ThotDjehuty
d780ed81d7
Adds 9 new top-level / sub-modules to the Rust API only (no Python
bindings yet), with at least one analytic unit test per module.
New Rust modules:
- optimal_control::matrix_riccati (RK4 backward solver)
- timeseries_utils::nonsync_covariance (Hayashi-Yoshida)
- timeseries_utils::wavelet (Haar / Daubechies DWT and MODWT)
- risk_measures (VaR, CVaR, projected sub-gradient CVaR minimisation)
- graph::laplacian + graph::spectral_clustering (Jacobi + k-means++)
- topology (Vietoris-Rips persistent homology, bottleneck distance)
- volterra (Caputo Adams, Markovian lift, second-kind Volterra,
Fourier inversion of characteristic functions)
- signatures (truncated tensor signature, log-sig, random reservoir,
Salvi-Cass-Lyons signature kernel, shuffle product)
All previously stable APIs untouched; abi3-py38 ABI preserved.
New module tests: 29/29 passing. Pre-existing 5 unrelated failures
unchanged.
52 lines
1.5 KiB
ReStructuredText
52 lines
1.5 KiB
ReStructuredText
Discrete and Maximum-Overlap Wavelet Transforms
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The module :code:`timeseries_utils::wavelet` provides Haar and Daubechies
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wavelet transforms with periodic boundary handling.
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Filter banks
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------------
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For an orthogonal scaling filter :math:`\{h_k\}_{k=0}^{L-1}` the quadrature
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mirror filter (QMF) is
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.. math::
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g_k = (-1)^k\, h_{L - 1 - k},
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so that :math:`\sum_k h_k = \sqrt{2}` and :math:`\sum_k g_k = 0`.
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DWT (one level, periodic)
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-------------------------
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For an input vector :math:`x \in \mathbb{R}^N` with :math:`N` even,
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.. math::
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a_n = \sum_{k=0}^{L-1} h_k\, x_{(2n + k)\bmod N},
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\qquad
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d_n = \sum_{k=0}^{L-1} g_k\, x_{(2n + k)\bmod N},
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\qquad n = 0, \dots, N/2 - 1.
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Successive levels apply the same filter to the previous approximation
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:math:`a^{(j)}`.
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MODWT (Maximum Overlap)
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-----------------------
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The MODWT does not downsample: at level :math:`j`, the filter is dilated
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by inserting :math:`2^{j-1} - 1` zeros between successive taps and applied
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in a periodic convolution. The result is shift-invariant.
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API
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---
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.. code-block:: rust
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pub enum WaveletFamily { Haar, Daubechies(u8) }
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pub fn scaling_filter(family: WaveletFamily) -> Result<Vec<f64>>;
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pub fn qmf(h: &[f64]) -> Vec<f64>;
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pub fn dwt_step(x: &[f64], h: &[f64], g: &[f64]) -> (Vec<f64>, Vec<f64>);
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pub fn dwt(x: &[f64], family: WaveletFamily, levels: usize) -> Result<Vec<Vec<f64>>>;
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pub fn modwt_step(x: &[f64], h: &[f64], g: &[f64], level: usize) -> (Vec<f64>, Vec<f64>);
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