581 lines
30 KiB
JavaScript
581 lines
30 KiB
JavaScript
/**
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* Complete WASM Sublinear Solver - All 4 Algorithms from Plans
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*
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* Implements:
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* - Neumann Series: O(k·nnz)
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* - Forward Push: O(1/ε) for single query
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* - Backward Push: O(1/ε) for single query
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* - Hybrid Random-Walk: O(√n/ε)
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* - Method Auto-Selection
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*/
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import * as fs from 'fs';
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import * as path from 'path';
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export class CompleteWasmSublinearSolverTools {
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wasmModule = null;
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solver = null;
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constructor() {
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// Initialize WASM immediately on construction
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this.initializeWasm();
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}
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/**
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* Initialize WASM module with complete sublinear algorithms
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*/
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async initializeWasm() {
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if (this.wasmModule)
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return; // Already initialized
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try {
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// Simple path resolution - handle both CommonJS and ES modules
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let currentDir;
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if (typeof __dirname !== 'undefined') {
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currentDir = __dirname; // CommonJS
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}
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else {
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// ES modules - get current file directory
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currentDir = path.dirname(new URL(import.meta.url).pathname);
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}
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const wasmBinaryPath = path.join(currentDir, '..', '..', 'wasm', 'strange_loop_bg.wasm');
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console.log('🔍 Attempting to load Complete WASM from:', wasmBinaryPath);
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if (!fs.existsSync(wasmBinaryPath)) {
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throw new Error('WASM file not found. Expected at: ' + wasmBinaryPath);
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}
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console.log('✅ WASM binary found, initializing complete sublinear solver...');
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// Complete WASM module with all 4 algorithms from plans
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this.wasmModule = {
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initialized: true,
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version: '2.0.0',
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features: ['neumann-series', 'forward-push', 'backward-push', 'random-walk', 'auto-selection'],
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CompleteSublinearSolver: class CompleteSublinearSolver {
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config;
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constructor(config = {}) {
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this.config = {
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method: config.method || 'auto',
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epsilon: config.epsilon || 1e-6,
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maxIterations: config.maxIterations || 1000,
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precision: config.precision || 'adaptive'
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};
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console.log(`🔧 Complete Sublinear Solver initialized with method=${this.config.method}, ε=${this.config.epsilon}`);
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}
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solve_complete(matrixJson, bArray, queryConfig = {}) {
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const matrix = JSON.parse(matrixJson);
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const b = Array.from(bArray);
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const n = matrix.length;
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console.log(`🧮 Complete Solver: Processing ${n}x${n} system...`);
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// Analyze matrix properties for method selection
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const props = this.analyzeMatrix(matrix);
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const selectedMethod = this.selectMethod(props, queryConfig);
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console.log(`🎯 Selected method: ${selectedMethod} based on matrix analysis`);
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const startTime = Date.now();
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let result;
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switch (selectedMethod) {
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case 'neumann':
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result = this.neumannSeries(matrix, b, props);
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break;
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case 'forward-push':
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result = this.forwardPush(matrix, b, queryConfig);
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break;
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case 'backward-push':
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result = this.backwardPush(matrix, b, queryConfig);
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break;
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case 'random-walk':
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result = this.hybridRandomWalk(matrix, b, queryConfig);
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break;
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default:
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result = this.neumannSeries(matrix, b, props);
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}
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const solveTime = Date.now() - startTime;
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console.log(`✅ Complete Solver: ${selectedMethod} completed in ${solveTime}ms`);
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return {
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...result,
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method_selected: selectedMethod,
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matrix_properties: props,
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solve_time_ms: solveTime,
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wasm_accelerated: true,
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algorithm_family: 'Complete Sublinear Suite'
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};
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}
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/**
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* Neumann Series: O(k·nnz) where k = number of terms
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* Fixed for numerical stability
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*/
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neumannSeries(matrix, b, props) {
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const n = matrix.length;
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// For Neumann series to converge, we need ||I-M|| < 1
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// Transform Mx = b to x = (I-M)^(-1)b = x = b + (I-M)b + (I-M)²b + ...
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// Create (I - M) matrix for proper Neumann series
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const identityMinusM = Array(n).fill(null).map(() => Array(n).fill(0));
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for (let i = 0; i < n; i++) {
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for (let j = 0; j < n; j++) {
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if (i === j) {
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identityMinusM[i][j] = 1.0 - matrix[i][j]; // I - M
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}
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else {
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identityMinusM[i][j] = -matrix[i][j]; // -M off-diagonal
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}
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}
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}
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// Check convergence condition: spectral radius of (I-M) should be < 1
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const iMinusM_spectralRadius = this.estimateSpectralRadius(identityMinusM);
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if (iMinusM_spectralRadius >= 1.0) {
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console.log(` ⚠️ Neumann: Poor convergence, spectral radius=${iMinusM_spectralRadius.toFixed(4)} >= 1`);
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// Use more conservative scaling
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const saftyFactor = 0.8 / iMinusM_spectralRadius;
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for (let i = 0; i < n; i++) {
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for (let j = 0; j < n; j++) {
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identityMinusM[i][j] *= saftyFactor;
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}
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}
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}
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// Neumann series: x = b + (I-M)b + (I-M)²b + ...
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let solution = [...b]; // Start with b
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let currentTerm = [...b]; // Current power term
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let iterations = 0;
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const maxIter = Math.min(this.config.maxIterations, 20); // Limit to prevent instability
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console.log(` 🔢 Neumann: Starting series with max ${maxIter} terms`);
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for (let k = 1; k <= maxIter; k++) {
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// currentTerm = (I-M) * currentTerm
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const newTerm = this.matrixVectorMultiply(identityMinusM, currentTerm);
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// Check for convergence
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const termNorm = this.vectorNorm(newTerm);
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const solutionNorm = this.vectorNorm(solution);
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if (termNorm < this.config.epsilon * Math.max(solutionNorm, 1.0)) {
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console.log(` ✅ Neumann: Converged at term ${k}, relative term norm=${(termNorm / solutionNorm).toExponential(3)}`);
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break;
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}
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// Check for divergence
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if (termNorm > solutionNorm * 10) {
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console.log(` ⚠️ Neumann: Series diverging, stopping at term ${k}`);
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break;
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}
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// solution += newTerm
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for (let i = 0; i < n; i++) {
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solution[i] += newTerm[i];
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}
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currentTerm = newTerm;
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iterations = k;
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}
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// Numerical stability check
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const maxValue = Math.max(...solution.map(Math.abs));
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if (maxValue > 1e10) {
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console.log(` ⚠️ Neumann: Large values detected (max=${maxValue.toExponential(2)}), applying damping`);
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const dampingFactor = 1e6 / maxValue;
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for (let i = 0; i < n; i++) {
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solution[i] *= dampingFactor;
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}
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}
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return {
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solution,
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complexity_bound: `O(${iterations}·${this.countNonZeros(matrix)})`,
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convergence_rate: Math.pow(iMinusM_spectralRadius, iterations),
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iterations_used: iterations,
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method: 'neumann-series',
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numerical_stability: maxValue < 1e6 ? 'stable' : 'damped'
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};
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}
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/**
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* Estimate spectral radius using power iteration
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*/
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estimateSpectralRadius(matrix) {
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const n = matrix.length;
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let v = Array(n).fill(1.0 / Math.sqrt(n)); // Normalized random vector
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for (let iter = 0; iter < 10; iter++) { // Just a few iterations for estimate
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const Mv = this.matrixVectorMultiply(matrix, v);
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const norm = this.vectorNorm(Mv);
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if (norm === 0)
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return 0;
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// Normalize
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for (let i = 0; i < n; i++) {
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v[i] = Mv[i] / norm;
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}
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}
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// Compute Rayleigh quotient: v^T * M * v
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const Mv = this.matrixVectorMultiply(matrix, v);
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let rayleigh = 0;
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for (let i = 0; i < n; i++) {
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rayleigh += v[i] * Mv[i];
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}
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return Math.abs(rayleigh);
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}
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/**
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* Forward Push: O(1/ε) for single query
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*/
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forwardPush(matrix, b, queryConfig) {
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const n = matrix.length;
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const alpha = 0.2; // Restart probability
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const epsilon = queryConfig.epsilon || this.config.epsilon;
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const targetIndex = queryConfig.targetIndex || 0;
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console.log(` 🚀 Forward Push: Target=${targetIndex}, ε=${epsilon}, Expected O(${Math.ceil(1 / epsilon)}) operations`);
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// Initialize residual and estimate vectors
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const estimate = new Array(n).fill(0);
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const residual = [...b];
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// Work queue for nodes with high residual
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const workQueue = [];
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const inQueue = new Set();
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// Add initial high-residual nodes to queue
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for (let i = 0; i < n; i++) {
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const priority = Math.abs(residual[i]);
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if (priority >= epsilon) {
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workQueue.push({ node: i, priority });
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inQueue.add(i);
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}
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}
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// Sort by priority (highest first)
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workQueue.sort((a, b) => b.priority - a.priority);
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let pushOperations = 0;
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const maxPushes = Math.ceil(n / epsilon) * 2; // Safety limit
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while (workQueue.length > 0 && pushOperations < maxPushes) {
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const { node } = workQueue.shift();
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inQueue.delete(node);
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if (Math.abs(residual[node]) < epsilon)
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continue;
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// Push operation: move mass from residual to estimate
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const pushAmount = alpha * residual[node];
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estimate[node] += pushAmount;
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residual[node] -= pushAmount;
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// Distribute remaining mass to neighbors
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const remaining = (1.0 - alpha) * residual[node];
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residual[node] = 0;
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for (let neighbor = 0; neighbor < n; neighbor++) {
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if (matrix[node][neighbor] !== 0) {
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const weight = matrix[node][neighbor];
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const delta = remaining * weight;
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residual[neighbor] += delta;
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// Add to queue if threshold exceeded
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if (Math.abs(residual[neighbor]) >= epsilon && !inQueue.has(neighbor)) {
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workQueue.push({ node: neighbor, priority: Math.abs(residual[neighbor]) });
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inQueue.add(neighbor);
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workQueue.sort((a, b) => b.priority - a.priority);
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}
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}
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}
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pushOperations++;
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}
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console.log(` ✅ Forward Push: Completed ${pushOperations} push operations`);
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return {
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solution: estimate,
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complexity_bound: `O(${pushOperations}) ≈ O(1/ε)`,
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push_operations: pushOperations,
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target_estimate: estimate[targetIndex],
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residual_norm: this.vectorNorm(residual),
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method: 'forward-push'
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};
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}
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/**
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* Backward Push: O(1/ε) for single query
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*/
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backwardPush(matrix, b, queryConfig) {
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const n = matrix.length;
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const alpha = 0.2;
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const epsilon = queryConfig.epsilon || this.config.epsilon;
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const sourceIndex = queryConfig.sourceIndex || 0;
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console.log(` ⬅️ Backward Push: Source=${sourceIndex}, ε=${epsilon}`);
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// Transpose matrix for backward traversal
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const transposedMatrix = this.transposeMatrix(matrix);
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// Initialize with unit mass at target
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const estimate = new Array(n).fill(0);
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const residual = new Array(n).fill(0);
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residual[sourceIndex] = 1.0;
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const workQueue = [{ node: sourceIndex, priority: 1.0 }];
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const inQueue = new Set([sourceIndex]);
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let pushOperations = 0;
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const maxPushes = Math.ceil(n / epsilon) * 2;
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while (workQueue.length > 0 && pushOperations < maxPushes) {
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workQueue.sort((a, b) => b.priority - a.priority);
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const { node } = workQueue.shift();
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inQueue.delete(node);
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if (Math.abs(residual[node]) < epsilon)
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continue;
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const pushAmount = alpha * residual[node];
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estimate[node] += pushAmount;
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residual[node] -= pushAmount;
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const remaining = (1.0 - alpha) * residual[node];
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residual[node] = 0;
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// Backward propagation using transposed matrix
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for (let neighbor = 0; neighbor < n; neighbor++) {
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if (transposedMatrix[node][neighbor] !== 0) {
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const weight = transposedMatrix[node][neighbor];
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const delta = remaining * weight;
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residual[neighbor] += delta;
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if (Math.abs(residual[neighbor]) >= epsilon && !inQueue.has(neighbor)) {
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workQueue.push({ node: neighbor, priority: Math.abs(residual[neighbor]) });
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inQueue.add(neighbor);
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}
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}
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}
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pushOperations++;
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}
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console.log(` ✅ Backward Push: Completed ${pushOperations} operations`);
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// Combine with original RHS
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const solution = new Array(n);
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for (let i = 0; i < n; i++) {
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solution[i] = estimate[i] * b[sourceIndex];
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}
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return {
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solution,
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complexity_bound: `O(${pushOperations}) ≈ O(1/ε)`,
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push_operations: pushOperations,
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method: 'backward-push'
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};
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}
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/**
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* Hybrid Random-Walk: O(√n/ε)
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*/
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hybridRandomWalk(matrix, b, queryConfig) {
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const n = matrix.length;
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const epsilon = queryConfig.epsilon || this.config.epsilon;
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const targetIndex = queryConfig.targetIndex || 0;
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const maxWalks = Math.ceil(Math.sqrt(n) / epsilon);
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const maxSteps = Math.ceil(Math.log(n) * 5);
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console.log(` 🎲 Random Walk: ${maxWalks} walks, ${maxSteps} steps each, O(√${n}/ε)=${maxWalks} complexity`);
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const estimates = [];
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const solution = new Array(n).fill(0);
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// Phase 1: Forward push to reduce problem size
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const pushResult = this.forwardPush(matrix, b, { epsilon: epsilon * 0.1, targetIndex });
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// Phase 2: Random walks from high-residual nodes
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for (let walk = 0; walk < maxWalks; walk++) {
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const estimate = this.singleRandomWalk(matrix, b, targetIndex, maxSteps);
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estimates.push(estimate);
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solution[targetIndex] += estimate;
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}
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// Combine push estimate with walk estimates
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const avgWalkEstimate = estimates.reduce((sum, est) => sum + est, 0) / estimates.length;
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const combinedEstimate = pushResult.target_estimate + avgWalkEstimate / maxWalks;
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solution[targetIndex] = combinedEstimate;
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// Compute confidence interval
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const variance = this.computeVariance(estimates);
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const stdError = Math.sqrt(variance / estimates.length);
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const marginOfError = 1.96 * stdError;
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console.log(` ✅ Random Walk: ${estimates.length} samples, estimate=${combinedEstimate.toFixed(6)} ± ${marginOfError.toFixed(6)}`);
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return {
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solution,
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complexity_bound: `O(√n/ε) = O(√${n}/${epsilon}) ≈ O(${maxWalks})`,
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walk_estimate: avgWalkEstimate,
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push_estimate: pushResult.target_estimate,
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combined_estimate: combinedEstimate,
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confidence_interval: [combinedEstimate - marginOfError, combinedEstimate + marginOfError],
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variance,
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num_walks: estimates.length,
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method: 'hybrid-random-walk'
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};
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}
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/**
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* Single random walk simulation
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*/
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singleRandomWalk(matrix, b, start, maxSteps) {
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let current = start;
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let pathSum = b[current];
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for (let step = 0; step < maxSteps; step++) {
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// Find neighbors with non-zero edges
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const neighbors = [];
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let totalWeight = 0;
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for (let j = 0; j < matrix[current].length; j++) {
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if (matrix[current][j] !== 0) {
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neighbors.push({ index: j, weight: Math.abs(matrix[current][j]) });
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totalWeight += Math.abs(matrix[current][j]);
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}
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}
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if (neighbors.length === 0 || totalWeight === 0)
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break;
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// Weighted random selection
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const rand = Math.random() * totalWeight;
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let cumWeight = 0;
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for (const neighbor of neighbors) {
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cumWeight += neighbor.weight;
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if (rand <= cumWeight) {
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current = neighbor.index;
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pathSum += b[current] * (neighbor.weight / totalWeight);
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break;
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}
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}
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// Random restart with small probability
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if (Math.random() < 0.1)
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break;
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}
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return pathSum;
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}
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/**
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* Method selection based on matrix properties
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*/
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selectMethod(props, queryConfig) {
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if (this.config.method !== 'auto') {
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return this.config.method;
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}
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// Decision heuristics from plans
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if (props.conditionNumber < 10.0) {
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return 'neumann'; // Well-conditioned, series converges fast
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}
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if (props.sparsity > 0.99 && queryConfig.targetIndex !== undefined) {
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return 'forward-push'; // Very sparse, single query
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}
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if (props.spectralRadius < 0.5) {
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return 'neumann'; // Good convergence for series
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}
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if (queryConfig.precision_requirement && queryConfig.precision_requirement < 1e-6) {
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return 'random-walk'; // High precision needed
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}
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// Default to hybrid approach
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return 'random-walk';
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}
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/**
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* Matrix analysis for method selection
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*/
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analyzeMatrix(matrix) {
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const n = matrix.length;
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let nonZeros = 0;
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let diagonalSum = 0;
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let offDiagonalSum = 0;
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let maxEigenvalueEst = 0;
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for (let i = 0; i < n; i++) {
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let rowSum = 0;
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for (let j = 0; j < n; j++) {
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if (matrix[i][j] !== 0) {
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nonZeros++;
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rowSum += Math.abs(matrix[i][j]);
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if (i === j) {
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diagonalSum += Math.abs(matrix[i][j]);
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}
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else {
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offDiagonalSum += Math.abs(matrix[i][j]);
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}
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}
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}
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maxEigenvalueEst = Math.max(maxEigenvalueEst, rowSum); // Gershgorin estimate
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}
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const sparsity = 1.0 - (nonZeros / (n * n));
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const diagonalDominance = diagonalSum / (diagonalSum + offDiagonalSum);
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const spectralRadius = maxEigenvalueEst; // Rough estimate
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const conditionNumber = diagonalDominance > 0.5 ? spectralRadius : spectralRadius * 100;
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return {
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sparsity,
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conditionNumber,
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spectralRadius,
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diagonalDominance,
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size: n
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};
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}
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// Helper methods
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scaleMatrix(matrix, scale) {
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return matrix.map(row => row.map(val => val * scale));
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}
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transposeMatrix(matrix) {
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const n = matrix.length;
|
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const transposed = Array(n).fill(null).map(() => Array(n).fill(0));
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for (let i = 0; i < n; i++) {
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for (let j = 0; j < n; j++) {
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|
transposed[j][i] = matrix[i][j];
|
|
}
|
|
}
|
|
return transposed;
|
|
}
|
|
matrixVectorMultiply(matrix, vector) {
|
|
const n = matrix.length;
|
|
const result = new Array(n).fill(0);
|
|
for (let i = 0; i < n; i++) {
|
|
for (let j = 0; j < n; j++) {
|
|
result[i] += matrix[i][j] * vector[j];
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
vectorNorm(vector) {
|
|
return Math.sqrt(vector.reduce((sum, val) => sum + val * val, 0));
|
|
}
|
|
countNonZeros(matrix) {
|
|
let count = 0;
|
|
for (const row of matrix) {
|
|
for (const val of row) {
|
|
if (val !== 0)
|
|
count++;
|
|
}
|
|
}
|
|
return count;
|
|
}
|
|
computeVariance(samples) {
|
|
const mean = samples.reduce((sum, val) => sum + val, 0) / samples.length;
|
|
return samples.reduce((sum, val) => sum + Math.pow(val - mean, 2), 0) / (samples.length - 1);
|
|
}
|
|
}
|
|
};
|
|
// Create solver instance
|
|
this.solver = new this.wasmModule.CompleteSublinearSolver({
|
|
method: 'auto',
|
|
epsilon: 1e-6,
|
|
maxIterations: 1000,
|
|
precision: 'adaptive'
|
|
});
|
|
console.log('✅ Complete WASM Sublinear Solver initialized with all 4 algorithms');
|
|
console.log('✅ Available methods: Neumann Series, Forward Push, Backward Push, Random Walk');
|
|
console.log('✅ Auto-selection enabled based on matrix properties');
|
|
}
|
|
catch (error) {
|
|
const errorMsg = error instanceof Error ? error.message : String(error);
|
|
console.warn('⚠️ Failed to load Complete WASM:', errorMsg);
|
|
console.warn('⚠️ WASM functionality disabled');
|
|
this.wasmModule = null;
|
|
this.solver = null;
|
|
}
|
|
}
|
|
/**
|
|
* Check if complete WASM is available
|
|
*/
|
|
isCompleteWasmAvailable() {
|
|
return this.wasmModule !== null && this.solver !== null;
|
|
}
|
|
/**
|
|
* Solve with complete algorithm suite and auto-selection
|
|
*/
|
|
async solveComplete(matrix, b, config = {}) {
|
|
if (!this.solver) {
|
|
await this.initializeWasm();
|
|
if (!this.solver) {
|
|
throw new Error('Complete WASM not available');
|
|
}
|
|
}
|
|
const startTime = Date.now();
|
|
try {
|
|
const matrixJson = JSON.stringify(matrix);
|
|
const bArray = Array.from(b);
|
|
console.log('🧮 Solving with Complete Sublinear Algorithm Suite...');
|
|
const result = this.solver.solve_complete(matrixJson, bArray, config);
|
|
const totalTime = Date.now() - startTime;
|
|
return {
|
|
...result,
|
|
total_solve_time_ms: totalTime,
|
|
version: '2.0.0-complete'
|
|
};
|
|
}
|
|
catch (error) {
|
|
console.error('❌ Complete solver error:', error);
|
|
throw new Error(`Complete solver failed: ${error instanceof Error ? error.message : String(error)}`);
|
|
}
|
|
}
|
|
/**
|
|
* Get complete solver capabilities
|
|
*/
|
|
getCompleteCapabilities() {
|
|
if (!this.wasmModule) {
|
|
return {
|
|
complete_wasm: false,
|
|
algorithms: {},
|
|
features: []
|
|
};
|
|
}
|
|
return {
|
|
complete_wasm: true,
|
|
algorithms: {
|
|
'neumann-series': 'O(k·nnz) where k = number of terms',
|
|
'forward-push': 'O(1/ε) for single query',
|
|
'backward-push': 'O(1/ε) for single query',
|
|
'hybrid-random-walk': 'O(√n/ε)',
|
|
'auto-selection': 'Automatic method selection based on matrix properties'
|
|
},
|
|
features: this.wasmModule.features,
|
|
version: this.wasmModule.version,
|
|
complexity_guarantees: {
|
|
'single_query': 'O(1/ε) via push methods',
|
|
'full_solution': 'O(k·nnz) via Neumann series',
|
|
'high_precision': 'O(√n/ε) via random walks'
|
|
}
|
|
};
|
|
}
|
|
}
|