# Modeling and Simulation in Python

Chapter 17



In [1]:

# Configure Jupyter so figures appear in the notebook
%matplotlib inline

# Configure Jupyter to display the assigned value after an assignment
%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'

# import functions from the modsim.py module
from modsim import *



### Data

We have data from Pacini and Bergman (1986), "MINMOD: a computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test", Computer Methods and Programs in Biomedicine, 23: 113-122..



In [2]:



Here's what the glucose time series looks like.



In [3]:

plot(data.glucose, 'bo', label='glucose')
decorate(xlabel='Time (min)',
ylabel='Concentration (mg/dL)')



And the insulin time series.



In [4]:

plot(data.insulin, 'go', label='insulin')
decorate(xlabel='Time (min)',
ylabel='Concentration ($\mu$U/mL)')



For the book, I put them in a single figure, using subplot



In [5]:

subplot(2, 1, 1)
plot(data.glucose, 'bo', label='glucose')
decorate(ylabel='Concentration (mg/dL)')

subplot(2, 1, 2)
plot(data.insulin, 'go', label='insulin')
decorate(xlabel='Time (min)',
ylabel='Concentration ($\mu$U/mL)')

savefig('figs/chap17-fig01.pdf')



### Interpolation

We have measurements of insulin concentration at discrete points in time, but we need to estimate it at intervening points. We'll use interpolate, which takes a Series and returns a function:

The return value from interpolate is a function.



In [6]:

I = interpolate(data.insulin)



We can use the result, I, to estimate the insulin level at any point in time.



In [7]:

I(7)



I can also take an array of time and return an array of estimates:



In [8]:

t_0 = get_first_label(data)
t_end = get_last_label(data)
ts = linrange(t_0, t_end, endpoint=True)
I(ts)
type(ts)



Here's what the interpolated values look like.



In [9]:

plot(data.insulin, 'go', label='insulin data')
plot(ts, I(ts), color='green', label='interpolated')

decorate(xlabel='Time (min)',
ylabel='Concentration ($\mu$U/mL)')

savefig('figs/chap17-fig02.pdf')



Exercise: Read the documentation of scipy.interpolate.interp1d. Pass a keyword argument to interpolate to specify one of the other kinds of interpolation, and run the code again to see what it looks like.



In [10]:

# Solution goes here



Exercise: Interpolate the glucose data and generate a plot, similar to the previous one, that shows the data points and the interpolated curve evaluated at the time values in ts.



In [11]:

# Solution goes here



### Under the hood



In [12]:

source_code(interpolate)




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