Last Updated: 2023-08-14 14:31:52 Monday
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Relative Error (RE) — when used as a measure of precision — is the ratio of the absolute error of a measurement to the measurement being taken. In other words, this type of error is relative to the size of the item being measured. RE is expressed as a percentage and has no units.
这两个概念，常用来检查测量或计算的精确度。
设测量值为\(a\)，真实值为\(b\)，
绝对错误，absolute error:
abs_err = abs(a-b)
相对错误，relative error = absolute error/real value:
rel_err = abs(a-b)/abs(b)
举个例子：
cs231n课程作业中，有一个检查计算的gradient是否正确的接口，里面用到了通过查看相对错误特别小的方式，来确定计算的gradient的正确性：
...
ix = tuple([randrange(m) for m in x.shape])
oldval = x[ix]
x[ix] = oldval + h # increment by h
fxph = f(x) # evaluate f(x + h)
x[ix] = oldval - h # increment by h
fxmh = f(x) # evaluate f(x - h)
x[ix] = oldval # reset
grad_numerical = (fxph - fxmh) / (2 * h)
...
rel_error = abs(grad_numerical - grad_analytic) / abs(grad_numerical)
grad_numerical通过导数定义公式计算，一定是正确的，当grad_analytic非常接近前者时，也可认为正确。
本文链接：https://cs.pynote.net/math/202210254/
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