def nash_equilibrium(a):
size = a.shape
rows = size[0]
cols = size[1]
#-------------NEW PART--------------
k = a[0][0]
for i in range(0, rows):
for j in range(0, cols):
if k > a[i][j]:
k = a[i][j]
if k < 0:
k = -k + 1
else:
k = k + 1
for i in range(0, rows):
for j in range(0, cols):
a[i][j] = a[i][j] + k
#------------------------------------
a1 = a.transpose()
b1 = np.ones((1, cols), dtype=np.int)
c1 = np.ones((1, rows), dtype=np.int)
a2 = a
b2 = np.ones((1, rows), dtype=np.int)
c2 = np.ones((1, cols), dtype=np.int)
v = 1 / (lp(c1[0], -a1, -b1[0]).fun)
p = lp(c1[0], -a1, -b1[0]).x * v
v = -1 / (lp(-c2[0], a2, b2[0]).fun)
q = lp(-c2[0], a2, b2[0]).x * v
#-------------------------------------
v = v - k
#-------------------------------------
print(v)
print(p)
print(q)
return v, p, q
def lp_solve(cur_est_rets, limit_factors, cur_benchmark_wt, num_multi=5):
"""
线性规划计算函数：
输入：截面预期收益，约束条件（风险因子），截面标的指数成分股权重，个股权重约束倍数
输出：经优化后的组合内个股权重
"""
data = pd.concat([cur_est_rets, limit_factors, cur_benchmark_wt], axis=1)
data = data.dropna(how='any', axis=0)
cur_est_rets, limit_factors, cur_benchmark_wt = (data.iloc[:, 0:1],
data.iloc[:, 1:-1],
data.iloc[:, -1])
#****请勿改成简写形式（df /= df.sum()) 错误原因待查****
cur_benchmark_wt = cur_benchmark_wt / cur_benchmark_wt.sum()
c = cur_est_rets.values.flatten()
A_ub = None
b_ub = None
A_eq = np.r_[limit_factors.T.values,
np.repeat(1, len(limit_factors)).reshape(1, -1)]
b_eq = np.r_[np.dot(limit_factors.T, cur_benchmark_wt), np.array([1])]
bounds = tuple([(0, num_multi * wt_in_index)
for wt_in_index in cur_benchmark_wt.values])
res = lp(-c, A_ub, b_ub, A_eq, b_eq, bounds)
cur_wt = pd.Series(res.x, index=cur_est_rets.index)
return cur_wt
def checkFormClosure(contacts):
"""Checks planar form closure given a set of contact points and contact normals
:param contacts: List contact points. Each element should be of format (x,y,theta)
i.e. (x,y) contact location
and the direction of the contact normal specified by theta (radians)
:return result: A logical value where TRUE means form closure
:return output: Solution of the linear programming problem, if form closure is true.
Else null list.
Example Input:
contacts = [[3,5,4.712],[3,5,0.785],[12,5,4.712],[12,5,0.785]]
Output:
"""
contactCount = len(contacts)
# Generating wrench matrix F : (Mz, Fx, Fy)
F = [[0 for x in range(contactCount)] for y in range(3)]
for contactID in range(contactCount):
x, y, theta = contacts[contactID]
Fx = math.cos(theta)
Fy = math.sin(theta)
forceVector = [Fx, Fy, 0] # Force vector
pointVector = [x, y, 0] # Vector from origin to contact point
M = np.cross(pointVector, forceVector)
Mx, My, Mz = M
F[0][contactID] = Mz
F[1][contactID] = Fx
F[2][contactID] = Fy
f = [1 for x in range(contactCount)]
A = [[0 for x in range(contactCount)] for y in range(contactCount)]
for x in range(contactCount):
A[x][x] = -1
b = [-1 for x in range(contactCount)]
Aeq = F
beq = [0 for x in range(3)]
lpOutput = lp(f, A, b, Aeq, beq)
k = []
result = lpOutput.get("success")
if result:
k = lpOutput.get("x")
return result, k
def runLP(self, results, c_bnds, A_ub, b_ub_log, b_eq_log, fields,
water_sources):
"""
:params results: Pandas Dataframe of possible field combinations, used to store LP results
:params c_bnds: Pandas dataframe of c coefficients and bounds for each field and water source
:param A_ub: left hand side upper bounds
:param b_ub: right hand side upper bounds
:param b_eq_log: right hand equality constraints
:param fields: Pandas DataFrame of FarmField objects to consider
:param water_sources: Water Sources to consider
"""
#Create a list of all fields, column by column
f = []
for field in fields:
f += fields[field].tolist()
#End for
fields = f
if (type(results) != pd.DataFrame) or results.empty:
results = c_bnds.drop(["max_area", "bounds"], axis=1)
results["profit"] = np.zeros
results["farm_area"] = np.zeros
results["area_breakdown"] = np.zeros
#Build list of c, b_ub, and bounds for each combination of fields
temp_df = c_bnds.drop("max_area", axis=1)
c_length = len(A_ub[0])
for row in c_bnds.itertuples():
i = row.Index
#Skip rows that are all NaNs
if all(np.isnan(x) for x in row[1:]):
continue
#End if
c = []
for j in temp_df.iloc[i]:
if (type(j) is not list) and (type(j) is not tuple):
c.append(j if np.isnan(j) == False else 0)
elif type(j) is list:
b_ub = j
elif type(j) is tuple:
bounds = j
#End for
#Insert a list at an index as we
#need to include bounds for each GW+SW combination
b_ub_list = b_ub_log.iloc[0].tolist()
b_ub = []
#Generate maximum bounds for b_ub
#Generate a map between fields and Aub constraints
self.genAubMap(fields, water_sources)
#Calculate max area possible with each water source
max_ws_areas = [f.area for f in self.A_ub_map]
#Grab the maximum field area and farm area
max_field_areas = [f.area for f in np.unique(self.A_ub_map)]
max_b_ub = max_ws_areas + max_field_areas + [sum(max_field_areas)]
#Generate b_ub for each A_ub entry
#Calculate total sum for each right hand upper bound combination
for idx, ub in enumerate(A_ub):
temp = np.array([])
#Create association between Field-WaterSource irrigation area and b_ub True/False
for f, b in zip(b_ub_list, ub):
temp = np.append(temp, f) if b == True else temp
#End for
b_ub.append(min(sum(temp), max_b_ub[idx]))
#End for
assert len(A_ub) == len(
b_ub
), "Number of A ub rows must be equal to number of elements in b_ub"
try:
b_eq = b_eq_log.iloc[i].tolist()
except IndexError:
b_eq = []
#End try
#If there is only one equality constraint, ensure that it matches possible farm area
#LP crashes out if this is not set
if (len(b_eq) == 1):
b_eq[0] = bounds[1]
#End if
if len(fields) > 1:
#b_ub.append(c_bnds.iloc[i]['max_area'])
A_eq = A_ub[c_length:-1]
else:
A_eq = A_ub[c_length:]
#End if
try:
bounds = [(0, None)] * len(
c) #[(0, c_bnds['max_area'][0]) for b in b_ub_list ]
#bounds = [(0, min(b, c_bnds['max_area'][0])) for b in b_ub_list]
A_eq = [
A_eq[j] for j in xrange(len(b_eq))
if np.isnan(b_eq[j]) == False
]
b_eq = [
x for x in b_eq if str(x) != 'nan'
] #Template is copied from b_ub which has extra elements; remove the unneeded entries
if (len(A_eq) == 0) and (len(b_eq) == 0):
A_eq = None
b_eq = None
#End if
# assert len(A_eq) == len(b_eq), "Number of equality constraints do not match ({A} != {b}, A_eq != b_eq)".format(A=len(A_eq), b=len(b_eq))
res = lp(c=c,
A_ub=A_ub,
A_eq=A_eq,
b_ub=b_ub,
b_eq=b_eq,
bounds=bounds)
except (ValueError, IndexError) as e:
print "====================="
print c_bnds
print "c: ", c
print "A_ub: ", A_ub
print "b_ub: ", b_ub
print "--------------"
print "A_ub[c]: ", A_ub[c_length:]
print "A_eq: ", A_eq
print "b_eq: ", b_eq
print "Bounds:", bounds
print "b_eq_log: "
print b_eq_log
print len(c)
print len(A_ub)
print len(b_ub)
print "===================\n"
print e
print e.args
print "===================\n"
import sys
sys.exit('Error occured during LP')
#End try
if res.success is False:
print "-------------------"
print res
print "c: ", c
print "A_ub: ", A_ub
print "b_ub", b_ub
print "A_eq", A_eq
print "b_eq", b_eq
print "bounds: ", bounds
print "c_length: ", c_length
print results
print "------------------\n\n"
print "LP failed!"
import sys
sys.exit()
#End if
#import sys; sys.exit('Exit inside LP run for debug')
#Area of each field/water source, (estimated) profit made, area breakdown
row = np.append(res.x, [res.fun, sum(res.x)]).tolist() + [
'| '.join(str(e) for e in res.x.tolist())
]
results.loc[i] = row
#End for
return results
Aeq[pss["plants"] + pss["stocks"]:, :] = NA[pss["plants"] + pss["stocks"]:, :]
# load cost array of arcs dimensions
C = np.array([
100, 200, 100, 200, 150, 150, 150, 150, 200, 100, 200, 100, 100, 150, 200,
100, 150, 200, 200, 150, 100, 200, 150, 100
])
# "linear equality constraint" of nodes dimensions
b = np.array(
[20, 30, 10, 40, 30, 10, 0, 0, 0, 0, -30, -40, -10, -20, -20, -20])
# Initialize Split b to b for upper bound and b for equal constraints
bub = np.zeros(b.shape)
beq = np.zeros(b.shape)
bub[:pss["plants"] + pss["stocks"]] = b[:pss["plants"] + pss["stocks"]]
beq[pss["plants"] + pss["stocks"]:] = b[pss["plants"] + pss["stocks"]:]
## load bounds of arcs dimensions
#ubs = np.array([np.inf,np.inf,np.inf,np.inf,10,5,10,5,5,5,3,3,6,3,6,3,3,3,np.inf,np.inf,np.inf,np.inf,np.inf])
bounds = np.zeros((C.shape[0])).astype(tuple)
for i in range(0, C.shape[0]):
bounds[i] = (0, np.inf)
bounds = tuple(bounds)
# solve the linear prog for simplex and interior point
res = lp(C, A_ub=Aub, A_eq=Aeq, b_ub=bub, b_eq=beq, bounds=bounds)
res_ip = lp(C, A_eq=NA, b_eq=b, bounds=bounds, method='interior-point')
b_eq = [area]
#Costs per Ha of producing the negated profit
# A_ub = [
# [Wheat.water_use_ML_per_Ha, Canola.water_use_ML_per_Ha, Tomato.water_use_ML_per_Ha],
# ]
A_ub = [Wheat.water_use_ML_per_Ha, Canola.water_use_ML_per_Ha, Tomato.water_use_ML_per_Ha]
#Constraints to producing negated profit
b_ub = [
water_entitlement
]
bounds = [(0, area), (0, area), (0, area)]
res = lp(c, A_eq=A_eq, b_eq=b_eq, A_ub=A_ub, b_ub=b_ub, bounds=bounds, options={"disp": True})
print(res)
print c
print A_ub
print b_ub
# print (tomato_cost - tomato_profit) * area
# print (wheat_cost - wheat_profit) * area
# print (canola_cost - canola_profit) * area
def runLP(self, results, c_bnds, A_ub, b_ub_log, b_eq_log, fields, water_sources):
"""
:params results: Pandas Dataframe of possible field combinations, used to store LP results
:params c_bnds: Pandas dataframe of c coefficients and bounds for each field and water source
:param A_ub: left hand side upper bounds
:param b_ub: right hand side upper bounds
:param b_eq_log: right hand equality constraints
:param fields: Pandas DataFrame of FarmField objects to consider
:param water_sources: Water Sources to consider
"""
#Create a list of all fields, column by column
f = []
for field in fields:
f += fields[field].tolist()
#End for
fields = f
if (type(results) != pd.DataFrame) or results.empty:
results = c_bnds.drop(["max_area", "bounds"], axis=1)
results["profit"] = np.zeros
results["farm_area"] = np.zeros
results["area_breakdown"] = np.zeros
#Build list of c, b_ub, and bounds for each combination of fields
temp_df = c_bnds.drop("max_area", axis=1)
c_length = len(A_ub[0])
for row in c_bnds.itertuples():
i = row.Index
#Skip rows that are all NaNs
if all( np.isnan(x) for x in row[1:] ):
continue
#End if
c = []
for j in temp_df.iloc[i]:
if (type(j) is not list) and (type(j) is not tuple):
c.append(j if np.isnan(j) == False else 0)
elif type(j) is list:
b_ub = j
elif type(j) is tuple:
bounds = j
#End for
#Insert a list at an index as we
#need to include bounds for each GW+SW combination
b_ub_list = b_ub_log.iloc[0].tolist()
b_ub = []
#Generate maximum bounds for b_ub
#Generate a map between fields and Aub constraints
self.genAubMap(fields, water_sources)
#Calculate max area possible with each water source
max_ws_areas = [f.area for f in self.A_ub_map]
#Grab the maximum field area and farm area
max_field_areas = [f.area for f in np.unique(self.A_ub_map)]
max_b_ub = max_ws_areas + max_field_areas + [sum(max_field_areas)]
#Generate b_ub for each A_ub entry
#Calculate total sum for each right hand upper bound combination
for idx, ub in enumerate(A_ub):
temp = np.array([])
#Create association between Field-WaterSource irrigation area and b_ub True/False
for f, b in zip(b_ub_list, ub):
temp = np.append(temp, f) if b == True else temp
#End for
b_ub.append(min(sum(temp), max_b_ub[idx]))
#End for
assert len(A_ub) == len(b_ub), "Number of A ub rows must be equal to number of elements in b_ub"
try:
b_eq = b_eq_log.iloc[i].tolist()
except IndexError:
b_eq = []
#End try
#If there is only one equality constraint, ensure that it matches possible farm area
#LP crashes out if this is not set
if (len(b_eq) == 1):
b_eq[0] = bounds[1]
#End if
if len(fields) > 1:
#b_ub.append(c_bnds.iloc[i]['max_area'])
A_eq = A_ub[c_length:-1]
else:
A_eq = A_ub[c_length:]
#End if
try:
bounds = [(0, None)] * len(c) #[(0, c_bnds['max_area'][0]) for b in b_ub_list ]
#bounds = [(0, min(b, c_bnds['max_area'][0])) for b in b_ub_list]
A_eq = [A_eq[j] for j in xrange(len(b_eq)) if np.isnan(b_eq[j]) == False]
b_eq = [x for x in b_eq if str(x) != 'nan'] #Template is copied from b_ub which has extra elements; remove the unneeded entries
if (len(A_eq) == 0) and (len(b_eq) == 0):
A_eq = None
b_eq = None
#End if
# assert len(A_eq) == len(b_eq), "Number of equality constraints do not match ({A} != {b}, A_eq != b_eq)".format(A=len(A_eq), b=len(b_eq))
res = lp(c=c, A_ub=A_ub, A_eq=A_eq, b_ub=b_ub, b_eq=b_eq, bounds=bounds)
except (ValueError, IndexError) as e:
print "====================="
print c_bnds
print "c: ", c
print "A_ub: ", A_ub
print "b_ub: ", b_ub
print "--------------"
print "A_ub[c]: ", A_ub[c_length:]
print "A_eq: ", A_eq
print "b_eq: ", b_eq
print "Bounds:", bounds
print "b_eq_log: "
print b_eq_log
print len(c)
print len(A_ub)
print len(b_ub)
print "===================\n"
print e
print e.args
print "===================\n"
import sys; sys.exit('Error occured during LP')
#End try
if res.success is False:
print "-------------------"
print res
print "c: ", c
print "A_ub: ", A_ub
print "b_ub", b_ub
print "A_eq", A_eq
print "b_eq", b_eq
print "bounds: ", bounds
print "c_length: ", c_length
print results
print "------------------\n\n"
print "LP failed!"
import sys; sys.exit()
#End if
#import sys; sys.exit('Exit inside LP run for debug')
#Area of each field/water source, (estimated) profit made, area breakdown
row = np.append(res.x, [res.fun, sum(res.x)]).tolist() + ['| '.join(str(e) for e in res.x.tolist())]
results.loc[i] = row
#End for
return results
# transform Node to Node matrix to Node Arc matrix, using the function made in basic utils EX0
# We need 2 matrix, the A_eq matrix that corresponds to the NA matrix, and the time constraint array
NA, arcs = nodoNodoANodoArco(NN)
Aeq = NA
Aub = [[3,1,3,1,3,3,5]]
# load cost array of arcs dimensions
C = np.array([2,1,2,5,2,1,2])
# "linear equality constraint" of nodes dimensions. Equality constraints for each node for flow
# and upper bound for total time constraint T
T = 8 # From the exercise
beq = np.array([1,0,0,0,0,-1])
bub = [T]
## load bounds of arcs dimensions
bounds = np.zeros((C.shape[0])).astype(tuple)
for i in range(0, C.shape[0]):
bounds[i] = (0,np.inf)
bounds = tuple(bounds)
# solve the linear prog for simplex and interior point
res = lp(C, A_eq=Aeq, b_eq=beq, A_ub=Aub, b_ub=bub, bounds=bounds)
def checkForceClosure(bodies, contacts):
"""Checks planar force closure given a set of objects and contact information
:param masses: List of object bodies. Each element should be of format (ID,x,y,mass)
i.e.
ID : Body ID (0 to N-1 if the number of bodies are N)
(x,y): Location of mass center
mass : Mass of the body in kg
:param contacts: List contact points. Each element should be of format (a,b,x,y,theta,u)
i.e.
a,b : Bodies in contact
(x,y) : contact location
theta : of the contact normal specified in radians
(Contact normal is into body a)
u : Coulomb Friction coefficient
:return result: A logical value where TRUE means force closure
:return output: Solution of the linear programming problem, if force closure is true.
Else null list.
Examples
========
Input:
bodies = [[1, 25, 35, 2], [2, 66, 42, 10]]
contacts = [[1, 2, 60, 60, 3.1416, 0.5], [1, 0, 0, 0, 1.5708, 0.5], [2, 0, 60, 0, 1.5708, 0.5], [2, 0, 72, 0, 1.5708, 0.5]]
Output:
Force closure successfull. k vector: [ 0.00, 6.21, 3.42, 15.84, 15.04, 12.91, 48.62, 38.34 ]
Input:
bodies = [[1, 25, 35, 2], [2, 66, 42, 5]]
contacts = [[1, 2, 60, 60, 3.1416, 0.5], [1, 0, 0, 0, 1.5708, 0.1], [2, 0, 60, 0, 1.5708, 0.5], [2, 0, 72, 0, 1.5708, 0.5]]
Output:
Force closure fail
"""
bodyCount = len(
bodies
) + 1 # Body 0 (Stationary Ground) in not provided as a seperate input item
contactCount = len(contacts)
wrenchCount = contactCount * 2
# Generating Ext Wrench matrix (Body Weight Wrenches) Fext : (Mz, Fx, Fy)
FextList = [0 for x in range(bodyCount)]
for body in bodies:
ID, x, y, mass = body
point = [x, y]
theta = 3 / 2 * math.pi # Gravity acts downwards - 270 degrees
force = mass * 10 # Gravitational acceleration taken as 10 m/s2
FextList[ID] = forceToWrench(point, theta, force)
# Generating List of contact wrench matrices. Each element F : (Mz, Fx, Fy)
Flist = [[[0 for x in range(wrenchCount)] for y in range(3)]
for z in range(bodyCount)]
for contactID in range(contactCount):
bodyA, bodyB, x, y, theta, u = contacts[contactID]
frictionAngle = math.atan(u)
# Friction cone left edge
WrenchL = forceToWrench((x, y), theta + frictionAngle)
wrenchLID = contactID * 2
# Friction cone right edge
WrenchR = forceToWrench((x, y), theta - frictionAngle)
wrenchRID = (contactID * 2) + 1
# bodyA : Contact normal is into body A
for var in range(3):
Flist[bodyA][var][wrenchLID] = WrenchL[var]
Flist[bodyA][var][wrenchRID] = WrenchR[var]
# bodyB : Contact normal is out of body B
for var in range(3):
Flist[bodyB][var][wrenchLID] = -WrenchL[var]
Flist[bodyB][var][wrenchRID] = -WrenchR[var]
# Remove Stationary ground from Wrench lists
FextList.pop(0)
Flist.pop(0)
f = [1 for x in range(wrenchCount)]
A = [[0 for x in range(wrenchCount)] for y in range(wrenchCount)]
for x in range(wrenchCount):
A[x][x] = -1
b = [0 for x in range(contactCount * 2)]
Aeq = []
for F_ in Flist:
Aeq = Aeq + F_
beq = []
for b_ in FextList:
beq = beq + b_
beq = map(lambda x: -x, beq) # Since Fk = -Fext
lpOutput = lp(f, A, b, Aeq, beq, method='interior-point')
k = []
result = lpOutput.get("success")
if result:
k = lpOutput.get("x")
return result, k
def fit_hard(self, trainx, trainy):
"""
Hard margin case (mainly for testing):
Compute the optimal weight vector to classify (trainx, trainy) using the
Scipy function 'linprog'.
The variable assignment for l = 4 samples is given by
x = (alpha_1, alpha_2, alpha_3, alpha_4, b, eps)
leading to l + 2 = 6 variables.
Parameters
----------
trainx : numpy array of floats, num_train_samples-by-num_features
Input training samples
trainy : list of numpy array of floats or integers num_train_samples-by-one
Input training labels
Returns
-------
self : object
"""
print "Fitting hard margin using Scipy linprog...\n"
[self.num_train_samples, self.num_features] = trainx.shape
# trainx and testx in 'predict', trainy for kernel, and testy for 'plot2d'
self.trainx = trainx
self.trainy = trainy
# Constraints from data (halfspaces), this is the transpose of K
Ktraintrans = get_label_adjusted_train_kernel(trainx,
trainy,
kernel=self.kernel,
degree=self.degree,
gamma=self.gamma,
coef0=self.coef0)
# Objective function
c = np.vstack((np.zeros((self.num_train_samples + 1, 1)), 1)).flatten()
a_ub = np.hstack((-Ktraintrans, -np.ones((self.num_train_samples, 1))))
# b_ub = np.zeros((self.num_train_samples, 1))
b_ub = np.zeros(self.num_train_samples)
lb = np.hstack((-np.ones(self.num_train_samples + 1), -1e9))
ub = np.hstack((np.ones(self.num_train_samples + 1), 1e9))
# Scipy lp solver: use bland option?)
result = lp(c=c,
A_ub=a_ub,
b_ub=b_ub,
bounds=zip(lb, ub),
options=dict(bland=True))
if result.message == 'Optimization failed. Unable to ' \
'find a feasible starting point.':
print result
if result.status > 0:
print 'Scipy linprog did not terminate successfully. status = %d' \
% result.status
weight_opt = result.x
self.weight_opt = weight_opt[:-1]
self.eps_opt = weight_opt[-1]
self.fun_opt = result.fun
if np.abs(self.eps_opt - self.fun_opt) >= 0.00001:
warnings.warn('\neps_opt is not identical to fun_opt. eps_opt - fun_opt = %0.6f. ' \
% (self.eps_opt - self.fun_opt))
if np.abs(self.eps_opt) <= 0.00001:
warnings.warn('\neps_opt is close to zero. Data not separable. ')
# [Wheat.water_use_ML_per_Ha, Canola.water_use_ML_per_Ha, Tomato.water_use_ML_per_Ha],
# ]
A_ub = [
Wheat.water_use_ML_per_Ha, Canola.water_use_ML_per_Ha,
Tomato.water_use_ML_per_Ha
]
#Constraints to producing negated profit
b_ub = [water_entitlement]
bounds = [(0, area), (0, area), (0, area)]
res = lp(c,
A_eq=A_eq,
b_eq=b_eq,
A_ub=A_ub,
b_ub=b_ub,
bounds=bounds,
options={"disp": True})
print(res)
print c
print A_ub
print b_ub
# print (tomato_cost - tomato_profit) * area
# print (wheat_cost - wheat_profit) * area
# print (canola_cost - canola_profit) * area
def update_bid(self):
# Define the number of steps the perfect foresight optimization should look in the future.
n_step = self.forecast_horizon
if self.bidding_solver == "linprog":
""" Linear program """
# To derive the bid for this time step, a linear optimization (linprog) determines the optimal amount of
# hydrogen that should be produced depending on the electricity price and the demand for the next ?2 weeks?.
# This requires perfect foresight and in order to formulate a linear optimization problem, the temperature
# dependent electrolyzer efficiency is not taken into account.
#
# The optimization problem is formulated in the way:
# min c * x
# s.t. A * x <= b
# x >= 0 and x < max. producible hydrogen
#
# Here, x is a vector with the amount of hydrogen produced each time step, c is the estimated cost function
# for each time step (EEX spot marked costs are used), A * x <= b is used to make sure that the storage
# never falls below the min. storage level (safety buffer).
# Number of time steps of the future used for the optimization.
# Define the electricity costs [EUR/kWh].
c = self.model.data.utility_pricing_profile[self.current_step:self.
current_step + n_step]
# Define the inequality matrix (A) and vector (b) that make sure that at no time step the storage is below
# the wanted buffer value.
# The matrix A is supposed to sum up all hydrogen produced for each time step, therefore A is a lower
# triangular matrix with all entries being -1 (- because we want to make sure that the hydrogen amount does
# not fall below a certain amount, thus the <= must be turned in a >=, therefore A and b values are all set
# negative).
A = [[-1] * (i + 1) + [0] * (n_step - i - 1)
for i in range(n_step)]
# Append A by the negative of itself to set the boundaries that the storage cannot be more than full.
A_append = [[1] * (i + 1) + [0] * (n_step - i - 1)
for i in range(n_step)]
A += A_append
# The b value is the sum of the demand for each time step (- because see comment above).
cumsum_h2_demand = self.h2_demand[self.
current_step:self.current_step +
n_step]
cumsum_h2_demand = [-float(x) for x in cumsum_h2_demand]
# Accumulate all demands over time.
cumsum_h2_demand = np.cumsum(cumsum_h2_demand).tolist()
# Now the usable hydrogen is added to all values of b except the last one. This allows stored hydrogen to be
# used but will force the optimization to have at least as much hydrogen stored at the end of the looked at
# time frame as there is now stored.
b = [
x + self.stored_hydrogen - self.storage_buffer
for x in cumsum_h2_demand
]
b_append = [-x + self.storage_size for x in b]
b[-1] -= self.stored_hydrogen - self.storage_buffer
b += b_append
# Define the bounds for the hydrogen produced.
x_bound = ((0, self.max_production_per_step), ) * n_step
# Do the optimization with linprog.
opt_res = lp(c, A, b, method="interior-point", bounds=x_bound)
# Return the optimal value for this time slot [kg]
if opt_res.success:
opt_production = opt_res.x.tolist()
else:
# Case: Linprog couldn't derive optimal result, thus produce as much H2 as possible.
opt_production = [self.max_production_per_step]
# print("Electrolyzer bidding - Optimization success is {}".format(opt_res.success))
electrolyzer_log.info(
"Electrolyzer bidding - Optimization success is {}".format(
opt_res.success))
elif self.bidding_solver == "quadprog":
""" Quadratic program """
from cvxopt import matrix, solvers
# The optimization problem is formulated in the way:
# min 0.5 x^T * P * x + q^T * x
# s.t. G * x <= d
# x >= 0 and x < max. producible hydrogen
# Define the electricity costs [EUR/kWh].
c = self.model.data.utility_pricing_profile[self.current_step:self.
current_step + n_step]
# The quadratic matrix P is a diagonal matrix containing the values of c on the diagonal.
# Create an eye matrix with the size of c.
P = np.eye(len(c))
# Multiply c with the eye matrix and convert the matrix back to a list.
P = P * c
# q is a vector consisting of 1.5 * max_production_per_step / 0.4 * 2 * c. The formula is derived by the
# assumption, that the electrolyzer cell voltage rises linearly from 1.5 V when off to 1.9 V when on max.
# power. The costs are the energy needed multiplied by the energy costs, which can be boiled down to the
# form (w/o constants) C = (1.5 + 0.4 x / x_max) * x * c, where x_max is the max. H2 production per step.
# Hereof the quadratic formulation can be derived.
q = [
1.5 * self.max_production_per_step / 0.4 * 2 * cost
for cost in c
]
# Define the inequality matrix (A) and vector (b) that make sure that at no time step the storage is below
# the wanted buffer value.
# The matrix A is supposed to sum up all hydrogen produced for each time step, therefore A is a lower
# triangular matrix with all entries being -1 (- because we want to make sure that the hydrogen amount does
# not fall below a certain amount, thus the <= must be turned in a >=, therefore A and b values are all set
# negative).
A = [[-1.0] * (i + 1) + [0.0] * (n_step - i - 1)
for i in range(n_step)]
# Append A by the negative of itself to set the boundaries that the storage cannot be more than full.
A_append = [[1.0] * (i + 1) + [0.0] * (n_step - i - 1)
for i in range(n_step)]
A += A_append
# The constraints that x can only be between 0 and max. production have to be inserted via the matrix A.
A += np.eye(n_step).tolist()
eye_neg = -np.eye(n_step)
A += eye_neg.tolist()
A = np.array(A).T.tolist()
# The b value is the sum of the demand for each time step (- because see comment above).
cumsum_h2_demand = self.h2_demand[self.
current_step:self.current_step +
n_step]
cumsum_h2_demand = [-float(x) for x in cumsum_h2_demand]
# Accumulate all demands over time.
cumsum_h2_demand = np.cumsum(cumsum_h2_demand).tolist()
# Now the usable hydrogen is added to all values of b except the last one. This allows stored hydrogen to be
# used but will force the optimization to have at least as much hydrogen stored at the end of the looked at
# time frame as there is now stored.
""" IDEA: Maybe the goal should be to have a filling level of half the storage at the end of the opt. """
b = [
x + self.stored_hydrogen - self.storage_buffer
for x in cumsum_h2_demand
]
b_append = [-x + self.storage_size for x in b]
b[-1] -= self.stored_hydrogen - self.storage_buffer
b += b_append
# Set the x boundaries (0 <= x <= max. H2 production per step).
b += [self.max_production_per_step for _ in range(n_step)]
b += [0 for _ in range(n_step)]
# Convert all the lists needed to cvxopt matrix format.
P = matrix(P)
q = matrix(q)
G = matrix(A)
d = matrix(b)
# Silence the optimizer output.
solvers.options['show_progress'] = False
# Do the optimization with linprog.
opt_res = solvers.qp(P, q, G, d)
# Transform cvxopt matrix format to list.
if opt_res['status'] == 'optimal':
opt_production = np.array(opt_res['x']).tolist()
opt_production = [x[0] for x in opt_production]
else:
opt_production = [self.max_production_per_step]
# Return the optimal value for this time slot [kg]
# print("Electrolyzer bidding - Optimization status is '{}'".format(opt_res['status']))
electrolyzer_log.info("Optimization status is '{}'".format(
opt_res['status']))
elif self.bidding_solver == "dummy":
""" Return a dummy bid """
opt_production = [0.1]
c = [30]
elif self.bidding_solver == "stepwise":
# Get the amount of hydrogen missing from the storage buffer [kg].
min_amount_needed = min(
self.max_production_per_step,
max(0, self.storage_buffer - self.stored_hydrogen))
# Approximate the electricity needed to produce the missing buffer mass (assume efficiency of 65 %) [kWh].
min_bid = min_amount_needed * 33.3 / 0.65
# Amount of H2 that can be stored [kg]
max_mass_storable = min(self.max_production_per_step,
self.storage_size - self.stored_hydrogen)
# Approximate the electricity buyable to fill storage (assume efficiency of 65 %) [kWh].
max_bid = max_mass_storable * 33.3 / 0.65
# Generate the bids.
# Bids are in the format [price [EUR/kWh], volume[kWh], ID]
bids = []
if min_bid > 0:
# Case: There is an amount that should definitely be bought.
bids.append([0.25, min_bid, self.id])
# Subtract the amount needed from the amount that could be bought on top of that.
max_bid -= min_bid
if max_bid > 0:
# Split max bid to 4 equal sections, one for 20 ct/kWh, one for 15, 10, and 5.
bids.append([self.stepwise_bid_price[0], max_bid / 4, self.id])
bids.append([self.stepwise_bid_price[1], max_bid / 4, self.id])
bids.append([self.stepwise_bid_price[2], max_bid / 4, self.id])
bids.append([self.stepwise_bid_price[3], max_bid / 4, self.id])
# Place the bids
for bid in bids:
self.model.auction.bid_list.append(bid)
return
else:
""" No valid solver """
raise ValueError('Electrolyzer: No valid solver name given.')
# self.plot_optimization_result(opt_production, cumsum_h2_demand, c)
# Return the energy value needed for the optimized production and the price [kWh, EUR/kWh]
energy_demand = self.get_power_by_production(
opt_production[0]) * self.interval_time / 60
price = c[0]
if energy_demand == 0:
# Case: Do not bid.
self.bid = None
self.trading_state = None
else:
# Case: Bid on energy.
self.bid = [price, energy_demand, self.id]
self.trading_state = "buying"
def solve(self):
res = lp(self.c, self.A_ub, self.b, self.A_eq, self.d)
if res['status'] != 0:
return res['message']
return res['x'].reshape(self.shape)
# solve the linear prog for simplex and interior point
results = [] # Empty array for values of primal equation
landas = [] # Empty array for values of lambda
tolerance = 0.01 # Level of tolerance for the difference of lambda
landa = 0.01 # Init Lambda
landaNext = 0.01 # Init lambda Next = lambda
diff = np.inf # Init difference to infinity
i = 1 # Init counter i, 1 for the step divisor.
# Loop while the difference between lambda_i and lambda_i+1 is less than the setted tolerance
while diff > tolerance and i < 150:
# Update Value of lambda for the lambda obtained in previous iteration
landa = landaNext
# Calculate the C~ = C + lambda*t and minimize using linprog
CplusLambdaT = C + landa * t
res = lp(CplusLambdaT, A_eq=Aeq, b_eq=beq, bounds=bounds)
# Calculate the primal value with the result of the minimization for plotting later
primal = res.fun - T * landa
# Calculate the gradient of C*X + lambda(t*x + T)
gradient = np.dot(t, res.x) - T
# Update Value of step, inversily proportional to the index of iteration
step = 1 / i
# Calculate the next lambda by moving the value "step" over the gradient
# and compute difference between current lambda
landaNext = landa + step * gradient
diff = abs(landaNext - landa)
# Update index value, and append calculated values to list for plotting later
i += 1
results.append(primal)
landas.append(landa)
print(i, step, gradient, landa, landaNext, diff)
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
# transform Node to Node matrix to Node Arc matrix, using the function made in basic utils EX0
NA, arcs = nodoNodoANodoArco(NN)
# load cost array of arcs dimensions
C = np.array(
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1])
# "linear equality constraint" of nodes dimensions
b = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
## load bounds of arcs dimensions
ubs = np.array([
np.inf, np.inf, np.inf, np.inf, 10, 5, 10, 5, 5, 5, 3, 3, 6, 3, 6, 3, 3, 3,
np.inf, np.inf, np.inf, np.inf, np.inf
])
bounds = np.zeros((C.shape[0])).astype(tuple)
for i in range(0, C.shape[0]):
bounds[i] = (0, ubs[i])
bounds = tuple(bounds)
# solve the linear prog for simplex and interior point
res = lp(C, A_eq=NA, b_eq=b, bounds=bounds)
res_ip = lp(C, A_eq=NA, b_eq=b, bounds=bounds, method='interior-point')
def min_cost(self, groups=['F 19-30','M 19-30'] , **kwargs):
if len(self.ndf) == 0 or len(self.foods_spreadsheet) == 0:
raise Exception("Please get a nutrition dataframe/spreadsheet for food first." )
def average_of_groups(group,table):
if len(group) == 1:
return table[group[0]]
return table[group[0]] + average_of_groups(group[1:],table)
min_table = pd.read_csv('./diet_minimums.csv').set_index('Nutrition')
max_table = pd.read_csv('./diet_maximums.csv').set_index('Nutrition')
min_of_groups = average_of_groups(groups,min_table) / len(groups)
max_of_groups = average_of_groups(groups,max_table) / len(groups)
def test1(ndf):
ndf['NDB Quantity'] = ndf[['Quantity','Units']].T.apply(lambda x : ndb.ndb_units(x['Quantity'],x['Units']))
ndf['NDB Price'] = ndf['Price']/ndf['NDB Quantity']
return ndf
df = pd.read_csv(self.foods_spreadsheet)
df['Quantity'] = [float(i)for i in df['Quantity']]
df['Price'] = [float(i[1:])for i in df['Price']]
if 'price_delta' in kwargs:
df['Price'] = df['Price'].where(df['Food'] != kwargs['price_delta'][0], df['Price']* (1 + (kwargs['price_delta'][1])/100) )
df = test1(df)
D = self.ndf
df.dropna(how='any')
Prices = df.groupby('Food')['NDB Price'].min()
regx1 = "[fFmM]{1}"
regx2 = r"[^\w ]+"
tol = 1e-6 # Numbers in solution smaller than this (in absolute value) treated as zeros
c = Prices.apply(lambda x:x.magnitude).dropna()
# Compile list that we have both prices and nutritional info for; drop if either missing
# Drop nutritional information for foods we don't know the price of,
# and replace missing nutrients with zeros.
Aall = D[c.index].fillna(0)
# Drop rows of A that we don't have constraints for.
Amin = Aall.loc[min_of_groups.index]
Amax = Aall.loc[max_table.index]
# Minimum requirements involve multiplying constraint by -1 to make <=.
A = pd.concat([-Amin,Amax])
b = pd.concat([-min_of_groups,max_of_groups]) # Note sign change for min constraints
result = lp(c, A, b, method='interior-point',options = {"presolve":False,'maxiter':5000.0})
# Put back into nice series
diet = pd.Series(result.x,index=c.index)
if 'price_delta' not in kwargs:
self.ot = str(result.fun)
self.result_comp = diet[diet >= tol]
self.result_cost = str(result.fun)
temp1 = 'the average of the (' + ', '.join(groups) + ')' if len(groups) > 1 else groups[0]
print("Cost of diet for %s is $%4.2f per day." % (temp1,result.fun))
print("\nYou'll be eating (in 100s of grams or milliliters):")
print(diet[diet >= tol]) # Drop items with quantities less than precision of calculation
tab = pd.DataFrame({"Outcome":np.abs(A).dot(diet),"Recommendation":np.abs(b)})
print("\nWith the following nutritional outcomes of interest:")
print(tab)
print("\nConstraining nutrients are:")
excess = tab.diff(axis=1).iloc[:,1]
print(excess.loc[np.abs(excess) < tol].index.tolist())
# Coeficientes de Función
cFuncionMin = [1, 1] # 1x + 1y
# Coeficientes de Restricciones
aRestricciones = [[50, 24], [30, 33]] # [50x + 24y], [30x + 33y]
bRestricciones = [2400, 2100]
# Límites
limitesX = (0, None)
limitesY = (0, None)
#%% PROGRAMA
# Configuraciones para ejecutar algoritmo de optimización
cFuncionMax = -np.array(cFuncionMin) # Maximización en lugar de minimización
limites = (limitesX, limitesY)
# Ejecución de optimización
solucion = lp(cFuncionMax, A_ub = aRestricciones, b_ub = bRestricciones, bounds = limites)
funcionReal = - solucion.fun # Ocurrió una maximización en lugar de una minimización
#%% IMPRESIÓN DE RESULTADOS
print()
print('Resultado de ejecución:')
print(solucion)
print()
print('Solución:')
print('X = {:.4f}'.format(solucion.x[0]))
print('Y = {:.4f}'.format(solucion.x[1]))
print('Función evaluada en solución: {:.4f}'.format(funcionReal))
# Drop nutritional information for foods we don't know the price of,
# and replace missing nutrients with zeros.
Aall = D[c.index].fillna(0)
# Drop rows of A that we don't have constraints for.
Amin = Aall.loc[bmin.index]
Amax = Aall.loc[bmax.index]
# Minimum requirements involve multiplying constraint by -1 to make <=.
A = pd.concat([-Amin, Amax])
b = pd.concat([-bmin, bmax]) # Note sign change for min constraints
# Now solve problem!
result = lp(c, A, b, method='interior-point')
# Put back into nice series
diet = pd.Series(result.x, index=c.index)
'''
print("Cost of diet for %s is $%4.2f per day." % (group,result.fun))
print("\nYou'll be eating (in 100s of grams or milliliters):")
print(diet[diet >= tol]) # Drop items with quantities less than precisionof calculation.'''
tab = pd.DataFrame({
"Outcome": np.abs(A).dot(diet),
"Recommendation": np.abs(b)
})
'''print("\nWith the following nutritional outcomes of interest:")
print(tab)
def lp_solve(date, cur_est_rets, limit_factors, cur_benchmark_wt, industry_map, stocks_in_index_wei=1, num_multi=5):
"""
线性规划计算函数：
输入：截面预期收益，约束条件（风险因子），截面标的指数成分股权重，个股权重约束倍数
输出：经优化后的组合内个股权重
"""
'''
scipy.optimize.linprog(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, bounds=None, method='interior-point',
callback=None, options=None, x0=None)
minimize:
c @ x
such that:
A_ub @ x <= b_ub
A_eq @ x == b_eq
lb <= x <= ub
'''
# b_eq是基准的风险暴露，通过是组合的风险暴露与基准的风险暴露相同，达到风险因子中性、行业中性的目的
# np.r_ 是按列拼接成一个maxic，就是在风险因子权重等于指数风险因子权重，且权重和为1。
# 行业虚拟变量
dummies = pd.get_dummies(industry_map[industry_map.columns[0]])
# 合并
data = pd.concat([cur_est_rets, limit_factors, cur_benchmark_wt, dummies], axis=1)
# 仅在成份股中选股
if stocks_in_index_wei == 1:
# 把不在成份股的都删掉了
data = data.dropna(how='any', axis=0)
cur_est_rets, limit_factors, cur_benchmark_wt, dummies = (data[cur_est_rets.columns], data[limit_factors.columns],
data[cur_benchmark_wt.columns], data[dummies.columns])
cur_benchmark_wt = cur_benchmark_wt / cur_benchmark_wt.sum()
c = cur_est_rets.values.flatten()
A_ub = None
b_ub = None
A_eq = np.r_[limit_factors.T.values, dummies.T.values, np.repeat(1, len(limit_factors)).reshape(1, -1)]
b_eq = np.r_[np.dot(limit_factors.T, cur_benchmark_wt), np.dot(dummies.T, cur_benchmark_wt),
np.array([1]).reshape(-1, 1)]
np.repeat(1, 6).reshape(1, -1)
# 股票权重的bounds,最小是0，最大是指数权重的5倍。
bounds = tuple([(0, num_multi * wt_in_index) for wt_in_index in cur_benchmark_wt.values])
try:
res = lp(-c, A_ub, b_ub, A_eq, b_eq, bounds)
except Exception as e:
res = lp(-c, A_ub, b_ub, A_eq, b_eq, bounds, method='interior-point')
print('{}简单方法未解出来'.format(date))
cur_wt = pd.Series(res.x, index=cur_est_rets.index)
# (cur_wt > 0).sum()
# (cur_wt > 0.01).sum()
# 可以选出部分的非成份股
else:
# 把不在成份股的股票权重nan部分变为0，这样后面就不会被删除
data[cur_benchmark_wt.columns] = data[cur_benchmark_wt.columns].fillna(0)
# 删除其他的nan
data = data.dropna(how='any', axis=0)
cur_est_rets, limit_factors, cur_benchmark_wt, dummies = (data[cur_est_rets.columns], data[limit_factors.columns],
data[cur_benchmark_wt.columns], data[dummies.columns])
cur_benchmark_wt = cur_benchmark_wt / cur_benchmark_wt.sum()
# 判断是否为成份股
not_in_benchmark = deepcopy(cur_benchmark_wt)
not_in_benchmark[cur_benchmark_wt == 0.0] = 1
not_in_benchmark[cur_benchmark_wt != 0.0] = 0
c = cur_est_rets.values.flatten()
A_ub = not_in_benchmark.T.values
b_ub = np.array([1 - stocks_in_index_wei])
A_eq = np.r_[limit_factors.T.values, dummies.T.values, np.repeat(1, len(limit_factors)).reshape(1, -1)]
b_eq = np.r_[np.dot(limit_factors.T, cur_benchmark_wt), np.dot(dummies.T, cur_benchmark_wt),
np.array([1]).reshape(-1, 1)]
# 得到行业权重
tmp = pd.concat([cur_benchmark_wt, industry_map], axis=1).fillna(0)
grouped = tmp.groupby(tmp.columns[-1])
tmp_indus_wei = pd.Series()
for k, v in grouped:
su = v[cur_benchmark_wt.columns].sum().values[0]
tmp_indus_wei[k] = su
tmp['indus_wei'] = None
for i in range(0, len(tmp.index)):
tmp.loc[tmp.index[i], 'indus_wei'] = tmp_indus_wei[tmp.loc[tmp.index[i], '申万一级行业']]
bounds_tmp = []
for v in tmp['indus_wei'].values:
if v > 0:
bounds_tmp.append([(0, v/3)])
else:
bounds_tmp.append([(0, 0.0001)])
bounds1 = tuple(bounds_tmp)
bounds = tuple([(0, 1) for i in cur_benchmark_wt.values])
res = lp(-c, A_ub, b_ub, A_eq, b_eq, bounds, method='interior-point')
res.x
cur_wt11 = pd.Series(res.x, index=cur_est_rets.index)
(cur_wt11 > 0).sum()
(cur_wt11 > 0.001).sum()
(cur_wt11 > 0.03).sum()
cur_wt11.sum()
res = lp(-c, A_ub, b_ub, A_eq, b_eq, bounds)
cur_wt = pd.Series(res.x, index=cur_est_rets.index)
return cur_wt