Floww Knaeple - 5 months ago 31

R Question

I have written the following function for multiplying two matrices

`A`

`B`

`f <- function(A,B){`

m<-nrow(A)

n<-ncol(A)

n<-nrow(B)

p<-ncol(B)

Result<-matrix(0,nrow = m,ncol = p)

for(i in 1:m){

for(j in 1:p){

for(k in 1:n){

Result[i,j]<-Result[i,j]+A[i,k]*B[k,j]

}

}

}

return(Result)

}

How would I adjust my function code to multiple 3 or more, i.e., a random number of matrices rather than just 2?

Answer

You just iteratively apply two-matrix multiplication. Let `f`

be the fundamental function multiplying two matrices `A`

and `B`

. Normally we use the internal one `%*%`

, but you can use the one defined in your question.

Since the number of matrices are unknown, I suggest using `...`

. We collect all matrices input into a "matrix list" by `list(...)`

, then use `Reduce`

to cumulatively apply two-operand matrix multiplication.

```
g <- function (...) Reduce(f, list(...))
```

Note, it is your responsibility to ensure the matrix dimension are conformable, especially when you have a lot of matrices. In the following, I would just use square matrices as an example.

```
set.seed(0)
A <- matrix(rnorm(4),2)
B <- matrix(rnorm(4),2)
C <- matrix(rnorm(4),2)
f <- "%*%"
g(A, B, C)
# [,1] [,2]
#[1,] -3.753667 0.08634328
#[2,] -0.161250 -1.54194176
```

And this is as same as:

```
A %*% B %*% C
# [,1] [,2]
#[1,] -3.753667 0.08634328
#[2,] -0.161250 -1.54194176
```