What's the reason for different memory consumption for sparse row and column vectors?

See below:

>> a = sparse(1e12,1);
>> b = sparse(1,1e9);
>> whos a b
Name                  Size                    Bytes  Class     Attributes
a         1000000000000x1                        32  double    sparse    
b                     1x1000000000       8000000024  double    sparse    

>> clear all
>> c = sparse(1,1e10);
Error using sparse
Requested 1x10000000000 (74.5GB) array exceeds maximum array size preference.
Creation of arrays greater than this limit may take a long time and cause 
MATLAB to become unresponsive. See array size limit or preference panel for 
more information.

Answer 1

[Peng Liu]

% The minimum data storage requirement formula for a double m x n sparse 
% matrix with nnz non-zero elements, including the index data, is as 
% follows on a 32-bit system:
% 
% max(nnz(x),1) * (4 + 8) + (size(x,2)+1)*4;  % 32-bit
% max(nnz(x),1) * (8 + 8) + (size(x,2)+1)*8;  % 64-bit
% 
% nnz * 4 = Storing the row index of the non-zero elements
% nnz * 8 = Storing the non-zero double element values themselves
% (n+1)*4 = Storing the cumulative number of non-zero elements thru column
% 
% For 64-bit systems using 8-byte integers for the indexing you can replace
% the 4's above with 8's.

[Walter Roberson]

Yup, so with you having requested many columns in the second version, it needs lots of memory.

Answer 2

[Walter Roberson]

http://www.mathworks.com/help/pdf_doc/otherdocs/simax.pdf