Re: [deal.II] Supported matrix/vector to LinearOperator

[陈敏]

Thanks, Luca.

I learn a lot. Since I use TrilinosWrapper::MPI::Vector,
TrilinosWrapper::SolveDirect can't use in linear_operator.
Since I can't get the precondition from linear_operator directly, I will
creat a inverse_operator without precondition.

Best,
Chen

Luca Heltai  于2022年4月20日周三 15:25写道：

> > While I can't get the entity of the matrix, I want to get the
> precondition directly from a linear_operator.
>
>
> > SparseMatrix M;
> > auto op_M = linear_operator(M);
> > TrilinosWrapper::PreconditionILU prec_M(op_M);
>
> This you cannot do. It is the other way around. Preconditioners need
> matrices (linear operator only store information about the *action* of the
> matrix, or of the various operations. Think of it this way: A*B*C*D_inv is
> still a linear operator. What matrix should this return to you?)
>
> This is how you should use it, if you want your preconditioner to be a
> linear operator:
>
> TrilinosWrapper::PreconditionILU prec_M_mat(M);
> auto op prec_M = linear_operator(M, prec_M_mat);
>
> > Can I get the entity of matrix G by TrilinosWrapper::MPI::SparseMatrix G
> = op_G; or the precondition of op_G?
>
> Nope. This, again, does not make sense.
>
> A Matrix is a linear operator (therefore you can create a linear operator
> from a matrix), but a linear operator is just an action (therefore you
> cannot create a matrix from a linear operator).
>
> L
>
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Re: [deal.II] Supported matrix/vector to LinearOperator

[Luca Heltai]

> While I can't get the entity of the matrix, I want to get the precondition 
> directly from a linear_operator. 


> SparseMatrix M; 
> auto op_M = linear_operator(M); 
> TrilinosWrapper::PreconditionILU prec_M(op_M);

This you cannot do. It is the other way around. Preconditioners need matrices 
(linear operator only store information about the *action* of the matrix, or of 
the various operations. Think of it this way: A*B*C*D_inv is still a linear 
operator. What matrix should this return to you?)

This is how you should use it, if you want your preconditioner to be a linear 
operator:

TrilinosWrapper::PreconditionILU prec_M_mat(M);
auto op prec_M = linear_operator(M, prec_M_mat);

> Can I get the entity of matrix G by TrilinosWrapper::MPI::SparseMatrix G = 
> op_G; or the precondition of op_G?

Nope. This, again, does not make sense.

A Matrix is a linear operator (therefore you can create a linear operator from 
a matrix), but a linear operator is just an action (therefore you cannot create 
a matrix from a linear operator).

L

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Re: [deal.II] Supported matrix/vector to LinearOperator

[Luca Heltai]

The issue is within Trilinos itself.

The TrilinosPayload (thanks JP!) provides an interface to Epetra_LinearOperator 
(Trilinos version of our LinearOperator). However, it cannot access matrix 
elements, as it is not thought for matrix based operations. 

You can, however, create a direct solver, wrap it into a LinearOperator, and 
use the direct solver as a preconditioner, or as one block of a Block 
preconditioner/solver. Simple workflow:

YourDirectSolverHere Ainv;

Ainv.initialze(A); // A is the actual Trilinos Matrix here, not a linear 
operator, since direct solvers need access to the matrix entries

auto Aop = linear_operator(A);
auto AinvOp = linear_operator(A, Ainv);

Now you can use Aop and AinvOp, i.e., 

auto S = Bt*AinvOp*B;

would crate a Schur complement.

Take a look at step-70, in the solve() function. There you have an example on 
how to use them with a block system.

L.

> On 19 Apr 2022, at 19:19, Jean-Paul Pelteret  wrote:
> 
> Dear Chen,
> 
> Bruno pointed you to the exact example that I was going to. It is certainly 
> possible to use linear operators as preconditioners for solvers.
> 
> It looks like support for TrilinosWrappers::SolverDirect has not yet been 
> implemented:
> https://github.com/dealii/dealii/blob/master/tests/lac/linear_operator_10.cc#L371-L414
> I cannot recall what the reason was — maybe the class is simply missing some 
> functions that are defined for the iterative solvers?
> 
> As for one of your early questions which Bruno did already answer: I must 
> admit that I do not know if the PETSc linear algebra is compatible with 
> linear operators. We had to write a special TrilinosPayload for the Trilinos 
> linear algebra classes in order for them to work correctly (with the Trilinos 
> solvers, at least), and such a wrapper doesn’t exist for PETSc. But maybe it 
> works just fine if you stick to the deal.II solvers? If you try this out, it 
> would be interesting to know if it works or not.
> 
> Best,
> J-P
> 
>> On 19. Apr 2022, at 17:27, Bruno Turcksin  wrote:
>> 
>> Chen,
>> 
>> I am not sure if TrilinosWrappers::SolverDirect is supported but for your 
>> second point, you can use the linear_operator as a preconditioner. That's 
>> exactly what's done here for example. The preconditioner is wrapped in a 
>> LinearOperator and this LinearOperator is then used as preconditioner.
>> 
>> Best,
>> 
>> Bruno
>> 
>> On Tuesday, April 19, 2022 at 10:39:17 AM UTC-4 hkch...@gmail.com wrote:
>> Hi everyone,
>> 
>> More questions:
>> 1. where can I find the supported linear solver of Trilinos of 
>> linear_operator? TrilinosWrappers::SolverDirect seems not to be supported by 
>> the linear_operator
>> 2. Does linear_operator can be a preconditioner? for example, SparseMatrix 
>> A, B, C, D, E, F; Matrix G=A-B*C^{-1}*D-E^{-1}*F; So Matrix G can only 
>> represent by a linear_operator, not its entity. I want to get its inverse by 
>> inverse_operator using some linear solvers as: PreconditionILU prec_G(op_G); 
>> const auto op_G_inv = inverse_operator(G, Solver, prec_G); But it seems that 
>> the precondition of linear_operator is not supported. Is there any solution?
>> 
>> best 
>> Chen
>> 
>> 在2022年4月18日星期一 UTC+8 22:07:36 写道：
>> Bruno Turcksin
>> Thank you! it really helpful!
>> 
>> best
>> chen
>> 在2022年4月18日星期一 UTC+8 21:07:45 写道：
>> Chen,
>> 
>> Yes, LinearOperator does support Trilinos and PETSc matrices. LinearOperator 
>> even supports your own matrix type as long as you define vmult and Tvmult 
>> (see here)
>> 
>> Best,
>> 
>> Bruno
>> 
>> On Monday, April 18, 2022 at 4:19:42 AM UTC-4 hkch...@gmail.com wrote:
>> Hi everyone,
>> 
>> When solving a block matrix system, the LinearOperator is a useful tool. My 
>> question is whether the LinearOpertor supports Matrix type (the same as the 
>> Vector type) like PETSCWrapper::MPI::SparseMatrix or 
>> TrilinosWrapper::MPI::SparseMatrix?
>> 
>> Best
>> Chen
>> 
>> -- 
>> The deal.II project is located at http://www.dealii.org/
>> For mailing list/forum options, see 
>> https://groups.google.com/d/forum/dealii?hl=en
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>> "deal.II User Group" group.
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> 
> 
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Re: [deal.II] Supported matrix/vector to LinearOperator

[hkch...@gmail.com]

Thanks, Bruno and Jean-Paul. I will not use the 
TrilinosWrapper::SolverDirect in inverse_operator, replaced by an iterative 
solver. But Bruno, this example initializes a precondition by a matrix 

preconditioner.initialize(system_matrix, data);

While I can't get the entity of the matrix, I want to get the precondition 
directly from a linear_operator. 

SparseMatrix M; 
auto op_M = linear_operator(M); 
TrilinosWrapper::PreconditionILU prec_M(op_M); 

Or in other hands, Can I get the entity of a matrix from the 
linear_operator? For example: 

SparseMatrix A, B, C, D, E, F;
linear_operator op_A, op_B, op_C, op_D, op_E, op_F;
inverse_operator  inv_C(op_C, solver, prec_C), inv_E(op_E, solver, prec_E);
linear_operator op_G=op_A-op_B*inv_C*op_D-inv_E*op_F;

Can I get the entity of matrix G by TrilinosWrapper::MPI::SparseMatrix G = 
op_G; or the precondition of op_G?

auto prec_G = linear_operator(op_G, TrilinosWrapper::PreconditionILU); seems 
don't wok.

Best,
Chen

在2022年4月20日星期三 UTC+8 00:19:46 写道：

> Dear Chen,
>
> Bruno pointed you to the exact example that I was going to. It is 
> certainly possible to use linear operators as preconditioners for solvers.
>
> It looks like support for TrilinosWrappers::SolverDirect has not yet been 
> implemented:
>
> https://github.com/dealii/dealii/blob/master/tests/lac/linear_operator_10.cc#L371-L414
> I cannot recall what the reason was — maybe the class is simply missing 
> some functions that are defined for the iterative solvers?
>
> As for one of your early questions which Bruno did already answer: I must 
> admit that I do not know if the PETSc linear algebra is compatible with 
> linear operators. We had to write a special TrilinosPayload 
> 
>  for 
> the Trilinos linear algebra classes in order for them to work correctly 
> (with the Trilinos solvers, at least), and such a wrapper doesn’t exist for 
> PETSc. But maybe it works just fine if you stick to the deal.II solvers? If 
> you try this out, it would be interesting to know if it works or not.
>
> Best,
> J-P
>
> On 19. Apr 2022, at 17:27, Bruno Turcksin  wrote:
>
> Chen,
>
> I am not sure if TrilinosWrappers::SolverDirect is supported but for your 
> second point, you can use the linear_operator as a preconditioner. That's 
> exactly what's done here 
> 
>  for example. The preconditioner is wrapped in a LinearOperator and this 
> LinearOperator is then used as preconditioner.
>
> Best,
>
> Bruno
>
> On Tuesday, April 19, 2022 at 10:39:17 AM UTC-4 hkch...@gmail.com wrote:
>
>> Hi everyone,
>>
>> More questions:
>> 1. where can I find the supported linear solver of Trilinos of 
>> linear_operator? TrilinosWrappers::SolverDirect seems not to be supported 
>> by the linear_operator
>> 2. Does linear_operator can be a preconditioner? for example, SparseMatrix 
>> A, B, C, D, E, F; Matrix G=A-B*C^{-1}*D-E^{-1}*F; So Matrix G can only 
>> represent by a linear_operator, not its entity. I want to get its inverse 
>> by inverse_operator using some linear solvers as: PreconditionILU 
>> prec_G(op_G); const auto op_G_inv = inverse_operator(G, Solver, prec_G); But 
>> it seems that the precondition of linear_operator is not supported. Is 
>> there any solution?
>>
>> best 
>> Chen
>>
>> 在2022年4月18日星期一 UTC+8 22:07:36 写道：
>>
>>> Bruno Turcksin
>>> Thank you! it really helpful!
>>>
>>> best
>>> chen
>>> 在2022年4月18日星期一 UTC+8 21:07:45 写道：
>>>
 Chen,

 Yes, LinearOperator does support Trilinos and PETSc matrices. 
 LinearOperator even supports your own matrix type as long as you define 
 vmult and Tvmult (see here 
 
 )

 Best,

 Bruno

 On Monday, April 18, 2022 at 4:19:42 AM UTC-4 hkch...@gmail.com wrote:

> Hi everyone,
>
> When solving a block matrix system, the LinearOperator is a useful 
> tool. My question is whether the LinearOpertor supports Matrix type (the 
> same as the Vector type) like PETSCWrapper::MPI::SparseMatrix or 
> TrilinosWrapper::MPI::SparseMatrix?
>
> Best
> Chen
>

> -- 
> The deal.II project is located at http://www.dealii.org/
> For mailing list/forum options, see 
> https://groups.google.com/d/forum/dealii?hl=en
> --- 
> You received this message because you are subscribed to the Google Groups 
> "deal.II User Group" group.
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> email to dealii+un...@googlegroups.com.
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>  
> 

Re: [deal.II] Supported matrix/vector to LinearOperator

[Jean-Paul Pelteret]

Dear Chen,

Bruno pointed you to the exact example that I was going to. It is certainly 
possible to use linear operators as preconditioners for solvers.

It looks like support for TrilinosWrappers::SolverDirect has not yet been 
implemented:
https://github.com/dealii/dealii/blob/master/tests/lac/linear_operator_10.cc#L371-L414
 

I cannot recall what the reason was — maybe the class is simply missing some 
functions that are defined for the iterative solvers?

As for one of your early questions which Bruno did already answer: I must admit 
that I do not know if the PETSc linear algebra is compatible with linear 
operators. We had to write a special TrilinosPayload 

 for the Trilinos linear algebra classes in order for them to work correctly 
(with the Trilinos solvers, at least), and such a wrapper doesn’t exist for 
PETSc. But maybe it works just fine if you stick to the deal.II solvers? If you 
try this out, it would be interesting to know if it works or not.

Best,
J-P

> On 19. Apr 2022, at 17:27, Bruno Turcksin  wrote:
> 
> Chen,
> 
> I am not sure if TrilinosWrappers::SolverDirect is supported but for your 
> second point, you can use the linear_operator as a preconditioner. That's 
> exactly what's done here 
> 
>  for example. The preconditioner is wrapped in a LinearOperator and this 
> LinearOperator is then used as preconditioner.
> 
> Best,
> 
> Bruno
> 
> On Tuesday, April 19, 2022 at 10:39:17 AM UTC-4 hkch...@gmail.com 
>  wrote:
> Hi everyone,
> 
> More questions:
> 1. where can I find the supported linear solver of Trilinos of 
> linear_operator? TrilinosWrappers::SolverDirect seems not to be supported by 
> the linear_operator
> 2. Does linear_operator can be a preconditioner? for example, SparseMatrix A, 
> B, C, D, E, F; Matrix G=A-B*C^{-1}*D-E^{-1}*F; So Matrix G can only represent 
> by a linear_operator, not its entity. I want to get its inverse by 
> inverse_operator using some linear solvers as: PreconditionILU prec_G(op_G); 
> const auto op_G_inv = inverse_operator(G, Solver, prec_G); But it seems that 
> the precondition of linear_operator is not supported. Is there any solution?
> 
> best 
> Chen
> 
> 在2022年4月18日星期一 UTC+8 22:07:36 > 写道：
> Bruno Turcksin
> Thank you! it really helpful!
> 
> best
> chen
> 在2022年4月18日星期一 UTC+8 21:07:45> 写道：
> Chen,
> 
> Yes, LinearOperator does support Trilinos and PETSc matrices. LinearOperator 
> even supports your own matrix type as long as you define vmult and Tvmult 
> (see here 
> )
> 
> Best,
> 
> Bruno
> 
> On Monday, April 18, 2022 at 4:19:42 AM UTC-4 hkch...@gmail.com <> wrote:
> Hi everyone,
> 
> When solving a block matrix system, the LinearOperator is a useful tool. My 
> question is whether the LinearOpertor supports Matrix type (the same as the 
> Vector type) like PETSCWrapper::MPI::SparseMatrix or 
> TrilinosWrapper::MPI::SparseMatrix?
> 
> Best
> Chen
> 
> -- 
> The deal.II project is located at http://www.dealii.org/ 
> 
> For mailing list/forum options, see 
> https://groups.google.com/d/forum/dealii?hl=en 
> 
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> .
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>  
> .

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Re: [deal.II] Supported matrix/vector to LinearOperator

[Bruno Turcksin]

Chen,

I am not sure if TrilinosWrappers::SolverDirect is supported but for your 
second point, you can use the linear_operator as a preconditioner. That's 
exactly what's done here 

 
for example. The preconditioner is wrapped in a LinearOperator and this 
LinearOperator is then used as preconditioner.

Best,

Bruno

On Tuesday, April 19, 2022 at 10:39:17 AM UTC-4 hkch...@gmail.com wrote:

> Hi everyone,
>
> More questions:
> 1. where can I find the supported linear solver of Trilinos of 
> linear_operator? TrilinosWrappers::SolverDirect seems not to be supported 
> by the linear_operator
> 2. Does linear_operator can be a preconditioner? for example, 
> SparseMatrix A, B, C, D, E, F; Matrix G=A-B*C^{-1}*D-E^{-1}*F; So Matrix 
> G can only represent by a linear_operator, not its entity. I want to get 
> its inverse by inverse_operator using some linear solvers as: PreconditionILU 
> prec_G(op_G); const auto op_G_inv = inverse_operator(G, Solver, prec_G); But 
> it seems that the precondition of linear_operator is not supported. Is 
> there any solution?
>
> best 
> Chen
>
> 在2022年4月18日星期一 UTC+8 22:07:36 写道：
>
>> Bruno Turcksin
>> Thank you! it really helpful!
>>
>> best
>> chen
>> 在2022年4月18日星期一 UTC+8 21:07:45 写道：
>>
>>> Chen,
>>>
>>> Yes, LinearOperator does support Trilinos and PETSc matrices. 
>>> LinearOperator even supports your own matrix type as long as you define 
>>> vmult and Tvmult (see here 
>>> 
>>> )
>>>
>>> Best,
>>>
>>> Bruno
>>>
>>> On Monday, April 18, 2022 at 4:19:42 AM UTC-4 hkch...@gmail.com wrote:
>>>
 Hi everyone,

 When solving a block matrix system, the LinearOperator is a useful 
 tool. My question is whether the LinearOpertor supports Matrix type (the 
 same as the Vector type) like PETSCWrapper::MPI::SparseMatrix or 
 TrilinosWrapper::MPI::SparseMatrix?

 Best
 Chen

>>>

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Re: [deal.II] Supported matrix/vector to LinearOperator

[hkch...@gmail.com]

Hi everyone,

More questions:
1. where can I find the supported linear solver of Trilinos of 
linear_operator? TrilinosWrappers::SolverDirect seems not to be supported 
by the linear_operator
2. Does linear_operator can be a preconditioner? for example, SparseMatrix 
A, B, C, D, E, F; Matrix G=A-B*C^{-1}*D-E^{-1}*F; So Matrix G can only 
represent by a linear_operator, not its entity. I want to get its inverse 
by inverse_operator using some linear solvers as: PreconditionILU 
prec_G(op_G); const auto op_G_inv = inverse_operator(G, Solver, prec_G); But 
it seems that the precondition of linear_operator is not supported. Is 
there any solution?

best 
Chen

在2022年4月18日星期一 UTC+8 22:07:36 写道：

> Bruno Turcksin
> Thank you! it really helpful!
>
> best
> chen
> 在2022年4月18日星期一 UTC+8 21:07:45 写道：
>
>> Chen,
>>
>> Yes, LinearOperator does support Trilinos and PETSc matrices. 
>> LinearOperator even supports your own matrix type as long as you define 
>> vmult and Tvmult (see here 
>> 
>> )
>>
>> Best,
>>
>> Bruno
>>
>> On Monday, April 18, 2022 at 4:19:42 AM UTC-4 hkch...@gmail.com wrote:
>>
>>> Hi everyone,
>>>
>>> When solving a block matrix system, the LinearOperator is a useful tool. 
>>> My question is whether the LinearOpertor supports Matrix type (the same as 
>>> the Vector type) like PETSCWrapper::MPI::SparseMatrix or 
>>> TrilinosWrapper::MPI::SparseMatrix?
>>>
>>> Best
>>> Chen
>>>
>>

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Re: [deal.II] Supported matrix/vector to LinearOperator

[hkch...@gmail.com]

One more question: where I can find the support linear solver of Trilinos 
of linear_operator? TrilinosWrappers::SolverDirect seem not be supported by 
the linear_operator

best 
chen 

在2022年4月18日星期一 UTC+8 22:07:36 写道：

> Bruno Turcksin
> Thank you! it really helpful!
>
> best
> chen
> 在2022年4月18日星期一 UTC+8 21:07:45 写道：
>
>> Chen,
>>
>> Yes, LinearOperator does support Trilinos and PETSc matrices. 
>> LinearOperator even supports your own matrix type as long as you define 
>> vmult and Tvmult (see here 
>> 
>> )
>>
>> Best,
>>
>> Bruno
>>
>> On Monday, April 18, 2022 at 4:19:42 AM UTC-4 hkch...@gmail.com wrote:
>>
>>> Hi everyone,
>>>
>>> When solving a block matrix system, the LinearOperator is a useful tool. 
>>> My question is whether the LinearOpertor supports Matrix type (the same as 
>>> the Vector type) like PETSCWrapper::MPI::SparseMatrix or 
>>> TrilinosWrapper::MPI::SparseMatrix?
>>>
>>> Best
>>> Chen
>>>
>>

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Re: [deal.II] Supported matrix/vector to LinearOperator

[hkch...@gmail.com]

Bruno Turcksin
Thank you! it really helpful!

best
chen
在2022年4月18日星期一 UTC+8 21:07:45 写道：

> Chen,
>
> Yes, LinearOperator does support Trilinos and PETSc matrices. 
> LinearOperator even supports your own matrix type as long as you define 
> vmult and Tvmult (see here 
> 
> )
>
> Best,
>
> Bruno
>
> On Monday, April 18, 2022 at 4:19:42 AM UTC-4 hkch...@gmail.com wrote:
>
>> Hi everyone,
>>
>> When solving a block matrix system, the LinearOperator is a useful tool. 
>> My question is whether the LinearOpertor supports Matrix type (the same as 
>> the Vector type) like PETSCWrapper::MPI::SparseMatrix or 
>> TrilinosWrapper::MPI::SparseMatrix?
>>
>> Best
>> Chen
>>
>

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Re: [deal.II] Supported matrix/vector to LinearOperator

[Bruno Turcksin]

Chen,

Yes, LinearOperator does support Trilinos and PETSc matrices. 
LinearOperator even supports your own matrix type as long as you define 
vmult and Tvmult (see here 

)

Best,

Bruno

On Monday, April 18, 2022 at 4:19:42 AM UTC-4 hkch...@gmail.com wrote:

> Hi everyone,
>
> When solving a block matrix system, the LinearOperator is a useful tool. 
> My question is whether the LinearOpertor supports Matrix type (the same as 
> the Vector type) like PETSCWrapper::MPI::SparseMatrix or 
> TrilinosWrapper::MPI::SparseMatrix?
>
> Best
> Chen
>

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[deal.II] Supported matrix/vector to LinearOperator

[陈敏]

Hi everyone,

When solving a block matrix system, the LinearOperator is a useful tool. My
question is whether the LinearOpertor supports Matrix type (the same as the
Vector type) like PETSCWrapper::MPI::SparseMatrix or
TrilinosWrapper::MPI::SparseMatrix?

Best
Chen

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