MaRC::root_find() is not reliable as implemented

[ossama-othman]

MaRC::root_find() as implemented is not suitable for all cases. It suffers from a few deficiencies:

• The step value h used when numerically computing the first derivative of the supplied function may not be suitable for all cases. An attempt should be made to automate selection of that step value. See Section 5.7 in the book "Numerical Recipes in C".
• There is a potential division by zero in the Newton-Raphson implementation if the computed derivative is zero.
• The search bracket used after the first attempt at finding the root fails seems rather large. Leverage something like a hybrid bisection / Newton-Raphson approach to address this problem. The hybrid approach would also address the fixed step value used during the search. See Section 9.4 of "Numerical Recipes in C".

These issues should be addressed so that other code in MaRC that call MaRC::root_find(), such as the conformal projections, work reliably in all cases.

[ossama-othman]

As of commit 11eebbe6, a version of MaRC::root_find() that implements the hybrid bisection / Newton-Raphson approach found in Section 9.4 of "Numerical Recipes in C" is now available. That commit also improves the step value used when computing the first derivative.