[newchem-cpp] transcribe gaussj

[ChristopherBignamini]

$\textcolor{red}{\textbf{MWA EDIT:}}$

This was originally proposed as brittonsmith#48

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This should be reviewed after #386 is merged

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This PR introduces a C++ function written "from-scratch" that is intended to replace the gaussj_g Fortran subroutine. The purpose was to avoid the licensing issues of the gaussj_g routine (since it had been ripped out of Numerical Recipes)

In the original PR, @ChristopherBignamini notes that "Implementation is quite basic and while it passes Grackle test it could have numerical issues in case of bad conditioned matrices."

[mabruzzo]

I took a quick look to investigate why CI is failing. (I haven't had a chance to look at everything in context yet, but let's get CI working first)

I made a few suggestions to address the issues:

• you aren't including <cmath> (to take absolute values). Plus, I don't think you need to be including <numeric>
• I suggested the use of std::fabs over std::abs (this isn't essential, but I generally think it is a little less confusing to people more familiar with C)

You are also going to need to adjust the loops. CI is complaining about mixing unsigned indices with signed loop bounds

After you do all that, you are going to need to format this file (this is why pre-commit.ci is failing). I would strongly recommend that you use pre-commit for this rather than directly invoking clang-format.¹ The easiest thing to do is add a GitHub comment that just says:

pre-commit.ci autofix

The continuous integration will then push a commit to your branch to adjusti the formatting. (If you really want to run it locally, the documentation provides additional context)

Footnotes

1. If you choose to manually invoke clang-format, you'll need to match the exact version of clang-format referenced in the pre-commit file. ↩

[ChristopherBignamini]

pre-commit.ci autofix

[mabruzzo]

Suggested change

	// See LICENSE file for license and copyright information
	/// @file gaussj_g.hpp
	/// @brief Implementation of Gauss-Jordan elimination for solving linear systems
	//===----------------------------------------------------------------------===//
	//
	// See the LICENSE file for license and copyright information
	// SPDX-License-Identifier: NCSA AND BSD-3-Clause
	//
	//===----------------------------------------------------------------------===//
	///
	/// @file
	/// Declares the function for Gauss-Jordan elimination
	///
	//===----------------------------------------------------------------------===//

[mabruzzo]

Suggested change

	#include <cmath>
	//===----------------------------------------------------------------------===//
	//
	// See the LICENSE file for license and copyright information
	// SPDX-License-Identifier: NCSA AND BSD-3-Clause
	//
	//===----------------------------------------------------------------------===//
	///
	/// @file
	/// Implementation of Gauss-Jordan elimination for solving linear systems
	///
	//===----------------------------------------------------------------------===//
	#include <cmath>

[ChristopherBignamini]

@mabruzzo @brittonsmith the 4x4 LinAlgCase was failing with an error of 4e-15, the same test now passes after increasing the tolerance to 5e-15. If you prefer, I can try to change the precision by using long double.