算法：有没有数据的线性趋势？ [英] Algorithm: is there a linear trend in data?

问题描述

我具有由整数x = [X1，...，XN]的数组psented连续输入的数据重新$ P $，N。1 000 000每两个元件满足以下的条件×〔1] - ; ×〔1 + 1]。

I am having a continuously incoming data represented by an array of integer x = [x1,...,xn], n<1 000 000. Each two elements satisfy the following condition x[i] < x[i + 1].

我需要检测尽可能快这样的断点，其中这些数据端部的线性趋势并变换成二次趋势。数据总是以线性趋势...

I need to detected as fast as possible such a breakpoint, where the linear trend of these data ends and transforms into a quadratic trend. The data always starts with linear trend...

我试图来计算

k = (x[i+1] - x[i])/ (x[i] - x[i-1]) 

不过这个测试不是太可靠的...也许还有一个更简单和有效的统计检验......回归线的计算是在这种情况下慢...

but this test not too reliable... Maybe there is a more simple and efficent statistic test... The computation of the regression line is slow in this case...

感谢您的帮助......

Thanks for your help...

推荐答案

其实你计算函数的导数。也许你应该使用更多的点来计算它如5，看五点型板

Actually you calculate a derivative of the function. Possibly you should use more points for calculating it e.g. 5, see Five-point stencil

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