Newton's Method

programming
1

@kirupa, I liked your email about calculating π so I came to share the “math heavy computation” I’m forcing my computer do for me. It’s Newton’s method, implemented in R, which is used to find the roots of a function:

nmet = function(f, g, t = 1e-10) {
  while(abs(f(g)) > t) {
    g = g - f(g) / nder(f, g)
  }
  return(g)
}

It also uses a numerical approximation of the derivative:

nder = function(f, x, h = 1e-3) {
  return((f(x + h) - f(x - h)) / 2 / h)
}

And we can see how it approximates the root of x2-5 over three iterations from a starting guess of 4 (red) to a final value of ~√5 (blue):

image
image1020×592 16.1 KB

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2

That is really nice! I also like how nice and compact R is :slight_smile:

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3

R is all I use now, but everyday I find something new and confusing about it. If I could still use ActionScript, I would!

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4

Did you ever explore Python? That’s where a lot of people seem to be jumping to these days.

5

No, but I have thought about looking into it. I believe there are already a lot of packages for Python relating to statistics, and even biology more generally.

There are also biology-related programs like PyMOL which I use frequently and can be scripted with Python.

So, I really probably should learn it. Do you use Python? What’s the best way to get into it?

Given how much I miss ActionScript, why don’t I just get into JavaScript? I never should’ve thrown away that disc for Macromedia Studio 8; maybe it would still work!

6

I’m strongly considering creating programming tutorials for Python this year. It’s a very forgiving language with a clean syntax. It is also one of the most popular languages - just a few hairs shy of JavaScript’s massive popularity!

For the types of activities you are describing, Python may be a better fit than JavaScript.

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7

I was surprised to see R was also growing quite rapidly, and even more surprised that Java is still so popular.

If you do make Python tutorials, I’ll be your first reader!

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8

Haha! Please don’t wait until I do that. My ability to generate new content keeps getting slower and slower! :turtle:

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