https://stats.stackexchange.com/a/417915/69508

417915_69508.py

import numpy as np

def scale(x, a=0, b=1):
    if a > b:
        a, b = b, a
    min_x = np.min(x)
    xout = (x - min_x) / (np.max(x) - min_x)
    xout *= (b - a)
    xout += a
    sigma_in = np.std(x, ddof=1)
    mu_in = np.mean(x)
    sigma_out = np.std(xout, ddof=1)
    mu_out = np.mean(xout)
    return (x - mu_in) * sigma_out / sigma_in + mu_out

if __name__ == '__main__':
    x = np.array([1, 3, 4, 5, -1, -7])
    print(scale(x, a=-1, b=1))