[petsc-dev] MATCOMPOSITE as fallback for matrix-matrix multiplication

[Jed Brown]

One could imagine PETSc written so that all Mat operations like
transpose and products return lazy representations, with a method that
makes it explicit.  Would eliminate all the Transpose variants in the
matrix products, for example, and enable an implementation to choose
order of operations for chained products.

"Smith, Barry F. via petsc-dev" <petsc-dev at mcs.anl.gov> writes:

>> On Mar 11, 2019, at 1:28 PM, Isaac, Tobin G <tisaac at cc.gatech.edu> wrote:
>> 
>> 
>> Okay, but do you have an opinion on the original issue: should we
>> always return a matrix from various matrix-matrix routines, even if it
>> has limited functionality?
>
>    I'm fine with it always returning the composite matrix unless you have a specific use case that would require MAT_INITIAL_MATRIX_GET_VALUES
>
>    Barry
>
>> 
>> On Mon, Mar 11, 2019 at 06:09:55PM +0000, Smith, Barry F. wrote:
>>> 
>>>   Sounds like overkill on the complexity meter.
>>> 
>>>   Barry
>>> 
>>> 
>>>> On Mar 11, 2019, at 6:15 AM, Isaac, Tobin G via petsc-dev <petsc-dev at mcs.anl.gov> wrote:
>>>> 
>>>> One thought: we could extend MatReuse with MAT_INITIAL_MATRIX_GET_VALUES to indicate that a matrix that implements MatGetValues() is desired, to allow some user intent.
>>>> 
>>>> 
>>>> On March 9, 2019 7:44:06 PM EST, Matthew Knepley <knepley at gmail.com> wrote:
>>>>> On Sat, Mar 9, 2019 at 4:42 PM Isaac, Tobin G via petsc-dev <
>>>>> petsc-dev at mcs.anl.gov> wrote:
>>>>> 
>>>>>> 
>>>>>> Let's say I want to do Newton-Krylov on some DAG of computations.
>>>>>> Building the Jacobian is programmatic from the chain rule, requiring
>>>>>> just a lot of matrix-matrix multiplications in the correct sequence.
>>>>>> 
>>>>>> If it really is more efficient for two Jacobians to be contracted
>>>>> into
>>>>>> a matrix with random access, that's great, but if it's not, or if
>>>>>> the appropriate implementation of MatMatMult_X_Y does not exist,
>>>>>> having a MATCOMPOSITE is better than nothing.
>>>>>> 
>>>>>> So why not make MATCOMPOSITE something that our matrix-matrix
>>>>>> multiplication routines return when a specialization isn't found?
>>>>>> It moves the "Not Implemented" warning from MatMatMult() to
>>>>>> whenever I try to do something other than multiply with the output,
>>>>>> but in some situations that's desirable.
>>>>>> 
>>>>>> I'd be interested to hear what people think.
>>>>>> 
>>>>> 
>>>>> I think this is a good idea. The most important thing is to maintain
>>>>> transparency, so that the output
>>>>> makes this clear in -ksp_view and we are easily able to see what
>>>>> someone
>>>>> has produced.
>>>>> 
>>>>> Matt
>>>>> 
>>>>> 
>>>>>> Thanks,
>>>>>> Toby
>>>>>> 
>>>>>> 
>>>>>> 
>>>