add new sparse ect algo

[yemeen]

speed up ect computation using sparse complex representation

Description

using the fact that the ect only changes at critical thresholds, we can calculate those thresholds for each face, and skip a lot of unnecessary computation.

fourier_circle_100_complexity_3:
  Baseline ECT:  0.0106s ± 0.0036s
  Optimized ECT: 0.0022s ± 0.0011s
  Baseline/Optimized: 4.85x

fourier_circle_1000_complexity_3:
  Baseline ECT:  0.0555s ± 0.0155s
  Optimized ECT: 0.0271s ± 0.0122s
  Baseline/Optimized: 2.05x

fourier_circle_10000_complexity_3:
  Baseline ECT:  0.2417s ± 0.0309s
  Optimized ECT: 0.0815s ± 0.0129s
  Baseline/Optimized: 2.96x

fourier_circle_100000_complexity_5:
  Baseline ECT:  1.2620s ± 0.0675s
  Optimized ECT: 0.6715s ± 0.0059s
  Baseline/Optimized: 1.88x

spiral_1000_complexity_2:
  Baseline ECT:  0.0562s ± 0.0057s
  Optimized ECT: 0.0237s ± 0.0138s
  Baseline/Optimized: 2.37x

lemniscate_1000_complexity_3:
  Baseline ECT:  0.0890s ± 0.0446s
  Optimized ECT: 0.0343s ± 0.0113s
  Baseline/Optimized: 2.59x

star_1000_complexity_5:
  Baseline ECT:  0.0868s ± 0.0228s
  Optimized ECT: 0.0336s ± 0.0103s
  Baseline/Optimized: 2.58x

random_walk_1000_complexity_2:
  Baseline ECT:  0.0868s ± 0.0318s
  Optimized ECT: 0.0292s ± 0.0097s
  Baseline/Optimized: 2.98x

spiral_5000_complexity_3:
  Baseline ECT:  0.1218s ± 0.0100s
  Optimized ECT: 0.0555s ± 0.0068s
  Baseline/Optimized: 2.20x

star_5000_complexity_5:
  Baseline ECT:  0.1415s ± 0.0286s
  Optimized ECT: 0.0561s ± 0.0146s
  Baseline/Optimized: 2.52x


CW_ECT RESULTS:
----------------------------------------
dirs_8_thresh_10:
  Baseline ECT:  0.0019s ± 0.0015s
  Optimized ECT: 0.0006s ± 0.0003s
  Baseline/Optimized: 3.06x

dirs_36_thresh_36:
  Baseline ECT:  0.0048s ± 0.0019s
  Optimized ECT: 0.0007s ± 0.0003s
  Baseline/Optimized: 7.18x

dirs_360_thresh_360:
  Baseline ECT:  0.0127s ± 0.0076s
  Optimized ECT: 0.0010s ± 0.0006s
  Baseline/Optimized: 12.22x

Motivation and Context

took too long for 4 million leaves

How has this been tested?

test_ect already tests this class

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• [ x] New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)

Checklist

• [x ] My code follows the code style of this project. (make clean)
• [x ] I have incremented the version number in the pyproject.toml file.
• [ x] I have added tests to cover my changes.
• [ x] All new and existing tests passed. (make tests)

[lizliz]

So fast!