[FIXED] Expand distance between values in pandas dataframe

Issue

How to expand distance between values in pandas dataframe?

  A
1 3
2 5
3 6
5 5
6 9

I want to increase the distance between adjacent elements by x times, for example by two times.

Expected output:

  A B
1 3 3
2 5 7  # (3 + 2 * 2)
3 6 9  # (7 + 1 * 2)
5 5 7  # (9 - 1 * 2)
6 9 15 # (7 + 4 * 2)

Solution

You can actually use a vectorial code as suggested by @MatBailie:

df['B'] = df['A']*2 - df['A'].iloc[0]

For generic code with any N:

N = 2
df['B'] = df['A']*N - df['A'].iloc[0]*(N-1)

Output:

   A  B(N=1)  B(N=2)  B(N=3)
1  3       3       3       3
2  5       5       7       9
3  6       6       9      12
5  5       5       7       9
6  9       9      15      21

Some explanation is however needed to understand why:

For each step, assuming a(n) the current value and b(n) the output. The output b(n) is equal to b(n-1) + (a(n) - a(n-1)) * 2, which is equal to b(n-2) + (a(n-1) - a(n-2)) * 2 + (a(n) - a(n-1)) * 2 which simplifies to b(n-2) + (a(n) - a(n-1)) * 2). By recursion, this becomes b(n) = b(0) + (a(n) - a(0))*2 which is b(n) = 2*a(n) - a(0) if n=2 since b(0) = a(0), in the generic case this is b(n) = a(n)*N - a(0)*(N-1).

Output:

   A   B
1  3   3
2  5   7
3  6   9
5  5   7
6  9  15

---

Original answer:

You probably can't solve it in a vectorial way since your nth value depends on the output of the step n-1, I believe you must iterate:

def expand_dist(s):
    s = list(s)
    prev = s[0]
    out = []
    for v in s:
        out.append(prev+(v-prev)*2)
    return out

df['B'] = expand_dist(df['A'])

Answered By - mozway