Matrix Multiplication using loop

Question

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

Matrix A:

2   3
4   2

Code:

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

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

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

Expected Output:

c <- b %*% a

c

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

d <- c %*% a

d

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

e <- d %*% a

e

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

f <- e %*% a

f

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

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

the logic is different in the earlier question posted.

Do you need all matrices or only the last result? You can write your own function for this task. — jogo, Dec 12 '17 at 09:11
Possible duplicate of [Matrix Multiplication for loop of n number of months](https://stackoverflow.com/questions/47765860/matrix-multiplication-for-loop-of-n-number-of-months) — Ronak Shah, Dec 12 '17 at 09:29
there are some changes in the multiplication of matrix. logic is different. — , Dec 12 '17 at 09:30

jogo · Accepted Answer · 2017-12-12T10:09:52.220

You can do:

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)

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)
}

Without defining a new function you can do:

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

Matrix Multiplication using loop

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