Optimized fast_array_util.py through vectorization

[DarkMatterCompiler]

The optimized version vectorizes the cumulative trapezoidal integration over blocks, reducing nested loops and handling size normalization for each block efficiently, ensuring the output matches the expected shape.

closes issue #2910

🚦 Testing

How did you test these changes?
this notebook has the testing i performed
https://colab.research.google.com/drive/1HJ_4_YrRZ57ikMqC_oOsGq2dnn5LfuC_?usp=sharing

[tardis-bot]

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Hi, human.

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Please add your name and email to .mailmap in your current branch and push the changes to this pull request.

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[tardis-bot]

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Hi human,
I ran ruff on the latest commit (a2e3967).
Here are the outputs produced.
Results can also be downloaded as artifacts here.
Summarised output:

5	E999	[ ] SyntaxError: Expected ',', found ':'
1	F401	[*] `numba.prange` imported but unused

Complete output(might be large):

.mailmap:1:38: E999 SyntaxError: Expected an expression
CHANGELOG.md:4:15: E999 SyntaxError: Expected ',', found ':'
CITATION.cff:3:1: E999 SyntaxError: Invalid annotated assignment target
README.rst:1:1: E999 SyntaxError: Expected a statement
docs/resources/credits.rst:1:1: E999 SyntaxError: Expected a statement
tardis/plasma/properties/continuum_processes/fast_array_util.py:4:25: F401 [*] `numba.prange` imported but unused
Found 6 errors.
[*] 1 fixable with the `--fix` option.

[tardis-bot]

*beep* *bop*
Hi human,
I ran benchmarks as you asked comparing master (87e4ae1) and the latest commit (a2e3967).
Here are the logs produced by ASV.
Results can also be downloaded as artifacts here.

Significantly changed benchmarks:

All benchmarks:

Benchmarks that have stayed the same:

| Change   | Before [d73192c5] <master>   | After [a2e3967f]    | Ratio   | Benchmark (Parameter)                                                                                                               |
|----------|------------------------------|---------------------|---------|-------------------------------------------------------------------------------------------------------------------------------------|
|          | 6.13±0.8μs                   | 6.85±0.7μs          | ~1.12   | transport_montecarlo_vpacket.BenchmarkMontecarloMontecarloNumbaVpacket.time_trace_vpacket                                           |
|          | 1.97±0.01ms                  | 1.75±0.02ms         | ~0.89   | transport_montecarlo_main_loop.BenchmarkTransportMontecarloMontecarloMainLoop.time_montecarlo_main_loop                             |
|          | 55.8±30μs                    | 46.3±30μs           | ~0.83   | transport_montecarlo_interaction.BenchmarkTransportMontecarloInteraction.time_line_scatter                                          |
|          | 762±400ns                    | 531±100ns           | ~0.70   | opacities_opacity.BenchmarkMontecarloMontecarloNumbaOpacities.time_compton_opacity_calculation                                      |
|          | 38.9±10μs                    | 24.8±7μs            | ~0.64   | transport_montecarlo_packet_trackers.BenchmarkTransportMontecarloPacketTrackers.time_generate_rpacket_last_interaction_tracker_list |
|          | 571±200ns                    | 622±100ns           | 1.09    | opacities_opacity.BenchmarkMontecarloMontecarloNumbaOpacities.time_photoabsorption_opacity_calculation                              |
|          | 7.27±2μs                     | 7.96±2μs            | 1.09    | transport_montecarlo_vpacket.BenchmarkMontecarloMontecarloNumbaVpacket.time_trace_vpacket_volley                                    |
|          | 3.02±0.01ms                  | 3.18±0ms            | 1.05    | opacities_opacity_state.BenchmarkOpacitiesOpacityState.time_opacity_state_initialize('scatter')                                     |
|          | 38.9±0.2s                    | 39.2±0.04s          | 1.01    | run_tardis.BenchmarkRunTardis.time_run_tardis                                                                                       |
|          | 39.0±0.02μs                  | 39.3±0.01μs         | 1.01    | transport_montecarlo_packet_trackers.BenchmarkTransportMontecarloPacketTrackers.time_generate_rpacket_tracker_list                  |
|          | 1.04±0m                      | 1.04±0m             | 1.00    | run_tardis.BenchmarkRunTardis.time_run_tardis_rpacket_tracking                                                                      |
|          | 2.09±0m                      | 2.09±0m             | 1.00    | spectrum_formal_integral.BenchmarkTransportMontecarloFormalIntegral.time_FormalIntegrator_functions                                 |
|          | 1.18±0μs                     | 1.16±0μs            | 0.99    | transport_geometry_calculate_distances.BenchmarkTransportGeometryCalculateDistances.time_calculate_distance_boundary                |
|          | 2.41±2μs                     | 2.38±2μs            | 0.99    | transport_montecarlo_estimators_radfield_estimator_calcs.BenchmarkMontecarloMontecarloNumbaPacket.time_update_line_estimators       |
|          | 51.4±20μs                    | 51.0±30μs           | 0.99    | transport_montecarlo_interaction.BenchmarkTransportMontecarloInteraction.time_line_emission                                         |
|          | 2.72±0.4ms                   | 2.68±0.4ms          | 0.99    | transport_montecarlo_single_packet_loop.BenchmarkTransportMontecarloSinglePacketLoop.time_single_packet_loop                        |
|          | 3.17±0.6μs                   | 3.14±0.7μs          | 0.99    | transport_montecarlo_vpacket.BenchmarkMontecarloMontecarloNumbaVpacket.time_trace_bad_vpacket                                       |
|          | 738±40ns                     | 725±2ns             | 0.98    | transport_montecarlo_interaction.BenchmarkTransportMontecarloInteraction.time_thomson_scatter                                       |
|          | 4.06±0.02ms                  | 3.92±0.03ms         | 0.97    | opacities_opacity_state.BenchmarkOpacitiesOpacityState.time_opacity_state_initialize('macroatom')                                   |
|          | 212±0.02ns                   | 206±0.1ns           | 0.97    | spectrum_formal_integral.BenchmarkTransportMontecarloFormalIntegral.time_intensity_black_body                                       |
|          | 3.51±0.3μs                   | 3.37±0.4μs          | 0.96    | transport_montecarlo_vpacket.BenchmarkMontecarloMontecarloNumbaVpacket.time_trace_vpacket_within_shell                              |
|          | 571±100ns                    | 541±100ns           | 0.95    | opacities_opacity.BenchmarkMontecarloMontecarloNumbaOpacities.time_pair_creation_opacity_calculation                                |
|          | 1.62±0.3μs                   | 1.52±0.4μs          | 0.94    | transport_geometry_calculate_distances.BenchmarkTransportGeometryCalculateDistances.time_calculate_distance_line                    |
|          | 70.2±3ms                     | 64.5±0.09ms         | 0.92    | transport_montecarlo_packet_trackers.BenchmarkTransportMontecarloPacketTrackers.time_rpacket_trackers_to_dataframe                  |

If you want to see the graph of the results, you can check it here

[DarkMatterCompiler]

Optimized fast_array_util.py
the optimized version vectorizes the cumulative trapezoidal integration over blocks #2911 #2757