About 5.1 Arrays

Hi Daniel,

Thanks for your detail advice.  I completely understand your explain.

But I can't resolve what does "a" stand for there?

a[1,1,1] is 1 * 1 * 1 = 1
a[2,1,1] is 2 * 1 * 1 = 2
a[2,4,2] is 2 * 4 * 2 = 16
a[3,4,2] is 3 * 4 * 2 = 24

?


B.R.
Stephen L







----- Original Message ----
From: Daniel Nordlund <djnordlund at frontier.com>
To: r-help at r-project.org
Sent: Fri, November 5, 2010 11:54:15 PM
Subject: Re: [R] About 5.1 Arrays

-----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


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