Mapping a value to an interval

[JazonKuer]

Hi,

Let's say I have a variable coordinate=234321, and a variable scale=5000 (a constant, but should also be able to be e.g. 4000). Now, I want to translate this coordinate into an interval [-scale/2, +scale/2] that can contain it, starting on an even 10000nd of the coordinate itself.

So for example, in the case of 234321, the interval would be [232500,237500]. 234321 is inside that interval. Another example would be 239580 => [237500,242500]. One caveat though, this last example would also be satisfied in [235000,240000], however since it's more closer to the mean of that first interval, that should be the preferred one. So the function should kind of decide what interval to return depending on if it's on either side of a "scale/4" value or not, if you get what I mean. How can I write a generic function, that can take a coordinate and a scale as inputs, and produce this interval as an output?

[menator01]

What have you tried?

[JazonKuer]

What have you tried?

I've tried checking the steps/4 intervals on an incremental basis, including overlapping backwards and forwards into the neighbouring intervals, like:

baseCoord = coordinate // 10000*10000
remainder = round(coordinate/100)/10%10

if remainder <= 1.25:
   min = baseCoord - scale/2
elif remainder <= 3.75:
   min = baseCoord
elif remainder <= 6.25:
   min = baseCoord + scale/2
elif remainder <= 8.75:
   min = baseCoord
else:
   min = baseCoord*1.5

return [min, min+scale]

But I thought there must be a pure computational solution without the need for the conditionals, or what do you think? :-)

[Gribouillis]

The conditions on the interval are unclear. What do you do when the scale is 5387?

[JazonKuer]

The conditions on the interval are unclear. What do you do when the scale is 5387?

Sorry, have clarified. It's a constant, but should work with e.g. both 4000 and 5000.

[Gribouillis]

Here is my proposal

__version__ = '2023.03.17.1'

def rounding(precision, value):
    y = 0.5 if value >= 0 else -0.5
    return precision * int(y + value / precision)

def interval(coord, scale):
    u = rounding(100, coord)
    m = u + scale // 2
    return (2 * u - m, m)

if __name__ == '__main__':
    from random import randint

    for i in range(10):
        x = randint(0, 1000000)
        print(x, interval(x, 5000))

Output:
883300 (880800, 885800)
879406 (876900, 881900)
797201 (794700, 799700)
499782 (497300, 502300)
834873 (832400, 837400)
670688 (668200, 673200)
726577 (724100, 729100)
657842 (655300, 660300)
230323 (227800, 232800)
738326 (735800, 740800)

[deanhystad]

This works for your particular examples.

def ranger(value, range_=5000):
    half_range = range_ / 2
    bottom = value // half_range * half_range
    return (bottom, bottom + range_)


print(ranger(234321), ranger(239580))

Output:
(232500.0, 237500.0) (237500.0, 242500.0)

[JazonKuer]

Here is my proposal

__version__ = '2023.03.17.1'

def rounding(precision, value):
    y = 0.5 if value >= 0 else -0.5
    return precision * int(y + value / precision)

def interval(coord, scale):
    u = rounding(100, coord)
    m = u + scale // 2
    return (2 * u - m, m)

if __name__ == '__main__':
    from random import randint

    for i in range(10):
        x = randint(0, 1000000)
        print(x, interval(x, 5000))

Output:
883300 (880800, 885800)
879406 (876900, 881900)
797201 (794700, 799700)
499782 (497300, 502300)
834873 (832400, 837400)
670688 (668200, 673200)
726577 (724100, 729100)
657842 (655300, 660300)
230323 (227800, 232800)
738326 (735800, 740800)

Thanks, unfortunately if the scale or half the scale should be added to an even 10000nd of the coordinate, these values are not valid. For a scale of 5000 it will either end on 0000, 2500, 5000, or 7500.

[JazonKuer]

This works for your particular examples.

def ranger(value, range_=5000):
    half_range = range_ / 2
    bottom = value // half_range * half_range
    return (bottom, bottom + range_)


print(ranger(234321), ranger(239580))

Output:
(232500.0, 237500.0) (237500.0, 242500.0)

Try it with 235000. Here, I'd like it to return (232500, 237500) since the input would be in the middle of that interval. Now it returns (235000, 240000). Any idea how to achieve that?

[Gribouillis]

For a scale of 5000 it will either end on 0000, 2500, 5000, or 7500.

Only replace 100 by 500 in the interval() function. However what are the valid values when the scale is 4000 ?

73874 (71500, 76500)
919227 (916500, 921500)
448634 (446000, 451000)
196040 (193500, 198500)
767177 (764500, 769500)
972937 (970500, 975500)
146383 (144000, 149000)
345814 (343500, 348500)
685618 (683000, 688000)
578875 (576500, 581500)

Edit: if you replace the rounding by 2500 instead of 500 it gives

73874 (71500, 76500)
919227 (916500, 921500)
448634 (446000, 451000)
196040 (193500, 198500)
767177 (764500, 769500)
972937 (970500, 975500)
146383 (144000, 149000)
345814 (343500, 348500)
685618 (683000, 688000)
578875 (576500, 581500)