Scipy 矩阵乘法优化
Scipy optimization with matrix multiplication
我试过用spicy.optimize.minimize解决一个矩阵乘法优化问题，但是，结果给我一个维数错误，谁能帮我解决一下？
import numpy as np
from scipy.optimize import minimize
# define known variables, mu, sigma, rf
mu = np.matrix([[0.12],
[0.08],
[0.05]])
sigma = np.matrix([[0.5, 0.05, 0.03],
[0.05, 0.4, 0.01],
[0.03, 0.01, 0.2]])
rf = 0.02
def objective_fun(x):
'''
This is the objective function
'''
s = np.sqrt(x.T * sigma * x)/(mu.T * x - rf)
return s
def constraint(x):
con = 1
for i in np.arange(0,3):
con = con - x[i]
return con
# set up the boundaries for x
bound_i = (0, np.Inf)
bnds = (bound_i, bound_i, bound_i)
#set up the constraints for x
con = {'type':'eq', 'fun':constraint}
# initial guess for variable x
x = np.matrix([[0.5],
[0.3],
[0.2]])
sol = minimize(objective_fun, x, method = 'SLSQP', bounds = bnds, constraints = con)
错误给我：
ValueError Traceback (most recent call last)
<ipython-input-31-b8901077b164> in <module>
----> 1 sol = minimize(objective_fun, x, method = 'SLSQP', bounds = bnds, constraints = con)
e:\Anaconda3\lib\site-packages\scipy\optimize\_minimize.py in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
606 elif meth == 'slsqp':
607 return _minimize_slsqp(fun, x0, args, jac, bounds,
--> 608 constraints, callback=callback, **options)
609 elif meth == 'trust-constr':
610 return _minimize_trustregion_constr(fun, x0, args, jac, hess, hessp,
e:\Anaconda3\lib\site-packages\scipy\optimize\slsqp.py in _minimize_slsqp(func, x0, args, jac, bounds, constraints, maxiter, ftol, iprint, disp, eps, callback, **unknown_options)
397
398 # Compute objective function
--> 399 fx = func(x)
400 try:
401 fx = float(np.asarray(fx))
e:\Anaconda3\lib\site-packages\scipy\optimize\optimize.py in function_wrapper(*wrapper_args)
324 def function_wrapper(*wrapper_args):
325 ncalls[0] += 1
--> 326 return function(*(wrapper_args + args))
327
328 return ncalls, function_wrapper
<ipython-input-28-b1fb2386a380> in objective_fun(x)
3 This is the objective function
4 '''
----> 5 s = np.sqrt(x.T * sigma * x)/(mu.T * x - rf)
6 return s
e:\Anaconda3\lib\site-packages\numpy\matrixlib\defmatrix.py in __mul__(self, other)
218 if isinstance(other, (N.ndarray, list, tuple)) :
219 # This promotes 1-D vectors to row vectors
--> 220 return N.dot(self, asmatrix(other))
221 if isscalar(other) or not hasattr(other, '__rmul__') :
222 return N.dot(self, other)
ValueError: shapes (1,3) and (1,3) not aligned: 3 (dim 1) != 1 (dim 0)
但是，我写的每一个函数我都单独尝试过，最后都没有错误，比如，如果在代码中定义了x矩阵之后，我只是运行 objective_fun(x)在控制台中，我立即得到了答案：
optimize_fun(x)
matrix([[5.90897598]])
这意味着我的函数可以正确地进行矩阵乘法，那么这里的代码有什么问题吗？
minimize() 的文档说 x0 应该是 (n,) 形状的数组，但您试图将其视为 (3,1) 数组。我不确定 minimize() 的内部工作原理，但我怀疑当它跨过拟合参数的不同值时，它会转换为它认为需要的格式。无论如何，以下小的更正使代码有效。
import numpy as np
from scipy.optimize import minimize
# define known variables, mu, sigma, rf
mu = np.matrix([[0.12],
[0.08],
[0.05]])
sigma = np.matrix([[0.5, 0.05, 0.03],
[0.05, 0.4, 0.01],
[0.03, 0.01, 0.2]])
rf = 0.02
def objective_fun(x):
'''
This is the objective function
'''
x = np.expand_dims(x, 1) # convert the (3,) shape to (3,1). Then we can do our normal matrix math on it
s = np.sqrt(x.T * sigma * x)/(mu.T * x - rf) # Transposes so the shapes are correct
return s
def constraint(x):
con = 1
for i in np.arange(0,3):
con = con - x[i]
return con
# set up the boundaries for x
bound_i = (0, np.Inf)
bnds = (bound_i, bound_i, bound_i)
#set up the constraints for x
con = {'type':'eq', 'fun':constraint}
# initial guess for variable x
x = np.array([0.5, 0.3, 0.2]) # Defining the initial guess as an (3,) array)
sol = minimize(objective_fun, x, method = 'SLSQP', bounds = bnds, constraints = con)
print(sol) # and the solution looks reasonable
输出
fun: 5.86953830952583
jac: array([-1.70555401, -1.70578796, -1.70573896])
message: 'Optimization terminated successfully.'
nfev: 32
nit: 6
njev: 6
status: 0
success: True
x: array([0.42809911, 0.29522438, 0.27667651])
查看我添加的评论，了解您需要做什么。
我试过用spicy.optimize.minimize解决一个矩阵乘法优化问题，但是，结果给我一个维数错误，谁能帮我解决一下？
import numpy as np
from scipy.optimize import minimize
# define known variables, mu, sigma, rf
mu = np.matrix([[0.12],
[0.08],
[0.05]])
sigma = np.matrix([[0.5, 0.05, 0.03],
[0.05, 0.4, 0.01],
[0.03, 0.01, 0.2]])
rf = 0.02
def objective_fun(x):
'''
This is the objective function
'''
s = np.sqrt(x.T * sigma * x)/(mu.T * x - rf)
return s
def constraint(x):
con = 1
for i in np.arange(0,3):
con = con - x[i]
return con
# set up the boundaries for x
bound_i = (0, np.Inf)
bnds = (bound_i, bound_i, bound_i)
#set up the constraints for x
con = {'type':'eq', 'fun':constraint}
# initial guess for variable x
x = np.matrix([[0.5],
[0.3],
[0.2]])
sol = minimize(objective_fun, x, method = 'SLSQP', bounds = bnds, constraints = con)
错误给我：
ValueError Traceback (most recent call last)
<ipython-input-31-b8901077b164> in <module>
----> 1 sol = minimize(objective_fun, x, method = 'SLSQP', bounds = bnds, constraints = con)
e:\Anaconda3\lib\site-packages\scipy\optimize\_minimize.py in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
606 elif meth == 'slsqp':
607 return _minimize_slsqp(fun, x0, args, jac, bounds,
--> 608 constraints, callback=callback, **options)
609 elif meth == 'trust-constr':
610 return _minimize_trustregion_constr(fun, x0, args, jac, hess, hessp,
e:\Anaconda3\lib\site-packages\scipy\optimize\slsqp.py in _minimize_slsqp(func, x0, args, jac, bounds, constraints, maxiter, ftol, iprint, disp, eps, callback, **unknown_options)
397
398 # Compute objective function
--> 399 fx = func(x)
400 try:
401 fx = float(np.asarray(fx))
e:\Anaconda3\lib\site-packages\scipy\optimize\optimize.py in function_wrapper(*wrapper_args)
324 def function_wrapper(*wrapper_args):
325 ncalls[0] += 1
--> 326 return function(*(wrapper_args + args))
327
328 return ncalls, function_wrapper
<ipython-input-28-b1fb2386a380> in objective_fun(x)
3 This is the objective function
4 '''
----> 5 s = np.sqrt(x.T * sigma * x)/(mu.T * x - rf)
6 return s
e:\Anaconda3\lib\site-packages\numpy\matrixlib\defmatrix.py in __mul__(self, other)
218 if isinstance(other, (N.ndarray, list, tuple)) :
219 # This promotes 1-D vectors to row vectors
--> 220 return N.dot(self, asmatrix(other))
221 if isscalar(other) or not hasattr(other, '__rmul__') :
222 return N.dot(self, other)
ValueError: shapes (1,3) and (1,3) not aligned: 3 (dim 1) != 1 (dim 0)
但是，我写的每一个函数我都单独尝试过，最后都没有错误，比如，如果在代码中定义了x矩阵之后，我只是运行 objective_fun(x)在控制台中，我立即得到了答案：
optimize_fun(x)
matrix([[5.90897598]])
这意味着我的函数可以正确地进行矩阵乘法，那么这里的代码有什么问题吗？
minimize() 的文档说 x0 应该是 (n,) 形状的数组，但您试图将其视为 (3,1) 数组。我不确定 minimize() 的内部工作原理，但我怀疑当它跨过拟合参数的不同值时，它会转换为它认为需要的格式。无论如何，以下小的更正使代码有效。
import numpy as np
from scipy.optimize import minimize
# define known variables, mu, sigma, rf
mu = np.matrix([[0.12],
[0.08],
[0.05]])
sigma = np.matrix([[0.5, 0.05, 0.03],
[0.05, 0.4, 0.01],
[0.03, 0.01, 0.2]])
rf = 0.02
def objective_fun(x):
'''
This is the objective function
'''
x = np.expand_dims(x, 1) # convert the (3,) shape to (3,1). Then we can do our normal matrix math on it
s = np.sqrt(x.T * sigma * x)/(mu.T * x - rf) # Transposes so the shapes are correct
return s
def constraint(x):
con = 1
for i in np.arange(0,3):
con = con - x[i]
return con
# set up the boundaries for x
bound_i = (0, np.Inf)
bnds = (bound_i, bound_i, bound_i)
#set up the constraints for x
con = {'type':'eq', 'fun':constraint}
# initial guess for variable x
x = np.array([0.5, 0.3, 0.2]) # Defining the initial guess as an (3,) array)
sol = minimize(objective_fun, x, method = 'SLSQP', bounds = bnds, constraints = con)
print(sol) # and the solution looks reasonable
输出
fun: 5.86953830952583
jac: array([-1.70555401, -1.70578796, -1.70573896])
message: 'Optimization terminated successfully.'
nfev: 32
nit: 6
njev: 6
status: 0
success: True
x: array([0.42809911, 0.29522438, 0.27667651])
查看我添加的评论，了解您需要做什么。