如何找到向量'；满足R中某些线性约束的s值（仅整数）？

给定一个向量和一个和，例如极限=c（1,2,5,6,7,6）和 总和=10。 给定的约束条件是：

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x1这里有一种方法可以得到所有可能的解决方案

library(partitions)

allPartitions <- compositions(10, 6, include.zero = FALSE)
limits <- c(1, 2, 5, 6, 7, 6) 
good <- apply(allPartitions, 2, function(x) all(x <= limits))
results <- allPartitions[, good]

或者，更简洁、更高效：

> results <- sweep(blockparts(limits-1,10-6), 1, c(1,1,1,1,1,1), "+")
> t(results)

 [1,] 1 2 4 1 1 1
 [2,] 1 1 5 1 1 1
 [3,] 1 2 3 2 1 1
 [4,] 1 1 4 2 1 1
 [5,] 1 2 2 3 1 1
 [6,] 1 1 3 3 1 1
 [7,] 1 2 1 4 1 1
 [8,] 1 1 2 4 1 1
 [9,] 1 1 1 5 1 1
[10,] 1 2 3 1 2 1
[11,] 1 1 4 1 2 1
[12,] 1 2 2 2 2 1
[13,] 1 1 3 2 2 1
[14,] 1 2 1 3 2 1
[15,] 1 1 2 3 2 1
[16,] 1 1 1 4 2 1
[17,] 1 2 2 1 3 1
[18,] 1 1 3 1 3 1
[19,] 1 2 1 2 3 1
[20,] 1 1 2 2 3 1
[21,] 1 1 1 3 3 1
[22,] 1 2 1 1 4 1
[23,] 1 1 2 1 4 1
[24,] 1 1 1 2 4 1
[25,] 1 1 1 1 5 1
[26,] 1 2 3 1 1 2
[27,] 1 1 4 1 1 2
[28,] 1 2 2 2 1 2
[29,] 1 1 3 2 1 2
[30,] 1 2 1 3 1 2
[31,] 1 1 2 3 1 2
[32,] 1 1 1 4 1 2
[33,] 1 2 2 1 2 2
[34,] 1 1 3 1 2 2
[35,] 1 2 1 2 2 2
[36,] 1 1 2 2 2 2
[37,] 1 1 1 3 2 2
[38,] 1 2 1 1 3 2
[39,] 1 1 2 1 3 2
[40,] 1 1 1 2 3 2
[41,] 1 1 1 1 4 2
[42,] 1 2 2 1 1 3
[43,] 1 1 3 1 1 3
[44,] 1 2 1 2 1 3
[45,] 1 1 2 2 1 3
[46,] 1 1 1 3 1 3
[47,] 1 2 1 1 2 3
[48,] 1 1 2 1 2 3
[49,] 1 1 1 2 2 3
[50,] 1 1 1 1 3 3
[51,] 1 2 1 1 1 4
[52,] 1 1 2 1 1 4
[53,] 1 1 1 2 1 4
[54,] 1 1 1 1 2 4
[55,] 1 1 1 1 1 5

>结果t（结果）
[1,] 1 2 4 1 1 1
[2,] 1 1 5 1 1 1
[3,] 1 2 3 2 1 1
[4,] 1 1 4 2 1 1
[5,] 1 2 2 3 1 1
[6,] 1 1 3 3 1 1
[7,] 1 2 1 4 1 1
[8,] 1 1 2 4 1 1
[9,] 1 1 1 5 1 1
[10,] 1 2 3 1 2 1
[11,] 1 1 4 1 2 1
[12,] 1 2 2 2 2 1
[13,] 1 1 3 2 2 1
[14,] 1 2 1 3 2 1
[15,] 1 1 2 3 2 1
[16,] 1 1 1 4 2 1
[17,] 1 2 2 1 3 1
[18,] 1 1 3 1 3 1
[19,] 1 2 1 2 3 1
[20,] 1 1 2 2 3 1
[21,] 1 1 1 3 3 1
[22,] 1 2 1 1 4 1
[23,] 1 1 2 1 4 1
[24,] 1 1 1 2 4 1
[25,] 1 1 1 1 5 1
[26,] 1 2 3 1 1 2
[27,] 1 1 4 1 1 2
[28,] 1 2 2 2 1 2
[29,] 1 1 3 2 1 2
[30,] 1 2 1 3 1 2
[31,] 1 1 2 3 1 2
[32,] 1 1 1 4 1 2
[33,] 1 2 2 1 2 2
[34,] 1 1 3 1 2 2
[35,] 1 2 1 2 2 2
[36,] 1 1 2 2 2 2
[37,] 1 1 1 3 2 2
[38,] 1 2 1 1 3 2
[39,] 1 1 2 1 3 2
[40,] 1 1 1 2 3 2
[41,] 1 1 1 1 4 2
[42,] 1 2 2 1 1 3
[43,] 1 1 3 1 1 3
[44,] 1 2 1 2 1 3
[45,] 1 1 2 2 1 3
[46,] 1 1 1 3 1 3
[47,] 1 2 1 1 2 3
[48,] 1 1 2 1 2 3
[49,] 1 1 1 2 2 3
[50,] 1 1 1 1 3 3
[51,] 1 2 1 1 1 4
[52,] 1 1 2 1 1 4
[53,] 1 1 1 2 1 4
[54,] 1 1 1 1 2 4
[55,] 1 1 1 1 1 5

这是一个优化问题。如果x是非整数，则可能有无穷多个解。查看

lpSolve

软件包小插图

library(partitions)

allPartitions <- compositions(10, 6, include.zero = FALSE)
limits <- c(1, 2, 5, 6, 7, 6) 
good <- apply(allPartitions, 2, function(x) all(x <= limits))
results <- allPartitions[, good]

> t(results)
      [,1] [,2] [,3] [,4] [,5] [,6]
 [1,]    1    2    4    1    1    1
 [2,]    1    1    5    1    1    1
 [3,]    1    2    3    2    1    1
 [4,]    1    1    4    2    1    1
 [5,]    1    2    2    3    1    1
 [6,]    1    1    3    3    1    1
 [7,]    1    2    1    4    1    1
 [8,]    1    1    2    4    1    1
 [9,]    1    1    1    5    1    1
[10,]    1    2    3    1    2    1
[11,]    1    1    4    1    2    1
[12,]    1    2    2    2    2    1
[13,]    1    1    3    2    2    1
[14,]    1    2    1    3    2    1
[15,]    1    1    2    3    2    1
[16,]    1    1    1    4    2    1
[17,]    1    2    2    1    3    1
[18,]    1    1    3    1    3    1
[19,]    1    2    1    2    3    1
[20,]    1    1    2    2    3    1
[21,]    1    1    1    3    3    1
[22,]    1    2    1    1    4    1
[23,]    1    1    2    1    4    1
[24,]    1    1    1    2    4    1
[25,]    1    1    1    1    5    1
[26,]    1    2    3    1    1    2
[27,]    1    1    4    1    1    2
[28,]    1    2    2    2    1    2
[29,]    1    1    3    2    1    2
[30,]    1    2    1    3    1    2
[31,]    1    1    2    3    1    2
[32,]    1    1    1    4    1    2
[33,]    1    2    2    1    2    2
[34,]    1    1    3    1    2    2
[35,]    1    2    1    2    2    2
[36,]    1    1    2    2    2    2
[37,]    1    1    1    3    2    2
[38,]    1    2    1    1    3    2
[39,]    1    1    2    1    3    2
[40,]    1    1    1    2    3    2
[41,]    1    1    1    1    4    2
[42,]    1    2    2    1    1    3
[43,]    1    1    3    1    1    3
[44,]    1    2    1    2    1    3
[45,]    1    1    2    2    1    3
[46,]    1    1    1    3    1    3
[47,]    1    2    1    1    2    3
[48,]    1    1    2    1    2    3
[49,]    1    1    1    2    2    3
[50,]    1    1    1    1    3    3
[51,]    1    2    1    1    1    4
[52,]    1    1    2    1    1    4
[53,]    1    1    1    2    1    4
[54,]    1    1    1    1    2    4
[55,]    1    1    1    1    1    5

> results <- sweep(blockparts(limits-1,10-6), 1, c(1,1,1,1,1,1), "+")
> t(results)

 [1,] 1 2 4 1 1 1
 [2,] 1 1 5 1 1 1
 [3,] 1 2 3 2 1 1
 [4,] 1 1 4 2 1 1
 [5,] 1 2 2 3 1 1
 [6,] 1 1 3 3 1 1
 [7,] 1 2 1 4 1 1
 [8,] 1 1 2 4 1 1
 [9,] 1 1 1 5 1 1
[10,] 1 2 3 1 2 1
[11,] 1 1 4 1 2 1
[12,] 1 2 2 2 2 1
[13,] 1 1 3 2 2 1
[14,] 1 2 1 3 2 1
[15,] 1 1 2 3 2 1
[16,] 1 1 1 4 2 1
[17,] 1 2 2 1 3 1
[18,] 1 1 3 1 3 1
[19,] 1 2 1 2 3 1
[20,] 1 1 2 2 3 1
[21,] 1 1 1 3 3 1
[22,] 1 2 1 1 4 1
[23,] 1 1 2 1 4 1
[24,] 1 1 1 2 4 1
[25,] 1 1 1 1 5 1
[26,] 1 2 3 1 1 2
[27,] 1 1 4 1 1 2
[28,] 1 2 2 2 1 2
[29,] 1 1 3 2 1 2
[30,] 1 2 1 3 1 2
[31,] 1 1 2 3 1 2
[32,] 1 1 1 4 1 2
[33,] 1 2 2 1 2 2
[34,] 1 1 3 1 2 2
[35,] 1 2 1 2 2 2
[36,] 1 1 2 2 2 2
[37,] 1 1 1 3 2 2
[38,] 1 2 1 1 3 2
[39,] 1 1 2 1 3 2
[40,] 1 1 1 2 3 2
[41,] 1 1 1 1 4 2
[42,] 1 2 2 1 1 3
[43,] 1 1 3 1 1 3
[44,] 1 2 1 2 1 3
[45,] 1 1 2 2 1 3
[46,] 1 1 1 3 1 3
[47,] 1 2 1 1 2 3
[48,] 1 1 2 1 2 3
[49,] 1 1 1 2 2 3
[50,] 1 1 1 1 3 3
[51,] 1 2 1 1 1 4
[52,] 1 1 2 1 1 4
[53,] 1 1 1 2 1 4
[54,] 1 1 1 1 2 4
[55,] 1 1 1 1 1 5