Question

To all:

This question pertains to some MS research I am doing.

What I want to do is seemingly simple. I have a text file of values( time, …..values). I then want to integrate from 0 to those values for all times, then save that value to a text file.

from numpy import *
from pylab import *
import os, sys, shutil
import math

#######################

#Load Data
data = loadtxt('wh.txt')

#Open file to save plots to
shutil.rmtree("wh_files")
os.makedirs("wh_files")
os.chdir("wh_files")

for i in range(0,100,1):
   int = trapz(data[i,:],axis=0)
   print int
   savetxt('int.txt', int)

When I run this I get the following error:

  File "integral.py", line 19, in 
    savetxt('int.txt', int)
  File "/Library/Frameworks/Python.framework/Versions/2.6/lib/python2.6/site-packages/numpy/lib/npyio.py", line 960, in savetxt
    ncol = X.shape[1]
IndexError: tuple index out of range

I have been trying to solve this problem for a few days on an off now, but am yet to find a solution. I appreciate any help/comments you can give.

Answer 1

The value of int is a float but savetxt requires an array. You want to create a numpy array for all the integration results, then save it at the end using savetxt. I think something like this should do the trick:

int_array = apply_along_axis(trapz, 0, data)
savetxt('int.txt', int_array)

Keep in mind that this (along with your original example) will sum the time fields, rather than integrating across time. This will only yield valid results if the spacing along the x-axis is 1. Otherwise you’ll want to do something like this:

t = data[0,:]
int_array = apply_along_axis(trapz, 0, data[1:,:], t)
savetxt('int.txt', int_array)

Assuming the time fields are numeric.

edit: Further explanation of 2nd code section follows.

You’re using the trapezoidal rule to integrate a variety of values, which is an integration approximation technique that works by summing the average of successive y-values on a curve multiplied by the change in x between the two y-values. This amounts to calculating the area of a trapezoid that connects the two y-values and the x-axis, like so:

It’s not completely clear from your question, but it seemed that you were integrating the values across time, so that the x-axis would represent time. The x-values need to be incorporated to get the correct area of each trapezoid (the area of each trapezoid is (x₂ – x₁) * (y₂ + y₁) / 2 and the final integration result is the sum of all such areas).

The simplest way to incorporate these x-axis values is to pass it into the trapz function as the x parameter (see the docstring). In the example above, I used t = data[0,:] as the array of x values suchly.

Another caveat: if all spacing between x values are the same (so that x₂ – x₁ is a constant), you can save yourself some calculation by pulling this out of the summation and simply multiplying it at the end. This functionality is available through the trapz function with the dx parameter. So, if you’re time measurements were taken every 30 seconds, for example, you could replace the 2nd line in my 2nd example with:

int_array = apply_along_axis(trapz, 0, data[1:,:], None, 30)

Hope that helps.