熊猫系列的绝对值之和

Question

我正在尝试修改从gurobi网站获得的投资组合示例。在示例中，存在一个线性问题，该线性问题可以用[0，1]中的所有var解决。我想将其更改为[-1，1]范围，而不是vars.sum() == 1，我需要var的绝对值之和。

我尝试了很多事情... vars.abs_().sum()，abs_(vars).sum()等，无法完成。

#!/usr/bin/python
from gurobipy import *
from math import sqrt
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import os

def moneta():

    # Import (normalized) historical return data using pandas
    caminho = os.getcwd() + "\evo_val1h.csv"
    #caminho = os.getcwd() + "\evo_val5min.csv"
    data = pd.DataFrame.from_csv(caminho)
    stocks = data.columns
    retorno = []

    # Calculate basic summary statistics for individual stocks
    stock_volatility = data.std()
    stock_return = data.mean()

    # Create an empty model
    m = Model('portfolio')

    # Add a variable for each stock
    vars = pd.Series(m.addVars(stocks, ub=1.0, lb=-1.0), index=stocks)
    # Objective is to minimize risk (squared).  This is modeled using the
    # covariance matrix, which measures the historical correlation between stocks.
    sigma = data.cov()
    portfolio_risk = sigma.dot(vars).dot(vars)
    m.setObjective(portfolio_risk, GRB.MINIMIZE)
    # Fix budget with a constraint
    m.addConstr(vars.sum() == 1, 'budget')
    print(vars)
    # Optimize model to find the minimum risk portfolio
    m.setParam('OutputFlag', 0)
    m.optimize()
    # Create an expression representing the expected return for the portfolio
    portfolio_return = stock_return.dot(vars)

    m.setObjective(portfolio_return - 80*portfolio_risk, GRB.MAXIMIZE)
    m.optimize()
    # Display minimum risk portfolio
    print('Minimum Risk Portfolio:\n')
    soma = 0.0
    for v in vars:
        if v.x > 0.03 or v.x < -0.03:
            print('\t%s\t: %g' % (v.varname, 100*v.x))
            soma += 100*v.x
            retorno.append(v.varname.replace("C", ""))
            retorno.append(str(v.x))
    print(soma)
    minrisk_volatility = sqrt(portfolio_risk.getValue())
    print('\nVolatility      = %g' % minrisk_volatility)
    minrisk_return = portfolio_return.getValue()
    print('Expected Return = %g' % minrisk_return)

    # Add (redundant) target return constraint
    target = m.addConstr(portfolio_return == minrisk_return, 'target')

    # Solve for efficient frontier by varying target return
    frontier = pd.Series()
    for r in np.linspace(stock_return.min(), stock_return.max(), 100):
        target.rhs = r
        m.optimize()
        frontier.loc[sqrt(portfolio_risk.getValue())] = r

    # Plot volatility versus expected return for individual stocks
    ax = plt.gca()
    ax.scatter(x=stock_volatility, y=stock_return,
               color='Blue', label='Individual Stocks')
    for i, stock in enumerate(stocks):
        if stock_return[i] > 0.05:
            ax.annotate(stock, (stock_volatility[i], stock_return[i]))


    # Plot volatility versus expected return for minimum risk portfolio
    ax.scatter(x=minrisk_volatility, y=minrisk_return, color='DarkGreen')
    ax.annotate('Minimum\nRisk\nPortfolio', (minrisk_volatility, minrisk_return),
                horizontalalignment='right')

    # Plot efficient frontier
    frontier.plot(color='DarkGreen', label='Efficient Frontier', ax=ax)

    # Format and display the final plot
    ax.axis([-0.05, 0.06, -0.01, 0.01])
    ax.set_xlabel('Volatility (standard deviation)')
    ax.set_ylabel('Expected Return')
    ax.legend()
    ax.grid()
    plt.show()
    return retorno
moneta()

由第33行插入：m.addConstr(vars.sum() == 1, 'budget') 我需要pd.Series vars的绝对值之和