R help - Sep 2004 - making custom function compute/return multiple items

Hello, I'm relatively new to R.  I've read the intro guide, but I
can't quite figure out how to:

I have a function:

Jcost <- function (theta, in, out) {
  a <- output - input %*% theta
  1/2 * t(a) %*% a
}

where 
"theta" is a 2x1 matrix
"in" is a 20x2 matrix
"out" is a 20x1 matrix
return value is a scaler

This works well when I only want to compute given 1 theta matrix.  How
do I compute several (say N) 2x1 theta matrices and get back N scaler
values?

Thanks!

-- 
-david
David Chu

chumpy town <chumpytown at gmail.com> writes:
> Hello, I'm relatively new to R.  I've read the intro guide, but I
> can't quite figure out how to:
> 
> I have a function:
> 
> Jcost <- function (theta, in, out) {
>   a <- output - input %*% theta
>   1/2 * t(a) %*% a
> }
> 
> where 
> "theta" is a 2x1 matrix
> "in" is a 20x2 matrix
> "out" is a 20x1 matrix
> return value is a scaler
> 
> This works well when I only want to compute given 1 theta matrix.  How
> do I compute several (say N) 2x1 theta matrices and get back N scaler
> values?
> 
> Thanks!
Two tricks:

(A) You can't do this
> matrix(1:10,10,1)-matrix(1:20,10,2)
Error in matrix(1:10, 10, 1) - matrix(1:20, 10, 2) :
        non-conformable arrays

but you can do this (vector recycling)
> as.vector(matrix(1:10,10,1))-matrix(1:20,10,2)
      [,1] [,2]
 [1,]    0  -10
 [2,]    0  -10
 [3,]    0  -10
 [4,]    0  -10
 [5,]    0  -10
 [6,]    0  -10
 [7,]    0  -10
 [8,]    0  -10
 [9,]    0  -10
[10,]    0  -10

so if you put your theta vectors into a 2xN matrix you can get a 20xN
"a" matrix.

(B) If "a" has more than one column, you can use diag(t(a)%*%a) to get
the N scalars that you want, but that computes all the cross-products
unnecessarily. It will be much better to use colSums(a^2).

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907

chumpy town <chumpytown <at> gmail.com> writes:

: 
: Hello, I'm relatively new to R.  I've read the intro guide, but I
: can't quite figure out how to:
: 
: I have a function:
: 
: Jcost <- function (theta, in, out) {
:   a <- output - input %*% theta
:   1/2 * t(a) %*% a
: }
: 
: where 
: "theta" is a 2x1 matrix
: "in" is a 20x2 matrix
: "out" is a 20x1 matrix
: return value is a scaler
: 
: This works well when I only want to compute given 1 theta matrix.  How
: do I compute several (say N) 2x1 theta matrices and get back N scaler
: values?

Assuming `theta' is 2xN, apply the formula over the columns, i.e. dimension
2,
of `theta'.

By the way, note that `in', which is used above as a parameter to
`Jcost', is
a reserved word in R and so should be avoided.

Jcost <- function(theta, input, output) 
      apply(as.matrix(theta), 2, function(theta) 
         1/2 * crossprod(output - input %*% theta))
      
Jcost(1:2, matrix(1:40,20), 1:20)
Jcost(3:4, matrix(1:40,20), 1:20)

# the following combines both of the above two lines into one:
Jcost(cbind(1:2, 3:4), matrix(1:40,20), 1:20)