矩阵乘法使用循环 [英] Matrix Multiplication using loop

问题描述

我有一个链式矩阵乘法问题.我只有一个输入矩阵A，将保存矩阵B<-矩阵A.需要按以下方式进行乘法

I have a matrix multiplication problem in a chain format. I only have a input Matrix A, will save Matrix B <- Matrix A. Need to multiply in the below fashion

C = B * A
D = C * A
E = D * A

A是每个月所有乘法的参考矩阵. 这个乘法链持续了18个月.

A is a reference matrix for all the multiplication for each month. this chain of multiplication taken places till 18 months.

矩阵A:

2   3
4   2

代码:

a = matrix( c(2, 3, 4, 2), nrow=2, ncol=2, byrow = TRUE) 
b <- a 
c <- b %*% a
d <- c %*% a
e <- d %*% a
f <- e %*% a
g <- f %*% a

每个时间A是将来与结果相乘的参考矩阵.重复了18次.

Each time A is the reference matrix for future multiplication with the result. This repeated for 18 times.

我必须手动对上述乘法进行18次校正，因此需要查找循环.

I have to manually right the above multiplication for 18 times, so looking for a loop.

预期输出:

c<-b％*％a

c <- b %*% a

c

     [,1] [,2]
[1,]   16   12
[2,]   16   16

d<-c％*％a

d <- c %*% a

d

     [,1] [,2]
[1,]   80   72
[2,]   96   80

e<-d％*％a

e <- d %*% a

e

     [,1] [,2]
[1,]  448  384
[2,]  512  448

f<-e％*％a

f <- e %*% a

f

     [,1] [,2]
[1,] 2432 2112
[2,] 2816 2432

因此应重复18次.请帮忙.提前致谢.

so this should be repeated for 18 times. Please help. Thanks in Advance.

在先前发布的问题中，逻辑是不同的.

the logic is different in the earlier question posted.

推荐答案

您可以这样做:

Mpow <- function(A, n) {
  if (n==1) return(list(A))
  L <- list(A)
  P <- A
  for (i in 2:n) {
    P <- P %*% A
    L[[i]] <- P
  }
  return(L)
}

a = matrix( c(2, 3, 4, 2), nrow=2, ncol=2, byrow = TRUE) 
Mpow(a, 1)
Mpow(a, 2)
Mpow(a, 18)

您将获得矩阵幂的列表.问题中的矩阵f是Mpow(a,5)的最后一个元素.
这是该函数的简短变体:

You will get a list of the powers of the matrix. The matrix f in the question is the last element of Mpow(a,5).
Here is short variant of the function:

Mpow <- function(A, n) {
  L <- list(A)
  if (n==1) return(L)
  P <- A
  for (i in 2:n) L[[i]] <- (P <- P %*% A)
  return(L)
}

无需定义新功能，您可以执行以下操作:

Without defining a new function you can do:

n <- 5
Reduce('%*%', rep(list(a), n), accumulate=TRUE)

这篇关于矩阵乘法使用循环的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！