是否有支持数据样本的 Min-Max 和 Sum 缩放的 python package？

Question

I've been looking for a python package/command that is able to scale a given data sample with a predefined min, max and total sum for the to-be scaled sample. I've attempted to use the MinMaxScaler() function of the sklearn.preprocessing package as in the example underneath.

Given a base sample:

from sklearn.preprocessing import MinMaxScaler
import pandas as pd

base_sample = pd.DataFrame([5 , 20 , 30 , 35, 45 , 60])

sample_min = 10
sample_max = 50

scaler = MinMaxScaler(feature_range = (sample_min , sample_max))
        
scaled_sample = scaler.fit_transform(base_sample)

print(scaled_sample)

Producing:

[[10.        ]
 [20.90909091]
 [28.18181818]
 [31.81818182]
 [39.09090909]
 [50.        ]]

With Sum:

print(scaled_sample.sum())
180.0

Yet what I need is a command that is able to do the above yet with a predefined different sum, for example based on the sum of the original sample:

print(base_sample.sum())
195

or any other predefined sum. In essence the values inbetween the min and max have to be scaled accordingly to match the sum without violating the min and max constraints. I've been doing this kind of exercise for a long time within a commercial tool that unfortunately does not allow me to have a look under the hood for the underlying formulation. Any suggestions on how to proceed would be very welcome.

Answer 1

Maybe this works,

scaled_sample/scaler.scale_

The scaler.scale_ is equivalent to (max - min) / (X.max(axis=0) - X.min(axis=0))

Answer 2

With a linear transformation, this is not possible. You cannot transform the values of a vector to an arbitrary minimum, maximum and sum. You can achieve this with non-linear transforms, given that you can scale certain weights more up/down than others to control the extrema while adjusting the sum (or vice versa). This would become an optimization problem, which has an infinite amount of answers as you can literally do anything with the transformed vector. You can limit this by setting the transformation function.