Sparse memory storage starts with a vector of pointers, with one element per column. The pointer content is 0 (NULL pointer) if the column has no non-zero entries.
For the columns that have non-zero entries, the above pointer points to a block of memory that is a paired list. The initial element of the pair is a row number. The second element of the pair is the value at the indicated row.
You are populating 20000 x 20000 randomly with 5% fill. The probability that at least one row in any given column will be selected is as close to 1 as to make no difference (about 1 minus 3e-446). So the marginal column vector pointer is going to be completely full, occupying 20000 * sizeof(pointer) = 20000*16 = 320000 bytes.
About 1 in 20 columns will be full, so approximately 1000 slots will need to be allocated per column. Each slot needs a 48 bit offset (row numbers can be up to 2^48-1) and an 8 byte value, 14 bytes total. That is provided that the offsets are stored as 48 bit instead of as 64 bit. So you should expect roughly 1000*14*20000 = 280000000 or 1000*16*20000 = 32000000 for the column values. Total 280320000 bytes or 32320000 bytes.
Comparing to the actual memory used, it appears that MATLAB uses the full 8 bytes for the offsets, and in practice was able to save a bit on the marginal vectors.
