[R-sig-Geo] Some comments on calculations with 'asc' (and 'kasc') objects with Adehabitat

[Mathieu Basille]

Dear Sander,

Calculations with objects of class 'asc' and 'kasc' are quite simple, as 
soon as you know that 'asc' ARE actually matrices and 'kasc' data 
frames. The difference is just that they have a few additional 
parameters ('xll', 'yll', 'cellsize' and 'type' - eventually 'levels' - 
for both and 'nrow' and 'ncol' for kasc). Note that the first value of 
the matrix (top-left corner) is actually the bottom-left corner of the 
map (clockwise rotation of 90° between the map and the matrix). Note 
also that each column of a 'kasc' represent one map (one variable). An 
illustration :

   data(puechabon)
   kasc <- puechabon$kasc
   asc <- getkasc(kasc, "Elevation")
   is.matrix(asc)
   # [1] TRUE
   is.data.frame(kasc)
   # [1] TRUE

Then, the calculations are exactly the same as for matrices or data 
frames. An exemple with a simple matrix :

   m <- matrix(1:20, nr = 5)
   mean(m)
   # [1] 10.5
   var(m)
   #      [,1] [,2] [,3] [,4]
   # [1,]  2.5  2.5  2.5  2.5
   # [2,]  2.5  2.5  2.5  2.5
   # [3,]  2.5  2.5  2.5  2.5
   # [4,]  2.5  2.5  2.5  2.5

The 'var' function applied to a matrix gives the variance-covariance 
matrix. To avoid that, just type :

   var(as.vector(m))
   # [1] 35

   sd(m)
   # [1] 1.581139 1.581139 1.581139 1.581139

The 'sd' function applied to a matrix returns a vector of the standard 
deviation of the columns. To avoid that :

   sd(as.vector(m))
   # [1] 5.91608


The same with a simple data frame :

   df <- cbind(a = 1:20, b = runif(20)*100, c = rnorm(20, 50, 10))
   mean(df)
   # [1] 38.64825

The 'mean' function gives the overall mean of the data frame. As for 
kasc we obviously need means for the columns, we can try :

   colMeans(df)
   #        a        b        c
   # 10.50000 56.74289 48.70187

   colSums(df)
   #        a         b         c
   # 210.0000 1134.8577  974.0374

For the variance or standard deviation, use the 'apply' function :

   apply(df, 2, var)
   #        a         b         c
   # 35.00000 748.78361  68.40536

   apply(df, 2, sd)
   #        a         b         c
   # 5.916080 27.363911  8.270753


Now, the same, but applied to a 'real' asc object.

   mean(asc)
   # [1] NA
   var(as.vector(asc))
   # Error in var(as.vector(asc)) : missing observations in cov/cor
   sd(as.vector(asc))
   # Error in var(x, na.rm = na.rm) : missing observations in cov/cor

For all these functions, you get something wrong because of the NAs. Use 
then the parameter na.rm = TRUE :

   mean(asc, na.rm = TRUE)
   # [1] 240.6568
   var(as.vector(asc), na.rm = TRUE)
   # [1] 7369.139
   sd(as.vector(asc), na.rm = TRUE)
   # [1] 85.84369

And with a kasc object :

   colSums(kasc)
   # Error in colSums(x, n, prod(dn), na.rm) : `x' must be numeric

You get an error because the variable 'Aspect' is a factor. We don't 
need to compute means and others statistics to this variable.

   colSums(kasc[-2])
   #  Elevation      Slope Herbaceous
   #         NA         NA         NA

Again, the same problem with the NAs, solved with the na.rm parameter :

   colSums(kasc[-2], na.rm = TRUE)
   #   Elevation       Slope  Herbaceous
   # 1053836.000   40881.457    1905.650

   colMeans(kasc[-2], na.rm = TRUE)
   #   Elevation       Slope  Herbaceous
   # 240.6567710   9.3357975   0.4351792

   apply(kasc[-2], 2, var, na.rm = TRUE)
   #    Elevation        Slope   Herbaceous
   # 7.369139e+03 6.208515e+01 5.703959e-02

   apply(kasc[-2], 2, sd, na.rm = TRUE)
   #  Elevation      Slope Herbaceous
   # 85.8436875  7.8794130  0.2388296


Finally, check the usefull functions 'summary' as applied to asc and kasc :

   summary(as.vector(asc))
   #    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's
   #    65.0   176.0   256.0   240.7   290.0   479.0  9052.0

   summary(kasc)
   #    Elevation            Aspect         Slope            
Herbaceous         #  Min.   :  65.0   NorthEast: 537   Min.   :   
0.000   Min.   :   0.0000    #  1st Qu.: 176.0   SouthEast:1504   1st 
Qu.:   3.124   1st Qu.:   0.2000    #  Median : 256.0   SouthWest:1262   
Median :   6.658   Median :   0.4222    #  Mean   : 240.7   
NorthWest:1076   Mean   :   9.336   Mean   :   0.4352    #  3rd Qu.: 
290.0   NA's     :9052   3rd Qu.:  13.710   3rd Qu.:   0.7000    #  
Max.   : 479.0                    Max.   :  40.631   Max.   :   0.7000 
   #  NA's   :9052.0                    NA's   :9052.000   NA's   
:9052.0000

I'll let Clément answer about your two first questions, that are far 
from my skills.

HTH,
Mathieu