Scaling range of values with negative numbers

问题:

How can I scale a set of values to fit a new range if they include negative numbers?

For example, I have a set of numbers (-10, -9, 1, 4, 10) which have to scaled to a range [0 1], such that -10 maps to 0, and 10 maps to 1.

The regular method for an arbitrary number 'x' would be: (x - from_min) * (to_max - to_min) / (from_max - from_min) + to_min

but this does not work for negative numbers. Any help is appreciated. Thanks!!

回答1:

I believe id does; in your example,

from_min = -10,
from_max = 10,
to_max = 1,
to_min = 0.

This yields

to_max - to_min = 1,
from_max - from_min = 20;

So using the formula

x -> (x - from_min) * (to_max - to_min) / (from_max - from_min) + to_min
   = (x - from_min) * 1 / 20 + 0
   = (x - from_min) / 20

yields

-10 -> (-10 + 10) / 20 = 0 / 20,
-9 -> (-9 + 10) / 20 = 1 / 20,
1 -> (1 + 10) / 20 = 11 / 20,
4 -> (4 + 10) / 20 = 14 / 20,
10 -> (10 + 10) / 20 = 20 / 20,

so all the resulting values are nonnegative. Furthermore, the original minimum -10 maps to to_min = 0 and the original maximum 10 maps to to_max = 1. If this doesn't work in your implementation, check if you mixed up integral types and floating-point types.

回答2:

Your formula works fine for negative numbers.

You have:

• from_min = -10
• from_max = 10
• to_min = 0
• to_max = 1

Substituting these into your formula:

(x - (-10)) * (1 - 0) / (10 - (-10)) + 0

Which simplifies to:

(x + 10) / 20