[LinearSystem] Update the "M, B, K factors" of the linear system when necessary

[leobois67]

Problem: calling mop.setSystemMBKMatrix(mFact, bFact, kFact, l_linearSolver.get()); actually ignores the factors except for the first time it is called.

Use case: In order to compute the gradient of a loss wrt some parameters, I want to solve linear systems with my own "M, B, K factors".

Solution: check for a change in the factors and update if necessary. This update is done in MatrixLinearSystem<TMatrix, TVector>::associateLocalMatrixTo().

Details: The factors passed to setSystemMBKMatrix() follow the path below:

MechanicalOperations::setSystemMBKMatrix()
> BaseMatrixLinearSystem::buildSystemMatrix()
    > BaseMatrixLinearSystem::preAssembleSystem() [virtual]
    > TypedMatrixLinearSystem<TMatrix, TVector>::preAssembleSystem()
        > TypedMatrixLinearSystem<TMatrix, TVector>::associateLocalMatrixToComponents() [virtual]
        > MatrixLinearSystem<TMatrix, TVector>::associateLocalMatrixToComponents()
            > MatrixLinearSystem<TMatrix, TVector>::associateLocalMatrixTo()

In this final method, the factors are only considered the first time the system is assembled because of this check:

auto it = componentLocalMatrix.find(pairs);
if (it == componentLocalMatrix.end())
{
    // use M, B, K factors
}

Which is why, after this check, we add the following code:

if (std::abs(localMatrix->m_cachedFactor - factor) > std::numeric_limits<SReal>::epsilon())
{
    localMatrix->setFactor(factor);
}

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[leobois67]

Also: now that I understand better how things work, I may actually be able to do what I want without this PR ;)

[alxbilger]

Your analysis makes sense. But the solution is wrong. m_cachedFactor is protected, therefore a direct access leads to a compilation error.

[alxbilger]

Suggested change

	if (std::abs(localMatrix->m_cachedFactor - factor) > std::numeric_limits<SReal>::epsilon())
	{
	localMatrix->setFactor(factor);
	}
	localMatrix->setFactor(factor);

I suggest to always set the factor even if it does not change since last time.

[leobois67]

Yep, that is what we did before adding the condition without checking that it compiled... I made the change.