Multidimensional Newton-Raphson method: Difference between revisions
Multidimensional Newton-Raphson method (view source)
Revision as of 20:01, 14 January 2021
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<pre>
Solution: [0.8936282344764825 0.8945270103905782 -0.04008928615915281]
</pre>
=={{header|Wren}}==
{{trans|Kotlin}}
{{libheader|Wren-matrix}}
{{libheader|Wren-fmt}}
<lang ecmascript>import "/matrix" for Matrix
import "/fmt" for Fmt
var solve = Fn.new { |funcs, jacobian, guesses|
var size = funcs.count
var gu1 = []
var gu2 = guesses.toList
var jac = Matrix.new(size, size)
var tol = 1e-8
var maxIter = 12
var iter = 0
while (true) {
gu1 = gu2
var g = Matrix.new([gu1]).transpose
var v = List.filled(size, 0)
for (i in 0...size) v[i] = funcs[i].call(gu1)
var f = Matrix.new([v]).transpose
for (i in 0...size) {
for (j in 0...size) jac[i, j] = jacobian[i][j].call(gu1)
}
var g1 = g - jac.inverse * f
gu2 = List.filled(size, 0)
for (i in 0...size) gu2[i] = g1[i][0]
iter = iter + 1
if (iter == maxIter) break
if ((0...size).all { |i| (gu2[i] - gu1[i]).abs <= tol }) break
}
return gu2
}
/* solve the two non-linear equations:
y = -x^2 + x + 0.5
y + 5xy = x^2
given initial guesses of x = y = 1.2
Example taken from:
http://www.fixoncloud.com/Home/LoginValidate/OneProblemComplete_Detailed.php?problemid=286
Expected results: x = 1.23332, y = 0.2122
*/
var f1 = Fn.new { |x| -x[0] * x[0] + x[0] + 0.5 - x[1] }
var f2 = Fn.new { |x| x[1] + 5 * x[0] * x[1] - x[0] * x[0] }
var funcs = [f1, f2]
var jacobian = [
[ Fn.new { |x| - 2 * x[0] + 1 }, Fn.new { |x| -1 } ],
[ Fn.new { |x| 5 * x[1] - 2 * x[0] }, Fn.new { |x| 1 + 5 * x[0] } ]
]
var guesses = [1.2, 1.2]
var sols = solve.call(funcs, jacobian, guesses)
Fmt.print("Approximate solutions are x = $.7f, y = $.7f", sols[0], sols[1])
/* solve the three non-linear equations:
9x^2 + 36y^2 + 4z^2 - 36 = 0
x^2 - 2y^2 - 20z = 0
x^2 - y^2 + z^2 = 0
given initial guesses of x = y = 1.0 and z = 0.0
Example taken from:
http://mathfaculty.fullerton.edu/mathews/n2003/FixPointNewtonMod.html (exercise 5)
Expected results: x = 0.893628, y = 0.894527, z = -0.0400893
*/
System.print()
var f3 = Fn.new { |x| 9 * x[0] * x[0] + 36 * x[1] *x[1] + 4 * x[2] * x[2] - 36 }
var f4 = Fn.new { |x| x[0] * x[0] - 2 * x[1] * x[1] - 20 * x[2] }
var f5 = Fn.new { |x| x[0] * x[0] - x[1] * x[1] + x[2] * x[2] }
funcs = [f3, f4, f5]
jacobian = [
[ Fn.new { |x| 18 * x[0] }, Fn.new { |x| 72 * x[1] }, Fn.new { |x| 8 * x[2] } ],
[ Fn.new { |x| 2 * x[0] }, Fn.new { |x| -4 * x[1] }, Fn.new { |x| -20 } ],
[ Fn.new { |x| 2 * x[0] }, Fn.new { |x| -2 * x[1] }, Fn.new { |x| 2 * x[2] } ]
]
guesses = [1, 1, 0]
sols = solve.call(funcs, jacobian, guesses)
Fmt.print("Approximate solutions are x = $.7f, y = $.7f, z = $.7f", sols[0], sols[1], sols[2]</lang>
{{out}}
<pre>
Approximate solutions are x = 1.2333178, y = 0.2122450
Approximate solutions are x = 0.8936282, y = 0.8945270, z = -0.0400893
</pre>
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