Multidimensional Newton-Raphson method: Difference between revisions

=={{header|C sharp|C#}}==

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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=={{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

 

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

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=={{header|Phix}}==

[[Matrix_multiplication#Phix]]<br>

See std distro for a complete runnable version.

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=={{header|Raku}}==

(formerly Perl 6)

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

# Mastering Algorithms with Perl

 

say "Solution: ", @solution;

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Solution: [0.8936282344764825 0.8945270103905782 -0.04008928615915281]

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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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