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Lab (Behind the Scenes)

How The Engine Runs

1) Age interpolation
Functions: buildAgeCurve, piecewiseLinearInterpolation, naturalCubicSplineInterpolation
2) Build constrained allocation
Functions: buildTargetWeights, applyBounds, computeAllocation
3) Root-correct rounded totals
Functions: correctBudgetAfterRounding, solveBisection, solveNewton
4) Diagnose numerical behavior
Functions: runLabSolvers, perturbAgeSensitivity, l2Norm, linfNorm

Algorithm To Function To Output

Numerical accuracy & stability
perturbAgeSensitivity, l2Norm, linfNorm to sensitivity and residual size shown below.
Linear algebra (Ax=b)
buildLabSystem, matVecMul, subVec to matrix/vector and residual metrics.
Linear solvers
gaussianEliminationPartialPivoting, jacobiSolver, gaussSeidelSolver to comparison and convergence chart.
Interpolation for age model
buildAgeCurve (spline/linear) to age-weight curve visual.
Root finding for budget correction
correctBudgetAfterRounding (Newton/Bisection safeguards) to budget match status and delta.

Live Solver Summary

gaussian
Converged: true
Iterations: 1
||r||2: 0.000e+0
||r||inf: 0.000e+0
jacobi
Converged: false
Iterations: 200
||r||2: 4.977e+64
||r||inf: 4.977e+64
Jacobi did not converge within max iterations.
gaussSeidel
Converged: false
Iterations: 200
||r||2: 2.948e+126
||r||inf: 2.354e+126
Gauss-Seidel did not converge within max iterations.
Show Ax = b
A =
[1.000, 0.000, -1.789]
[0.000, 1.000, -2.372]
[1.000, 1.000, 1.000]
b = [0.000, 0.000, 600.000]
Diagonal dominance: No

Convergence (Iterative Solvers)

Age Interpolation (Live)

Model: spline

Budget Correction (Live)

Method: newton
alpha: 0.992188
Total rounded: $600.00
Budget: $600.00
Difference: $0.00
Status: Exact match

Sensitivity Test (+1 Year Age)

Delta(Aiden) = 0.00
Delta(Mia) = 0.00
Delta(Uncle Chen) = 0.00
Max absolute change: 0.00
Relative residual proxy ||r||/||b||: 0.000e+0
Amplification proxy: 0.000
Floating-point effects: values are double precision approximations.