This PR is largely performance improvements related to hessian updating and fixes discrepancies between c++ and pyoptking #75 Tried a number of criteria for whether to include a step in the update procedure. No new criteria worked well generally. The first step is now included. This caused an alarming number of failures in the tests with ranged constraints and external forces various - these tests appear highly sensitive to the hessian and unstable. ranged coordinates are no longer included in the update procedure and external forces are now added to the system before updating the hessian.

[x] Hessian update now occurs using the most recent step.
[x] Hessian wasn't being updated in IRCs - this bug seems to have occured in the original rewrite of the IRC code.
[x] Constrained coordinates (ranged and frozen) are not updated - kept diagonal. Constrained steps are forced towards their desired values after the step so the forces and displacement can be inconsistent.
[x] Limited stepsize for constrained coordinates adjustments for stability. When far away from the constraint or when the constraint is far from the minimum large steps can be attempted due to needing a large adjustment to the constraint or large forces these large steps can amplified by the back transformation going very poorly for such a large step. This can lead to large oscillations jumping into the range (where forces are active) and outside where forces are inactive. In such cases the optimizer may never (or only with difficulty) settling on the constraint.
[x] External forces are now included in the hessian update. TODO Should use sympy to compute Hessian elements for external forces.
[x] Dimer coordinates accept strings or python objects now.
[x] Fix linear bend check. Method was checking whether 2*step not step was linear (past linear)
[x] Over the 86 tests, which track the number of steps required, we save 150 steps with these changes.
[ ] Check that this also fixes psi4's CI issues.

Codecov Report

Base: 84.01% // Head: 84.28% // Increases project coverage by +0.26% :tada:

Coverage data is based on head (67db2a4) compared to base (921f161). Patch coverage: 75.54% of modified lines in pull request are covered.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #77 +/- ## ========================================== + Coverage 84.01% 84.28% +0.26% ========================================== Files 34 34 Lines 6676 6701 +25 ========================================== + Hits 5609 5648 +39 + Misses 1067 1053 -14 ``` | [Impacted Files](https://codecov.io/gh/psi-rking/optking/pull/77?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King) | Coverage Δ | | |---|---|---| | [optking/bend.py](https://codecov.io/gh/psi-rking/optking/pull/77/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King#diff-b3B0a2luZy9iZW5kLnB5) | `93.04% <ø> (ø)` | | | [optking/cart.py](https://codecov.io/gh/psi-rking/optking/pull/77/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King#diff-b3B0a2luZy9jYXJ0LnB5) | `72.72% <ø> (ø)` | | | [optking/compute\_wrappers.py](https://codecov.io/gh/psi-rking/optking/pull/77/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King#diff-b3B0a2luZy9jb21wdXRlX3dyYXBwZXJzLnB5) | `87.09% <ø> (-0.31%)` | :arrow_down: | | [optking/exceptions.py](https://codecov.io/gh/psi-rking/optking/pull/77/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King#diff-b3B0a2luZy9leGNlcHRpb25zLnB5) | `100.00% <ø> (ø)` | | | [optking/frag.py](https://codecov.io/gh/psi-rking/optking/pull/77/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King#diff-b3B0a2luZy9mcmFnLnB5) | `88.96% <0.00%> (ø)` | | | [optking/loggingconfig.py](https://codecov.io/gh/psi-rking/optking/pull/77/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King#diff-b3B0a2luZy9sb2dnaW5nY29uZmlnLnB5) | `100.00% <ø> (ø)` | | | [optking/misc.py](https://codecov.io/gh/psi-rking/optking/pull/77/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King#diff-b3B0a2luZy9taXNjLnB5) | `82.97% <ø> (ø)` | | | [optking/oofp.py](https://codecov.io/gh/psi-rking/optking/pull/77/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King#diff-b3B0a2luZy9vb2ZwLnB5) | `64.86% <ø> (ø)` | | | [optking/printTools.py](https://codecov.io/gh/psi-rking/optking/pull/77/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King#diff-b3B0a2luZy9wcmludFRvb2xzLnB5) | `94.33% <0.00%> (ø)` | | | [optking/tors.py](https://codecov.io/gh/psi-rking/optking/pull/77/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King#diff-b3B0a2luZy90b3JzLnB5) | `96.03% <ø> (+0.88%)` | :arrow_up: | | ... and [26 more](https://codecov.io/gh/psi-rking/optking/pull/77/diff?src=pr&el=tree-more&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King) | | Help us with your feedback. Take ten seconds to tell us [how you rate us](https://about.codecov.io/nps?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King). Have a feature suggestion? [Share it here.](https://app.codecov.io/gh/feedback/?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=Rollin+King)

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psi-rking / optking

Hessian #77

Codecov Report