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# Copyright (C) 2016 EDF
# All Rights Reserved
# This code is published under the GNU Lesser General Public License (GNU LGPL)
import numpy as np
# Defines a simple gas storage for optimization and simulation
# No constraint on the storage at the end of optimization period (so the storage will be empty)
class OptimizeLake :
# Constructor
# p_withdrawalRate withdrawal rate between two time steps
def __init__(self, p_withdrawalRate) :
self.m_withdrawalRate = p_withdrawalRate
# define the diffusion cone for parallelism
# p_regionByProcessor region (min max) treated by the processor for the different regimes treated
# returns in each dimension the min max values in the stock that can be reached from the grid p_gridByProcessor for each regime
def getCone(self, p_regionByProcessor) :
extrGrid = list(range(1))
extrGrid[0][0] = p_regionByProcessor[0][0] - self.m_withdrawalRate
extrGrid[0][1] = 1e30
return extrGrid
# permits to actualize the time (needed for simulation)
def incrementActuTimeStep(self) :
return None
# defines a step in optimization
# p_grid grid at arrival step after command
# p_stock coordinate of the stock point to treat
# p_condEsp conditional expectation operator
# p_phiIn for each regime gives the solution calculated at the previous step ( next time step by Dynamic Programming resolution)
# for each regimes (column) gives the solution for each particle (row)
def stepOptimize(self, p_grid, p_stock, p_condEsp, p_phiIn) :
nbSimul = p_condEsp[0].getNbSimul()
solutionAndControl = list(range(2))
solutionAndControl[0] = np.zeros((nbSimul, 1))
solutionAndControl[1] = np.zeros((nbSimul, 1))
inflows = self.m_simulator.getParticles()[0,:].transpose()
# level min of the stock
minStorage = p_grid.getExtremeValues()[0][0]
maxStorage = p_grid.getExtremeValues()[0][1]
condExpSameStock = np.zeros(len(inflows))
cashSameStock = np.zeros(len(inflows))
for i in range(len(inflows)):
stockWithInflows = np.zeros(1)
stockWithInflows[0] = min(p_stock[0] + inflows[i], maxStorage)
if p_grid.isInside(stockWithInflows):
interpolatorCurrentStock = p_grid.createInterpolator(stockWithInflows)
# cash flow at current stock and previous step
cashSameStock[i] = interpolatorCurrentStock.apply(p_phiIn[0][i,:].transpose())
# conditional expectation at current stock point
condExpSameStock[i] = p_condEsp[0].getASimulation(i, interpolatorCurrentStock)
else:
cashSameStock[i] = - 1e30
condExpSameStock[i] = - 1e30
gainWithdrawal = np.zeros(len(inflows))
cashWithdrawalStock = np.zeros(len(inflows))
condExpWithdrawalStock = np.zeros(len(inflows))
withdrawalMax = np.zeros(nbSimul)
for i in range(len(inflows)):
stockWithIn = p_stock[0] + inflows[i]
withdrawalMax[i] = min(stockWithIn - minStorage, self.m_withdrawalRate)
if withdrawalMax[i] < (0. - 1e3 * 2.220446049250313e-16):
cashWithdrawalStock[i] = - 1e30
condExpWithdrawalStock[i] = - 1e30
gainWithdrawal = - 1e30
else:
stockWithInflows = np.zeros(1)
stockWithInflows[0] = min(stockWithIn - withdrawalMax[i], maxStorage)
interpolatorWithdrawalStock = p_grid.createInterpolator(stockWithInflows)
cashWithdrawalStock[i] = interpolatorWithdrawalStock.apply(p_phiIn[0][i,:].transpose())
condExpWithdrawalStock[i] = p_condEsp[0].getASimulation(i, interpolatorWithdrawalStock)
gainWithdrawal[i] = withdrawalMax[i]
solutionAndControl[0][:,0] = cashSameStock
solutionAndControl[1][:,0] = 0.
espCondMax = condExpSameStock
espCondWithdrawal = gainWithdrawal + condExpWithdrawalStock
solutionAndControl[0][:,0] = np.where(espCondWithdrawal > espCondMax, gainWithdrawal + cashWithdrawalStock, solutionAndControl[0][:,0])
solutionAndControl[1][:,0] = np.where(espCondWithdrawal > espCondMax, - withdrawalMax, solutionAndControl[1][:,0])
return solutionAndControl
# get number of regimes
def getNbRegime(self) :
return 1
# number of controls
def getNbControl(self):
return 1
# defines a step in simulation
# Notice that this implementation is not optimal. In fact no interpolation is necessary for this asset.
# This implementation is for test and example purpose
# p_grid grid at arrival step after command
# p_continuation defines the continuation operator for each regime
# p_state defines the state value (modified)
# p_phiInOut defines the value function (modified): size number of functions to follow
def stepSimulate(self, p_grid, p_continuation, p_state, p_phiInOut) :
ptStock = p_state.getPtStock()
ptStockMax = ptStock
# size of the stock
maxStorage = p_grid.getExtremeValues()[0][1]
# inflow
inflow = p_state.getStochasticRealization()[0]
# update storage
ptStockCur = ptStock.copy()
ptStockCur[0] += inflow
ptStockCur[0] = min(ptStockCur[0], maxStorage) # deverse if necessary
# if do nothing
espCondMax = -1.e30
if p_grid.isInside(ptStockCur):
espCondMax = p_continuation[0].getValue(ptStockCur, p_state.getStochasticRealization())
ptStockMax[0] += inflow
# gain to add at current point
phiAdd = 0.
# if withdrawal
# level min of the stock
minStorage = p_grid.getExtremeValues()[0][0]
withdrawalMax = min(p_state.getPtStock()[0] + inflow - minStorage, self.m_withdrawalRate)
if (0. < withdrawalMax ):
gainWithdrawal = withdrawalMax
# level reached
ptStockCur = ptStock + inflow - withdrawalMax
ptStockCur[0] = min(ptStockCur[0], maxStorage)
continuationWithdrawal = p_continuation[0].getValue(ptStockCur, p_state.getStochasticRealization())
espCondWithdrawal = gainWithdrawal + continuationWithdrawal
if espCondWithdrawal > espCondMax :
espCondMax = espCondWithdrawal
phiAdd = gainWithdrawal
ptStockMax[0] = ptStockCur[0]
# for return
p_state.setPtStock(ptStockMax)
p_phiInOut[0] += phiAdd
# Defines a step in simulation using interpolation in controls
# p_grid grid at arrival step after command
# p_control defines the controls
# p_state defines the state value (modified)
# p_phiInOut defines the value function (modified): size number of functions to follow
def stepSimulateControl(self, p_grid, p_control, p_state, p_phiInOut):
ptStock = p_state.getPtStock()
# size of the stock
maxStorage = p_grid.getExtremeValues()[0][1]
minStorage = p_grid.getExtremeValues()[0][0]
# inflow
inflow = p_state.getStochasticRealization()[0]
# get back control
control = p_control[0].getValue(ptStock, p_state.getStochasticRealization())
control = max(min(maxStorage - (ptStock[0] + inflow), control), minStorage - (ptStock[0] + inflow))
ptStock[0] += inflow + control
# for return
p_state.setPtStock(ptStock)
p_phiInOut[0] -= control
# get size of the function to follow in simulation
def getSimuFuncSize(self):
return 1
# store the simulator
def setSimulator(self, p_simulator):
self.m_simulator = p_simulator
# get the simulator back
def getSimulator(self):
return self.m_simulator
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