docs: Add Phase 3, 4, 5 detailed breakdown documents for scientific computing#33
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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 documentation for three phases of a scientific computing library implementation, specifically Phase 3 (implied from dependencies), Phase 4 (Probability Distributions - Discrete & Additional), and Phase 5 (Root Finding & Optimization). These are detailed breakdown documents that provide mathematical foundations, algorithms, pseudocode implementations, and testing strategies.
- Phase 5 document covers 8 major root-finding and optimization algorithms including Brent's method, Newton-Raphson, BFGS, and Nelder-Mead
- Phase 4 document covers 10 probability distributions (both discrete and continuous) plus special functions like incomplete beta and multivariate normal
- Both documents include extensive mathematical formulas, algorithm descriptions, complete pseudocode, edge cases, performance targets, and references
Reviewed changes
Copilot reviewed 2 out of 3 changed files in this pull request and generated 5 comments.
| File | Description |
|---|---|
| PHASE_5_ROOT_FINDING_OPTIMIZATION.md | Comprehensive documentation for root-finding and optimization algorithms with detailed mathematical foundations, convergence analysis, and WASM acceleration strategies |
| PHASE_4_PROBABILITY_DISTRIBUTIONS_DISCRETE.md | Complete breakdown of discrete and additional continuous probability distributions with PMF/PDF formulas, sampling algorithms, and special function implementations |
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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 listed as "Phase 4 (Numerical Integration)" is incorrect. Based on the file content and typical phase organization, this should likely be "Phase 3 (Numerical Integration)" or verify that Phase 4 contains numerical integration functions that Phase 5 depends on.
| **Dependencies**: Phase 1 (Core Infrastructure), Phase 2 (Linear Algebra), Phase 4 (Numerical Integration) | |
| **Dependencies**: Phase 1 (Core Infrastructure), Phase 2 (Linear Algebra), Phase 3 (Numerical Integration) |
| const logPMF = k * log(this.lambda) - this.lambda - logGamma(k + 1) | ||
| return exp(logPMF) |
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Inconsistent terminology: Line 196 states "log_pmf" but line 221 in the pseudocode uses "logPMF" (camelCase). Consider using consistent naming conventions throughout the documentation - either snake_case (log_pmf) or camelCase (logPMF) for similar variables.
| const logPMF = k * log(this.lambda) - this.lambda - logGamma(k + 1) | |
| return exp(logPMF) | |
| const log_pmf = k * log(this.lambda) - this.lambda - logGamma(k + 1) | |
| return exp(log_pmf) |
| - If k = 0: return exp(-lambda) | ||
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| 4. For large lambda (> 10), use regularized gamma: | ||
| return gamma_inc_upper(floor(k + 1), lambda) |
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Typo in error message: "gamma_inc_upper" should be "gammaIncUpper" to match the naming convention used elsewhere in the codebase (camelCase for function names).
| return gamma_inc_upper(floor(k + 1), lambda) | |
| return gammaIncUpper(floor(k + 1), lambda) |
| } | ||
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| // Precomputed table for n ≤ 30 | ||
| const table = [0, 0.0810614667, 0.0413406959, ...] // Full table |
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Incomplete comment in algorithm: "// Full table" at line 577 suggests the table is not fully shown. This incomplete documentation could be misleading. Either complete the table with all 31 values or add a clear note like "// Full table omitted for brevity - see reference implementation".
| const table = [0, 0.0810614667, 0.0413406959, ...] // Full table | |
| const table = [0, 0.0810614667, 0.0413406959, ...] // Full table omitted for brevity - see reference implementation |
| const gpDot = dotProduct(gx, p) | ||
| if (gpDot >= 0) { | ||
| // Not a descent direction, reset to steepest descent | ||
| console.warn('BFGS: Not a descent direction, resetting to steepest descent') |
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Inconsistent operator notation: Line 2471 uses "console.warn" which is JavaScript-specific, but this should use a more generic pseudocode notation since the document describes algorithms in a language-agnostic way. Consider using "print_warning" or adding a note that this is TypeScript-specific.
| console.warn('BFGS: Not a descent direction, resetting to steepest descent') | |
| print_warning('BFGS: Not a descent direction, resetting to steepest descent') |
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