Created by Davide Carpi (davide.carpi@gmail.com) in the scope of SMath project. Published by smath.
This is Open Source project. Sources shared under MIT Licence and available in public SVN repository.

Features of Nonlinear Solvers

Functions (135 items):

  • BDQRF("1:function", "2:condition", "3:condition") — Bisected Direct Quadratic Regula Falsi root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least 4 decimal places function precision.
  • BDQRF("1:function", "2:condition", "3:condition", "4:condition") — Bisected Direct Quadratic Regula Falsi root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision.
  • BDQRF("1:function", "2:condition", "3:condition", "4:condition", "5:condition") — Bisected Direct Quadratic Regula Falsi root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision or "5:condition" variable precision.
  • BDQRF("1:function", "2:condition", "3:condition", "4:condition", "5:condition", "6:number", "7:variable", "8:variable", "9:variable") — Bisected Direct Quadratic Regula Falsi root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision or "5:condition" variable precision. A "6:number" different from 0 set your custom max number of iterations, a "7:variable" different from 0 show you the number of iterations, a "8:variable" different from 0 show you a step-by-step summary and a "9:variable" different from 0 save a CSV summary into the current working directory.
  • Bisection("1:function", "2:condition", "3:condition") — Bisection root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least 4 decimal places function precision.
  • Bisection("1:function", "2:condition", "3:condition", "4:condition") — Bisection root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision.
  • Bisection("1:function", "2:condition", "3:condition", "4:condition", "5:condition") — Bisection root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision or "5:condition" variable precision.
  • Bisection("1:function", "2:condition", "3:condition", "4:condition", "5:condition", "6:variable", "7:variable", "8:variable") — Bisection root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision or "5:condition" variable precision. A "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory.
  • Brent("1:function", "2:condition", "3:condition") — Brent's root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least 4 decimal places function precision.
  • Brent("1:function", "2:condition", "3:condition", "4:condition") — Brent's root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision.
  • Brent("1:function", "2:condition", "3:condition", "4:condition", "5:condition") — Brent's root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision or "5:condition" variable precision.
  • Brent("1:function", "2:condition", "3:condition", "4:condition", "5:condition", "6:number", "7:variable", "8:variable", "9:variable") — Brent's root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision or "5:condition" variable precision. A "6:number" different from 0 set your custom max number of iterations, a "7:variable" different from 0 show you the number of iterations, a "8:variable" different from 0 show you a step-by-step summary and a "9:variable" different from 0 save a CSV summary into the current working directory.
  • Broyden("1:function", "2:condition") — Broyden's root-finding method of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places function(s) precision.
  • Broyden("1:function", "2:condition", "3:condition") — Broyden's root-finding method of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision.
  • Broyden("1:function", "2:condition", "3:condition", "4:condition") — Broyden's root-finding method of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision.
  • Broyden("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Broyden's root-finding method of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision. A "5:number" different from 0 set your custom max number of iterations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory.
  • FindRoot("1:function", "2:condition") — Find root(s) of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places function(s) precision.
  • FindRoot("1:function", "2:condition", "3:condition") — Find root(s) of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision.
  • FindRoot("1:function", "2:condition", "3:condition", "4:condition") — Find root(s) of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision.
  • GaussNewton.CD("1:function", "2:condition") — Gauss-Newton optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a constant step length.
  • GaussNewton.CD("1:function", "2:condition", "3:condition") — Gauss-Newton optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a constant step length.
  • GaussNewton.CD("1:function", "2:condition", "3:condition", "4:condition") — Gauss-Newton optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation. Alghorithm use a constant step length.
  • GaussNewton.CD("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Gauss-Newton optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation. A "5:number" different from 0 set your custom max number of iterations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a constant step length.
  • GaussNewton.GSS;CD("1:function", "2:condition") — Gauss-Newton optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GaussNewton.GSS;CD("1:function", "2:condition", "3:condition") — Gauss-Newton optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GaussNewton.GSS;CD("1:function", "2:condition", "3:condition", "4:condition") — Gauss-Newton optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GaussNewton.GSS;CD("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Gauss-Newton optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation. A "5:number" different from 0 set your custom max number of iterations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GaussNewton.GSS("1:function", "2:condition") — Gauss-Newton optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GaussNewton.GSS("1:function", "2:condition", "3:condition") — Gauss-Newton optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GaussNewton.GSS("1:function", "2:condition", "3:condition", "4:number", "5:variable", "6:variable", "7:variable") — Gauss-Newton optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:number" different from 0 set your custom max number of iterations, a "5:variable" different from 0 show you the number of iterations, a "6:variable" different from 0 show you a step-by-step summary and a "7:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GaussNewton("1:function", "2:condition") — Gauss-Newton optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a constant step length.
  • GaussNewton("1:function", "2:condition", "3:condition") — Gauss-Newton optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a constant step length.
  • GaussNewton("1:function", "2:condition", "3:condition", "4:number", "5:variable", "6:variable", "7:variable") — Gauss-Newton optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:number" different from 0 set your custom max number of iterations, a "5:variable" different from 0 show you the number of iterations, a "6:variable" different from 0 show you a step-by-step summary and a "7:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a constant step length.
  • GoldenSectionSearch.max("1:function", "2:condition", "3:condition") — Golden Section Search extremum finding of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least 4 decimal places variable precision.
  • GoldenSectionSearch.max("1:function", "2:condition", "3:condition", "4:condition") — Golden Section Search extremum finding of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" variable precision.
  • GoldenSectionSearch.max("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Golden Section Search extremum finding of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" variable precision. A "5:number" different from 0 set your custom max number of iterations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory.
  • GoldenSectionSearch.min("1:function", "2:condition", "3:condition") — Golden Section Search extremum finding of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least 4 decimal places variable precision.
  • GoldenSectionSearch.min("1:function", "2:condition", "3:condition", "4:condition") — Golden Section Search extremum finding of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" variable precision.
  • GoldenSectionSearch.min("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Golden Section Search extremum finding of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" variable precision. A "5:number" different from 0 set your custom max number of iterations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory.
  • Gradient.CD("1:function", "2:variable") — Numerical first order central differences of "1:function" evaluated at "2:variable"; returns Gradients or 1st order differentiations.
  • Gradient.CD("1:function", "2:variable", "3:variable") — Numerical first order central differences of "1:function" evaluated at "2:variable" using a "3:variable" perturbation; returns Gradients or 1st order differentiations.
  • Gradient("1:function", "2:variable") — First order derivatives of "1:function" evaluated at "2:variable"; returns Gradients or 1st order differentiations.
  • GradientAscent.GSS("1:function", "2:condition") — Gradient ascent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GradientAscent.GSS("1:function", "2:condition", "3:condition") — Gradient ascent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GradientAscent.GSS("1:function", "2:condition", "3:condition", "4:number", "5:variable", "6:variable", "7:variable") — Gradient ascent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:number" different from 0 set your custom max number of iterations, a "5:variable" different from 0 show you the number of iterations, a "6:variable" different from 0 show you a step-by-step summary and a "7:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GradientAscent("1:function", "2:condition") — Gradient ascent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a constant step length.
  • GradientAscent("1:function", "2:condition", "3:condition") — Gradient ascent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a constant step length.
  • GradientAscent("1:function", "2:condition", "3:condition", "4:number", "5:variable", "6:variable", "7:variable") — Gradient ascent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:number" different from 0 set your custom max number of iterations, a "5:variable" different from 0 show you the number of iterations, a "6:variable" different from 0 show you a step-by-step summary and a "7:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a constant step length.
  • GradientDescent.GSS("1:function", "2:condition") — Gradient descent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GradientDescent.GSS("1:function", "2:condition", "3:condition") — Gradient descent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GradientDescent.GSS("1:function", "2:condition", "3:condition", "4:number", "5:variable", "6:variable", "7:variable") — Gradient descent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:number" different from 0 set your custom max number of iterations, a "5:variable" different from 0 show you the number of iterations, a "6:variable" different from 0 show you a step-by-step summary and a "7:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • GradientDescent("1:function", "2:condition") — Gradient descent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a constant step length.
  • GradientDescent("1:function", "2:condition", "3:condition") — Gradient descent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a constant step length.
  • GradientDescent("1:function", "2:condition", "3:condition", "4:number", "5:variable", "6:variable", "7:variable") — Gradient descent optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:number" different from 0 set your custom max number of iterations, a "5:variable" different from 0 show you the number of iterations, a "6:variable" different from 0 show you a step-by-step summary and a "7:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a constant step length.
  • Hessian.CD("1:function", "2:variable") — Numerical second order central differences of "1:function" evaluated at "2:variable"; returns Hessians or 2nd order differentiations.
  • Hessian.CD("1:function", "2:variable", "3:variable") — Numerical second order central differences of "1:function" evaluated at "2:variable" using a "3:variable" perturbation; returns Hessians or 2nd order differentiations.
  • Hessian("1:function", "2:variable") — Second order derivatives of "1:function" evaluated at "2:variable"; returns Hessians or 2nd order differentiations.
  • HRE.B("1:function", "2:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Broyden's algorithm; calculation have at least 4 decimal places function(s) precision.
  • HRE.B("1:function", "2:condition", "3:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Broyden's algorithm; calculation have at least "3:condition" function(s) precision.
  • HRE.B("1:function", "2:condition", "3:condition", "4:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Broyden's algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision.
  • HRE.B("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Broyden's algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision. A "5:number" different from 0 set your custom number of homotopy transformations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory.
  • HRE.NR;CD("1:function", "2:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the central differences Newton's algorithm; calculation have at least 4 decimal places function(s) precision.
  • HRE.NR;CD("1:function", "2:condition", "3:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the central differences Newton's algorithm; calculation have at least "3:condition" function(s) precision.
  • HRE.NR;CD("1:function", "2:condition", "3:condition", "4:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the central differences Newton's algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision.
  • HRE.NR;CD("1:function", "2:condition", "3:condition", "4:condition", "5:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the central differences Newton's algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision. A "5:condition" different from 0 set your custom perturbation.
  • HRE.NR;CD("1:function", "2:condition", "3:condition", "4:condition", "5:condition", "6:number", "7:variable", "8:variable", "9:variable") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the central differences Newton's algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision. A "5:condition" different from 0 set your custom perturbation. A "6:number" different from 0 set your custom number of homotopy transformations, a "7:variable" different from 0 show you the number of iterations, a "8:variable" different from 0 show you a step-by-step summary and a "9:variable" different from 0 save a CSV summary into the current working directory.
  • HRE.NR("1:function", "2:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Newton's algorithm; calculation have at least 4 decimal places function(s) precision.
  • HRE.NR("1:function", "2:condition", "3:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Newton's algorithm; calculation have at least "3:condition" function(s) precision.
  • HRE.NR("1:function", "2:condition", "3:condition", "4:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Newton's algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision.
  • HRE.NR("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Newton's algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision. A "5:number" different from 0 set your custom number of homotopy transformations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory.
  • HRE.RK;CD("1:function", "2:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Runge-Kutta 4th order central differences algorithm; calculation have at least 4 decimal places function(s) precision.
  • HRE.RK;CD("1:function", "2:condition", "3:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Runge-Kutta 4th order central differences algorithm; calculation have at least "3:condition" function(s) precision.
  • HRE.RK;CD("1:function", "2:condition", "3:condition", "4:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Runge-Kutta 4th order central differences algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision.
  • HRE.RK;CD("1:function", "2:condition", "3:condition", "4:condition", "5:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Runge-Kutta 4th order central differences algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision. A "5:condition" different from 0 set your custom perturbation.
  • HRE.RK;CD("1:function", "2:condition", "3:condition", "4:condition", "5:condition", "6:number", "7:variable", "8:variable", "9:variable") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Runge-Kutta 4th order central differences algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision. A "5:condition" different from 0 set your custom perturbation. A "6:number" different from 0 set your custom number of homotopy transformations, a "7:variable" different from 0 show you the number of iterations, a "8:variable" different from 0 show you a step-by-step summary and a "9:variable" different from 0 save a CSV summary into the current working directory.
  • HRE.RK("1:function", "2:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Runge-Kutta 4th order algorithm; calculation have at least 4 decimal places function(s) precision.
  • HRE.RK("1:function", "2:condition", "3:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Runge-Kutta 4th order algorithm; calculation have at least "3:condition" function(s) precision.
  • HRE.RK("1:function", "2:condition", "3:condition", "4:condition") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Runge-Kutta 4th order algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision.
  • HRE.RK("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Homotopy root-estimation method of function(s) "1:function", giving an initial guess "2:condition" for each variable, using the Runge-Kutta 4th order algorithm; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision. A "5:number" different from 0 set your custom number of homotopy transformations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory.
  • Jacobian.CD("1:function", "2:variable") — Numerical first order central differences of "1:function" evaluated at "2:variable"; returns Jacobians or 1st order differentiations.
  • Jacobian.CD("1:function", "2:variable", "3:variable") — Numerical first order central differences of "1:function" evaluated at "2:variable" using a "3:variable" perturbation; returns Jacobians or 1st order differentiations.
  • Jacobian("1:function", "2:variable") — First order derivatives of "1:function" evaluated at "2:variable"; returns Jacobians or 1st order differentiations.
  • LevenbergMarquardt.CD("1:function", "2:condition") — Levenberg-Marquardt optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a constant step length.
  • LevenbergMarquardt.CD("1:function", "2:condition", "3:condition") — Levenberg-Marquardt optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a constant step length.
  • LevenbergMarquardt.CD("1:function", "2:condition", "3:condition", "4:condition") — Levenberg-Marquardt optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation. Alghorithm use a constant step length.
  • LevenbergMarquardt.CD("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Levenberg-Marquardt optimization algorithm of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation. A "5:number" different from 0 set your custom max number of iterations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a constant step length.
  • LevenbergMarquardt("1:function", "2:condition") — Levenberg-Marquardt optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a constant step length.
  • LevenbergMarquardt("1:function", "2:condition", "3:condition") — Levenberg-Marquardt optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a constant step length.
  • LevenbergMarquardt("1:function", "2:condition", "3:condition", "4:number", "5:variable", "6:variable", "7:variable") — Levenberg-Marquardt optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:number" different from 0 set your custom max number of iterations, a "5:variable" different from 0 show you the number of iterations, a "6:variable" different from 0 show you a step-by-step summary and a "7:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a constant step length.
  • mapUnknowns("1:function", "2:condition") — Symbolical variables' mapping; returns a vector of unassigned variables/elements contained in "1:function", according with the "2:condition" pattern.
  • mapUnknowns("1:function", "2:condition", "3:name") — Symbolical variables' mapping; returns a vector of unassigned elements contained in "1:function", according with the "2:condition" pattern, using "3:name" as unknown name.
  • NCGM.CD("1:function", "2:condition") — Nonlinear Conjugate Gradient Method optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NCGM.CD("1:function", "2:condition", "3:condition") — Nonlinear Conjugate Gradient Method optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NCGM.CD("1:function", "2:condition", "3:condition", "4:condition") — Nonlinear Conjugate Gradient Method optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NCGM.CD("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Nonlinear Conjugate Gradient Method optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation. A "5:number" different from 0 set your custom max number of iterations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NCGM("1:function", "2:condition") — Nonlinear Conjugate Gradient Method optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NCGM("1:function", "2:condition", "3:condition") — Nonlinear Conjugate Gradient Method optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NCGM("1:function", "2:condition", "3:condition", "4:number", "5:variable", "6:variable", "7:variable") — Nonlinear Conjugate Gradient Method optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:number" different from 0 set your custom max number of iterations, a "5:variable" different from 0 show you the number of iterations, a "6:variable" different from 0 show you a step-by-step summary and a "7:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NelderMead("1:function", "2:condition", "3:condition", "4:condition", "5:condition", "6:condition", "7:number", "8:variable", "9:variable", "10:variable") — Nelder-Mead optimization algorithm of function(s) "1:function", giving an initial simplex or an initial guess "2:condition"; calculation have "3:condition" standard deviation precision for function(s) on the simplex. A "4:number" different from 0 set your custom reflection coefficient, a "5:number" different from 0 set your custom contraction coefficient and a "6:number" different from 0 set your custom expansion coefficient. A "7:number" different from 0 set your custom max number of iterations, a "8:variable" different from 0 show you the number of iterations, a "9:variable" different from 0 show you a step-by-step summary and a "10:variable" different from 0 save a CSV summary into the current working directory.
  • NelderMead("1:function", "2:condition") — Nelder-Mead optimization algorithm of function(s) "1:function", giving an initial simplex or an initial guess "2:condition"; calculation have at least 4 decimal places standard deviation precision for function(s) on the simplex.
  • NelderMead("1:function", "2:condition", "3:condition") — Nelder-Mead optimization algorithm of function(s) "1:function", giving an initial simplex or an initial guess "2:condition"; calculation have "3:condition" standard deviation precision for function(s) on the simplex.
  • NelderMead("1:function", "2:condition", "3:condition", "4:condition", "5:condition", "6:condition") — Nelder-Mead optimization algorithm of function(s) "1:function", giving an initial simplex or an initial guess "2:condition"; calculation have "3:condition" standard deviation precision for function(s) on the simplex. A "4:number" different from 0 set your custom reflection coefficient, a "5:number" different from 0 set your custom contraction coefficient and a "6:number" different from 0 set your custom expansion coefficient.
  • NewtonMethod.CD("1:function", "2:condition") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision.
  • NewtonMethod.CD("1:function", "2:condition", "3:condition") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision.
  • NewtonMethod.CD("1:function", "2:condition", "3:condition", "4:condition") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation.
  • NewtonMethod.CD("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation. A "5:number" different from 0 set your custom max number of iterations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory.
  • NewtonMethod.GSS;CD("1:function", "2:condition") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NewtonMethod.GSS;CD("1:function", "2:condition", "3:condition") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NewtonMethod.GSS;CD("1:function", "2:condition", "3:condition", "4:condition") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NewtonMethod.GSS;CD("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:condition" different from 0 set your custom perturbation. A "5:number" different from 0 set your custom max number of iterations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NewtonMethod.GSS("1:function", "2:condition") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NewtonMethod.GSS("1:function", "2:condition", "3:condition") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NewtonMethod.GSS("1:function", "2:condition", "3:condition", "4:number", "5:variable", "6:variable", "7:variable") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:number" different from 0 set your custom max number of iterations, a "5:variable" different from 0 show you the number of iterations, a "6:variable" different from 0 show you a step-by-step summary and a "7:variable" different from 0 save a CSV summary into the current working directory. Alghorithm use a step length based on a Golden Section Search line search strategy.
  • NewtonMethod("1:function", "2:condition") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places variable(s) precision.
  • NewtonMethod("1:function", "2:condition", "3:condition") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision.
  • NewtonMethod("1:function", "2:condition", "3:condition", "4:number", "5:variable", "6:variable", "7:variable") — Newton's optimization algorithm of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have "3:condition" variable(s) precision. A "4:number" different from 0 set your custom max number of iterations, a "5:variable" different from 0 show you the number of iterations, a "6:variable" different from 0 show you a step-by-step summary and a "7:variable" different from 0 save a CSV summary into the current working directory.
  • NewtonRaphson.CD("1:function", "2:condition") — Newton's root-finding method of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places function(s) precision.
  • NewtonRaphson.CD("1:function", "2:condition", "3:condition") — Newton's root-finding method of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision.
  • NewtonRaphson.CD("1:function", "2:condition", "3:condition", "4:condition") — Newton's root-finding method of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision.
  • NewtonRaphson.CD("1:function", "2:condition", "3:condition", "4:condition", "5:condition") — Newton's root-finding method of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision. A "5:condition" different from 0 set your custom perturbation.
  • NewtonRaphson.CD("1:function", "2:condition", "3:condition", "4:condition", "5:condition", "6:number", "7:variable", "8:variable", "9:variable") — Newton's root-finding method of function(s) "1:function" using central differences, giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision. A "5:condition" different from 0 set your custom perturbation. A "6:number" different from 0 set your custom max number of iterations, a "7:variable" different from 0 show you the number of iterations, a "8:variable" different from 0 show you a step-by-step summary and a "9:variable" different from 0 save a CSV summary into the current working directory.
  • NewtonRaphson("1:function", "2:condition") — Newton's root-finding method of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least 4 decimal places function(s) precision.
  • NewtonRaphson("1:function", "2:condition", "3:condition") — Newton's root-finding method of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision.
  • NewtonRaphson("1:function", "2:condition", "3:condition", "4:condition") — Newton's root-finding method of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision.
  • NewtonRaphson("1:function", "2:condition", "3:condition", "4:condition", "5:number", "6:variable", "7:variable", "8:variable") — Newton's root-finding method of function(s) "1:function", giving an initial guess "2:condition" for each variable; calculation have at least "3:condition" function(s) precision or "4:condition" variable(s) precision. A "5:number" different from 0 set your custom max number of iterations, a "6:variable" different from 0 show you the number of iterations, a "7:variable" different from 0 show you a step-by-step summary and a "8:variable" different from 0 save a CSV summary into the current working directory.
  • Ridder("1:function", "2:condition", "3:condition") — Brent's root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least 4 decimal places function precision.
  • Ridder("1:function", "2:condition", "3:condition", "4:condition") — Brent's root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision.
  • Ridder("1:function", "2:condition", "3:condition", "4:condition", "5:condition") — Brent's root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision or "5:condition" variable precision.
  • Ridder("1:function", "2:condition", "3:condition", "4:condition", "5:condition", "6:number", "7:variable", "8:variable", "9:variable") — Brent's root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision or "5:condition" variable precision. A "6:number" different from 0 set your custom max number of iterations, a "7:variable" different from 0 show you the number of iterations, a "8:variable" different from 0 show you a step-by-step summary and a "9:variable" different from 0 save a CSV summary into the current working directory.
  • Secant("1:function", "2:condition", "3:condition") — Secant root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least 4 decimal places function precision.
  • Secant("1:function", "2:condition", "3:condition", "4:condition") — Secant root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision.
  • Secant("1:function", "2:condition", "3:condition", "4:condition", "5:condition") — Secant root-finding method of function "1:function", giving a couple of delimiters "2:condition" and "3:condition"; calculation have at least "4:condition" function precision or "5:condition" variable precision.
  • Secant("1:function", "2:condition", "3:condition", "4:condition", "5:condition", "6:number", "7:variable", "8:variable", "9:variable") — Secant root-finding method of function "1:function", giving a couple of initial guess "2:condition" and "3:condition"; calculation have at least "4:condition" function precision or "5:condition" variable precision. A "6:number" different from 0 set your custom max number of iterations, a "7:variable" different from 0 show you the number of iterations, a "8:variable" different from 0 show you a step-by-step summary and a "9:variable" different from 0 save a CSV summary into the current working directory.
  • Taylor("1:function", "2:variable", "3:number") — Taylor series expansion of "1:function" about the "2:variable" point up to the "3:number"th order.
  • Unknowns("variable") — Variables' detection; returns a vector of unassigned variables contained in "1:variable".