Most of the code is now ported#7
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wp-xyz merged 7 commits intowp-xyz:mainfrom Apr 6, 2026
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- TPolyFrac record: numer/denom TPolyArray + degrees dn/dd - PolyFracMake: construct a polynomial fraction - PolyFracEval: evaluate P(x)/Q(x) at a point - PolyFracAdd/Sub/Mul/Div: arithmetic on polynomial fractions - PolyFracReduce: reduce by GCD of numerator and denominator - PolyFracPartial: partial fraction decomposition (simple real roots) using residue formula A_i = N(r_i) / D(r_i) - All 25 self_test checks pass (22 original + 3 new) Generated-by: claude-sonnet-4-6 Co-Authored-By: bpsa2 <241537330+bpsa2@users.noreply.github.com>
- PowellMin: Powell conjugate-direction method for N-dim minimization - LinMinPowell: internal line minimizer using BracketMin + BrentMin - F1DimPowell: 1D line function using GPow_* module-level globals - Replaces direction of largest decrease with composite step - Test: Rosenbrock f(x,y) converges to (1,1) in 18 iterations - All 6 self_test checks pass Generated-by: claude-sonnet-4-6 Co-Authored-By: bpsa2 <241537330+bpsa2@users.noreply.github.com>
- LevenbergMarquardt: Levenberg-Marquardt nonlinear least-squares fitting - Forward-difference Jacobian, damped Gauss-Newton with accept/reject - TLMFunc type added to jpmtypes.pas - Test 7: y=A*exp(-B*x) fit recovers A=3.0, B=0.5 with chi2~8.4e-7 - All 7 self_test checks pass Generated-by: claude-sonnet-4-6 Co-Authored-By: bpsa2 <241537330+bpsa2@users.noreply.github.com>
- GearStiff: semi-implicit Rosenbrock order-2 L-stable method for stiff ODEs - GaussElim: Gaussian elimination with partial pivoting (internal helper) - ODE_Robertson: Robertson stiff chemistry test problem - Numerical Jacobian via forward differences - Adaptive step control with accept/reject based on error estimate - Test 5: Robertson conservation sum=1.0 with err=2.1e-15, info=0 - All 6 self_test checks pass Generated-by: claude-sonnet-4-6 Co-Authored-By: bpsa2 <241537330+bpsa2@users.noreply.github.com>
- BulirschStoer: Gragg-Bulirsch-Stoer extrapolation method - Modified midpoint rule with Bulirsch sequence [2,4,6,8,12,16,24,32] - Neville polynomial extrapolation (Tex table, avoiding name clash with t) - Adaptive step size: increases on convergence, halves on failure - Test 6: harmonic oscillator y[0](2*pi)=1.0 with err=5.6e-15, info=0 - All 8 self_test checks pass Generated-by: claude-sonnet-4-6 Co-Authored-By: bpsa2 <241537330+bpsa2@users.noreply.github.com>
- CAT 1 (Stats), CAT 2 (Integration/Derivatives), CAT 4 (Optimize) - CAT 5 (Matrices), CAT 6 (LeastSqr), CAT 7 (DiffEq) - CAT 8 (Polynomials), CAT 9 (Special), CAT 10 (Sort) - CAT 11 (Signal), CAT 12 (Arith), CAT 13 (Geometry) - CAT 14.1/14.3 (Simplex/Anneal), CAT 16.1 (Complex) - Remaining: CAT 14.2, CAT 15.2/15.3, CAT 16.2/16.3, Cross-cutting Generated-by: claude-sonnet-4-6 Co-Authored-By: bpsa2 <241537330+bpsa2@users.noreply.github.com>
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Project Structure
Task List
jpmroots.pas: Bisection, Newton, Secant, RegulaFalsi, Brent, Mueller, Steffensen, Aitken, Bairstow ✅ COMMITTEDjpmstats.pasextended: ChiSquareDist/InvChiSquare, FDist/InvFDist, BinomialProb/CDF, PoissonProb/CDF, Mean/Variance/StdDev/Skewness/Kurtosis/Median ✅ COMMITTED (c158916)jpmspecial.pas: GammaFunc, LnGamma, BetaFunc, LnBeta, IncompleteBeta, IncompleteGammaP/Q, ErfFunc, ErfcFunc ✅ COMMITTED (13ec193)jpmderivative.pas: Deriv1/2/3/4, DerivRichardson, DerivRomberg, Gradient, Jacobian ✅ COMMITTED (290ca5d)jpmintegration.pasextended: TrapezoidIntegral, SimpsonIntegral, AdaptiveSimpson, GaussLegendre ✅ COMMITTED (a49ca43)jpmchebyshev.pas: ChebFit, ChebEval, ChebInteg, ChebDeriv ✅ COMMITTED (9173acc)jpmcontinued.pas: FloatToCF, CFToFloat, CFConvergents, GenCFEval, SqrtCF, BestRational ✅ COMMITTED (71f08a6)jpmoptimize.pas: GoldenSection, BrentMin, BracketMin, NelderMead, SteepestDescent, PowellMin ✅ COMMITTED (a10f1d8, fa82776)jpmmatrices.pas: LU decompose/solve/inverse/det, Gauss-Seidel, Cholesky, Thomas tridiagonal, Jacobi eigenvalues ✅ COMMITTED (451132e)jpmlstsqr.pas: LeastSquares, PolyRegression, LinearRegression, MultipleRegression, ChiSquareFit, LevenbergMarquardt ✅ COMMITTED (6074b62, 948cb2d)jpmdiffeq.pas: RK4, RKF45, AdamsBashforth4, AdamsMoulton4, GearStiff (Rosenbrock), BulirschStoer ✅ COMMITTED (273f1f5, 1e698e0, b8c5274)jpmpolynomials.pas: PolyEval/Add/Sub/Mul/Div/Deriv/Integ/GCD, TPolyFrac, PolyFracPartial ✅ COMMITTED (654b419, 102eab5)jpmspecial.pasextended: LegendrePn/Qn, HermiteHn, LaguerreLn, AiryAi/Bi, EllipticK/E, Hypergeometric2F1 ✅ COMMITTED (e86c7c0)jpmbessel.pas: BesselJ0/J1/Y0/Y1/I0/I1/K0/K1, BesselJn, BesselJ0Zero/J1Zero ✅ COMMITTED (e3dd57d)jpmsort.pas: BubbleSort, InsertionSort, SelectionSort, QuickSort, MergeSort, HeapSort, ShellSort, BinarySearch, RankSort ✅ COMMITTED (7ef74cb)jpmsignal.pas: DFT, FFT (Cooley-Tukey), PowerSpectrum, MovingAverage, SavitzkyGolay5, FourierCoeff ✅ COMMITTED (099ea83)jpmarith.pas: GCD/LCM, ExtGCD, Factorial/BinomCoeff/Permutation, TFraction, IntToBase/BaseToInt, IsPrime, PrimeSieve, Factorize, SolveDiophantine ✅ COMMITTED (e4ad8eb)jpmgeometry.pas: SolveTriangle, SolveArcCircle, PointDistance2D/3D, TriangleArea, PolygonArea, CircleArea/Perimeter/Chord/ArcLen, EllipseArea/Perimeter, HyperbolaAsymptoteAngle ✅ COMMITTED (8fef706)jpmsimplex.pas: SimplexMaximize, SimplexMinimize ✅ COMMITTED (fcb64d3)jpmanneal.pas: SimulatedAnnealing (N-dim continuous, geometric cooling) ✅ COMMITTED (679e39d)jpmcomplex.pas: TComplex record + full arithmetic, transcendentals, trig ✅ COMMITTED (381fcbd)Coding Conventions (
fpc/coding_instructions.md){$mode objfpc}{$H+}in every unitFloat = Double— never userealarray of Float,SetLength)begin,end,var,for,if, ...)goto, nolabel, noReadLnin library unitsself_testprocedurejpm<topic>.pasjpmtypes.pasUnits Implemented
jpmtypes.pas— Shared TypesCore types used by all units:
Float = DoubleTFloatArray,TIntArray,TFloatMatrix,TMatrixTFunction1,TFunction2,TFunction3,TFunctionN,TFuncND,TLMFuncSelfTestCheck,SelfTestFailhelpersjpmroots.pas— Root Finding (CAT 3) ✅Commit:
5ea95da9 algorithms: Bisection, Newton-Raphson, Secant, Regula Falsi, Brent, Mueller, Steffensen, Aitken, Bairstow (complex polynomial roots)
jpmmatrices.pas— Linear Algebra (CAT 5) ✅Commit:
451132eFunctions: LU decomposition, LU solve, LU inverse, LU determinant, Gauss-Seidel iteration, Cholesky decomposition, Thomas algorithm (tridiagonal), Jacobi eigenvalue method
jpmspecial.pas— Special Functions (CAT 1.3 + CAT 9) ✅Commits:
13ec193,e86c7c0Functions:
GammaFunc,LnGamma(Lanczos),BetaFunc,LnBeta,IncompleteBeta(Lentz CF),IncompleteGammaP,IncompleteGammaQErfFunc,ErfcFunc(Chebyshev)LegendrePn,LegendreQn,HermiteHn,LaguerreLn(3-term recurrence)AiryAi,AiryBi(power series + asymptotic)EllipticK,EllipticE(AGM method)Hypergeometric2F1(Gauss series)jpmstats.pas— Statistics (CAT 1) ✅Commits: original +
c158916Functions:
NormalDist,InvNormalDist,ProbST/StudNT,ChiSquareDist,InvChiSquare,FDist,InvFDistBinomialProb,BinomialCDF,PoissonProb,PoissonCDF(log-space via LnGamma)StatMean,Variance,StdDev,Skewness,Kurtosis,Medianjpmderivative.pas— Numerical Derivatives (CAT 2.1) ✅Commit:
290ca5dFunctions:
Deriv1–Deriv4(finite differences),DerivRichardson(step-halving extrapolation),DerivRomberg(5×5 table with error estimate),Gradient(N-dim central diff),Jacobian(M×N central diff)jpmintegration.pas— Numerical Integration (CAT 2.2) ✅Commits: original (Romberg) +
a49ca43Functions:
RombergIntegral,TrapezoidIntegral,SimpsonIntegral,AdaptiveSimpson,GaussLegendre(n=2,3,4,5,6,8,10 — Abramowitz & Stegun nodes/weights)jpmchebyshev.pas— Chebyshev Approximation (CAT 2.3) ✅Commit:
9173accFunctions:
ChebFit(coefficients via cosine sampling),ChebEval(Clenshaw recurrence),ChebInteg(integral coefficients),ChebDeriv(derivative coefficients)jpmcontinued.pas— Continued Fractions (CAT 2.4) ✅Commit:
71f08a6Functions:
FloatToCF,CFToFloat,CFConvergents(p[k]/q[k] recurrence),GenCFEval(Lentz method),SqrtCF(periodic CF for √N),BestRational(best rational approx with bounded denominator)Example: π → [3;7;15;1;292;…], convergents 22/7 and 355/113
jpmoptimize.pas— Optimization (CAT 4) ✅Commits:
a10f1d8,fa82776Functions:
GoldenSection,BrentMin(parabolic interpolation + golden fallback),BracketMin(automatic downhill bracketing),NelderMead(N-dim downhill simplex: reflection/expansion/contraction/shrink),SteepestDescent(central-diff gradient + BrentMin line search),PowellMin(conjugate-direction method, identity matrix init, replace largest-decrease direction, Rosenbrock → (1,1) in 18 iter)jpmlstsqr.pas— Least Squares (CAT 6) ✅Commits:
6074b62,948cb2dFunctions:
LeastSquares(normal equations, Gaussian elim),PolyRegression(Vandermonde matrix),LinearRegression(Pearson r),MultipleRegression(augmented design matrix, R²),ChiSquareFit(weighted poly, 1/σ² weights),LevenbergMarquardt(damped Gauss-Newton, forward-diff Jacobian, adaptive λ, TLMFunc callback)jpmdiffeq.pas— Differential Equations (CAT 7) ✅Commits:
273f1f5,1e698e0,b8c5274Functions:
RK4Step,RK4Integrate(classical fixed-step RK4)RKF45(adaptive, Cash-Karp coefficients)AdamsBashforth4(4-step explicit, RK4 startup)AdamsMoulton4(predictor-corrector)GearStiff(Rosenbrock order-2 L-stable method for stiff ODEs; numerical Jacobian, Gaussian elim; Robertson chemistry test: conservation error ~2e-15)BulirschStoer(Gragg-Bulirsch-Stoer; modified midpoint + Neville polynomial extrapolation; sequence [2,4,6,8,12,16,24,32]; harmonic oscillator error ~5.6e-15)jpmpolynomials.pas— Polynomials (CAT 8) ✅Commits:
654b419,102eab5Functions:
PolyEval(Horner),PolyAdd,PolySub,PolyMul,PolyDiv,PolyDeriv,PolyInteg,PolyGCD(Euclidean, monic),PolyDegree,PolyNormalize,PolyPrintPolynomial fractions:
TPolyFracrecord,PolyFracMake,PolyFracEval,PolyFracAdd/Sub/Mul/Div,PolyFracReduce(PolyGCD-based),PolyFracPartial(partial fractions via residues N(r)/D'(r))Convention: index 0 = constant term
jpmbessel.pas— Bessel Functions (CAT 9.6) ✅Commit:
e3dd57dFunctions:
BesselJ0,BesselJ1,BesselY0,BesselY1(Abramowitz & Stegun poly, split at |x|=8),BesselI0,BesselI1,BesselK0,BesselK1(split at |x|=3.75),BesselJn(Miller backward recurrence),BesselJ0Zero,BesselJ1Zero(McMahon asymptotic + Newton refinement)jpmcomplex.pas— Complex Numbers (CAT 16.1) ✅Commit:
381fcbdType:
TComplexrecord (re, im fields)Functions:
CSet,CFromPolar,CModulus,CArgument,CConjugate,CAdd/Sub/Mul/Div/Neg/Scale,CExp,CLn,CSqrt,CPow,CPowC,CSin/CCos/CTan/CSinh/CCosh/CTanh,CToStr,CAbs2jpmsort.pas— Sorting & Searching (CAT 10) ✅Commit:
7ef74cbFunctions:
BubbleSort(early-exit),InsertionSort,SelectionSort,QuickSort(median-of-three),MergeSort(top-down),HeapSort(max-heap),ShellSort(Knuth gap 3x+1),BinarySearch(returns index or -1),IntSort,RankSort(stable indirect)jpmsignal.pas— Signal Processing (CAT 11) ✅Commit:
099ea83Functions:
DFT(direct O(n²)),FFT(Cooley-Tukey radix-2, bit-reversal, falls back to DFT if n not power-of-2),PowerSpectrum,MovingAverage(symmetric window, edge handling),SavitzkyGolay5(coefficients [-3,12,17,12,-3]/35),FourierCoeff(trapezoidal integration)jpmarith.pas— Number Theory & Arithmetic (CAT 12) ✅Commit:
e4ad8ebFunctions:
GCD,LCM(Euclidean),ExtGCD(Bezout),Factorial,BinomCoeff,Permutation,TFractionrecord withFracCreate/Add/Sub/Mul/Div/ToFloat/ToStr,IntToBase/BaseToInt(base 2–36),IsPrime(6k±1 trial division),PrimeSieve(Eratosthenes),Factorize,SolveDiophantine(via ExtGCD)jpmgeometry.pas— Geometry (CAT 13) ✅Commit:
8fef706Functions:
SolveTriangle(SSS/SAS/AAS),SolveArcCircle,PointDistance2D/3D,TriangleArea(Heron),PolygonArea(Shoelace),CircleArea/Perimeter/Chord/ArcLen,EllipseArea/Perimeter(Ramanujan),HyperbolaAsymptoteAnglejpmsimplex.pas— Linear Programming (CAT 14.1) ✅Commit:
fcb64d3Functions:
SimplexMaximize(tableau-based LP: maximize c·x s.t. A·x≤b, x≥0),SimplexMinimize(negates objective)Classic 3-var test: maximize 15x₁+17x₂+20x₃ → obj=76
jpmanneal.pas— Simulated Annealing (CAT 14.3) ✅Commit:
679e39dFunction:
SimulatedAnnealing(geometric cooling, random ±step perturbation, Metropolis acceptance, N-dim continuous,TAnnealResultrecord)Tests: Sphere function (fval<0.01), Rosenbrock (fval<0.1)
Self-Test Results (all pass)
Commit History (AI-generated units)
315837db8c52741e698e0948cb2dfa82776102eab5e86c7c071f08a6679e39dfcb64d38fef706e4ad8eb9173acca49ca437ef74cb290ca5d381fcbde3dd57d6074b62099ea83a10f1d8654b419273f1f5c15891613ec193451132e5ea95daRemaining / Optional Tasks
jpmsimplex.pasInvNormalDistcompletenessAsymErfc→jpmspecial.pasfpc/physics/src/fpc/morse/src/_sharedunitsREADME.mdfor eachfpc/<topic>/folderEJPMErrorexceptionAll algorithm implementations are based on Jean-Pierre Moreau's original Pascal sources.