[R] About 5.1 Arrays

[Daniel Nordlund]

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> On Behalf Of Stephen Liu
> Sent: Friday, November 05, 2010 7:57 AM
> To: Steve Lianoglou
> Cc: r-help at r-project.org
> Subject: Re: [R] About 5.1 Arrays
> 
> Hi Steve,
> 
> > It's not clear what you're having problems understanding. By
> > setting the "dim" attribute of your (1d) vector, you are changing
> > itsdimenensions.
> 
> I'm following An Introduction to R to learn R
> 
> On
> 
> 5.1 Arrays
> http://cran.r-project.org/doc/manuals/R-intro.html#Vectors-and-assignment
> 
> 
> It mentions:-
> ...
> For example if the dimension vector for an array, say a, is c(3,4,2) then
> there
> are 3 * 4 * 2 = 24 entries in a and the data vector holds them in the
> order
> a[1,1,1], a[2,1,1], ..., a[2,4,2], a[3,4,2].
> 
> 
> I don't understand "on .... =24 entries in a and the data vector holds
> them in
> the order a[1,1,1], a[2,1,1], ..., a[2,4,2], a[3,4,2]."  the order
> a[1,1,1],
> a[2,1,1], ..., a[2,4,2], a[3,4,2]?  What does it mean "the order a[1,1,1],
> a[2,1,1], ..., a[2,4,2], a[3,4,2]"?
> 
> Thanks
> 
> B.R.
> Stephen
> 
> 

Stephen,

Start with a vector of length = 12.  The vector, v, is stored in consecutive locations in memory, one after the other.  And 

> v <- 1:12
> v
 [1]  1  2  3  4  5  6  7  8  9 10 11 12

Now change then change the dimension of v to c(3,4), i.e. a matrix with 3 rows and 4 columns.  
 
> dim(v) <- c(3,4)
> v
     [,1] [,2] [,3] [,4]
[1,]    1    4    7   10
[2,]    2    5    8   11
[3,]    3    6    9   12

The values of v are still stored in memory in consecutive locations.  But now you refer to the first location as v[1,1], the second as v[2,1], third as v[3,1] ... and the 12th as v[3,4].  We sometimes talk about the values "going into" v[1,1] or more generally, v[i,j], but the values aren't going anywhere.  They are still stored in consecutive locations.  We are just changing how they are referred to when we change the dimensions.

So in the 2-dimensional matrix above, the values of the vector v "go into" the matrix in column order, i.e. the first column is filled first, then the second, ...  

Now, create a 24 element vector.

> v <- 1:24
> v
 [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Change the dimensions to a 3-dimensional array.

> dim(v) <- c(3,4,2)
> v
, , 1

     [,1] [,2] [,3] [,4]
[1,]    1    4    7   10
[2,]    2    5    8   11
[3,]    3    6    9   12

, , 2

     [,1] [,2] [,3] [,4]
[1,]   13   16   19   22
[2,]   14   17   20   23
[3,]   15   18   21   24

You can visualize a 3-dimensional array as a series of 2-dimensional arrays stacked on top of each other.  But this is just a convenient image.  The items are still stored consecutively in memory.  Notice that layer one in the stack was "filled" first, and the first layer was "filled" just like the previous 2-dimensional example.  But the items are still physically stored linearly, in consecutive locations in memory.

Hope this is helpful,

Dan

Daniel Nordlund
Bothell, WA USA