Creating (and Accessing) a Sparse Matrix with NA default entries

Question

After learning about the options for working with sparse matrices in R, I want to use the Matrix package to create a sparse matrix from the following data frame and have all other elements be NA.

     s    r d
1 1089 3772 1
2 1109  190 1
3 1109 2460 1
4 1109 3071 2
5 1109 3618 1
6 1109   38 7

I know I can create a sparse matrix with the following, accessing elements as usual:

> library(Matrix)
> Y <- sparseMatrix(s,r,x=d)
> Y[1089,3772]
[1] 1
> Y[1,1]
[1] 0

but if I want to have the default value to be NA, I tried the following:

  M <- Matrix(NA,max(s),max(r),sparse=TRUE)
  for (i in 1:nrow(X))
    M[s[i],r[i]] <- d[i]

and got this error

Error in checkSlotAssignment(object, name, value) : 
  assignment of an object of class "numeric" is not valid for slot "x" in an object of class "lgCMatrix"; is(value, "logical") is not TRUE

Not only that, I find that one takes much longer to access to elements.

> system.time(Y[3,3])
   user  system elapsed 
  0.000   0.000   0.003 
> system.time(M[3,3])
   user  system elapsed 
  0.660   0.032   0.995 

How should I be creating this matrix? Why is one matrix so much slower to work with?

Here's the code snippet for the above data:

X <- structure(list(s = c(1089, 1109, 1109, 1109, 1109, 1109), r = c(3772, 
190, 2460, 3071, 3618, 38), d = c(1, 1, 1, 2, 1, 7)), .Names = c("s", 
"r", "d"), row.names = c(NA, 6L), class = "data.frame")

Answer 1

Why do you want default NA values? As far as I know matrices are only sparse if they have zero-cells. As NA is a non-zero value, you loose all the benefits from the sparse matrix. A classic matrix is even more efficient if the matrix has hardly any zeros. A classic matrix is like a vector that will be cut according to the dimensions. So it only has to store the data vector and the dimensions. The sparse matrix stores only the non-zero values, but also stores there location. This is an advantage if and only if you have enough zero values.

Answer 2

Yes, Thierry's answer is definitely true I can say as co-author of the 'Matrix' package...

To your other question: Why is accessing "M" slower than "Y"? The main answer is that "M" is much much sparser than "Y" hence much smaller and -- depending on the sizes envolved and the RAM of your platform -- the access time is faster for much smaller objects, notably for indexing into them.