differintP 0.0.4 (Weyl, Riesz)

0.0.4

• Added Weyl and Riesz Fractional Derivative Functions:

  • Weyl: Implements the periodic, right-sided fractional derivative using an FFT-based method. For periodic functions, this operator produces phase-shifted analytical derivatives, and is especially well-suited for spectral methods.
  • Riesz: Implements the symmetric (two-sided) fractional derivative, also using FFT. For pure sines/cosines, the Riesz operator multiplies each Fourier mode by $-|k|^\alpha$, resulting in a real-valued, sign-flipped output (not a phase shift). Especially relevant in physics and PDEs.

• Testing Update:

  • Both Weyl and Riesz are covered by unittest and pytest-style tests for compatibility and reliability.
  • The test suite is transitioned from unittest to pytest for modern, flexible, and more expressive testing.

differintP 0.0.3

0.0.3 (7/4/2025)

• Redesigned GLpoint:
  Replaced the previous GLpoint implementation with a highly efficient, single-pass C++-style recurrence. The new method uses a Numba JIT-compiled kernel for substantial speed gains, directly computing the Grünwald-Letnikov fractional derivative at the endpoint in one loop over the function values.
  Legacy and alternative endpoint methods (GLpoint_direct, GLpoint_via_GL) have been moved to special.py for reference and comparison.

Benchmark Result for GLpoint:

count	differintP	differint	Speedup Factor
1+e2	0.0148 ms	0.0416 ms	x2.81
1+e3	0.0276 ms	0.4213 ms	x15.26
1+e4	0.0397 ms	3.8376 ms	x96.66
1+e5	0.3285 ms	36.303 ms	x110.5
1+e6	5.267 ms	385.9205 ms	x73.27
1+e7	51.2645 ms	3674.3541 ms	x71.67

• Optimized GLI implementation:

  • Rewrote core algorithm to use a Numba-accelerated helper for the main rolling-window convolution, matching the original literature.
  • Ensured correctness by flipping GL coefficients within the moving-window convolution.
  • Replaced class-based coefficient calculation with direct variable computation for improved clarity and efficiency.
  • All critical loops are now compiled with Numba for major speed improvements, especially at high grid resolutions.
  • Modernized function interface and added robust array conversion and shape checks.

Benchmark Result for GLI:

count	differintP	differint	Speedup Factor
1+e2	0.0760 ms	0.7582 ms	x6.06
1+e3	2.0336 ms	7.391 ms	x3.63
1+e4	155.7649 ms	128.3709 ms	x0.8
5+e4	3895.176 ms	15181.82 ms	x3.89

• Wiki Pages for

  • CaputoL1point CaputoL2point CaputoL2Cpoint CaputoFromRLpoint
  • CRONE GL GLpoint GLI GL_gpu
  • RL RLpoint PCsolver functions Namespaces

• Aditional test and test restructuring

• Restructuring the Namespaces

differintP 0.0.2

0.0.2 (7/3/2025)

• Optimized core functions: GL, RL, and RLpoint
• Added GPU-accelerated GL (GL_gpu) via CuPy (optional dependency)
• Modernized package setup and build system

GL:

count	differintP	differint
1+e2	0.0782 ms	0.2159 ms
1+e3	0.0942 ms	0.6401 ms
1+e4	0.487 ms	3.8757 ms
1+e5	9.1574 ms	38.2753 ms
1+e6	97.8466 ms	403.2405 ms
1+e7	*	*

RL

count	differintP	differint
1+e2	0.9003 ms	4.054 ms
1+e3	15.8491 ms	418.7378 ms
1+e4	1372.8949 ms	3.8757 ms

RLpoint

count	differintP	differint
1+e2	0.0874 ms	0.1039 ms
1+e3	0.1519 ms	0.9835 ms
1+e4	1.0374 ms	9.7152 ms
1+e5	12.5892 ms	108.2792 ms
1+e6	126.6893 ms	995.7722 ms
1+e7	1257.0316 ms	*