修正逆幂函数实现错误：cw_2_ZMA的逆函数ZMA_2_cw结果不符

Looking at your code, there are two key mistakes preventing the inverse function from working correctly:

1. Incorrect PCW Calculation #

The original function uses ZMA = C * PCW^(-0.88) where C = -(1000 * np.log(0.05))/144.7. To solve for PCW, you need to rearrange this equation properly:

• Start with ZMA = C / PCW^(0.88)
• Rearrange to PCW^(0.88) = C / ZMA
• Raise both sides to the power of 1/0.88: PCW = (C / ZMA)^(1/0.88)

Your current code uses (1/C) * ZMA^(-1/0.88), which is not equivalent to the correct expression. This is because (C/ZMA)^(1/0.88) = C^(1/0.88) * ZMA^(-1/0.88), not (1/C) * ZMA^(-1/0.88).

2. Wrong Conversion from PCW to cw #

In the original function, PCW = cw + bs, so solving for cw gives cw = PCW - bs. Your code incorrectly multiplies PCW by 1000 before subtracting bs—this extra multiplication is unnecessary and introduces a huge error.

Corrected Code #

Here's the fixed version of ZMA_2_cw:

import numpy as np

#define input arrays and variables
cw_array=np.arange(0,10,1)
bs = 1.592278e-4

#functions
def cw_2_ZMA(cw):
    PCW = np.add(cw, bs)
    ZMA = -(1000 * np.log(0.05) / 144.7)* np.power(PCW, -0.88)
    return ZMA

def ZMA_2_cw(ZMA):
    # Calculate the constant C from the original function
    C = -(1000 * np.log(0.05)) / 144.7
    # Correct PCW calculation
    PCW = np.power(C / ZMA, 1 / 0.88)
    # Correct conversion to cw
    cw = PCW - bs
    return cw

#execute functions
ZMA_calc=cw_2_ZMA(cw_array)
cw_calc=ZMA_2_cw(ZMA_calc)

#print arrays
print("cw_array=", cw_array[:])
print("cw_calc=", np.round(cw_calc[:],1))

Expected Output #

When you run this corrected code, the output will be:

('cw_array=', array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))
('cw_calc=', array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.]))

Now the inverse function accurately recovers the original cw_array values!

内容的提问来源于stack exchange，提问作者PythonForeCats