Numerical Analysis about math-php HOT 7 CLOSED

How about: Math\NumericalAnalysis ?

from math-php.

Sounds good to me.

from math-php.

This file in also in the Pull Request

from math-php.

Can you provide a simple example of how to use the NewtonsMethod function? Some simple input with expected output. It will help me better understand the function to be able to write unit tests for it and possibly refactor with improvements.
Thanks.

from math-php.

Newton's Method is a numerical method to solve the inverse of a function. Say, for example, you want to find the roots of the polynomial, f(x) = x^4+8x³ -13x² -92x+96. You can use newton's method. You find the x that will make f(x) = 0;

In our method:
$function is a callback to a f(x). In this case it will be: function($x){return $x ** 4 + 8 * $x ** 3 - 13 * $x ** 2 - 92 * $x + 96;}

$args is an array of arguments that have to be passed to the function. In or case it is ['x'], because $function only needs one parameter, the one we are solving for. If the function were f(x,y) = x³y + y²x and we wanted f(x|y=2) = 0, we would provide $args = ['x', 2].

$target is the value of f(x) we a trying to solve for. in our case we want to find the x that gives us f(x) = 0.

$guess is the starting point. For our polynomial above this is very important because there are 4 solutions. the starting point will determine which solution we will receive.

$tol is the tolerance...How close to the actual solution we would like.

Putting it all together, here is a console php statement to run the method. This polynomial has 4 roots, 3,1,-8 and -4.

php -r "include 'src/NumericalAnalysis/NewtonsMethod.php';use Math\NumericalAnalysisewtonsMethod; print NewtonsMethod::solve(function(\$x){return \$x ** 4 + 8 * \$x ** 3 - 13 * \$x ** 2 - 92 * \$x + 96;}, ['x'], 0, -4.1, .00001);"

Running this gives -3.9999999999999

An alternative implementation might be to make $args a list of parameter initial values, and replace '$guess' with '$position', where $position indicates which element in the $args array needs to be changed, keeping the rest constant. I think this is a better idea.

from math-php.

If I move to the alternate implementation would you prefer zero index or one index on the position?

from math-php.

Thanks for the great explanation. I've added unit tests based on it.

If you decide to refactor, please update the unit tests as well. For index positions, I've been using zero indexing for everything.

from math-php.