R help - Sep 2017 - building random matrices from vectors of random parameters

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))

Many thanks in advance...

I would try something like

n = 5
a <- rnorm(n,0.8,0.1)
so <- rnorm(n,0.5,0.1)
m <- rnorm(n,1.2,0.1)
mats = mapply(function(sa1, so1, m1) matrix(c(0,sa1*m1,so1,sa1),2,2,byrow=T),
                       a, so, m, SIMPLIFY = FALSE)
> mats
[[1]]
          [,1]      [,2]
[1,] 0.0000000 0.9129962
[2,] 0.4963598 0.7067311

[[2]]
          [,1]      [,2]
[1,] 0.0000000 1.0150316
[2,] 0.5489887 0.8469046

[[3]]
          [,1]      [,2]
[1,] 0.0000000 0.9516137
[2,] 0.3724521 0.8306535

[[4]]
          [,1]      [,2]
[1,] 0.0000000 1.0525355
[2,] 0.8075108 0.8314638

[[5]]
          [,1]      [,2]
[1,] 0.0000000 0.9400074
[2,] 0.4803386 0.7901753

On Wed, Sep 27, 2017 at 5:47 PM, Evan Cooch <evan.cooch at gmail.com>
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))
>
> Many thanks in advance...
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

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

Thanks for both the mapply and array approaches! However, although 
intended to generate the same result, they don't:

# mapply approach

n = 3
sa <- rnorm(n,0.8,0.1)
so <- rnorm(n,0.5,0.1)
m <- rnorm(n,1.2,0.1)
mats = mapply(function(sa1, so1, m1) 
matrix(c(0,sa1*m1,so1,sa1),2,2,byrow=T), sa, so, m, SIMPLIFY = FALSE)

print(mats)

[[1]]
 ????????? [,1]????? [,2]
[1,] 0.0000000 0.8643679
[2,] 0.4731249 0.7750431

[[2]]
 ????????? [,1]????? [,2]
[1,] 0.0000000 0.8838286
[2,] 0.5895258 0.7880983

[[3]]
 ????????? [,1]????? [,2]
[1,] 0.0000000 1.1491560
[2,] 0.4947322 0.9744166


Now, the array approach:

# array approach

ms <- array(c(rep(0, 3),sa*m,so,sa), c(3, 2, 2))

for (i in 1:n) { print(ms[i,,])

 ????????? [,1]????? [,2]
[1,] 0.0000000 0.4731249
[2,] 0.8643679 0.7750431

 ????????? [,1]????? [,2]
[1,] 0.0000000 0.5895258
[2,] 0.8838286 0.7880983

 ???????? [,1]????? [,2]
[1,] 0.000000 0.4947322
[2,] 1.149156 0.9744166


These matrices are the transpose of those returned by the mapply 
approach. To see if one approach or the other is 'confused', I simply 
rerun setting sd=0 for the parameters -- thus, every matrix will be the 
same. The correct matrix would be:

 ???? [,1] [,2]
[1,]? 0.0 0.96
[2,]? 0.5 0.80


In fact, this is what is returned by the mapply approach, while the 
array approach returns the transpose. I gather the 'missing step' is to 
use aperm, but haven't figured out how to get that to work...yet.


On 9/28/2017 5:11 AM, Duncan Murdoch wrote:
> ms <- array(c(rep(0, 5),sa*m,so,sa), c(5, 2, 2)) 

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