Question

Write a function to find the indices of a time series in which the absolute value of the derivative is above a particular threshold. This is somewhat based on work we’ve done in this chapter. The function:

(a) should be named where_deriv_large.

(b) should take two arguments: times, data (in that order).

(c) (509 only) should have a third argument in which the value of the threshold can be passed.

(d) should return a tuple. The first element is the indices of the derivative that exceed a particular threshold. The second element is the count of the number of values of the derivative exceed the threshold The third element is the (signed) derivative values for the entire time series.

Let’s set the threshold to nominally be 5000. So, your function will find where (wink) the absolute value of the derivative of a time series is larger than 5000.

Test your function using the data we’ve used in this chapter: where p_vars

Write your function in a module named time_series.py.

idx, cnt, deriv = where_deriv_large(p_vars['times'], p_vars['data'])

Answer 1

#import the required libraries

def where_deriv_large(t,d): #declare and define the function with times and data as arguments

def f(x):

return abs(x) # return absolute value

dx = f(x).diff(x) # derivative dx

dx

(re(x)*Derivative(re(x), x) + im(x)*Derivative(im(x), x))/Abs(x) # perform derivative calculation

thr=0 # assign the threshold value

tuple=() # declare function for tuple

if thr>5000: # test condition if threshold is greater than 5000

tuple[0]= # consider the indices of element which satistfies the test condition

tuple[1]= # consider the count values that satisfy above condition

tuple[2]= # consider derivative values of entire time series (dx)

return tuple() # return tuple with the above three values

Note: The above pseudocode is written in Python Programming language.