[Python-ideas] PEP 485: A Function for testing approximate equality

[Paul Moore]

On 26 January 2015 at 19:42, Chris Barker <chris.barker at noaa.gov> wrote:
> OK -- here is a real-life application

[details snipped]

> The simplist iterative solution is something like this: recast the
> equation as:
>
> k_2 = omega**2 / (g * tanh(k_1 * h))
>
>  - guess a k_1
>  - compute k_2
>  - check if k_2 is close to k_1
>  - if not, set k_1 to k_2 repeat.

[more details snipped]

> In fact, you write a generic iteration routine:
>
> def iterate(func, x_initial, *args):
>     """
>     iterate to find a solution to the function passed in
>
>     func should be a function that takes x as a first argument,
>     and computes an approximation to x as a result.
>
>     x_initial is an initial guess for the unknown value
>     """
>     x_1 = x_initial
>     while True:
>         x_2 = func(x_1, *args)
>         if is_close_to(x_2, x_1):
>             break
>         x_1 = x_2
>     return x_2

The point I was trying to make earlier (which came across as "nobody
should be coding their own Newton iterations") is essentially this -
surely iterating a relation until the value you need converges is a
common operation, and libraries exist that do this for you? And those
libraries would already have their own "is the result close enough"
calculation (possibly tunable via arguments to the routine). Do people
actually write the low-level algorithms by hand, so that a building
block like is_close is worthwhile? The lack of people coming up with
use cases suggests to me that maybe it isn't.

FWIW, a quick google search came up with scipy.optimize.fixed_point,
which is, AFAICT, the equivalent of your iterate(). (You probably know
better than I do if that's the case).

Paul