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## Re: I wrote fluid advection code: How to make this more elegant?

 From: Taylan Ulrich Bayırlı/Kammer Subject: Re: I wrote fluid advection code: How to make this more elegant? Date: Sun, 24 Jan 2016 18:46:43 +0100 User-agent: Gnus/5.13 (Gnus v5.13) Emacs/24.5 (gnu/linux)

```Arne Babenhauserheide <address@hidden> writes:

> Taylan Ulrich Bayırlı/Kammer writes:
>>> The original version was in Python:
>>>
>>>     psi[i] - c1*(psi[i+1] - psi[i-1]) + c2*(psi[i+1] - 2.0*psi[i] +
>>> psi[i-1])
>>>
>>> My port to Scheme looks like this:
>>>
>>>     (let ((newvalue (+ (- (psir i)
>>>                           (* c1 (- (psir (+ i 1)) (psir (- i 1)))))
>>>                        (* c2 (+ (- (psir (+ i 1)) (* 2 (psir i)))
>>>                                 (psir (- i 1)))))))
>>>       (array-set! psinew newvalue i))
>>
>> Guile supports SRFI-105, so that could be:
>>
>>     {{psi[i] - {c1 * {psi[{i + 1}] - psi[{i - 1}]}}} + {c2 * {{psi[{i + 1}]
>> - {2 * psi[i]}} + psi[{i - 1}]}}}
>
> That’s already pretty close — I wonder why I didn’t think of the psi[i]
> form.
>
> I think a + around the equation would actually help here:
>
>     (+ psi[i]
>        (* -1 c1 {psi[{i + 1}] - psi[{i - 1}]})
>        (* c2 {{psi[{i + 1}] - {2 * psi[i]}} + psi[{i - 1}]}))
>
> Though neoteric expressions combined with curly infix make this even
> easier: p{i + 1} → (p (+ i 1))

Good call, I had forgotten that's included in SRFI 105.  (Thought it was
just for x[y].)

> (though this did not work for me in the REPL right now — did I miss
> something?)

Any SRFI 105 syntax must appear within {}, so that would have to be
e.g. {p{i + 1}}, although if it appears within a larger {} block then it
won't have that annoyance.

> So the function psir could be used to have elegant access to elements:
>
>     (+ psi[i]
>        (* -1 c1 {psi[{i + 1}] - psi[{i - 1}]})
>        (* c2 {{psi[{i + 1}] - {2 * psi[i]}} + psi[{i - 1}]}))
>
>>     {psi[i] - c1 * {psi[i + 1] - psi[i - 1]} + c2 * {psi[i + 1] - 2 * psi[i]
>> + psi[i - 1]}}
>
> That looks roughly as readable as the Python version. With the + around
> I think it becomes better:
>
>     (+ psi[i]
>        (* -1 c1 {psi[i + 1] - psi[i - 1]})
>        (* c2 {{psi[i + 1] - {2 * psi[i]}} + psi[i - 1]}))

I agree mixing in some prefix notation actually makes things more