[petsc-users] Matrix Construction Question

[Adam Byrd]

Matt,

Alright, that means I need to continue learning how to use MatSetValues().
With my 6x6 example I tried filling it with four 3x3 sub matrices, but when
I do that I get the error 'sum of local sizes 12 does not equal global
size.' I had 4 processors each calling MatSetValues for their own 3x3.
Graphically, I arranged the nodes 0 1

                                                                       2 3
where process 0 had global rows 0-2 and global columns 0-2; process 1 had
0-2, 3-5; process 2 had 3-5, 0-2; and process 3 had 3-5, 3-5. From the
documentation, I think this should be correct, but I'm not sure. Also, which
format would you recommend for storing the matrix?


Jack,

I'm a summer intern just getting started with this project, so I don't know
all the details yet (I can ask though). I know I need to find the Green's
function which will involve the trace of the inverted Hamiltonian, as well
as the rest of the matrix. I have inquired about avoiding the inversion
altogether, but my instructor doesn't believe there is a way around it. Once
I've worked through the math I want to explore other options though.

Respectfully,
Adam

On Tue, Jun 28, 2011 at 6:08 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Tue, Jun 28, 2011 at 5:01 PM, Adam Byrd <adam1.byrd at gmail.com> wrote:
>
>> Actually, it's quite sparse. In the 3600x3600 there are only just 4
>> nonzero entries in each row. This means it's 99.9% empty. My smaller 6x6
>> example is dense, but it's only practice building and manipulating matrices.
>>
>
> Ah, then its easy. Just call MatSetValues() with each block. Then use MUMPS
> to do a sparse direct solve.
>
>   Matt
>
>
>> Respectfully,
>> Adam
>>
>>
>> On Tue, Jun 28, 2011 at 5:55 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>
>>> It sounds like you have a dense matrix (from your example). Is this true?
>>> If so, you should use Elemental (on Google Code).
>>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>>  On Tue, Jun 28, 2011 at 8:55 AM, Adam Byrd <adam1.byrd at gmail.com>wrote:
>>>
>>>> Hi,
>>>>
>>>> I'm rather new to PETSc and trying to work out the best way to create
>>>> and fill a large sparse matrix distributed over many processors. Currently,
>>>> my goal is to create a 3600x3600 matrix in units of 12x12 blocks with
>>>> several blocks on any given node. I'd like to create the matrix in such a
>>>> way that each node only holds the information in it's handful of blocks and
>>>> not the entire matrix. Eventually, this matrix is to be inverted (I know,
>>>> inversion should be avoided, but as this is a Hamiltonian matrix from which
>>>> I need the Green's function, I'm unaware of a way to forgo carrying out the
>>>> inversion). Additionally, the values will be changed slightly and the matrix
>>>> will be repeatedly inverted. It's structure will remain the same. In order
>>>> to learn how to do this is I am starting with a small 6x6 matrix broken into
>>>> four 3x3 blocks and distributed one block per node. I've been able to create
>>>> a local 3x3 matrix on each node, with it's own values, and with the global
>>>> row/column IDs correctly set to [0, 1, 2] or [3, 4, 5] depending on where
>>>> the block is in the matrix. My problem manifests when I try to create the
>>>> larger matrix from the individual smaller ones. When the matrix is
>>>> constructed I'm trying to use MatSetValues and having each node pass in it's
>>>> 3x3 block. I end up with an error that the sum of local lengths 12x12 does
>>>> not match the global length 6x6. It appears as though this is from passing
>>>> in four 3x3s and the program interpreting that as a 12x12 instead of as a
>>>> 6x6 with the blocks in a grid.
>>>>
>>>> My question is then: is it possible to fill a matrix as a grid of
>>>> blocks, or can I only fill it in groups of rows or columns? Also, am I
>>>> approaching this problem the correct way, or are there more efficient ways
>>>> of building this matrix with the ultimate goal of inverting it?
>>>>
>>>> I have included my copy of a modified example if it helps. I do
>>>> apologize if this is answered somewhere in the documentation, I have been
>>>> unable to find a solution.
>>>>
>>>> Respectfully,
>>>> Adam
>>>>
>>>
>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>
>>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
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