R help - Jun 2009 - sampling quadrats of increasing size in a list of matrices

Dear R-Users,

I have a problem and I have already surveyed different packages 
especially in the Spatial-TASK view but did not find something 
applicable. :(

I am looking for a solution on how to sample increasing sizes of 
"quadrats" in a list of matrices. Each matrix is a binary raster map
and
I want to know if there is a 1 or only 0 s in the sampling unit 
(quadrat, e.g. 4x4 cells). This block has to vary in size so that each 
time the area of the matrix (think of a map) is sampled, the areas I am 
looking at are becoming larger. That means, in the first run cellsize 
would 1x1 than 2x2 than 4x4 than 8x8 than 16x16 up to 64x64 which is the 
final size of a matrix.

Furthermore, I need this done on a list object consisting of a set of 
matrices, all with the same size (64x64). The list is 100 objects
"tall".

The result should be a again a vector for each matrix with the length of 
possible steps to sample the quadrat. This vector should report for each 
sampling unit a 1 if there is a 1 somewhere otherwise the value should 
be zero.

e.g. this is matrix number 90 from my list ( only showing a subset from 
16 x16)

     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] 
[,13] [,14] [,15] [,16]
 [1,]    0    0    1    1    1    0    1    1    1     1     1     0     
0     0     1     1
 [2,]    0    1    1    1    0    1    0    1    1     0     1     1     
1     1     1     1
 [3,]    1    0    1    1    1    1    0    1    1     1     1     1     
0     1     0     1
 [4,]    0    0    0    0    1    0    0    1    1     0     1     1     
1     1     1     1
 [5,]    1    1    1    1    1    0    0    1    0     1     1     0     
0     0     0     0
 [6,]    1    0    1    1    0    0    0    0    0     1     1     1     
1     0     1     1
 [7,]    1    1    0    1    1    1    1    1    1     1     1     1     
1     0     1     0
 [8,]    1    1    1    1    1    0    1    0    1     1     1     0     
1     1     1     1
 [9,]    1    0    1    0    1    1    1    1    1     1     0     1     
1     1     1     1
[10,]    1    1    1    1    1    1    1    0    1     0     0     0     
0     1     1     1
[11,]    0    1    0    1    1    1    0    1    1     0     0     1     
1     1     1     1
[12,]    1    1    1    1    0    1    1    1    1     1     0     1     
1     1     0     0
[13,]    1    1    1    1    1    1    1    0    0     1     1     1     
1     1     0     0
[14,]    1    1    0    1    1    0    0    1    0     0     1     1     
1     0     1     1
[15,]    0    1    1    1    0    1    1    0    1     1     0     1     
0     1     1     1
[16,]    0    1    1    0    1    0    1    1    1     0     1     1     
1     1     0     0

with sample size of 2x2 (4 cells) one would need 64 steps to sample all 256
hence the result vector should have a length of 64. I think there is 
only one spot  row 4 col.6,7 row 5 col.6,7 that has only zeros.

increasing the sample size to 8x8 would need a vector of length 32, 
possibly without any zero.
the matrices have an decreasing amount of 1s, so the rasters from 1-20 
are more dominated by zeros.

in a second step; the sampling should be with a random nonoverlapping 
placement of these sampling units. but I will post this question separately.






Your kind help will be highly appreciated!


Jens

-- 
+++++++++++++++++++++++++++++++++++++++++
Dipl.Biol. Jens Oldeland
University of Hamburg
Biocentre Klein Flottbek and Botanical Garden
Ohnhorststr. 18
22609 Hamburg,
Germany

Tel:    0049-(0)40-42816-407
Fax:    0049-(0)40-42816-543
Mail: 	Oldeland at botanik.uni-hamburg.de
        Jens.Oldeland at DLR.de  (for attachments > 2mb!!)
http://www.biologie.uni-hamburg.de/bzf/fbda005/fbda005.htm
+++++++++++++++++++++++++++++++++++++++++

Jens Oldeland wrote:
> 
> I am looking for a solution on how to sample increasing sizes of 
> "quadrats" in a list of matrices. Each matrix is a binary raster
map and
> I want to know if there is a 1 or only 0 s in the sampling unit 
> (quadrat, e.g. 4x4 cells). 
> 

You could just use a few loops to index the submatrices/quadrats, maybe
something like this.  

set.seed(7)
x<-matrix(sample(c(0,1), 256, replace=TRUE, prob=c(.8,.2)),  nrow=16,
byrow=TRUE)
# matrix size (16)
n<-nrow(x)
#quadrat sizes (1  2  4  8 16)
q<-  2^(0:sqrt(n))
# store results in list
quads<-vector("list", length(q) )
names(quads)<-q
for (i in 1:length(q) ) 
{
   z<-c()    
   for(j in 1:(n-q[i]+1) )    
   {
      for(k in 1:(n-q[i]+1))
      {
         y<-x[j:(j+q[i]-1), k:(k+q[i]-1)]
         #do something with submatrix
         z<-c(z, ifelse( sum(y)>0, 1,0))
         #z<-c(z, sum(y) ) 
        
      }
   }
   quads[[i]]<-z
}

#empty quads
sapply(quads, function(x) sum(x==0))
  1   2   4   8  16 
206  91   3   0   0 
# total number of quadrats sampled
sapply(quads, length)
#or
(n-q+1)^2


For random sampling, try replacing 1:(n-q[i]+1)  with  sample( 1:(n-q[i]+1),
replace=TRUE) ?

Also, if you have a list of matrices, then maybe combine the code above into
a function and then apply it to your list using lapply.


Chris Stubben

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