Implement symmetric positive definite tensor interpolation with weights

[amgebauer]

This PR implements a tensor interpolation of symmetric positive definite tensors. The interpolation is (in contrast to existing one from @dragos-ana) purely based on normalized weights.

I also rewrote some parts of the tensor interpolation algorithms based on Tensors (instead of Matrix).

I use it to interpolate a pure stretch tensor input field.

[Copilot]

Pull request overview

This PR implements symmetric positive definite (SPD) tensor interpolation using normalized weights for interpolating pure stretch tensor input fields. The implementation uses the R-LOG method (rotation-logarithmic eigenvalue interpolation) and refactors existing tensor interpolation algorithms to use the new Tensor classes instead of Matrix classes.

Key Changes:

• Adds interpolate_spd() function for SPD tensor interpolation using R-LOG method
• Refactors rotation vector/matrix conversion functions to use Tensor instead of Matrix
• Introduces SymmetricPositiveDefiniteInterpolation template for use with interpolated input fields
• Adds comprehensive unit tests for the new interpolation functionality

Reviewed changes

Copilot reviewed 8 out of 9 changed files in this pull request and generated 9 comments.

Show a summary per file

File	Description
tests/list_of_tests.cmake	Adds new test case for constant prestretch field
tests/input_files/mixture_prestress_constant_field.4C.yaml	New test configuration for prestretch field interpolation
src/mixture/src/4C_mixture_prestress_strategy_prescribed.hpp	Updates template parameters to use SPD interpolation
src/mixture/src/4C_mixture_prestress_strategy_prescribed.cpp	Updates template instantiation for SPD interpolation
src/global_legacy_module/4C_global_legacy_module_validmaterials.cpp	Updates material input specification for SPD interpolation
src/core/linalg/tests/4C_linalg_utils_tensor_interpolation_test.cpp	Adds unit tests for diagonal and rotated SPD tensor interpolation
src/core/linalg/src/dense/4C_linalg_utils_tensor_interpolation.hpp	Declares new SPD interpolation functions and helper utilities
src/core/linalg/src/dense/4C_linalg_utils_tensor_interpolation.cpp	Refactors rotation vector/matrix conversion to use Tensor types

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[dragos-ana]

Looks good, thanks for adding this!
I added some comments --- the main one addresses eigenvector alignment for multiple eigenvalues. I would wait for the rework from @abhi-satheesh before properly addressing it, but we should be aware that the underlying problem exists (at least it existed at the time when I first implemented the interpolation framework).