[R] Lots of huge matrices, for-loops, speed

[Moshe Olshansky]

Another possibility is to use explicit formula, i.e. if you are doing linear regression like y = a*x + b then the explicit formulae are:

a = (meanXY - meanX*meanY)/(meanX2 - meanX^2)
b = (meanY*meanX2 - meanX*meanXY)/(meanX2 - meanX^2)

where meanX is mean(x), meanXY is mean(x*y), meanX2 is mean(x^2), etc.

So if x is your time vector you could do something like:

meanY <- matrix(0,nrow=4000,ncol=3500)
meanXY <- matrix(0,nrow=4000,ncol=3500)
meanY2 <- matrix(0,nrow=4000,ncol=3500)

for (i in 1:80)
{
A <- read.table(file[i])
meanY = meanY +A
meanXY <- meanXY + x[i]*A
meanY2 <- meanY2 + A*A
}

now:
meanY <- meanY/80
meanXY <- meanXY/80
meanY2 <- meanY2/80
meanX <- mean(x)
meanX2 <- mean(x*x)

and now use the above formulae to compute regression coefficients.

You will need space for 4 4000x3500 matrices and this should not be a problem.
Once a and b are found you can use meanX,meanX2,meanXY,meanY,meanY2 to compute R2 as well.





--- On Mon, 7/7/08, Zarza <s.schmidtlein at uni-bonn.de> wrote:

> From: Zarza <s.schmidtlein at uni-bonn.de>
> Subject: [R]  Lots of huge matrices, for-loops, speed
> To: r-help at r-project.org
> Received: Monday, 7 July, 2008, 1:39 AM
> Hello,
> we have 80 text files with matrices. Each matrix represents
> a map (rows for
> latitude and columns for longitude), the 80 maps represent
> steps in time. In
> addition, we have a vector x of length 80. We would like to
> compute a
> regression between matrices (response through time) and x
> and create maps
> representing coefficients, r2 etc. Problem: the 80 matrices
> are of the size
> 4000 x 3500 and we were running out of memory. We computed
> line by line and
> the results for each line were appended to output grids.
> This works. But -
> for each line, 80 text files must be scanned and output
> must be written. And
> there are several for-loops involved. This takes a lot of
> time (about a
> week). I read the contributions related to speeding up code
> and maybe
> vectorizing parts of the procedure could help a bit.
> However, I am a
> neophyte (as you may see from the code below) and did not
> find a way by now.
> I would appreciate very much any suggestions for speeding
> up the procedure.
> Thanks, Zarza 
> 
> 
> 
> 
> The code (running but sloooooow):
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> regrid <- function (infolder, x, outfolder) {
> 
> # List of input files
> setwd (infolder)
> filelist <- dir (pattern=".*.asc$", full.names
> = F)
> 
> # Dimensions (making use of the header information coming
> with
> # the .asc-input files, ESRI-format)
> hd <- read.table (filelist [1], nrows = 6)
> cols <- hd[1,2]	
> rows <- hd[2,2]
> times <- length (filelist)
> items <- 4 + ncol (x)
> 
> # Prepare output
> out1 <- matrix (numeric (times * cols), ncol = cols)
> out2 <- matrix (numeric (items * cols), ncol = items)
> out3 <- as.numeric (items)
> 
> # Prepare .asc-files
> filenames <- c("R2", "adj.R2",
> "p", "b0", colnames (x))
> for (i in 1:items) {
> write.table (hd, file = paste (outfolder, filenames
> [i],".asc",sep =""),
>   quote=F, row.names=F, col.names=F) }
> rm (hd)
> 
> # Prepare regression
> xnam <- paste ("x[,",
> 1:(ncol(x)),"]", sep="")
> form <- paste("y ~ ", paste(xnam,
> collapse="+"))
> rm (xnam)
> 
> # Loop through rows
> for (j in 1:rows) {
>   getgrid <- function (j) {
>     print (paste
> ("Row",j,"/",rows),quote = F)
> 
>   # Read out multi-temporal response values for one
> grid-row of cells
>   for (k in 1:times)
>     {
>     getslice <-  function (k) {
>           values <- scan (filelist [k], what=0,
> na.strings = "-9999", 
>             skip = (5 + j), nlines = 1, nmax = cols,
> quiet=T)
>           values  }
>     out1[k,] <- getslice (k)
>     }
>     
>   # Regression
>   for (l in 1:cols)
>     {
>     y <- as.vector (out1 [,l])
>     if    (length (y) > length (na.omit (y)))
>           {           
>                setNA <- function (l) {
>                NAs <- rep (NA, length (out3)) 
>                NAs }
>           out2[l,] <- setNA (l)  
>           }             
>     else  
>           {             
>           regression <- function (l) {
>                model <- lm (as.formula(form))
>                out3[1] <- summary (model)$r.squared
>                out3[2] <- summary (model)$adj.r.squared
>                        f <- summary (model)$fstatistic
>                out3[3] <- 1-pf(f[1],f[2],f[3])
>                out3[4:items] <- coef(model)[1:(1 +
> ncol(x))]
>                out3 }
>           out2[l,] <- regression (l) 
>           }
>      }
>   out2
>   }
> fillrow <- getgrid (j)
> 
> # Append results to output files
> for (m in 1:items) {
>   write.table (t(fillrow [,m]), file = paste (outfolder,
> filenames [m], 
>     ".asc", sep =""), append=T,
> quote=F, na = as.character (-9999), 
>        row.names = F, col.names = F, dec=".") }
> }
> }    
> -- 
> View this message in context:
> http://www.nabble.com/Lots-of-huge-matrices%2C-for-loops%2C-speed-tp18303230p18303230.html
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> 
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