[R] building random matrices from vectors of random parameters

[Duncan Murdoch]

On 27/09/2017 8:47 PM, Evan Cooch wrote:
> Suppose I have interest in a matrix with the following symbolic
> structure (specified by 3 parameters: sa, so, m):
> 
> matrix(c(0,sa*m,so,sa),2,2,byrow=T)
> 
> What I can't figure out is how to construct a series of matrices, where
> the elements/parameters are rnorm values. I'd like to construct separate
> matrices, with each matrix in the series using the 'next random
> parameter value'. While the following works (for generating, say, 5 such
> random matrices)
> 
> replicate(5,matrix(c(0,rnorm(1,0.8,0.1)*rnorm(1,1.2,0.1),rnorm(1,0.5,0.1),rnorm(1,0.8,0.1)),2,2,byrow=T))
> 
> its inelegant, and a real pain if the matrix gets large (say, 20 x 20).
> 
> I'm wondering if there is an easier way. I tried
> 
>   > sa <- rnorm(5,0.8,0.1)
>   > so <- rnorm(5,0.5,0.1)
>   > m <- rnorm(5,1.2,0.1)
> 
> matrix(c(0,sa*m,so,sa),2,2,byrow=T)
> 
> but that only returns a single matrix, not 5 matrices as I'd like. I
> also tried several variants of the 'replicate' approach (above), but
> didn't stumble across anything that seemed to work.
> 
> So, is there a better way than something like:
> 
> replicate(5,matrix(c(0,rnorm(1,0.8,0.1)*rnorm(1,1.2,0.1),rnorm(1,0.5,0.1),rnorm(1,0.8,0.1)),2,2,byrow=T))
> 

Peter's mapply solution is probably the best.  Another that might be a 
little faster (but more obscure) is to use a 3-index array.  I think 
this is what you'd want, with sa, so, and m as defined above:

ms <- array(c(rep(0, 5),sa*m,so,sa), c(5, 2, 2))

Then matrix i will be stored as ms[i,,].

Duncan Murdoch