ThotDjehuty
142 lines
6.3 KiB
Python
142 lines
6.3 KiB
Python
"""Replace the 4 remaining ASCII diagram blocks in mathematical_foundations.md
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with {figure} directives pointing to the new SVGs.
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"""
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import pathlib
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MD = pathlib.Path(__file__).parent / "theory" / "mathematical_foundations.md"
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text = MD.read_text(encoding="utf-8")
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# ── 1. HMM regime state machine → fig_hmm_regime ──────────────────────────
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old1 = '''\
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```
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HMM regime state machine (K = 3)
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┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄
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A₁₂ → A₂₃ →
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┌─────────────┐ ┌─────────────┐ ┌─────────────┐
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│ State 1 │──────▶│ State 2 │──────▶│ State 3 │
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│ Bull │◀──────│ Neutral │◀──────│ Bear │
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└─────────────┘ └─────────────┘ └─────────────┘
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← A₂₁ ← A₃₂
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Emission B_k(y) = 𝒩(μ_k, σ_k²):
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┌────────┬────────┬────────┬──────────────────┐
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│ State │ μ │ σ │ Character │
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├────────┼────────┼────────┼──────────────────┤
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│ Bull │ +0.05 │ 0.12 │ high return, low vol │
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│ Neutral│ 0.00 │ 0.18 │ flat, medium vol │
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│ Bear │ -0.08 │ 0.35 │ crash, high vol │
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└────────┴────────┴────────┴──────────────────┘
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(self-transition: A₁₁=0.97, A₂₂=0.97, A₃₃=0.90)
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```'''
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new1 = '''\
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```{figure} ../_static/diagrams/fig_hmm_regime.svg
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:align: center
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:width: 90%
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HMM $K=3$ state machine with Bull / Neutral / Bear regimes and Gaussian emission
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parameters. Self-transitions $A_{11}=A_{22}=0.97$, $A_{33}=0.90$.
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```'''
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# ── 2. Viterbi trellis → fig_viterbi_trellis ───────────────────────────────
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old2 = '''\
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```
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Viterbi trellis (K=3, T=4)
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┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄
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State t=1 t=2 t=3 t=4
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1 ○─────────▶○─────────▶○─────────▶○
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╲ ╳
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2 ○─────────▶●─────────▶●─────────▶○ ● = MAP path
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╲ ╲ ╲
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3 ○─────────▶○─────────▶○─────────▶○
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δ_t(k) = max_j [δ_{t−1}(j) · A_jk · B_k(y_t)]
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ψ_t(k) = argmax_j ← backtrack pointer
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Traceback: z_4★ ← z_3★ ← z_2★ ← z_1★ via ψ
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```'''
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new2 = r'''\
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```{figure} ../_static/diagrams/fig_viterbi_trellis.svg
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:align: center
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:width: 82%
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Viterbi trellis ($K=3$, $T=4$). Filled nodes mark the MAP (most probable) state
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sequence; arrows show transition candidates. Backtracking via $\psi_t(k)$ recovers
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$z_1^\star \to z_4^\star$.
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```'''
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# ── 3. Standard vs natural gradient (text comparison) → fig_std_vs_nat_gradient
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old3 = '''\
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```
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Standard vs natural gradient
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┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄
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Standard: θ_{k+1} = θ_k − η·∇ℒ Natural: θ_{k+1} = θ_k − η·ℐ(θ)^{−1}∇ℒ
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────────────────────────────────────────────
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┌────────────────────┐ ┌────────────────────┐
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│ Flat ℝᵈ geometry │ │ Riemannian metric ℐ(θ) │
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│ Ignores curvature │ │ Adapts to geometry │
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│ Slow on ill-cond ℐ │ │ Reparam invariant │
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│ O(κ(ℐ)) iters │ │ O(1) on exp families │
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└────────────────────┘ └────────────────────┘
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On Gaussian / exponential family: ℐ⁻¹∇ℒ = MLE step → 1 iteration!
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```'''
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new3 = '''\
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```{figure} ../_static/diagrams/fig_std_vs_nat_gradient.svg
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:align: center
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:width: 88%
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Standard versus natural gradient: geometric properties. On exponential families
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the natural gradient equals the MLE Newton step, achieving convergence in one
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iteration.
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```'''
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# ── 4. Matrix Lie group hierarchy → fig_lie_group_hierarchy ─────────────────
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old4 = '''\
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```
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Matrix Lie group hierarchy
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┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄
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GL(n,ℝ) ─ all invertible n×n real matrices
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│
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├──▶ SL(n,ℝ) det = 1
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│
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├──▶ O(n) RᵀR = I (orthogonal)
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│ └─▶ SO(n) det = +1 (pure rotations)
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│ ↳ portfolio factor rotation, PCA constraints
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│
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└──▶ Sp(2n,ℝ) preserves symplectic form ω
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↳ Hamiltonian mechanics, PMP §4.2 / §10.4
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H(n) Heisenberg ─ upper triangular, 1s on diagonal
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↳ path-signature feature maps
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```'''
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new4 = r'''\
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```{figure} ../_static/diagrams/fig_lie_group_hierarchy.svg
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:align: center
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:width: 90%
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Matrix Lie group hierarchy: subgroup inclusions and their quantitative-finance
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applications. $SO(n)$ underpins PCA factor rotation; $\mathrm{Sp}(2n,\mathbb{R})$
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governs Hamiltonian mechanics (PMP §10.4); $H(n)$ drives path-signature features.
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```'''
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replacements = [(old1, new1), (old2, new2), (old3, new3), (old4, new4)]
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for i, (old, new) in enumerate(replacements, 1):
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if old in text:
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text = text.replace(old, new, 1)
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print(f" Block {i}: replaced OK")
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else:
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print(f" Block {i}: NOT FOUND — check encoding/whitespace")
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MD.write_text(text, encoding="utf-8")
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print("Done.")
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