Given a parameter p, be any float or integer.
For example, let p=4
| time | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Numbers | a1 | a1*(0.5)^(1/p)^(2-1) | a1*(0.5)^(1/p)^(2-1) | a1*(0.5)^(1/p)^(3-1) | a1*(0.5)^(1/p)^(4-1) |
| Numbers | nan | a2 | a2*(0.5)^(1/p)^(3-2) | a2*(0.5)^(1/p)^(4-2) | a2*(0.5)^(1/p)^(5-2) |
| Numbers | nan | nan | a3 | a3*(0.5)^(1/p)^(4-3) | a3*(0.5)^(1/p)^(5-3) |
| Numbers | nan | nan | nan | a4 | a4*(0.5)^(1/p)^(5-4) |
| Number | nan | nan | nan | nan | a5 |
| Final Results | a1 | sum of column 2 | sum of column 3 | sum of column 4 | sum of column 5 |
Numbers like a1,a2,a3,a4,a5,…,at is given, our goal is to find the Final Results. Combining the answer provided by mozway, I wrote the following function which works well. It is a matrix way to solve the problem.
def hl(p,column):
a = np.arange(len(copy_raw))
factors = (a[:,None]-a)
factors = np.where(factors<0, np.nan, factors)
inter = ((1/2)**(1/p))**factors
copy_raw[column] = np.nansum(copy_raw[column].to_numpy()*inter, axis=1)
However, I don’t think this method will work well if we are dealing with large dataframe. Are there any better way to fix the problem? (In this case, faster = better.)
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Answer
Assuming your number of rows is not too large, you can achieve this with numpy broadcasting:
First create a 2D array of factors:
a = np.arange(len(df)) factors = (a[:,None]-a) factors = np.where(factors<0, np.nan, factors) # array([[ 0., nan, nan, nan, nan], # [ 1., 0., nan, nan, nan], # [ 2., 1., 0., nan, nan], # [ 3., 2., 1., 0., nan], # [ 4., 3., 2., 1., 0.]])
Then map to your data and sum:
df['number2'] = np.nansum(df['number'].to_numpy()*(1/2)**factors, axis=1)
example output:
Index Time number number2 0 0 1997-WK01 1 1.0000 1 1 1997-WK02 2 2.5000 2 2 1997-WK03 3 4.2500 3 3 1997-WK04 2 4.1250 4 4 1997-WK05 4 6.0625
intermediate:
df['number'].to_numpy()*(1/2)**factors # array([[1. , nan, nan, nan, nan], # [0.5 , 2. , nan, nan, nan], # [0.25 , 1. , 3. , nan, nan], # [0.125 , 0.5 , 1.5 , 2. , nan], # [0.0625, 0.25 , 0.75 , 1. , 4. ]])