# 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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