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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 StOptGrids
import StOptReg
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 OptimizeGasStorage :
# Constructor
# p_maxLevel size of the storage
# p_injectionRate injection rate per time step
# p_withdrawalRate withdrawal rate between two time steps
# p_injectionCost injection cost
# p_withdrawalCost withdrawal cost
def __init__(self, p_injectionRate, p_withdrawalRate, p_injectionCost, p_withdrawalCost) :
self.m_injectionRate = p_injectionRate
self.m_withdrawalRate = p_withdrawalRate
self.m_injectionCost = p_injectionCost
self.m_withdrawalCost = p_withdrawalCost
# 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 = np.zeros(1)
extrGrid[0] = p_regionByProcessor[0] - self.m_withdrawalRate
extrGrid[1] = p_regionByProcessor[1] + self.m_injectionRate
return extrGrid
# 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 = self.m_simulator.getNbSimul()
actuStep = self.m_simulator.getActuStep()
solutionAndControl = list(range(2))
solutionAndControl[0] = np.zeros((nbSimul, 1))
solutionAndControl[1] = np.zeros((nbSimul, 1))
# Spot price
spotPrice = self.m_simulator.fromParticlesToSpot(self.m_simulator.getParticles())
# level if injection
# size of the stock
maxStorage = p_grid.getExtremeValues()[0][1]
injectionMax = min(maxStorage - p_stock[0], self.m_injectionRate)
injectionStock = p_stock + injectionMax
# level if withdrawal
# level min of the stock
minStorage = p_grid.getExtremeValues()[0][0]
withdrawalMax = min(p_stock[0] - minStorage, self.m_withdrawalRate)
withdrawalStock = p_stock - withdrawalMax
if (injectionMax < -1e-10):
solutionAndControl[0].fill(-1.e30)
solutionAndControl[1].fill(0.)
# not an admissible point
return solutionAndControl
condExpSameStock = []
# Suppose that non injection and no withdrawal
#############################################
# create interpolator at current stock point
if p_grid.isInside(p_stock):
interpolatorCurrentStock = p_grid.createInterpolator(p_stock)
# cash flow at current stock and previous step
cashSameStock = interpolatorCurrentStock.applyVec(p_phiIn[0])
# conditional expectation at current stock point
condExpSameStock = actuStep * p_condEsp[0].getAllSimulations(interpolatorCurrentStock).squeeze()
# injection
###########
gainInjection = []
if (injectionMax > 0):
# interpolator for stock level if injection
interpolatorInjectionStock = p_grid.createInterpolator(injectionStock)
# cash flow at previous step at injection level
cashInjectionStock = interpolatorInjectionStock.applyVec(p_phiIn[0]).squeeze()
# conditional expectation at injection stock level
condExpInjectionStock = actuStep * p_condEsp[0].getAllSimulations(interpolatorInjectionStock).squeeze()
# instantaneous gain if injection
gainInjection = -injectionMax * (spotPrice + self.m_injectionCost)
# withdrawal
############
gainWithdrawal = []
if (withdrawalMax >0):
# interpolator for stock level if withdrawal
interpolatorWithdrawalStock = p_grid.createInterpolator(withdrawalStock)
# cash flow at previous step at injection level
cashWithdrawalStock = interpolatorWithdrawalStock.applyVec(p_phiIn[0]).squeeze()
# conditional expectation at withdrawal stock level
condExpWithdrawalStock = actuStep * p_condEsp[0].getAllSimulations(interpolatorWithdrawalStock).squeeze()
# instantaneous gain if withdrawal
gainWithdrawal = withdrawalMax * (spotPrice - self.m_withdrawalCost)
# do the arbitrage
##################
if (len(gainWithdrawal) > 0) & (len(gainInjection) > 0):
# all point admissible
solutionAndControl[0][:,0] = np.multiply(actuStep, cashSameStock).transpose()
solutionAndControl[1][:,0] = 0.
espCondInjection = gainInjection + condExpInjectionStock
espCondInjectionSuperiorToCondExpSameStock = espCondInjection > condExpSameStock
solutionAndControl[0][:,0] = np.where(espCondInjectionSuperiorToCondExpSameStock, gainInjection + actuStep * cashInjectionStock, solutionAndControl[0][:,0])
solutionAndControl[1][:,0] = np.where(espCondInjectionSuperiorToCondExpSameStock, injectionMax, solutionAndControl[1][:,0])
condExpSameStock = np.where(espCondInjectionSuperiorToCondExpSameStock, espCondInjection, condExpSameStock)
espCondWithdrawal = gainWithdrawal + condExpWithdrawalStock
solutionAndControl[0][:,0] = np.where(espCondWithdrawal > condExpSameStock, gainWithdrawal + actuStep * cashWithdrawalStock, solutionAndControl[0][:,0])
solutionAndControl[1][:,0] = np.where(espCondWithdrawal > condExpSameStock, - withdrawalMax, solutionAndControl[1][:,0])
elif len(gainWithdrawal) > 0:
if len(condExpSameStock) > 0:
solutionAndControl[0][:,0] = np.multiply(actuStep, cashSameStock).transpose()
solutionAndControl[1][:,0] = 0.
espCondWithdrawal = gainWithdrawal + condExpWithdrawalStock
solutionAndControl[0][:,0] = np.where(espCondWithdrawal > condExpSameStock, gainWithdrawal + actuStep * cashWithdrawalStock, solutionAndControl[0][:,0])
solutionAndControl[1][:,0] = np.where(espCondWithdrawal > condExpSameStock, - withdrawalMax, solutionAndControl[1][:,0])
else:
solutionAndControl[0][:,0] = gainWithdrawal + actuStep * cashWithdrawalStock
solutionAndControl[1][:,0] = - withdrawalMax
elif len(gainInjection) > 0:
if len(condExpSameStock) > 0:
solutionAndControl[0][:,0] = np.multiply(actuStep, cashSameStock).transpose()
solutionAndControl[1][:,0] = 0.
espCondInjection = gainInjection + condExpInjectionStock
espCondInjectionSuperiorToCondExpSameStock = espCondInjection > condExpSameStock
solutionAndControl[0][:,0] = np.where(espCondInjectionSuperiorToCondExpSameStock, gainInjection + actuStep * cashInjectionStock, solutionAndControl[0][:,0])
solutionAndControl[1][:,0] = np.where(espCondInjectionSuperiorToCondExpSameStock, injectionMax, solutionAndControl[1][:,0])
else:
solutionAndControl[0][:,0] = gainInjection + actuStep * cashInjectionStock
solutionAndControl[1][:,0] = injectionMax
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)
def stepSimulate(self, p_grid, p_continuation, p_state, p_phiInOut) :
actuStep = self.m_simulator.getActuStep()
actu = self.m_simulator.getActu()
# optimal stock attained
ptStockCur = p_state.getPtStock()
control = np.zeros_like(ptStockCur)
# spot price
spotPrice = self.m_simulator.fromOneParticleToSpot(p_state.getStochasticRealization())
espCondMax = -1.e30
if p_grid.isInside(ptStockCur):
continuationDoNothing = actuStep * p_continuation[0].getValue(p_state.getPtStock(), p_state.getStochasticRealization())
espCondMax = continuationDoNothing
# gain to add at current point
phiAdd = 0
# size of the stock
maxStorage = p_grid.getExtremeValues()[0][1]
# if injection
injectionMax = min(maxStorage - p_state.getPtStock()[0], self.m_injectionRate)
if injectionMax>0:
continuationInjection = actuStep * p_continuation[0].getValue(p_state.getPtStock() + injectionMax, p_state.getStochasticRealization())
gainInjection = - injectionMax * (spotPrice + self.m_injectionCost)
espCondInjection = gainInjection + continuationInjection
if espCondInjection > espCondMax :
espCondMax = espCondInjection
phiAdd = gainInjection
control[0] = injectionMax
# if withdrawal
# level min of the stock
minStorage = p_grid.getExtremeValues()[0][0]
withdrawalMax = min(p_state.getPtStock()[0] - minStorage, self.m_withdrawalRate)
if withdrawalMax >0:
gainWithdrawal = withdrawalMax * (spotPrice - self.m_withdrawalCost)
continuationWithdrawal = actuStep * p_continuation[0].getValue(p_state.getPtStock() - withdrawalMax, p_state.getStochasticRealization())
espCondWithdrawal = gainWithdrawal + continuationWithdrawal
if espCondWithdrawal > espCondMax :
espCondMax = espCondWithdrawal
phiAdd = gainWithdrawal
control[0] = -withdrawalMax
# for return
p_state.setPtStock(ptStockCur+control)
p_phiInOut += phiAdd * actu
# 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):
actu = self.m_simulator.getActu()
ptStock = p_state.getPtStock()
# spot price
spotPrice = self.m_simulator.fromOneParticleToSpot(p_state.getStochasticRealization())
# optimal control
control = p_control[0].getValue(p_state.getPtStock(), p_state.getStochasticRealization())
maxStorage = p_grid.getExtremeValues()[0][1]
minStorage = p_grid.getExtremeValues()[0][0]
control = max(min(maxStorage - ptStock[0], control), minStorage - ptStock[0])
if control > 0:
p_phiInOut[0] -= control * (spotPrice + self.m_injectionCost) * actu
elif control < 0:
p_phiInOut[0] -= control * (spotPrice - self.m_withdrawalCost) * actu
ptStock[0] += control
p_state.setPtStock(ptStock)
# 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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