Multidimensional Newton-Raphson method: Difference between revisions

;Task:

Create a program that finds and outputs the root of a system of nonlinear equations

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For matrix inversion and matrix and vector definitions - see C# source from [[Gaussian elimination]]

using System;

 

}

}

using System;

 

}

}

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2.54258545959024

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We follow the Kotlin example of coding our own matrix methods rather than using a third party library.

 

import (

sol = solve(fs, jacob, guesses)

fmt.Printf("Approximate solutions are x = %.7f, y = %.7f, z = %.7f\n", sol[0], sol[1], sol[2])

 

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Approximate solutions are x = 0.8936282, y = 0.8945270, z = -0.0400893

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=={{header|Julia}}==

NLsolve is a Julia package for nonlinear systems of equations, with the Newton-Raphson method one of the choices for solvers.

# (x, y) -> ((x+3)*(y^3-7)+18, sin(y*exp(x)-1))

using NLsolve

 

println(nlsolve(f!, j!, [ 0.1; 1.2], method = :newton))

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Results of Nonlinear Solver Algorithm

* Jacobian Calls (df/dx): 4

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=={{header|Kotlin}}==

 

As neither the JDK nor the Kotlin Standard Library have matrix functions built in, most of the functions used have been taken from other tasks.

 

import kotlin.math.abs

val (xx2, yy2, zz2) = solve(funcs2, jacobian2, guesses2)

System.out.printf("Approximate solutions are x = %.7f, y = %.7f, z = %.7f\n", xx2, yy2, zz2)

 

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# https://github.com/pierre-vigier/Perl6-Math-Matrix

# Mastering Algorithms with Perl

 

say "Solution: ", @solution;

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gu1 = gu2

return gu2

 

 

 

 

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=={{header|zkl}}==

This doesn't use Newton-Raphson (with derivatives) but a hybrid algorithm.

 

// two functions of two variables: f(x,y)=0

v.format(11,8).println(); // answer overwrites initial guess

 

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A condensed solver (for a different set of functions):

GSL.multiroot_fsolver(T( fcn(x,y){ 1.0 - x }, fcn(x,y){ 10.0*(y - x*x) }),v)

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Another example:

fxyzs:=T(

fcn(x,y,z){ x*x*9 + y*y*36 + z*z*4 - 36 }, // 9x^2 + 36y^2 + 4z^2 - 36 = 0

(v=GSL.multiroot_fsolver(fxyzs,v)).format(12,8).println();

 

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