[R] How to select multiple cells in a matrix and perform an operation on corresponding cells in another matrix of the same size?

[Jim Lemon]

On 03/25/2014 01:02 AM, Vermeulen, Lucie wrote:
> I am trying to write an R script to do pollution routing in world rivers, and need some help on selecting matrix cell coordinates and applying these to other matrices of the same dimension.
>
> My data: I have several matrices corresponding to hydrological parameters of world rivers on a half degree grid (360 rows, 720 columns). These matrices represent flow accumulation (how many cells flow into this cell), flow direction (which of the 8 surrounding cells does the load of certain cell flow to) and pollutant load.
>
> My idea: compute pollutant load in each grid cell from the start to the end of a river. I can base this on flow accumulation (low to high). However, each river basin can have multiple cells with the same flow accumulation value.
>
> The problem: I need to select all matrix cells of each value of flow accumulation (low to high), find their coordinates (row,column), and transfer the corresponding pollutant load to the correct adjacent cell using the flow direction matrix. I have tried various ways, but selecting the coordinates of the correct cells and applying these to another matrix I cannot get to work.
> ...

Hi Lucie,
I had a look at this and I think what you want to do is to step through 
time intervals, transferring a combination of flow rates and pollution 
loads from cell to cell. At each time interval, the downstream cells 
will be updated with a value that reflects the amount of pollutants in 
those cells. It seems that you want to ignore evaporation and absorption.

This might do what you want.

# assume three flow rates
flowmat<-matrix(sample(1:3,100,TRUE),nrow=10)
# directions are 1 to 8 starting at North and going clockwise
dirmat<-matrix(sample(1:8,100,TRUE),nrow=10)
# some values for pollutant concentration (?)
pollmat<-matrix(runif(100),nrow=10)
dimmat<-dim(flowmat)
# these translate the "direction" value into row and column changes
rowdirs<-c(0,1,1,1,0,-1,-1,-1)
coldirs<-c(1,1,0,-1,-1,-1,0,1)
# the matrix to be updated
newpollmat<-matrix(0,nrow=dimmat[1],ncol=dimmat[2])
for(flow in unique(flowmat)) {
  # this yields a matrix where all cells of a given flow are TRUE
  selected_cells<-flowmat == flow
  for(row in 1:dimmat[1]) {
   for(col in 1:dimmat[2]) {
    # only update the selected cells
    if(selected_cells[row,col]) {
     newrow<-row+rowdirs[dirmat[row,col]]
     newcol<-col+coldirs[dirmat[row,col]]
     # don't go out of the matrix
     if(newx >= 1 && newx <= 10 && newy > = 1 && newy <= 10)
      # update the new pollutant matrix
      newpollmat[newrow,newcol]<-pollmat[row,col]*flowmat[row,col]
    }
   }
  }
}

The above can be done in the inner two loops as it accounts for the flow 
rate in the calculation. You will probably want to update the "edge" 
cells with their original values or wrap values from the opposite edge 
if that is appropriate.

Jim