如何解决使用 m.time 随时间使用其先前值更新 gekko 变量
考虑 gekko 中的方程,其中包含 MV、m.Var、m.CV 和 m.Param 矩阵,其中包括基于非线性回归的最大化问题。
如何将时间相关决策变量“covar”添加到当前代码中,以便:
covar(在时间 t) = [1,gekko_attr1 ** attr1_pow,gekko_attr2 ** attr2_pow,gekko_attr3 ** attr3_pow] * covar(在时间 t-1) * Transpose([1,* attr2_pow,gekko_attr3 ** attr3_pow]) + 常数
数据集:
https://drive.google.com/file/d/10tVHghTvRThsDfyzprINdlVTtJTUbSyQ/view?usp=sharing
def gekko_fun():
xm1 = np.array(data['Attr1'])
xm2 = np.array(data['Attr2'])
xm3 = np.array(data['Attr3'])
ym = np.array(data['Result'])
m = GEKKO(remote=False)
# parameters
gekko_attr1 = m.Param(value = xm1)
gekko_attr2 = m.Param(value = xm2)
gekko_attr3 = m.Param(value = xm3)
intercept = m.MV(lb=0,name="Intercept")
attr1_multiplier = m.MV(lb=0)
attr2_multiplier = m.MV(lb=0)
attr3_multiplier = m.MV(lb=0)
intercept_lambda = m.MV(lb=0,ub = 1)
attr1_lambda = m.MV(lb=0,ub = 1)
attr2_lambda = m.MV(lb=0,ub = 1)
attr3_lambda = m.MV(lb=0,ub = 1)
attr1_pow = m.MV(lb=0,ub=1)
attr2_pow = m.MV(lb=0,ub=1)
attr3_pow = m.MV(lb=0,ub=1)
intercept.STATUS = 1
attr1_multiplier.STATUS = 1
attr2_multiplier.STATUS = 1
attr3_multiplier.STATUS = 1
intercept_lambda.STATUS = 1
attr1_lambda.STATUS = 1
attr2_lambda.STATUS = 1
attr3_lambda.STATUS = 1
attr1_lambda_pow.STATUS = 1
attr2_lambda_pow.STATUS = 1
attr3_lambda_pow.STATUS = 1
control_value = m.CV(value=ym)
control_value.STATUS=1
pred_value = m.Var
error = m.Var
maximized_value = m.Var
m.options.IMODE = 2
m.options.MAX_ITER = 999
m.Equation(pred_value == (
np.dot(
[[1,gekko_attr1**attr1_pow,gekko_attr2**attr2_pow,gekko_attr3**attr3_pow]],#multiply
np.add(
np.dot(
[
[intercept_lambda,0],[0,attr1_lambda,attr2_lambda,attr3_lambda]
],#multiply
[
[intercept],[attr1_multiplier],[attr2_multiplier],[attr3_multiplier]
]
),#add
np.dot(
[
[attr1_multiplier,attr2_multiplier,attr3_multiplier],[attr1_multiplier,attr3_multiplier]
],#multiply
[
[gekko_attr1**attr1_pow],[gekko_attr2**attr2_pow],[gekko_attr3**attr3_pow]
]
)
)
)
))
m.Equation(error==control_value-pred_value)
m.Equation(maximized_value == -m.log(covar) - covar*(error)**2)
m.Maximize(maximized_value)
我是 Gekko 的新手,如果我能得到一些帮助来解决这个问题,我将不胜感激。 感谢您抽出宝贵时间。
解决方法
如果存在离散时间方程而不是连续时间方程(例如微分方程),则使用 IMODE=3
(默认)并使用数组构建变量。这是 x[t] = x[t-1]+1
的示例问题。
from gekko import GEKKO
m = GEKKO()
x = m.Array(m.Var,10)
for i in range(9):
m.Equation(x[i+1]==x[i]+1)
m.Minimize((x[9]-10)**2)
m.solve()
print(x)
解决方案是:
---------------------------------------------------
Solver : IPOPT (v3.12)
Solution time : 5.399999994551763E-003 sec
Objective : 0.000000000000000E+000
Successful solution
---------------------------------------------------
[[1.0] [2.0] [3.0] [4.0] [5.0] [6.0] [7.0] [8.0] [9.0] [10.0]]
Numpy 矩阵运算也可以用于 Gekko 数组。下面是一个例子:
from gekko import GEKKO
import numpy as np
m = GEKKO(remote=False)
ni = 3; nj = 2; nk = 4
# solve AX=B
A = m.Array(m.Var,(ni,nj),lb=0)
X = m.Array(m.Var,(nj,nk),lb=0)
AX = np.dot(A,X)
B = m.Array(m.Var,lb=0)
# equality constraints
m.Equations([AX[i,j]==B[i,j] for i in range(ni) \
for j in range(nk)])
m.Equation(5==m.sum([m.sum([A[i][j] for i in range(ni)]) \
for j in range(nj)]))
m.Equation(2==m.sum([m.sum([X[i][j] for i in range(nj)]) \
for j in range(nk)]))
# objective function
m.Minimize(m.sum([m.sum([B[i][j] for i in range(ni)]) \
for j in range(nk)]))
m.solve()
print(A)
print(X)
print(B)
这是另一个例子:
import numpy as np
from gekko import GEKKO
m = GEKKO(remote=False)
# Random 3x3
A = np.random.rand(3,3)
# Random 3x1
b = np.random.rand(3,1)
# Gekko array 3x3
p = m.Array(m.Param,(3,3))
# Gekko array 3x1
y = m.Array(m.Var,1))
# Dot product of A p
x = np.dot(A,p)
# Dot product of x y
w = np.dot(x,y)
# Dot product of p y
z = np.dot(p,y)
# Trace (sum of diag) of p
t = np.trace(p)
# solve Ax = b
s = m.axb(A,b)
m.solve()
对于以后的问题,请发布 Minimal,Reproducible example 以更好地诊断问题。
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