provisdom.solvers

A comprehensive Clojure library for numerical optimization, root-finding, interpolation, and regression. Built on Hipparchus, OjAlgo, jcobyla, and Incanter.

Namespaces

Root-Finding

• root-solvers — Univariate root-finding with multiple algorithms: Brent-Dekker, modified Newton-Raphson, Muller, plus Hipparchus methods (bisection, Brent, Illinois, Pegasus, Ridders, secant, Regula-Falsi). Includes quadratic equation solver.

• integer-root-solvers — Bisection algorithm for strictly increasing discrete functions. Returns the minimum integer with function value ≥ 0.

• plateau-root-solvers — Root-finding for monotonic functions that return plateau values. Supports univariate and multivariate cases.

Optimization

• optimize-univariate — Brent optimizer for 1D minimization/maximization over bounded intervals.

• integer-optimize — Custom integer maximizer that exponentially focuses search around a guess. Handles functions with at most one sign change in derivative.

• linear-programming — Two-phase Simplex Method. Minimizes/maximizes linear objectives subject to linear constraints (equality, ≤, ≥).

• quadratic-programming — Minimizes (1/2)x^T P x + q^T x subject to equality and inequality constraints using OjAlgo.

• nonlinear-programming — Multiple solvers for nonlinear optimization:

  • Constrained: Cobyla for inequality constraints
  • Unbounded: Powell, Nelder-Mead, Multi-directional Simplex, Conjugate Gradient (Polak-Ribière, Fletcher-Reeves)
  • Bounded: BOBYQA, Cobyla, CMA-ES (evolutionary, handles non-smooth/non-convex objectives)

Constraint Satisfaction

• nonlinear-constraints-without-objective — Finds variable values that satisfy nonlinear constraints:
  • Nonlinear Least Squares (Levenberg-Marquardt, Gauss-Newton)
  • Nonlinear Ordered Constraints (prioritized constraint satisfaction)

Interpolation

• interpolation — Comprehensive interpolation functions:
  • 1D: cubic spline, Akima, LOESS, linear, polynomial, Neville, quadratic, cubic-clamped, Hermite
  • 2D: polynomial, bicubic, bicubic-Hermite, bilinear
  • 3D: tricubic
  • N-D: microsphere interpolation
  • Slope interpolation variants for derivatives

Regression

• logistic-regression — Iteratively Reweighted Least Squares (IRLS) with optional ridge regularization.

• multinomial-logistic-regression — IRLS for multi-class classification.

• generalized-regression-neural-network — GRNN for non-parametric regression with automatic spread parameter optimization.

Linear Systems

• iterative-linear-least-squares — Iterative solvers for symmetric linear systems (A × y = b): SYMMLQ and Conjugate Gradient methods.

Usage

(require '[provisdom.solvers.root-solvers :as root])
(require '[provisdom.solvers.nonlinear-programming :as nlp])
(require '[provisdom.solvers.interpolation :as interp])

;; Find root of f(x) = x³ - 3x
(root/root-solver
  {::root/univariate-f (fn [x] (- (* x x x) (* 3 x)))
   ::root/guess 2.0
   ::root/interval [-5.0 5.0]})

;; Minimize f(x,y) = x² + y² subject to bounds
(nlp/bounded-nonlinear-programming-without-evolutionary
  {::nlp/objective (fn [da] (let [[x y] da] (+ (* x x) (* y y))))
   ::nlp/vars-guess [1.0 1.0]
   ::nlp/var-intervals [[-10.0 10.0] [-10.0 10.0]]})

;; Cubic spline interpolation
(let [f (interp/interpolation-1D
          {::interp/x-vals [0.0 1.0 2.0 3.0]
           ::interp/f-vals [0.0 1.0 4.0 9.0]})]
  (f 1.5))

Dependencies

• Hipparchus — root-finding, optimization, interpolation, least squares (replaces Apache Commons Math)
• OjAlgo — linear and quadratic programming
• jcobyla — constrained nonlinear optimization (COBYLA algorithm)
• Incanter — 2D interpolation (bicubic, bilinear, polynomial)

License

Copyright © 2018-2026 Provisdom Corp.

Distributed under the GNU Lesser General Public License version 3.0.