Moved mat_mul operations outside inner loops and

[dseyler]

Current situation

After profiling a 500k element structural mechanics simulation, I noticed several mat_mul function calls that were unnecessarily repeated within loops, as discussed in issue 602.

These occurred at:

• mat_models.cpp lines 1695-1696
• sv_struct.cpp line 750
• ustruct.cpp line 144

and have now been moved outside their loops.

Additionally, while investigating, it was noticed that many of these mat_mul operations were of fixed-size arrays with sizes known at compilation. These can be optimized with fixed-size Eigen maps, which run 3-4x faster than the generic mat_mul operation.

New fixed-size functions were defined in mat_mul.cpp:

• mat_mul_fixed()
• mat_mul_fixed_rows()

These functions are then dispatched within mat_mul() so developers do not need to distinguish between these differences.

///
/// Used when sizes are known at compile time.
template <int M, int K, int N>
inline void mat_mul_fixed(const Array<double>& A, const Array<double>& B, Array<double>& C)
{
  Eigen::Map<const Eigen::Matrix<double, M, K>> a(A.data());
  Eigen::Map<const Eigen::Matrix<double, K, N>> b(B.data());
  Eigen::Map<Eigen::Matrix<double, M, N>>       c(C.data());

  c.noalias() = a * b;
}

And in mat_mul:

{ 
  // Fixed-shape fast paths for the products that dominate the element loops.
  //
  //   3x3 * 3x3     F*S in struct_3d; vx*Fi, ddev*Fit, Fi*ddev_Fit and the
  //                 potential-viscosity products in mat_models; F^T*F in cep
  //   3x3 * 3xeNoN  ddev*Nx_Fi and vx_Fi*Nx_Fi in the viscous tangent
  //   6x6 * 6x3     the material stiffness product D*B in struct_3d/ustruct_3d_m
  if (A.nrows() == 3 && A.ncols() == 3 && B.nrows() == 3 &&
      result.nrows() == 3 && result.ncols() == B.ncols()) {
    if (B.ncols() == 3) {
      mat_mul_fixed<3, 3, 3>(A, B, result);
    } else {
      mat_mul_fixed_rows<3, 3>(A, B, result);
    }
    return;
  }

In total, these changes decreased runtime by ~21%.

I suspect this number could increase much more if we correctly implement eigen arrays throughout sv_struct.cpp and mat_models.cpp as many arrays are of size nsd or enon, which have a discrete number of values and can be optimized similarly. I tested this on the viscosity models alone and found another 10% improvement (can open an issue about this, but the code is too messy for this PR)

Release Notes

• Moved mat_mul outside loops in several locations
• Implemented fixed-shape mat_mul functions
• mat_mul directs arrays with know sizes at compilation down these paths

Code of Conduct & Contributing Guidelines

• I agree to follow the Code of Conduct and Contributing Guidelines.

[claude]

Claude Code Review

This pull request is from a fork — automated review is disabled. A repository maintainer can comment @claude review to run a one-time review.

[dseyler]

Sorry, opened with wrong branch. Reopening with the correct one!