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MATRIX 2.3:提升Excel矩阵运算与规划求解能力

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根据提供的文件信息,以下为相关的知识点详细说明: 标题知识点: "Matrix for Excel" 提示我们该文件可能与在Microsoft Excel中使用矩阵相关功能的软件或工具有关。Excel是微软公司的电子表格程序,广泛应用于数据分析、财务模型、报告以及其他多种办公场景中。在Excel中利用矩阵能够处理更复杂的数学问题,包括线性代数运算等。 描述知识点: 描述中提到的"MATRIX 2.3-Matrix and Linear Algebra functions for EXCEL" 揭示了这个文件是关于名为 MATRIX 2.3 的插件,它为Excel增添了强大的矩阵运算和线性代数功能。这表明 MATRIX 2.3 插件是专门设计用于扩展Excel的数学处理能力,使其能够执行更高级的数学运算,这对于需要进行复杂数据分析和数学建模的专业人士来说非常有用。 插件可以嵌入到Excel中,这意味着它提供了额外的功能集,用户无需离开Excel界面即可执行矩阵运算和规划求解等任务。矩阵运算是处理多维数组数据的关键技术,而规划求解则广泛应用于优化问题,如资源分配、成本最小化等。 描述中还提到该插件不支持Vista系统。Vista指的是微软公司推出的Windows Vista操作系统,而该插件仅支持Windows XP和Windows Server 2003。这说明在使用MATRIX 2.3时需要考虑到操作系统兼容性问题。 标签知识点: 标签中列出了"Matrix Excel 规划求解 矩阵 插件"等关键词,这些关键词均指向了与插件相关的功能和用途。从标签可以看出,该插件的主要功能包括在Excel中进行矩阵运算和规划求解。 文件名称列表知识点: 文件名称列表中提供了两个与学习使用该插件相关的文件:“MatrixTutorial.part1.pdf” 和 “MatrixTutorial.part2.pdf”,这些是教学指南或者教程。"part1" 和 "part2" 表明教程被分成了至少两个部分,用户可能需要按照顺序阅读这些文件来完整地学习如何使用MATRIX 2.3插件。 "MATRIX 2.3-Matrix and Linear Algebra functions for EXCEL.zip" 是一个压缩文件,它可能包含插件程序本身以及所有相关文件。ZIP是一种常用的文件压缩格式,它能减少文件大小,便于传输和存储。压缩文件的出现表明用户可能需要先解压这个文件,才能进行插件的安装和使用。 总结以上信息,我们可以得出: - MATRIX 2.3 是一个专为Excel设计的插件,目的是为了增强Excel处理矩阵和线性代数运算的能力。 - 插件适用于较旧的Windows操作系统,但不支持Windows Vista。 - 插件包含一个用户教程,分为至少两个部分,并且可能需要解压后安装。 - 插件在矩阵运算和规划求解方面表现强大,可广泛应用于科学计算、数据分析等领域。 为确保正确使用插件并完全掌握其功能,用户应当遵循教程的指导,安装前确认操作系统兼容性,并对线性代数和矩阵理论具备基本的理解。插件的使用能够提高工作效率,特别是在进行大量数学运算和数据分析时更为显著。

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import cvxpy as cp import numpy as np import pandas as pd data = pd.read_excel('附件1.xlsx') X = data.iloc[1:, 1:2] Y = data.iloc[1:, 2:3] W = data.iloc[2:, 3:4] # 收集点垃圾量(i=1..n) xi = X.values.flatten() # 转换为一维数组 (n,) yi = Y.values.flatten() # 转换为一维数组 (n,) wi = W.values.flatten() # 转换为一维数组 (n,) # 定义参数 n = 30 # 收集点数量(i=1..n,0为处理厂) K = 30 # 车辆总数 Q = 5 # 最大载重 # 计算距离矩阵dij(i,j=0..n) dij = np.zeros((n+1, n+1)) for i in range(n+1): for j in range(n+1): dij[i, j] = np.sqrt((xi[i] - xi[j])**2 + (yi[i] - yi[j])**2) x = cp.Variable((n+1, n+1, K), boolean=True) # x_ijv: 车辆v从i到j y = cp.Variable((n, K), boolean=True) # y_iv: 车辆v服务收集点i(i=1..n,索引0..n-1) z = cp.Variable(K, boolean=True) # z_v: 使用车辆v u = cp.Variable((n+1, K), nonneg=True) # u_iv: 车辆v访问i后的累计载重(i=0..n,u[0,v]=0) objective = cp.Minimize(cp.sum(cp.sum(cp.sum(dij @ x, axis=2), axis=1), axis=0)) # 约束条件 constraints = [] # 1. 每个收集点被 exactly 一辆车服务(i=1..n,对应y的索引0..n-1) for i in range(n): constraints.append(cp.sum(y[i, :]) == 1) # 2. 流量守恒(i=1..n,处理厂i=0的约束在6中) for i in range(1, n+1): # 收集点i(1..n,y索引i-1) for v in range(K): constraints.append(cp.sum(x[i, :, v]) == y[i-1, v]) # 离开i的次数等于服务i的次数 constraints.append(cp.sum(x[:, i, v]) == y[i-1, v]) # 进入i的次数等于服务i的次数 # 3. 载重约束 for v in range(K): constraints.append(cp.sum(wi * y[:, v]) <= Q * z[v]) # 4. MTZ约束(子回路消除) for v in range(K): constraints.append(u[0, v] == 0) # 处理厂出发时载重为0 for i in range(1, n+1): # 收集点i(1..n,wi[i-1]) constraints.append(u[i, v] >= wi[i-1]) # 载重下限 constraints.append(u[i, v] <= Q) # 载重上限 for j in range(1, n+1): if i != j: constraints.append(u[i, v] - u[j, v] + Q * x[i, j, v] <= Q - wi[j-1]) # 5. 车辆使用约束:服务收集点则使用车辆 for i in range(n): for v in range(K): constraints.append(y[i, v] <= z[v]) # 6. 出发返回约束(处理厂i=0,出发到收集点1..n,返回从收集点1..n到0) for v in range(K): constraints.append(cp.sum(x[0, 1:, v]) == z[v]) # 出发次数等于车辆使用 constraints.append(cp.sum(x[1:, 0, v]) == z[v]) # 返回次数等于车辆使用 # 建立问题并求解 problem = cp.Problem(objective, constraints) problem.solve() # 输出结果(示例,需根据实际需求处理) print("最优目标值:", problem.value) print("使用的车辆:", z.value)D:\python\python.exe D:\35433\Documents\数模练习\电工杯\问题1.py D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 1 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 2 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 3 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 4 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 5 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 6 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 7 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 8 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 9 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 10 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 11 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 12 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 13 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 14 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 15 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 16 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 17 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 18 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 19 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 20 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 21 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 22 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 23 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 24 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 25 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 26 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 27 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 28 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 29 times so far. D:\python\Lib\site-packages\cvxpy\expressions\expression.py:674: UserWarning: This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit 30 times so far. D:\python\Lib\site-packages\cvxpy\reductions\solvers\solving_chain_utils.py:41: UserWarning: The problem has an expression with dimension greater than 2. Defaulting to the SCIPY backend for canonicalization.