I've looked at the Matrix package and at their slides. I was trying to understand what is the intution and the meaning behind the arguments in the dgCMatrix class. I understand that

• @i gives the zero-based row indeces of the non-zero entries in the matrix.
• @j gives the zero-based column indeces of the non-zero entries in the matrix.
• @x gives the non-zero elements at the (i,j) positions.

However I don't understand the meaning of the pointer @p. The documentation says

numeric (integer-valued) vector of pointers, one for each column (or row), to the initial (zero-based) index of elements in the column (or row).

This is not very informative. In the "detail" section, on the same page they explain more

If i or j is missing then p must be a non-decreasing integer vector whose first element is zero. It provides the compressed, or “pointer” representation of the row or column indices, whichever is missing. The expanded form of p, rep(seq_along(dp),dp) where dp <- diff(p), is used as the (1-based) row or column indices.

Which to me is definitely non-intuitive. Can someone provide a simple explanation of what p represents? I've created a Minimal Working Example but feel free to create a new one.

Minimal Working Example

# Define non-zero values and their row/col indeces
i_indeces <- c(1, 3, 4, 6, 8, 9)
j_indeces <- c(2, 9, 6, 3, 9, 10)
values <- c(60, 20, 10, 40, 30, 50)
# Create the sparse matrix
A <- sparseMatrix(
    i=i_indeces,
    j=j_indeces,
    x=values,
    dims=c(10, 20)
)

Where

> str(A)
Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
  ..@ i       : int [1:6] 0 5 3 2 7 8
  ..@ p       : int [1:21] 0 0 1 2 2 2 3 3 3 5 ...
  ..@ Dim     : int [1:2] 10 20
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
  ..@ x       : num [1:6] 60 40 10 20 30 50
  ..@ factors : list()

and

> A
10 x 20 sparse Matrix of class "dgCMatrix"

 [1,] . 60  . . .  . . .  .  . . . . . . . . . . .
 [2,] .  .  . . .  . . .  .  . . . . . . . . . . .
 [3,] .  .  . . .  . . . 20  . . . . . . . . . . .
 [4,] .  .  . . . 10 . .  .  . . . . . . . . . . .
 [5,] .  .  . . .  . . .  .  . . . . . . . . . . .
 [6,] .  . 40 . .  . . .  .  . . . . . . . . . . .
 [7,] .  .  . . .  . . .  .  . . . . . . . . . . .
 [8,] .  .  . . .  . . . 30  . . . . . . . . . . .
 [9,] .  .  . . .  . . .  . 50 . . . . . . . . . .
[10,] .  .  . . .  . . .  .  . . . . . . . . . . .

Note

I understand that rep(seq_along(diff(A@p)), diff(A@p)) is a rearranged form of j_indeces but I still don't understand what it means.