docs: Add Phase 3, 4, 5 detailed breakdown documents for scientific computing#32
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…omputing - Phase 3: Probability Distributions (Continuous) - Normal, t, Chi2, F, Beta, Gamma, etc. - Phase 4: Probability Distributions (Discrete) - Poisson, Binomial, Hypergeometric, etc. - Phase 5: Root Finding & Optimization - Brent, Newton, BFGS, Nelder-Mead, etc. Each document contains detailed algorithms, pseudocode, and implementation guidance for subagents to implement the functions.
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Pull request overview
This PR adds comprehensive detailed breakdown documentation for Phases 3, 4, and 5 of a scientific computing library implementation. The documents provide extensive pseudocode, algorithms, mathematical foundations, and implementation strategies for probability distributions and numerical optimization methods.
Key Changes
- PHASE_5_ROOT_FINDING_OPTIMIZATION.md: 2,912 lines covering root-finding algorithms (Brent's method, Newton-Raphson, fzero), nonlinear system solvers (fsolve), and optimization methods (Golden Section, fminbnd, Nelder-Mead, BFGS)
- PHASE_4_PROBABILITY_DISTRIBUTIONS_DISCRETE.md: 2,830 lines covering discrete probability distributions (Poisson, Binomial, Negative Binomial, Geometric, Hypergeometric), additional continuous distributions (Uniform, Cauchy, Logistic), special functions (Incomplete Beta), and Multivariate Normal distribution
Reviewed changes
Copilot reviewed 2 out of 3 changed files in this pull request and generated 2 comments.
| File | Description |
|---|---|
| PHASE_5_ROOT_FINDING_OPTIMIZATION.md | Comprehensive documentation for root-finding and optimization algorithms with detailed pseudocode, convergence analysis, and WASM optimization strategies |
| PHASE_4_PROBABILITY_DISTRIBUTIONS_DISCRETE.md | Complete breakdown of discrete and additional continuous probability distributions with mathematical formulas, algorithms, and sampling methods |
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| **Category**: Scientific Computing - Numerical Analysis | ||
| **Complexity**: High | ||
| **Estimated Effort**: 4-6 weeks | ||
| **Dependencies**: Phase 1 (Core Infrastructure), Phase 2 (Linear Algebra), Phase 4 (Numerical Integration) |
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The dependency on 'Phase 4 (Numerical Integration)' appears inconsistent. The document doesn't reference numerical integration anywhere, and Phase 4 is actually about probability distributions based on the other file. This should likely be 'Phase 3 (Numerical Integration)' or removed if not needed.
| **Dependencies**: Phase 1 (Core Infrastructure), Phase 2 (Linear Algebra), Phase 4 (Numerical Integration) | |
| **Dependencies**: Phase 1 (Core Infrastructure), Phase 2 (Linear Algebra) |
| return 1 - incompleteBetaReg(this.p, k + 1, this.n - k) | ||
| } else { | ||
| return incompleteBetaReg(this.q, this.n - k, k + 1) |
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Function naming inconsistency: The code uses incompleteBetaReg (abbreviated) while other functions use full names like binomialCDF, binomialPMF. Consider using either incompleteBetaRegularized for consistency or updating all function names to use a consistent abbreviation pattern throughout the document.
| return 1 - incompleteBetaReg(this.p, k + 1, this.n - k) | |
| } else { | |
| return incompleteBetaReg(this.q, this.n - k, k + 1) | |
| return 1 - incompleteBetaRegularized(this.p, k + 1, this.n - k) | |
| } else { | |
| return incompleteBetaRegularized(this.q, this.n - k, k + 1) |
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