invA function in linear_algebra.h library is not general (i.e. no pivoting)

[bornhoft]

Expected Behavior

Supposed to provide the inverse of a general square matrix.

Actual Behavior

Doesn't work for pivoting matrices

Steps to Reproduce the Problem

1. Run the quad_2x2 example test case and print the Jacobian inside of the get_element_jacobian functions

Ideas to Fix

1. Implement a general QR decomposition using Kokkos Kernels (see test_linear_algebra.cpp -> test_batched_math_inv_2x2_offdiagonal_QR). The issue with adding this is it requires additional working views (both vectors / matrices) that need to be preallocated on the GPU.

2. For now, we can add analytic inverse matrices for 2x2 and 3x3 matrices (may be the best long term solution for the jacobian).