (dot([[1,2],[3,4]],[5,6]) == [17, 39]).all()
def lm_recalculate_eta_sigma(eta, y, phi1, phi2):
"""
Accepts eta (K+J)-size vector,
also y (a D-size vector of reals),
also two phi D-size vectors of NxK matrices.
Returns new sigma squared update (a double).
ηnew ← (E[ATA])-1 E[A]Ty
σ2new ← (1/D) {yTy - yTE[A]ηnew}
(Note that A is the D X (K + J) matrix whose rows are the vectors ZdT for document and comment concatenated.)
(Also note that the dth row of E[A] is φd, and E[ATA] = Σd E[ZdZdT] .)
(Also, note that E[Z] = φ := (1/N)Σnφn, and E[ZdZdT] = (1/N2)(ΣnΣm!=nφd,nφd,mT + Σndiag{φd,n})
"""
ensure(len(phi1) == len(phi2))
D = len(phi1)
Nd,K = phi1[0].shape
Nc,J = phi2[0].shape
Ndc, KJ = (Nd+Nc,K+J)
#print 'e_a...'
E_A = np.zeros((D, KJ))
for d in xrange(D):
E_A[d,:] = calculate_EZ_from_small_phis(phi1[d], phi2[d])
#print 'inverse...'
E_ATA_inverse = calculate_E_ATA_inverse_from_small_phis(phi1, phi2)
#print 'new eta...'
#new_eta = matrix_multiply(matrix_multiply(E_ATA_inverse, E_A.T), y)
new_eta = np.dot(np.dot(E_ATA_inverse, E_A.T), y)
if np.sum(np.abs(new_eta)) > (KJ * KJ * 5):
print 'ETA is GOING CRAZY {0}'.format(eta)
print 'aborting the update!!!'
else:
eta[:] = new_eta
# todo: don't do this later
# keep sigma squared fix
#import pdb; pdb.set_trace()
#new_sigma_squared = (1.0 / D) * (np.dot(y, y) - np.dot(np.dot(np.dot(np.dot(y, E_A), E_ATA_inverse), E_A.T), y))
new_sigma_squared = 1.0
return new_sigma_squared
def partial_slda_update_phi(text, phi, gamma, beta, y_d, eta, sigma_squared):
"""Same as slda update phi, but eta may be smaller than total number of topics.
So only some of the topics contribute to y.
"""
(N, K) = phi.shape
Ks = len(eta)
phi_sum = np.sum(phi[:,:Ks], axis=0)
Ns = (N * sigma_squared)
ElogTheta = graphlib.dirichlet_expectation(gamma)
front = (-1.0 / (2 * N * Ns))
eta_dot_eta = front * (eta * eta)
pC = ((1.0 * y_d / Ns) * eta) + eta_dot_eta
right_eta_times_const = (front * 2 * eta)
if isinstance(text, np.ndarray):
# if text is in array form, do an approximate fast matrix update
phi_minus_n = -(phi[:,:Ks] - phi_sum)
phi[:,:] = ElogTheta + np.log(beta[:,text].T)
phi[:,:Ks] += pC
phi[:,:Ks] += np.dot(np.matrix(np.dot(phi_minus_n, eta)).T, np.matrix(right_eta_times_const))
graphlib.log_row_normalize(phi)
phi[:,:] = np.exp(phi[:,:])
else:
# otherwise, iterate through each word
for n,word,count in iterwords(text):
phi_sum -= phi[n,:Ks]
pB = np.log(beta[:,word])
pD = (np.dot(eta, phi_sum) * right_eta_times_const)
# must exponentiate and normalize immediately!
phi[n,:] = ElogTheta + pB
phi[n,:] += pC + pD
phi[n,:] -= graphlib.logsumexp(phi[n,:]) # normalize in logspace
phi[n,:] = np.exp(phi[n,:])
# add this back into the sum
# unlike in LDA, this cannot be computed in parallel
phi_sum += phi[n,:Ks]
return phi
def calculate_EZZT_from_small_phis(phi1, phi2):
"""
Accepts a big phi matrix (like ((Nd+Nc) x (K+J))
Calculates E[ZdZdT].
Returns the final matrix ((K+J) x (K+J)).
(Also, E[ZdZdT] = (1/N2)(ΣNΣm!=nφd,nφd,mT + ΣNdiag{φd,n})
"""
Nd,K = phi1.shape
Nc,J = phi2.shape
(Ndc, KJ) = (Nd+Nc, K+J)
inner_sum = np.zeros((KJ, KJ))
p1 = np.matrix(phi1)
p2 = np.matrix(phi2)
for i in xrange(K):
for j in xrange(K):
m = np.dot(np.matrix(p1[:,i]), np.matrix(p1[:,j]).T)
inner_sum[i,j] = np.sum(m) - np.sum(np.diagonal(m))
for i in xrange(J):
for j in xrange(J):
m = np.dot(np.matrix(p2[:,i]), np.matrix(p2[:,j]).T)
inner_sum[K+i,K+j] = np.sum(m) - np.sum(np.diagonal(m))
for i in xrange(K):
for j in xrange(J):
m = np.dot(np.matrix(p1[:,i]), np.matrix(p2[:,j]).T)
inner_sum[i,K+j] = np.sum(m)
for i in xrange(J):
for j in xrange(K):
m = np.dot(np.matrix(p2[:,i]), np.matrix(p1[:,j]).T)
inner_sum[K+i,j] = np.sum(m)
big_phi_sum = np.concatenate((np.sum(phi1, axis=0),
np.sum(phi2, axis=0)), axis=1)
ensure(big_phi_sum.shape == (KJ,))
inner_sum += np.diagonal(big_phi_sum)
inner_sum /= (Ndc * Ndc)
return inner_sum
def test_dot_constant(self):
from numpypy import array, dot
a = array(range(5))
b = a.dot(2.5)
for i in xrange(5):
assert b[i] == 2.5 * a[i]
c = dot(4, 3.0)
assert c == 12.0
c = array(3.0).dot(array(4))
assert c == 12.0
def lm_elbo_y_from_small_phis(y, eta, phiD, phiC, sigma_squared):
"""
Calculates some terms in the elbo for a document.
Same as in sLDA.
E[log p(y|Z1:N,η,σ2)] = (–1/2)log 2πσ2 – (1/2σ2)[y2– 2yηTE[Z] + ηTE[ZZT]η]
Test:
Should be the same as slda_elbo_y when phiD and phiC are catercorner concatenated.
"""
elbo = 0.0
ss = sigma_squared
elbo += (-0.5) * np.log(2 * np.pi * ss)
ez = calculate_EZ_from_small_phis(phiD, phiC)
ezzt = calculate_EZZT_from_small_phis(phiD, phiC)
nEZZTn = np.dot(np.dot(eta, ezzt), eta)
elbo += (-0.5 / ss) * (y*y - (2 * y * np.dot(eta, ez)) + nEZZTn)
return elbo
def slda_elbo_y(y, eta, phi, sigma_squared):
"""
Calculates some terms in the elbo for a document.
Same as in sLDA.
E[log p(y|Z1:N,η,σ2)] = (–1/2)log 2πσ2 – (1/2σ2)[y2– 2yηTE[Z] + ηTE[ZZT]η]
"""
elbo = 0.0
ss = sigma_squared
elbo += (-0.5) * np.log(2 * np.pi * ss)
#print 'will calculate ez...'
ez = calculate_EZ(phi)
#print 'will calculate ezzt...'
ezzt = calculate_EZZT(phi)
#print 'will calculate nEZZTn...'
nEZZTn = np.dot(np.dot(eta, ezzt), eta)
#print 'will sum up elbo...'
elbo += (-0.5 / ss) * (y*y - (2 * y * np.dot(eta, ez)) + nEZZTn)
return elbo
def update(self, input_values, trace=False ):
# This is a forward operation in the network. This is how we
# calculate the network output from a set of input signals.
output = input_values
if trace: tracelist = [ output ]
for i, weight_layer in enumerate(self.weights):
# Loop over the network layers and calculate the output
if i == 0:
output = np.dot( output, weight_layer[1:,:] ) + weight_layer[0:1,:] # implicit bias
else:
output = np.dot( output, weight_layer[1:,:] ) + weight_layer[0:1,:] # implicit bias
output = self.activation_functions[i]( output )
if trace: tracelist.append( output )
if trace: return tracelist
return output
def test_dot_out(self):
from numpypy import arange, dot
a = arange(12).reshape(3, 4)
b = arange(12).reshape(4, 3)
out = arange(9).reshape(3, 3)
c = dot(a, b, out=out)
assert (c == out).all()
assert (c == [[42, 48, 54], [114, 136, 158], [186, 224, 262]]).all()
out = arange(9, dtype=float).reshape(3, 3)
exc = raises(ValueError, dot, a, b, out)
assert exc.value[0] == ('output array is not acceptable (must have the '
'right type, nr dimensions, and be a C-Array)')
def _unoptimized_slda_update_phi(text, phi, gamma, beta, y_d, eta, sigma_squared):
"""
Update phi in LDA.
phi is N x K matrix.
gamma is a K-size vector
update phid:
φd,n ∝ exp{ E[log θ|γ] +
E[log p(wn|β1:K)] +
(y / Nσ2) η —
[2(ηTφd,-n)η + (η∘η)] / (2N2σ2) }
Note that E[log p(wn|β1:K)] = log βTwn
"""
(N, K) = phi.shape
#assert len(eta) == K
#assert len(gamma) == K
#assert beta.shape[0] == K
phi_sum = np.sum(phi, axis=0)
Ns = (N * sigma_squared)
ElogTheta = graphlib.dirichlet_expectation(gamma)
ensure(len(ElogTheta) == K)
pC = (1.0 * y_d / Ns * eta)
eta_dot_eta = (eta * eta)
front = (-1.0 / (2 * N * Ns))
for n,word,count in iterwords(text):
phi_sum -= phi[n]
ensure(len(phi_sum) == K)
pB = np.log(beta[:,word])
pD = (front * (((2 * np.dot(eta, phi_sum) * eta) + eta_dot_eta))
)
ensure(len(pB) == K)
ensure(len(pC) == K)
ensure(len(pD) == K)
# must exponentiate and sum immediately!
#phi[n,:] = np.exp(ElogTheta + pB + pC + pD)
#phi[n,:] /= np.sum(phi[n,:])
# log normalize before exp for numerical stability
phi[n,:] = ElogTheta + pB + pC + pD
phi[n,:] -= graphlib.logsumexp(phi[n,:])
phi[n,:] = np.exp(phi[n,:])
# add this back into the sum
# unlike in LDA, this cannot be computed in parallel
phi_sum += phi[n]
return phi
def update(self, input_values, trace=False):
# This is a forward operation in the network. This is how we
# calculate the network output from a set of input signals.
output = input_values
if trace: tracelist = [output]
for i, weight_layer in enumerate(self.weights):
# Loop over the network layers and calculate the output
if i == 0:
output = np.dot(output, weight_layer[1:, :]) + weight_layer[
0:1, :] # implicit bias
else:
output = np.dot(output, weight_layer[1:, :]) + weight_layer[
0:1, :] # implicit bias
output = self.activation_functions[i](output)
if trace: tracelist.append(output)
if trace: return tracelist
return output
def lm_E_step_for_doc(global_iteration,
d, document, comment,
alphaD, alphaC,
betaD, betaC,
gammaD, gammaC,
phiD, phiC,
y, eta, sigma_squared):
"""Given phi and gamma matrices and document of the document.
Recalculate phi and gamma repeatedly iteratively.
Uses local elbo calculation to check for convergence.
"""
print "starting E step on doc {0}".format(d)
graphlib.initialize_random(phiD)
graphlib.initialize_random(phiC)
i = 0
last_local_elbo, local_elbo = graphlib.INITIAL_ELBO - 100, graphlib.INITIAL_ELBO
while graphlib.elbo_did_not_converge(local_elbo, last_local_elbo, i,
criterion=0.1, max_iter=20):
print 'will update gamma...'
# update gammas
lda_update_gamma(alphaD, phiD, gammaD)
lda_update_gamma(alphaC, phiC, gammaC)
Nd,Kd = phiD.shape
print 'will update phis...'
# update phis (note we have to pass the right part of eta!)
slda_update_phi(document, phiD, gammaD, betaD, y[d], eta[:Kd], sigma_squared)
slda_update_phi(comment, phiC, gammaC, betaC, y[d], eta[Kd:], sigma_squared)
print 'will calculate y...'
# update the response variable
# y = ηTE[Z] = ηTφ [ where φ = 1/N * Σnφn ]
y[d] = np.dot(eta, calculate_EZ_from_small_phis(phiD, phiC))
if i % 2 == 0:
print 'will calculate elbo...'
# calculate new ELBO
last_local_elbo = local_elbo
local_elbo = lm_local_elbo(document, comment, alphaD, alphaC, betaD, betaC, gammaD, gammaC, phiD, phiC, y[d], eta, sigma_squared)
i += 1
#print {'beta': (betaD, betaC), 'gamma': (gammaD, gammaC), 'phi': (phiD, phiC), 'y': y, 'eta': eta}
print "{2}: e-step iteration {0} ELBO: {1}".format(i, local_elbo, global_iteration)
print "{2}: done e-step on doc {3}: {0} iterations ELBO: {1}".format(i, local_elbo, global_iteration, d)
return i
def calculate_EZZT(big_phi):
"""
Accepts a big phi matrix (like (N x K)
Calculates E[ZdZdT].
Returns the final matrix (K x K).
(Also, E[ZdZdT] = (1/N2)(ΣNΣm!=nφd,nφd,mT + ΣNdiag{φd,n})
"""
(N, K) = big_phi.shape
inner_sum = np.empty((K, K))
for i in xrange(K):
for j in xrange(K):
inner_sum[i,j] = np.sum(np.multiply.outer(big_phi[:,i], big_phi[:,j])) - np.sum(np.dot(big_phi[:,i], big_phi[:,j]))
inner_sum += np.diag(np.sum(big_phi, axis=0))
inner_sum /= (N * N)
return inner_sum
def __run(score_task_knapsack, m_tasks, tasks, mac): n = len(tasks) Tu = [] Td = range(0, n) Pu = numpy.zeros(2, float) Z = 0 X = numpy.zeros(n, int) Tc = [] B = numpy.ones(2, float) P = numpy.zeros((n, 2), float) G = numpy.zeros(n, float) U = numpy.zeros(n, float) for x in range(0, n): P[x][0] = m_tasks[tasks[x]].CPU_usage / mac.free_CPU() P[x][1] = m_tasks[tasks[x]].mem_usage / mac.free_mem() keep_going = True cnt = math.sqrt(2) #w_cpu = 0.6 #w_mem = 1 - w_cpu #print "MAC = %d, ntasks = %d" % (mac.machine_ID, n) while keep_going : # step 2 del Tc Tc = [] for i in Td: if P[i][0] <= (1. - Pu[0]) and P[i][1] <= (1. - Pu[1]): Tc.append(i) #print "2" # step 3 # terminate if Tc = empty if len(Tc) == 0: keep_going = False else: # step 4 # (a) if (numpy.dot(Pu, Pu) == 0.): for i in Tc: d = sum(P[i]) G[i] = (score_task_knapsack(m_tasks[tasks[i]], mac) * cnt)/d # (b) else: mod_Pu = math.sqrt(numpy.dot(Pu, Pu)) E = numpy.array(Pu * (1./mod_Pu)) for i in Tc: d = numpy.dot(P[i], E) G[i] = score_task_knapsack(m_tasks[tasks[i]], mac) / d #print "4" # step 5 v_max = -1 i_max = 0 for i in Tc: if G[i] > v_max: v_max = G[i] i_max = i #print "5" # step 6 Tu.append(i_max) Td.remove(i_max) Pu = Pu + P[i_max] Z = Z + m_tasks[tasks[i_max]].CPU_usage #print "(%f, %f)" % (mac.capacity_CPU, mac.capacity_memory) #print Pu return Tu
def backpropagation(self, trainingset, ERROR_LIMIT = 1e-3, learning_rate = 0.3, momentum_factor = 0.9 ):
assert trainingset[0].features.shape[0] == self.n_inputs, \
"ERROR: input size varies from the defined input setting"
assert trainingset[0].targets.shape[0] == self.n_outputs, \
"ERROR: output size varies from the defined output setting"
training_data = np.array( [instance.features for instance in trainingset ] )
training_targets = np.array( [instance.targets for instance in trainingset ] )
MSE = ( ) # inf
neterror = None
momentum = collections.defaultdict( int )
batch_size = self.batch_size if self.batch_size != 0 else training_data.shape[0]
epoch = 0
while MSE > ERROR_LIMIT:
epoch += 1
for start in xrange( 0, len(training_data), batch_size ):
batch = training_data[start : start+batch_size]
input_layers = self.update( training_data, trace=True )
out = input_layers[-1]
error = out - training_targets
delta = error
MSE = np.mean( np.power(error,2) )
loop = itertools.izip(
xrange(len(self.weights)-1, -1, -1),
reversed(self.weights),
reversed(input_layers[:-1]),
)
for i, weight_layer, input_signals in loop:
# Loop over the weight layers in reversed order to calculate the deltas
if i == 0:
dropped = dropout( add_bias(input_signals).T, self.input_layer_dropout )
else:
dropped = dropout( add_bias(input_signals).T, self.hidden_layer_dropout )
# Calculate weight change
dW = learning_rate * np.dot( dropped, delta ) + momentum_factor * momentum[i]
if i!= 0:
"""Do not calculate the delta unnecessarily."""
# Skipping the bias weight during calculation.
weight_delta = np.dot( delta, weight_layer[1:,:].T )
# Calculate the delta for the subsequent layer
delta = np.multiply( weight_delta, self.activation_functions[i-1]( input_signals, derivative=True) )
# Store the momentum
momentum[i] = dW
# Update the weights
self.weights[ i ] -= dW
if epoch%1000==0:
# Show the current training status
print "* current network error (MSE):", MSE
print "* Converged to error bound (%.4g) with MSE = %.4g." % ( ERROR_LIMIT, MSE )
print "* Trained for %d epochs." % epoch
expectedValueFunction = np.zeros((nGridCapital,nGridProductivity),dtype=float)
# 4. We pre-build output for each point in the grid
for nProductivity in range(nGridProductivity):
mOutput[:,nProductivity] = vProductivity[nProductivity]*(vGridCapital**aalpha)
## 5. Main iteration
maxDifference = 10.0
tolerance = 0.0000001
iteration = 0
while(maxDifference > tolerance):
expectedValueFunction = np.dot(mValueFunction,mTransition.T)
for nProductivity in range(nGridProductivity):
# We start from previous choice (monotonicity of policy function)
gridCapitalNextPeriod = 0
for nCapital in range(nGridCapital):
valueHighSoFar = -100000.0
capitalChoice = vGridCapital[0]
for nCapitalNextPeriod in range(gridCapitalNextPeriod,nGridCapital):
consumption = mOutput[nCapital,nProductivity] - vGridCapital[nCapitalNextPeriod]
def backpropagation(self,
trainingset,
ERROR_LIMIT=1e-3,
learning_rate=0.3,
momentum_factor=0.9):
assert trainingset[0].features.shape[0] == self.n_inputs, \
"ERROR: input size varies from the defined input setting"
assert trainingset[0].targets.shape[0] == self.n_outputs, \
"ERROR: output size varies from the defined output setting"
training_data = np.array(
[instance.features for instance in trainingset])
training_targets = np.array(
[instance.targets for instance in trainingset])
MSE = () # inf
neterror = None
momentum = collections.defaultdict(int)
batch_size = self.batch_size if self.batch_size != 0 else training_data.shape[
0]
epoch = 0
while MSE > ERROR_LIMIT:
epoch += 1
for start in xrange(0, len(training_data), batch_size):
batch = training_data[start:start + batch_size]
input_layers = self.update(training_data, trace=True)
out = input_layers[-1]
error = out - training_targets
delta = error
MSE = np.mean(np.power(error, 2))
loop = itertools.izip(
xrange(len(self.weights) - 1, -1, -1),
reversed(self.weights),
reversed(input_layers[:-1]),
)
for i, weight_layer, input_signals in loop:
# Loop over the weight layers in reversed order to calculate the deltas
if i == 0:
dropped = dropout(
add_bias(input_signals).T,
self.input_layer_dropout)
else:
dropped = dropout(
add_bias(input_signals).T,
self.hidden_layer_dropout)
# Calculate weight change
dW = learning_rate * np.dot(
dropped, delta) + momentum_factor * momentum[i]
if i != 0:
"""Do not calculate the delta unnecessarily."""
# Skipping the bias weight during calculation.
weight_delta = np.dot(delta, weight_layer[1:, :].T)
# Calculate the delta for the subsequent layer
delta = np.multiply(
weight_delta,
self.activation_functions[i - 1](input_signals,
derivative=True))
# Store the momentum
momentum[i] = dW
# Update the weights
self.weights[i] -= dW
if epoch % 1000 == 0:
# Show the current training status
print "* current network error (MSE):", MSE
print "* Converged to error bound (%.4g) with MSE = %.4g." % (
ERROR_LIMIT, MSE)
print "* Trained for %d epochs." % epoch
def test_flatiter_array_conv(self):
from numpypy import array, dot
a = array([1, 2, 3])
assert dot(a.flat, a.flat) == 14
# 4. We pre-build output for each point in the grid
for nProductivity in range(nGridProductivity):
mOutput[:, nProductivity] = vProductivity[nProductivity] * (vGridCapital**
aalpha)
## 5. Main iteration
maxDifference = 10.0
tolerance = 0.0000001
iteration = 0
while (maxDifference > tolerance):
expectedValueFunction = np.dot(mValueFunction, mTransition.T)
for nProductivity in range(nGridProductivity):
# We start from previous choice (monotonicity of policy function)
gridCapitalNextPeriod = 0
for nCapital in range(nGridCapital):
valueHighSoFar = -100000.0
capitalChoice = vGridCapital[0]
for nCapitalNextPeriod in range(gridCapitalNextPeriod,
nGridCapital):
consumption = mOutput[
