Random with difference between outputs as constraint

[sydy]

I struggle to do it and tried different ways but couldn't find a solution.

TASK
Random function with constraints executed N-times.

The function should reply to the following conditions:
1. No elements < $1
2. No elements > $2
3. No differences between randomly generated elements < $3

Condition 1. and 2. are easy.
Its the 3. condition I can't handle.

Eg. of a (sorted) list that would reply to all conditions:
$1 = 0
$2 = 30
$3 = 5

N = 4
1. 5
2. 10
3. 16
4. 25
Any help would be appreciated.

[sydy]

Solved it with Javascript for now. I'm not really happy about javascript. It is not fast enough.
Anyway, if somebody can make some use of it. Here's the code.
I'm still interested in any cpu cheap solution with bach...

Greatings,
m


/** generates random integer between min and max (inclusive) **/
function generateRandomBetween(min, max){
return Math.random() * (max - min + 1) + min;
}


//test logically impossible
/**
var userDefinedMin = 5
var userDefinedMax = 17
var distance = 4
**/

// test logically possible
var n = 6; //number of generated points
var userDefinedMin = 20;
var userDefinedMax = 150;
var distance = 15;
var isDataSerieValid = true;
var envelopData = new Array(n);

//init Envelop Data
for (var i = 0; i < envelopData.length; i++) envelopData = userDefinedMin;
envelopData[n-1] = userDefinedMax;


// create envelop Data
for (i = 1; i <= envelopData.length-2; i++) {
logicalMinimum = envelopData[i-1]+distance;
logicalMaximum = (userDefinedMax - ((n-i-1)*distance));
if(logicalMaximum < logicalMinimum){
isDataSerieValid = false;
}
envelopData = generateRandomBetween(logicalMinimum,logicalMaximum);

}

// print data if it is valid
if (isDataSerieValid){
print(envelopData);
} else{
print("logisch nicht möglich ein array von min "+ userDefinedMin + " bis max " + userDefinedMax + " mit Distanz "+distance+" und länge "+ n +" zu definieren");
}

[danieleghisi]

Hi!
Have you considered using bach.constraints?

[sydy]

Hey Daniele,

Thanks a lot for your reply.

Yes, I did try constraints.
Here are the two actual solutions (the older posted in Javascript was in fact not complete).

randompoints.zip

solutions_with_javascript_and_bach

(11.29 KiB) Downloaded 178 times

I must admit the bach.constraints solutions is really a brute force method and gives for now only integer solutions (I want also floats).
If I turn on @engine 0, there are no solutions, with @engine 1, the solutions are partly wrong, with @engine 2 it works but in the meantime, you go and get a coffee. Of course, there must be ways to program it better in bach. I just don't know how to handle this for now.

If you have an idea of how to make the bach solution faster I'd be glad to have it. In javascript you have – so I believe more possibilities to make loops.
For now, javascript is like a flash compared to bach.

I put both solutions as an attachment – I couldn't add the javascript to the forum without compressing it.

Best and thanks for your help,
m

[danieleghisi]

Hi, I may have read your post too fast, but it seems to me that this is exactly what [drunk] does, just use the maximum step as your $3, and shift it to your $1.
Collect many drunk outputs and you are done.

[sydy]

really ? No, unfortunately not.
drunk has a stepsize limit, not a stepsize minimum. it will randomly choose a step size inside its stepsize limit...
I want the MinimalDistance_between_each_generated_element >= $3 (In other words, each point has a lower and higher distance from the next >= $3.)
As far as my small brain understands it, this can only be done by iterating through the random generation process, comparing each new result with all the older ones.
That's roughly what my javascript does and that's also what the bach.constraint patch I patched does (although in a more brutal way)...

eg.
RandomRange: min 5, max 25
MinimalDistance between generated points(lower,higher): 4
Number of points: 3

Point 1. random between 5, 25, let's say it returns: 10
Point 2. the next point must be a random which: >=5, <=10-4, >=10+4, <=25,
so the possible ranges left for the random "selection" are: 5-6, 13-25. let's say it returns 16
Point 3. the next point must >=5, <=10-4, >=10+4, <=16-4, >=16+ 4, <=25,
so the possible ranges left for the random "selection" are: 5-6, 20-25.

There are of course data sets which are not possible for instance:
RandomRange = 5,17
MinimalDistance = 4
Number of points to be generated: 5

(I use this for the x-axis of envelopes with a specific number of points which I want to be randomly generated but without having points closer than a specific distance to avoid clicks for instance.)
Hope this explanation was clearer.

AND – Sorry for writing messages that long.

[danieleghisi]

Yep, sorry. I misread your post, it couldn't have been that simple.

I still think you can solve it fairly easily though. Can this be something that goes more or less your way?

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</code></pre>

[sydy]

(It must be my awful English. In German I'd explain myself better) Your solution gives (not always!) the wrong results.
You can see it if you collect the extracted values, sort them and compare the differences:
The differences between the elements of the list should be >= mindist
If it's smaller than the results are wrong.

See my version with a little check routine at the end. (Try it at least 3 times or 5 if there are no wrong solutions at the beginning, they might come later).
I'm not sure you can do it the way you started it – at least not if you want always right solutions. I know the problem looks easy at the beginning but (I think) it's really much trickier...
But anyway, I don't want to bother you here anymore with my problem. I got a fast javascript solution now and that's not the end of the world.

Thanks for your help anyway.
M

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</code></pre>

[danieleghisi]

sydy – are you saying that you want the difference between ANY TWO extracted numbers to be >= K for some K? Because that's what your sort function at the end seem to imply... If so, why don't you just divide everything by K, extract ANY random integer (taken between, say, A/K and B/K) and then multiply the integer by K?

Again, I have the feeling that I'm missing something obvious... Sorry...

Daniele

[sydy]

It's me who's sorry. I think I don't explain the problem in a clear way – I tried though...

Could you patch me what you're proposing?
I must admit, I'm not sure if I understand fully what you want to do.

But yes, the distance between any two of the randomly extracted elements should be >= K

Good night

(I might probably end up by understanding that I made an Elephant out of moustique.)