Q on SparseArray representation
- To: mathgroup at smc.vnet.net
- Subject: [mg113952] Q on SparseArray representation
- From: kj <no.email at please.post>
- Date: Fri, 19 Nov 2010 05:08:44 -0500 (EST)
In[1]:= SparseArray[RandomInteger[{1, 4}, {10, 2}] ->
RandomInteger[{1, 9}, 10]]
Out[1]= SparseArray[<8>, {4, 4}]
In[2]:= InputForm[%]
Out[2]= SparseArray[Automatic, {4, 4}, 0,
{1, {{0, 1, 3, 4, 8}, {{3}, {4}, {1}, {4}, {4}, {1}, {3},
{2}}}, {8, 9, 6, 2, 4, 7, 1, 4}}]
I find this canonical form intriguing, and would like to understand
it. The first three terms of the SparseArray arguments list (namely
Automatic, {4, 4}, and 0) are easy to rationalize. But I'm stumped
by the last term, namely:
{1, {{0, 1, 3, 4, 8}, {{3}, {4}, {1}, {4}, {4}, {1}, {3}, {2}}},
{8, 9, 6, 2, 4, 7, 1, 4}}
In fact, this term is not 100% opaque. Its last element, namely
{8, 9, 6, 2, 4, 7, 1, 4}
consists of the non-zero elements of the array, although they appear
in an order whose relation to their oder in the array I cannot
figure out:
/ \
| 0 0 8 0 |
| 6 0 0 9 |
| 0 0 0 2 |
| 7 4 1 4 |
\ /
Similarly, its element at position {2, 2}, namely
{{3}, {4}, {1}, {4}, {4}, {1}, {3}, {2}}
contains the numbers of the columns of the entries listed in the
last element. Thus we see that 8 appears in column 3, 9 in column
4, 6 in column 1, etc.
It's the remaining two items that I cannot figure out at all.
These are the members at positions {1} and {2, 1}. The former is
simply the number 1. What does this mean? The latter is the list
{0, 1, 3, 4, 8}. All I can say about this list is that in all
cases of SparseArray I've examined, its firts element is always 0,
and its length is 1 more than the number of rows in the SparseArray.
Does anyone know what this list of numbers represents?
TIA!
~kj