Implement evaluateDerivRatios in J1 and J2

[ye-luo]

Proposed changes

Implement J1 and J2. JeeI will be next.
Remove unnecessary get_neighbours in DT.

Running on diamondC_1x1x1
"use_nonlocalpp_deriv" is cheap to run now.
From "gradient_test"

# use_nonlocalpp_deriv = no
Param_Name  Value    Numeric            Analytic       Percent
eC_0 -2.0322e-01  5.8930e-03  5.8919e-03  1.9518e-02
eC_1 -1.6256e-01  -1.5658e-03  -1.5656e-03  1.6832e-02
...
eC_6 -4.4453e-02  1.1006e-03  1.0739e-03  2.4258e+00
eC_7 -2.1351e-02  -1.5482e-01  -1.5449e-01  2.1335e-01
uu_0 2.7977e-01  -3.6705e-05  -1.0604e-04  -1.8889e+02
uu_1 2.1726e-01  7.1735e-03  6.6674e-03  7.0540e+00
...
uu_6 2.9160e-02  -3.9518e-02  -3.5624e-02  9.8537e+00
uu_7 1.2240e-02  1.6430e-01  1.6897e-01  -2.8403e+00
...
ud_6 4.1459e-02  -5.6726e-02  -5.5265e-02  2.5760e+00
ud_7 1.6906e-02  5.9920e-02  5.5935e-02  6.6501e+00

  Execution time = 6.5431e+01

develop branch

# use_nonlocalpp_deriv = yes
Param_Name  Value    Numeric            Analytic       Percent
eC_0 -2.0322e-01  5.8930e-03  5.8919e-03  1.9524e-02
eC_1 -1.6256e-01  -1.5658e-03  -1.5656e-03  1.6872e-02
...
eC_6 -4.4453e-02  1.1006e-03  1.1006e-03  -3.6409e-03
eC_7 -2.1351e-02  -1.5482e-01  -1.5482e-01  1.4062e-05
uu_0 2.7977e-01  -3.6705e-05  -3.3317e-05  9.2291e+00
uu_1 2.1726e-01  7.1735e-03  7.1750e-03  -2.1123e-02
...
uu_6 2.9160e-02  -3.9518e-02  -3.9518e-02  5.7571e-05
uu_7 1.2240e-02  1.6430e-01  1.6430e-01  -9.4842e-06
ud_0 4.6311e-01  -3.0363e-04  -3.0126e-04  7.7817e-01
ud_1 3.5640e-01  2.4801e-02  2.4800e-02  2.3507e-03
...
ud_6 4.1459e-02  -5.6726e-02  -5.6726e-02  -1.3851e-05
ud_7 1.6906e-02  5.9920e-02  5.9920e-02  -3.2892e-05

  Execution time = 2.4349e+02

this PR

# use_nonlocalpp_deriv = yes
Param_Name  Value    Numeric            Analytic       Percent
eC_0 -2.0322e-01  5.8930e-03  5.8919e-03  1.9518e-02
eC_1 -1.6256e-01  -1.5658e-03  -1.5656e-03  1.6832e-02
...
eC_6 -4.4453e-02  1.1006e-03  1.1006e-03  -3.6651e-03
eC_7 -2.1351e-02  -1.5482e-01  -1.5482e-01  1.4176e-05
uu_0 2.7977e-01  -3.6705e-05  -3.3317e-05  9.2298e+00
uu_1 2.1726e-01  7.1735e-03  7.1750e-03  -2.1132e-02
...
uu_6 2.9160e-02  -3.9518e-02  -3.9518e-02  5.6447e-05
uu_7 1.2240e-02  1.6430e-01  1.6430e-01  -9.4301e-06
ud_0 4.6311e-01  -3.0363e-04  -3.0126e-04  7.7797e-01
ud_1 3.5640e-01  2.4801e-02  2.4800e-02  2.3539e-03
...
ud_6 4.1459e-02  -5.6726e-02  -5.6726e-02  -1.3694e-05
ud_7 1.6906e-02  5.9920e-02  5.9920e-02  -3.2447e-05

  Execution time = 4.7143e+01

use_nonlocalpp_deriv significantly reduces the difference between Numeric and Analytic.
New code path is much faster.

What type(s) of changes does this code introduce?

• New feature
• Testing changes (e.g. new unit/integration/performance tests)

Does this introduce a breaking change?

• No

What systems has this change been tested on?

epyc-server

Checklist

• Yes. This PR is up to date with current the current state of 'develop'

[ye-luo]

Test this please

[ye-luo]

Test this please

[prckent]

Thanks Ye!

LGTM.