[petsc-users] Diagonalization of a 3D dense matrix

[Matthew Knepley]

On Mon, Jul 11, 2016 at 1:22 PM, Ketan Maheshwari <
ketancmaheshwari at gmail.com> wrote:

> Matthew,
>
> I am probably not using the right language but I meant that each element
> has three indices associated with it: x, y, z.
>
> Here is a snapshot:
>
> 1 10 55    5.7113635929515209e-03
>  1 10 56    4.2977490038287334e-03
>  1 10 57    2.8719519782193204e-03
>  1 10 58    1.4380140927001712e-03
>  1 10 59    9.9299930690365083e-17
>  1 11  0    0.0000000000000000e+00
>  1 11  1    1.5658614070601917e-03
>  1 11  2    3.1272842098367562e-03
>  1 11  3    4.6798423857521204e-03
>
> Where the first three columns are the coordinates and the last one is
> value.
>

This is not a matrix. A matrix is a linear operator on some space with a
finite basis: https://en.wikipedia.org/wiki/Matrix_(mathematics)
This is just a set of data points.

Most people would call this a vector, since you have an index I (which
consists of each independent triple) and a value V.


> Could you clarify the meaning of "diagonalization is not a clear concept"
> if it is applicable to this case.
>

There is no one definition of tensor diagonalization.

   Matt


> Thank you,
> --
> Ketan
>
>
> On Mon, Jul 11, 2016 at 1:15 PM, Matthew Knepley <knepley at gmail.com>
> wrote:
>
>> On Mon, Jul 11, 2016 at 12:05 PM, Ketan Maheshwari <
>> ketancmaheshwari at gmail.com> wrote:
>>
>>> Hello PETSC-ers,
>>>
>>> I am a research faculty at Univ of Pittsburgh trying to use PETSC/SLEPC
>>> to
>>> obtain the diagonalization of a large matrix using Lanczos or Davidson
>>> method.
>>>
>>> The matrix is a 3 dimensional dense matrix with a total of 216000
>>> elements.
>>>
>>> After looking into some of the examples in PETSC as well SLEPC
>>> implementations
>>> it seems like most of the implementations are with 2 dimensional
>>> matrices.
>>>
>>
>> You will have to explain what you mean by a "3D matrix". A matrix, by
>> definition, has only
>> rows and columns. You may mean a matrix generated from a 3D problem. That
>> should pose
>> no extra difficulty. You may mean a 3-index tensor, in which case
>> diagonalization is not a clear
>> concept.
>>
>>   Thanks,
>>
>>      Matt
>>
>>
>>> So, I was wondering if it is possible to express a 3 dimensional matrix
>>> object
>>> compatible to PETSC so that the SLEPC API could be used to obtain
>>> diagonalization.
>>>
>>> Any suggestions or pointers to documentation or examples would be of
>>> great
>>> help.
>>>
>>> Best,
>>> --
>>> Ketan
>>>
>>>
>>
>>
>> --
>> 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
>>
>
>
>
> --
> Ketan
>
>


-- 
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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