矩阵元素与向量值相乘

Question

我有一个矩阵 M，我想创建3个额外的矩阵，其中每个额外的矩阵都有 M 的某些 3x3 列切片乘以向量中的值，然后我将把得到的 3 个新矩阵存储在一个 list 中。

##create the initial matrix
M <- matrix(1:20, nrow = 4)

    [,1] [,2] [,3] [,4] [,5]
[1,]    1    5    9   13   17
[2,]    2    6   10   14   18
[3,]    3    7   11   15   19
[4,]    4    8   12   16   20

## coordinates in the matrix I want to alter 
iy <- c(1, 2, 3)
ix <- c(1, 4, 5)
coords <- as.data.frame(cbind(ix, iy))


## multiplier values
multis <- c(0.1, 2, 100)

我想要做的伪代码

mapply (function(multis, cords) {multis * M[coords$iy, coords$ix]})

期望的结果应该是什么样子

  [[1]]
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.1    5    9 13.0 17.0
[2,]  2.0    6   10  1.4 18.0
[3,]  3.0    7   11 15.0  1.1
[4,]  4.0    8   12 16.0 20.0

[[2]]
     [,1] [,2] [,3] [,4] [,5]
[1,]    2    5    9   13   17
[2,]    2    6   10   28   18
[3,]    3    7   11   15   38
[4,]    4    8   12   16   20

[[3]]
[,1] [,2] [,3] [,4] [,5]
[1,]  100    5    9   13   17
[2,]    2    6   10 1400   18
[3,]    3    7   11   15 1900
[4,]    4    8   12   16   20

- flee

---

你需要明确指出，乘法是指“按元素逐个相乘，使用3x1行向量”。不是矩阵乘法。 - smci

Answer 1

首先需要将coords强制转换为矩阵以便进行索引，然后反转列顺序。然后只需使用简单的lapply()循环即可。

coords <- as.matrix(coords)[, 2:1]
lapply(multis, function(x) {
    M[coords] <- M[coords] * x
    M
})

导致

[[1]]
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.1    5    9 13.0 17.0
[2,]  2.0    6   10  1.4 18.0
[3,]  3.0    7   11 15.0  1.9
[4,]  4.0    8   12 16.0 20.0

[[2]]
     [,1] [,2] [,3] [,4] [,5]
[1,]    2    5    9   13   17
[2,]    2    6   10   28   18
[3,]    3    7   11   15   38
[4,]    4    8   12   16   20

[[3]]
     [,1] [,2] [,3] [,4] [,5]
[1,]  100    5    9   13   17
[2,]    2    6   10 1400   18
[3,]    3    7   11   15 1900
[4,]    4    8   12   16   20

- Rich Scriven

Answer 2

另一种解决方案是使用一个已定义的函数，并针对每个“multis”使用“sapply”：

##create the initial matrix
M <- matrix(1:20, nrow = 4)

## coordinates in the matrix I want to alter 
Y <- c(1, 2, 3)
X <- c(1, 4, 5)
coords <- as.data.frame(cbind(X, Y))

## multiplier values
multis <- c(0.1, 2, 100)

## Modifying the specific coordinates.
modif.one.matrix <- function(one_multis, coords, M) {
    M_out <- M
    for(one_coord in 1:nrow(coords)) {
        M_out[coords$Y[one_coord], coords$X[one_coord]] <- M[coords$Y[one_coord], coords$X[one_coord]] * one_multis
    }
    return(M_out)
}

## Modifying one matrix
modif.one.matrix(multis[1], coords, M)
#     [,1] [,2] [,3] [,4] [,5]
#[1,]  0.1    5    9 13.0 17.0
#[2,]  2.0    6   10  1.4 18.0
#[3,]  3.0    7   11 15.0  1.9
#[4,]  4.0    8   12 16.0 20.0

## Modifying all the matrices
sapply(multis, modif.one.matrix, coords, M, simplify = FALSE)

#[[1]]
#     [,1] [,2] [,3] [,4] [,5]
#[1,]  0.1    5    9 13.0 17.0
#[2,]  2.0    6   10  1.4 18.0
#[3,]  3.0    7   11 15.0  1.9
#[4,]  4.0    8   12 16.0 20.0
#
#[[2]]
#     [,1] [,2] [,3] [,4] [,5]
#[1,]    2    5    9   13   17
#[2,]    2    6   10   28   18
#[3,]    3    7   11   15   38
#[4,]    4    8   12   16   20
#
#[[3]]
#     [,1] [,2] [,3] [,4] [,5]
#[1,]  100    5    9   13   17
#[2,]    2    6   10 1400   18
#[3,]    3    7   11   15 1900
#[4,]    4    8   12   16   20

- Thomas Guillerme