Programmatically finding "significant" data points

[Paul McGuire]

... dang touchy keyboard!

> Here is some sample data:
> data = [0.10, 0.50, 0.60, 0.40, 0.39, 0.50, 1.00, 0.80, 0.60, 1.20,
> 1.10, 1.30, 1.40, 1.50, 1.05, 1.20, 0.90, 0.70, 0.80, 0.40, 0.45, 0.35,
> 0.10]
>
> In this data, some of the significant points include:
> data[0]
> data[2]
> data[4]
> data[6]
> data[8]
> data[9]
> data[13]
> data[14]

Using the first derivative, and looking for sign changes, finds many of the 
values you marked as "significant".

-- Paul


data = [0.10, 0.50, 0.60, 0.40, 0.39, 0.50, 1.00, 0.80, 0.60, 1.20,
1.10, 1.30, 1.40, 1.50, 1.05, 1.20, 0.90, 0.70, 0.80, 0.40, 0.45, 0.35,
0.10]

delta = lambda (x1,x2) : x2-x1
dy_dx =[0]+map(delta,zip(data,data[1:]))
d2y_dx2 = [0]+map(delta,zip(dy_dx,dy_dx[1:]))

sgnChange = lambda (x1,x2) : x1*x2<0
sigs = map(sgnChange,zip(dy_dx,dy_dx[1:]))
print [i for i,v in enumerate(sigs) if v]
[2, 4, 6, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20]