Finding where a value lands between two numbers in Python

Question

I have a problem where I need to determine where a value lands between other values. This is an awful long question...but its a convoluted problem (at least to me).

The simplest presentation of the problem can be seen with the following data:

I have a value of 24.0. I need to determine where that value lands within six 'ranges'. The ranges are: 10, 20, 30, 40, 50, 60. I need to calculate where along the ranges, the value lands. I can see that it lands between 20 and 30. A simple if statement can find that for me.

My if statement for checking if the value is between 20 and 30 would be:

if value >=20 and value <=30:

Pretty simple stuff.

What I'm having trouble with is when I try to rank the output.

As an example, let's say that each range value is given an integer representation. 10 =1, 20=2, 30=3, 40=4, 50=5, 60=6, 70=7. Additionally, lets say that if the value is less than the midpoint between two values, it is assigned the rank output of the lower value. For example, my value of 24 is between 20 and 30 so it should be ranked as a "2".

This in and of itself is fairly straightforward with this example, but using real world data, I have ranges and values like the following:

• Value = -13 with Ranges = 5,35,30,25,-25,-30,-35
• Value = 50 with Ranges = 5,70,65,60,40,35,30
• Value = 6 with Ranges = 1,40,35,30,5,3,0

Another wrinkle - the orders of the ranges matter. In the above, the first range number equates to a ranking of 1, the second to a ranking of 2, etc as I mentioned a few paragraphs above.

The negative numbers in the range values were causing trouble until I decided to use a percentile ranking which gets rid of the negative values all together. To do this, I am using an answer from Map each list value to its corresponding percentile like this:

y=[stats.percentileofscore(x, a, 'rank') for a in x]

where x is the ranges AND the value I'm checking. Running the value=6 values above through this results in y being:

x = [1, 40, 35, 30, 5, 3, 0, 6]

y=[stats.percentileofscore(x, a, 'rank') for a in x]

Looking at "y", we see it as:

[25.0, 100.0, 87.5, 75.0, 50.0, 37.5, 12.5, 62.5]

What I need to do now is compare that last value (62.5) with the other values to see what the final ranking will be (rankings of 1 through 7) according to the following ranking map:

1=25.0
2=100.0
3=87.5
4=75.0
5=50.0
6=37.5
7=12.5

If the value lies between two of the values, it should be assigned the lower rank. In this example, the 62.5 value would have a final ranking value of 4 because it sits between 75.0 (rank=4) and 50.0 (rank=5).

If I take 'y' and break it out and use those values in multiple if/else statements it works for some but not all (the -13 example does not work correctly).

My question is this:

How can I programmatically analyze any value/range set to find the final ranking without building an enormous if/elif structure? Here are a few sample sets. Rankings are in order of presentation below (first value in Ranges =1 , second = 2, etc etc)

• Value = -13 with Ranges = 5, 35, 30, 25, -25, -30, -35 --> Rank = 4
• Value = 50 with Ranges = 5, 70, 65, 60, 40, 35, 30 --> Rank = 4
• Value = 6 with Ranges = 1, 40, 35, 30, 5, 3,0 --> Rank = 4
• Value = 24 with Ranges = 10, 20, 30, 40, 50, 60, 70 --> Rank = 2
• Value = 2.26 with Ranges = 0.1, 0.55, 0.65, 0.75, 1.75, 1.85, 1.95 --> Rank = 7
• Value = 31 with Ranges = 10, 20, 30, 40, 60, 70, 80 --> Rank = 3

I may be missing something very easy within python to do this...but I've bumped my head on this wall for a few days with no progress.

Any help/pointers are appreciated.

Answer 1

def checker(term):
    return term if term >= 0 else abs(term)+1e10

l1, v1 = [5, 35, 30, 25, -25, -30, -35], -13 # Desired: 4
l2, v2 = [5, 70, 65, 60, 40, 35, 30], 50 # Desired: 4
l3, v3 = [1, 40, 35, 30, 5, 3, 0], 6 # Desired: 4
l4, v4 = [10, 20, 30, 40, 50, 60, 70], 24 # Desired: 2
l5, v5 = [0.1, 0.55, 0.65, 0.75, 1.75, 1.85, 1.95], 2.26 # Desired: 7
l6, v6 = [10, 20, 30, 40, 60, 70, 80], 31 # Desired: 3

Result:

>>> print(*(sorted(l_+[val], key=checker).index(val) for
... l_, val in zip((l1,l2,l3,l4,l5,l6),(v1,v2,v3,v4,v5,v6))), sep='\n')
4
4
4
2
7
3

Answer 2

Taking the first example of -13.

y = [5, 35, 30, 25, -25, -30, -35]
value_to_check = -13

max_rank = len(y) # Default value in case no range found (as per 2.26 value example)

for ii in xrange(len(y)-1,0,-1):
    if (y[ii] <= value_to_check <= y[ii-1]) or (y[ii] >= value_to_check >= y[ii-1]):
        max_rank = ii
        break

>>> max_rank
4

In function form:

def get_rank(y, value_to_check):

    max_rank = len(y) # Default value in case no range found (as per 2.26 value example)

    for ii in xrange(len(y)-1,0,-1):
        if (y[ii] <= value_to_check <= y[ii-1]) or (y[ii] >= value_to_check >= y[ii-1]):
            max_rank = ii
            break

    return max_rank

When you call:

>>> get_rank(y, value_to_check)
4

Answer 3

This correctly finds the answer for all your data:

def get_rank(l,n):
    mindiff = float('inf')
    minindex = -1
    for i in range(len(l) - 1):
        if l[i] <= n <= l[i + 1] or l[i + 1] <= n <= l[i]:
            diff = abs(l[i + 1] - l[i])
            if diff < mindiff:
                mindiff = diff
                minindex = i
    if minindex != -1:
        return minindex + 1         
    if n > max(l):
        return len(l)
    return 1

>>> test()
[5, 35, 30, 25, -25, -30, -35] -13 Desired: 4 Actual: 4
[5, 70, 65, 60, 40, 35, 30] 50 Desired: 4 Actual: 4
[1, 40, 35, 30, 5, 3, 0] 6 Desired: 4 Actual: 4
[10, 20, 30, 40, 50, 60, 70] 24 Desired: 2 Actual: 2
[0.1, 0.55, 0.65, 0.75, 1.75, 1.85, 1.95] 2.26 Desired: 7 Actual: 7
[10, 20, 30, 40, 60, 70, 80] 31 Desired: 3 Actual: 3

For completeness, here is my test() function, but you only need get_rank for what you are doing:

>>> def test():
        lists = [[[5, 35, 30, 25, -25, -30, -35],-13,4],[[5, 70, 65, 60, 40, 35, 30],50,4],[[1, 40, 35, 30, 5, 3,0],6,4],[[10, 20, 30, 40, 50, 60, 70],24,2],[[0.1, 0.55, 0.65, 0.75, 1.75, 1.85, 1.95],2.26,7],[[10, 20, 30, 40, 60, 70, 80],31,3]]
        for l,n,desired in lists:
            print l,n,'Desired:',desired,'Actual:',get_rank(l,n)