testing: matrix forward mode, and (column-forward, row-reverse) mode.

[mindeye33]

From these two different implementations, we're getting same speed as forward mode with the "matrix forward mode" which is good for sanity check I suppose.

The column-forward, row reverse, was to test our idea about mixing the different modes.

Next step is:
For the element-by-element forward mode, and the column-forward row-reverse mode, we should only constrain to the elements of env2 that are relevant.

[mindeye33]

Timing on my mac:

• For small system:

./target/release/overhead molecules/h2/sto3g.txt                                                   
--- Timing Reverse Mode dS ---
count 4
total ovlp time:    0.000021 sec
total dovlp time:   0.000046 sec
average ovlp time:  0.000005 sec
average dovlp time: 0.000012 sec
avg overhead:       2.156284
--- Timing Forward Mode dS ---
count 4
total ovlp time:    0.000001 sec
total dovlp time:   0.000132 sec
average ovlp time:  0.000000 sec
average dovlp time: 0.000033 sec
avg overhead:       88.058706
--- Timing Matrix Forward Mode dS ---
AD calls:           6
primal time:        0.000002 sec
total dovlp time:   0.000159 sec
avg dovlp time:     0.000026 sec
avg overhead:       92.994145
--- Timing Row Reverse Mode dS ---
AD calls:           4
primal time:        0.000002 sec
total dovlp time:   0.000105 sec
avg dovlp time:     0.000026 sec
avg overhead:       49.588235
dS and dS_for match
env2.len() 6

• And for bigger system:

./target/release/overhead molecules/c6h6/631g.txt                                                                   
--- Timing Reverse Mode dS ---
count 2304
total ovlp time:    0.001054 sec
total dovlp time:   0.016825 sec
average ovlp time:  0.000000 sec
average dovlp time: 0.000007 sec
avg overhead:       15.962207
--- Timing Forward Mode dS ---
count 2304
total ovlp time:    0.000916 sec
total dovlp time:   0.035719 sec
average ovlp time:  0.000000 sec
average dovlp time: 0.000016 sec
avg overhead:       39.001398
--- Timing Matrix Forward Mode dS ---
AD calls:           38
primal time:        0.000701 sec
total dovlp time:   0.039551 sec
avg dovlp time:     0.001041 sec
avg overhead:       56.454449
--- Timing Row Reverse Mode dS ---
AD calls:           10404
primal time:        0.000652 sec
total dovlp time:   3.121718 sec
avg dovlp time:     0.000300 sec
avg overhead:       4790.056028
dS and dS_for match
env2.len() 38