[Example] Add a scene checking the projection of mapped matrices

[fredroy]

Claude:

Adds a self-checking example for the assembly of force fields acting on mapped states.

The scene runs the same mechanical system twice: once with a spring acting directly on two top-level states, once with the same spring acting on two identity-mapped children. Since J = I, the projected matrix JTKJ must equal K, so both sub-trees must follow exactly the same trajectory.
A WriteState on each top-level state records the result, and the two files must be identical.

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This test is intended to show the validity of #6256 .
The mapped positions are supposed to be identical with the "direct" positions but with master it does not. (and it does with #6256)

Configuration	direct P1.x	mapped Q1.x	Result
union (before the fix)	0.457469	0.470485	DIFFERENT
cartesian product (the fix)	0.457469	0.457469	identical
#6260 + union	0.457469	0.470485	DIFFERENT
#6260 + cartesian product	0.457469	0.457469	identical

( I did the tests by myself 👀)

The output files does serve as a self-contained regression test but it can be added as a regular regression test as well.

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EDIT: converted to unit tests, with the following combinations:

Matrix	Linear system	Projection method
FullMatrix	MatrixLinearSystem	MatrixProjectionMethod
FullMatrix	MatrixLinearSystem	ConstantSparsityProjectionMethod
CompressedRowSparseMatrixd	MatrixLinearSystem	MatrixProjectionMethod
CompressedRowSparseMatrixd	MatrixLinearSystem	ConstantSparsityProjectionMethod
CompressedRowSparseMatrixd	ConstantSparsityPatternSystem	MatrixProjectionMethod
CompressedRowSparseMatrixd	ConstantSparsityPatternSystem	ConstantSparsityProjectionMethod

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Reviewers will merge this pull-request only if

• it builds with SUCCESS for all platforms on the CI.
• it does not generate new warnings.
• it does not generate new unit test failures.
• it does not generate new scene test failures.
• it does not break API compatibility.
• it is more than 1 week old (or has fast-merge label).

[alxbilger]

Excellent idea to have this scene. I thought I had something similar somewhere. There is intermediateMapping in examples/Component/LinearSystem/MatrixLinearSystem.scn, but I don't test it numerically.

Can Claude translate it to a C++ unit test? I also would like to apply this test on ConstantSparsityPatternSystem instead of MatrixLinearSystem and/or ConstantSparsityProjectionMethod instead of MatrixProjectionMethod (= 4 combinations).