[petsc-users] Matrix Construction Question

[Matthew Knepley]

On Tue, Jun 28, 2011 at 10:20 PM, Adam Byrd <adam1.byrd at gmail.com> wrote:

> 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?
>

1) With any error, send the Entire error message.

2) PETSc matrices are divided by rows, not rows and columns, see the manual
section. Rows & columns only makes sense for dense matrices

3) You can still set arbitrary blocks no matter how the matrix is divided

4) The error means you tried to set both local and global dimensions, and
they do not add up correctly. Just set the global dimensions

   Matt


> 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
>>
>
>


-- 
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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