How do I divide by the change in a list Y?

Question

Solution to this problem is solving delta y, see bottom of question in ** **

I am writing code for many different equations for linear regression. I have two lists with x and y values. One of my equations creates a new list w. The equation for the list w is (w=1/Δy^2) where y is a list. I have used equations that require lists before but never the change in a list.

I have w = [ 1/(deltay)**2 in zip(x,y)] But when I print that I get w [False]. So I dont think I am doing the delta y part right but I have no idea.

Each data point in the list y needs to have an uncertainty of 5%. Right now I am only concerned with w and the uncertainty in y. This w function is needed for something else.

In summary how can I code the equation (w=1/Δy^2) where delta y is a list and w is a list, thanks.

** Ok I have made some progress. I think I know how to solve this now. I have a list of y values. The uncertainty in each y value is 5%. So I need a new list deltay that is the old list y timesed by 0.05. So I am writing this deltay = [(i*0.05) for i in zip(y)] But I am getting the error TypeError: can't multiply sequence by non-int of type 'float'**

Do you want to have the slope (piecewise) or just the change in `y` from `y[i]` to `y[i+1]`? I don't quite get the role of `x`. — sim, Mar 02 '20 at 10:07
Ok I have made some progress. I think I know how to solve this now. I just need to generate a list of y times by 0.05. As this will act as my list delta y. So I am writing this` w = [ 1/(deltay)**2 in zip(x,y)]` But I am getting the error TypeError: can't multiply sequence by non-int of type 'float' — DwightConrad, Mar 02 '20 at 10:16

kederrac · Answer 1 · 2020-03-02T10:38:10.140

1

I suppose that your deltay variable is a numpy.array otherwise your code will raise an exception, so since you use a numpy.array you could use elementwise operations:

w =  1 / deltay ** 2

if your deltay it is not a numpy.array (as your last update shows) you can use list comprehension to compute your w:

deltay = [ i * 0.05 for i in y]
w = [1/x**2 for x in deltay]

edited Mar 02 '20 at 10:38

answered Mar 02 '20 at 10:11

kederrac

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sim · Accepted Answer · 2020-03-02T10:33:44.953

In principle what you want to have is an iterator over a sliding window. There are already several good posts on that matter available here (Rolling or sliding window iterator?).

We will make use of Daniel DiPaolo's suggested approach:

from itertools import islice

def window(seq, n=2):
    "Returns a sliding window (of width n) over data from the iterable"
    "   s -> (s0,s1,...s[n-1]), (s1,s2,...,sn), ...                   "
    it = iter(seq)
    result = tuple(islice(it, n))
    if len(result) == n:
        yield result
    for elem in it:
        result = result[1:] + (elem,)
        yield result

Now, getting the changes is easy:

xs = [1, 3, 4, 7, 10, 14]
ys = [3, 1, 2, 9, 13, -1]

# if you need the slope
w = [1/d**2 
     for d in 
         map(lambda pnts: (pnts[1][1]-pnts[0][1])/(pnts[1][0]-pnts[0][0]),  
             window(zip(xs, ys), 2))
    ]

# if you just need the change in y
w = [1/d**2 
     for d in 
         map(lambda y: y[1] - y[0], window(ys, 2))
    ]

To answer your edit:

Ok I have made some progress. I think I know how to solve this now. I have a list of y values. The uncertainty in each y value is 5%. So I need a new list deltay that is the old list y timesed by 0.05. So I am writing this deltay = [(i*0.05) for i in zip(y)] But I am getting the error TypeError: can't multiply sequence by non-int of type 'float'**

You should use [(i*0.05) for i in y]. If you use zip(y) all the entries you iterate over will be tuples.

How do I divide by the change in a list Y?

2 Answers2