01-numpy.md 36.3 KB
Newer Older
1
---
2
3
4
5
title: Analyzing Patient Data
teaching: 30
exercises: 0
questions:
Greg Wilson's avatar
Greg Wilson committed
6
- "How can I process tabular data files in Python?"
7
objectives:
Brian Jackson's avatar
Brian Jackson committed
8
- "Explain what a library is and what libraries are used for."
9
- "Import a Python library and use the functions it contains."
10
11
12
13
- "Read tabular data from a file into a program."
- "Assign values to variables."
- "Select individual values and subsections from data."
- "Perform operations on arrays of data."
14
- "Plot simple graphs from data."
15
keypoints:
Greg Wilson's avatar
Greg Wilson committed
16
17
18
19
20
21
- "Import a library into a program using `import libraryname`."
- "Use the `numpy` library to work with arrays in Python."
- "Use `variable = value` to assign a value to a variable in order to record it in memory."
- "Variables are created on demand whenever a value is assigned to them."
- "Use `print(something)` to display the value of `something`."
- "The expression `array.shape` gives the shape of an array."
22
- "Use `array[x, y]` to select a single element from a 2D array."
Greg Wilson's avatar
Greg Wilson committed
23
- "Array indices start at 0, not 1."
Dustin Lang's avatar
Dustin Lang committed
24
- "Use `low:high` to specify a `slice` that includes the indices from `low` to `high-1`."
Greg Wilson's avatar
Greg Wilson committed
25
26
27
28
29
- "All the indexing and slicing that works on arrays also works on strings."
- "Use `# some kind of explanation` to add comments to programs."
- "Use `numpy.mean(array)`, `numpy.max(array)`, and `numpy.min(array)` to calculate simple statistics."
- "Use `numpy.mean(array, axis=0)` or `numpy.mean(array, axis=1)` to calculate statistics across the specified axis."
- "Use the `pyplot` library from `matplotlib` for creating simple visualizations."
30
31
---

32
33
In this lesson we will learn how to work with arthritis inflammation datasets in Python. However,
before we discuss how to deal with many data points, let's learn how to work with single data values.
34

35
36
37
38
39
## Variables

Any Python interpreter can be used as a calculator:
~~~
3 + 5 * 4
Justin Pringle's avatar
Justin Pringle committed
40
~~~
41
{: .language-python}
Justin Pringle's avatar
Justin Pringle committed
42
~~~
43
44
45
23
~~~
{: .output}
46

47
48
49
50
51
This is great but not very interesting.
To do anything useful with data, we need to assign its value to a _variable_.
In Python, we can [assign]({{ page.root }}/reference/#assign) a value to a
[variable]({{ page.root }}/reference/#variable), using the equals sign `=`.
For example, to assign value `60` to a variable `weight_kg`, we would execute:
52

53
~~~
54
weight_kg = 60
Greg Wilson's avatar
Greg Wilson committed
55
~~~
56
{: .language-python}
57

58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
From now on, whenever we use `weight_kg`, Python will substitute the value we assigned to
it. In essence, **a variable is just a name for a value**.

In Python, variable names:

 - must begin with a letter, and
 - are [case sensitive]({{ page.root }}/reference/#case-sensitive).

This means that, for example:
 - `weight0` is a valid variable name, whereas `0weight` is not
 - `weight` and `Weight` are different variables

## Types of data
Python knows various types of data. The most common ones are:

* integer numbers
* floating point numbers, and
* strings.

In the example above, variabe `weight_kg` has an integer value of `60`.
To create a variable with a floating point value, we can execute:

~~~
weight_kg = 60.0
~~~
{: .language-python}

And to create a string we simply have to add single or double quotes around some text, for example:

~~~
weight_kg_text = 'weight in kilograms:'
~~~
{: .language-python}
91

92
93
## Using Variables in Python
To display the value of a variable to the screen in Python, we can use `print` function:
94

95
~~~
96
print(weight_kg)
Greg Wilson's avatar
Greg Wilson committed
97
~~~
98
{: .language-python}
99
100

~~~
101
60
Greg Wilson's avatar
Greg Wilson committed
102
~~~
103
{: .output}
104

105
106
107
108
109
110
111
112
113
114
115
116
We can display multiple things at once using only one `print` command:

~~~
print(weight_kg_text, weight_kg)
~~~
{: .language-python}
~~~
weight in kilograms: 60
~~~
{: .output}

Moreover, we can do arithmetics with variables right inside the `print` function:
117

118
~~~
119
print('weight in pounds:', 2.2 * weight_kg)
Greg Wilson's avatar
Greg Wilson committed
120
~~~
121
{: .language-python}
122
123

~~~
124
weight in pounds: 132.0
Greg Wilson's avatar
Greg Wilson committed
125
~~~
126
{: .output}
127

128
129
130
131
132
The above command, however, did not change the value of `weight_kg`:
~~~
print(weight_kg)
~~~
{: .language-python}
jstapleton's avatar
jstapleton committed
133

134
135
136
137
138
139
~~~
60
~~~
{: .output}

To change variable's value, we have to assign it a new one:
140

141
~~~
142
weight_kg = 65.0
143
print('weight in kilograms is now:', weight_kg)
Greg Wilson's avatar
Greg Wilson committed
144
~~~
145
{: .language-python}
146
147

~~~
148
weight in kilograms is now: 65.0
Greg Wilson's avatar
Greg Wilson committed
149
~~~
150
{: .output}
151

152
153
A variable is analoguous to a sticky note with a name written on it:
assigning value to a variable is like putting that sticky note on a particular value.
154

155
![Variables as Sticky Notes](../fig/python-sticky-note-variables-01.svg)
156

157
158
This means that assigning a value to one variable does **not** change the values of other variables.
For example, let's store the subject's weight in pounds in its own variable:
159

160
~~~
161
# There are 2.2 pounds per kilogram
Greg Wilson's avatar
Greg Wilson committed
162
weight_lb = 2.2 * weight_kg
163
print(weight_kg_text, weight_kg, 'and in pounds:', weight_lb)
Greg Wilson's avatar
Greg Wilson committed
164
~~~
165
{: .language-python}
166
167

~~~
168
weight in kilograms: 65.0 and in pounds: 143.0
Greg Wilson's avatar
Greg Wilson committed
169
~~~
170
{: .output}
171

172
![Creating Another Variable](../fig/python-sticky-note-variables-02.svg)
173

174
Let's now change `weight_kg`:
175

176
~~~
Greg Wilson's avatar
Greg Wilson committed
177
weight_kg = 100.0
178
print('weight in kilograms is now:', weight_kg, 'and weight in pounds is still:', weight_lb)
Greg Wilson's avatar
Greg Wilson committed
179
~~~
180
{: .language-python}
181
182

~~~
183
weight in kilograms is now: 100.0 and weight in pounds is still: 143.0
Greg Wilson's avatar
Greg Wilson committed
184
~~~
185
{: .output}
186

187
![Updating a Variable](../fig/python-sticky-note-variables-03.svg)
188

Brian Jackson's avatar
Brian Jackson committed
189
Since `weight_lb` doesn't remember where its value came from,
190
it isn't automatically updated when `weight_kg` changes.
191
192


Benjamin Laken's avatar
Benjamin Laken committed
193

194
195
196
197
Words are useful, but what's more useful are the sentences and stories we build with them.
Similarly, while a lot of powerful, general tools are built into languages like Python,
specialized tools built up from these basic units live in
[libraries]({{ page.root }}/reference/#library)
devendra1810's avatar
devendra1810 committed
198
199
that can be called upon when needed.

200
201
202
203
204
205
## Loading data into Python
In order to load our inflammation data, we need to access
([import]({{ page.root }}/reference/#import) in Python terminology) a library called
[NumPy](http://docs.scipy.org/doc/numpy/ "NumPy Documentation").  In general you should use this
library if you want to do fancy things with numbers, especially if you have matrices or arrays.  We
can import NumPy using:
devendra1810's avatar
devendra1810 committed
206
207
208
209

~~~
import numpy
~~~
210
{: .language-python}
devendra1810's avatar
devendra1810 committed
211

212
213
214
215
216
217
Importing a library is like getting a piece of lab equipment out of a storage locker and setting it
up on the bench. Libraries provide additional functionality to the basic Python package, much like
a new piece of equipment adds functionality to a lab space. Just like in the lab, importing too
many libraries can sometimes complicate and slow down your programs - so we only import what we
need for each program. Once we've imported the library, we can ask the library to read our data
file for us:
devendra1810's avatar
devendra1810 committed
218
219
220
221

~~~
numpy.loadtxt(fname='inflammation-01.csv', delimiter=',')
~~~
222
{: .language-python}
devendra1810's avatar
devendra1810 committed
223
224
225
226
227
228
229
230
231
232
233
234

~~~
array([[ 0.,  0.,  1., ...,  3.,  0.,  0.],
       [ 0.,  1.,  2., ...,  1.,  0.,  1.],
       [ 0.,  1.,  1., ...,  2.,  1.,  1.],
       ...,
       [ 0.,  1.,  1., ...,  1.,  1.,  1.],
       [ 0.,  0.,  0., ...,  0.,  2.,  0.],
       [ 0.,  0.,  1., ...,  1.,  1.,  0.]])
~~~
{: .output}

Trevor Bekolay's avatar
Trevor Bekolay committed
235
The expression `numpy.loadtxt(...)` is a [function call]({{ page.root }}/reference/#function-call)
236
237
238
239
that asks Python to run the [function]({{ page.root }}/reference/#function) `loadtxt` which
belongs to the `numpy` library. This [dotted notation]({{ page.root }}/reference/#dotted-notation)
is used everywhere in Python: the thing that appears before the dot contains the thing that
appears after.
Brian Jackson's avatar
Brian Jackson committed
240

Brian Jackson's avatar
Brian Jackson committed
241
As an example, John Smith is the John that belongs to the Smith family,
242
We could use the dot notation to write his name `smith.john`,
Brian Jackson's avatar
Brian Jackson committed
243
just as `loadtxt` is a function that belongs to the `numpy` library.
devendra1810's avatar
devendra1810 committed
244

245
246
247
248
`numpy.loadtxt` has two [parameters]({{ page.root }}/reference/#parameter): the name of the file
we want to read and the [delimiter]({{ page.root }}/reference/#delimiter) that separates values on
a line. These both need to be character strings (or [strings]({{ page.root }}/reference/#string)
for short), so we put them in quotes.
devendra1810's avatar
devendra1810 committed
249
250
251
252
253
254
255
256
257
258
259
260

Since we haven't told it to do anything else with the function's output,
the notebook displays it.
In this case,
that output is the data we just loaded.
By default,
only a few rows and columns are shown
(with `...` to omit elements when displaying big arrays).
To save space,
Python displays numbers as `1.` instead of `1.0`
when there's nothing interesting after the decimal point.

Brian Jackson's avatar
Brian Jackson committed
261
Our call to `numpy.loadtxt` read our file
devendra1810's avatar
devendra1810 committed
262
263
but didn't save the data in memory.
To do that,
264
265
266
we need to assign the array to a variable. Just as we can assign a single value to a variable, we
can also assign an array of values to a variable using the same syntax.  Let's re-run
`numpy.loadtxt` and save the returned data:
267

268
~~~
Greg Wilson's avatar
Greg Wilson committed
269
270
data = numpy.loadtxt(fname='inflammation-01.csv', delimiter=',')
~~~
271
{: .language-python}
272

273
This statement doesn't produce any output because we've assigned the output to the variable `data`.
Brian Jackson's avatar
Brian Jackson committed
274
If we want to check that the data have been loaded,
275
we can print the variable's value:
276

277
~~~
278
print(data)
Greg Wilson's avatar
Greg Wilson committed
279
~~~
280
{: .language-python}
281
282

~~~
Greg Wilson's avatar
Greg Wilson committed
283
[[ 0.  0.  1. ...,  3.  0.  0.]
284
285
 [ 0.  1.  2. ...,  1.  0.  1.]
 [ 0.  1.  1. ...,  2.  1.  1.]
286
 ...,
287
288
289
 [ 0.  1.  1. ...,  1.  1.  1.]
 [ 0.  0.  0. ...,  0.  2.  0.]
 [ 0.  0.  1. ...,  1.  1.  0.]]
Greg Wilson's avatar
Greg Wilson committed
290
~~~
291
{: .output}
292

Brian Jackson's avatar
Brian Jackson committed
293
294
Now that the data are in memory,
we can manipulate them.
295
First,
296
let's ask what [type]({{ page.root }}/reference/#type) of thing `data` refers to:
297

298
~~~
299
print(type(data))
Greg Wilson's avatar
Greg Wilson committed
300
~~~
301
{: .language-python}
302
303

~~~
304
<class 'numpy.ndarray'>
Greg Wilson's avatar
Greg Wilson committed
305
~~~
306
{: .output}
307

308
The output tells us that `data` currently refers to
Brian Jackson's avatar
Brian Jackson committed
309
an N-dimensional array, the functionality for which is provided by the NumPy library.
310
These data correspond to arthritis patients' inflammation.
Brian Jackson's avatar
Brian Jackson committed
311
The rows are the individual patients, and the columns
312
313
are their daily inflammation measurements.

314
> ## Data Type
315
316
>
> A Numpy array contains one or more elements
Brian Jackson's avatar
Brian Jackson committed
317
318
319
320
> of the same type. The `type` function will only tell you that
> a variable is a NumPy array but won't tell you the type of
> thing inside the array.
> We can find out the type
321
322
> of the data contained in the NumPy array.
>
323
> ~~~
324
325
> print(data.dtype)
> ~~~
326
> {: .language-python}
327
328
>
> ~~~
329
330
> dtype('float64')
> ~~~
331
> {: .output}
332
333
>
> This tells us that the NumPy array's elements are
334
> [floating-point numbers]({{ page.root }}/reference/#floating-point number).
335
{: .callout}
336

Brian Jackson's avatar
Brian Jackson committed
337
With the following command, we can see the array's [shape]({{ page.root }}/reference/#shape):
338

339
~~~
340
print(data.shape)
Greg Wilson's avatar
Greg Wilson committed
341
~~~
342
{: .language-python}
343
344

~~~
Greg Wilson's avatar
Greg Wilson committed
345
346
(60, 40)
~~~
347
{: .output}
348

349
350
The output tells us that the `data` array variable contains 60 rows and 40 columns. When we
created the variable `data` to store our arthritis data, we didn't just create the array; we also
351
created information about the array, called [members]({{ page.root }}/reference/#member) or
352
353
354
355
attributes. This extra information describes `data` in the same way an adjective describes a noun.
`data.shape` is an attribute of `data` which describes the dimensions of `data`. We use the same
dotted notation for the attributes of variables that we use for the functions in libraries because
they have the same part-and-whole relationship.
356

357
358
359
360
If we want to get a single number from the array, we must provide an
[index]({{ page.root }}/reference/#index) in square brackets after the variable name, just as we
do in math when referring to an element of a matrix.  Our inflammation data has two dimensions, so
we will need to use two indices to refer to one specific value:
361

362
~~~
363
print('first value in data:', data[0, 0])
Greg Wilson's avatar
Greg Wilson committed
364
~~~
365
{: .language-python}
366
367

~~~
Greg Wilson's avatar
Greg Wilson committed
368
369
first value in data: 0.0
~~~
370
{: .output}
371

372
~~~
373
print('middle value in data:', data[30, 20])
Greg Wilson's avatar
Greg Wilson committed
374
~~~
375
{: .language-python}
376
377

~~~
Greg Wilson's avatar
Greg Wilson committed
378
379
middle value in data: 13.0
~~~
380
{: .output}
381

382
383
The expression `data[30, 20]` accesses the element at row 30, column 20. While this expression may
not surprise you,
384
 `data[0, 0]` might.
Brian Jackson's avatar
Brian Jackson committed
385
Programming languages like Fortran, MATLAB and R start counting at 1
386
387
because that's what human beings have done for thousands of years.
Languages in the C family (including C++, Java, Perl, and Python) count from 0
388
389
390
391
392
because it represents an offset from the first value in the array (the second
value is offset by one index from the first value). This is closer to the way
that computers represent arrays (if you are interested in the historical
reasons behind counting indices from zero, you can read
[Mike Hoye's blog post](http://exple.tive.org/blarg/2013/10/22/citation-needed/)).
393
As a result,
Greg Wilson's avatar
Greg Wilson committed
394
if we have an M×N array in Python,
395
396
397
398
399
400
its indices go from 0 to M-1 on the first axis
and 0 to N-1 on the second.
It takes a bit of getting used to,
but one way to remember the rule is that
the index is how many steps we have to take from the start to get the item we want.

401
402
![Zero Index](../fig/python-zero-index.png)

403
> ## In the Corner
404
405
406
407
>
> What may also surprise you is that when Python displays an array,
> it shows the element with index `[0, 0]` in the upper left corner
> rather than the lower left.
Brian Jackson's avatar
Brian Jackson committed
408
> This is consistent with the way mathematicians draw matrices
409
> but different from the Cartesian coordinates.
410
> The indices are (row, column) instead of (column, row) for the same reason,
411
> which can be confusing when plotting data.
412
{: .callout}
413

414
## Slicing data
415
416
417
418
An index like `[30, 20]` selects a single element of an array,
but we can select whole sections as well.
For example,
we can select the first ten days (columns) of values
419
for the first four patients (rows) like this:
420

421
~~~
422
print(data[0:4, 0:10])
Greg Wilson's avatar
Greg Wilson committed
423
~~~
424
{: .language-python}
425
426

~~~
Greg Wilson's avatar
Greg Wilson committed
427
[[ 0.  0.  1.  3.  1.  2.  4.  7.  8.  3.]
428
429
430
 [ 0.  1.  2.  1.  2.  1.  3.  2.  2.  6.]
 [ 0.  1.  1.  3.  3.  2.  6.  2.  5.  9.]
 [ 0.  0.  2.  0.  4.  2.  2.  1.  6.  7.]]
Greg Wilson's avatar
Greg Wilson committed
431
~~~
432
{: .output}
433

434
435
436
The [slice]({{ page.root }}/reference/#slice) `0:4` means, "Start at index 0 and go up to, but not
including, index 4."Again, the up-to-but-not-including takes a bit of getting used to, but the
rule is that the difference between the upper and lower bounds is the number of values in the slice.
437
438

We don't have to start slices at 0:
439

440
~~~
441
print(data[5:10, 0:10])
Greg Wilson's avatar
Greg Wilson committed
442
~~~
443
{: .language-python}
444
445

~~~
Greg Wilson's avatar
Greg Wilson committed
446
[[ 0.  0.  1.  2.  2.  4.  2.  1.  6.  4.]
447
448
449
450
 [ 0.  0.  2.  2.  4.  2.  2.  5.  5.  8.]
 [ 0.  0.  1.  2.  3.  1.  2.  3.  5.  3.]
 [ 0.  0.  0.  3.  1.  5.  6.  5.  5.  8.]
 [ 0.  1.  1.  2.  1.  3.  5.  3.  5.  8.]]
Greg Wilson's avatar
Greg Wilson committed
451
~~~
452
{: .output}
453

454
455
456
457
We also don't have to include the upper and lower bound on the slice.  If we don't include the lower
bound, Python uses 0 by default; if we don't include the upper, the slice runs to the end of the
axis, and if we don't include either (i.e., if we just use ':' on its own), the slice includes
everything:
458

459
~~~
Greg Wilson's avatar
Greg Wilson committed
460
small = data[:3, 36:]
461
462
print('small is:')
print(small)
Greg Wilson's avatar
Greg Wilson committed
463
~~~
464
{: .language-python}
Brian Jackson's avatar
Brian Jackson committed
465
The above example selects rows 0 through 2 and columns 36 through to the end of the array.
466
467

~~~
Greg Wilson's avatar
Greg Wilson committed
468
small is:
469
470
471
[[ 2.  3.  0.  0.]
 [ 1.  1.  0.  1.]
 [ 2.  2.  1.  1.]]
Greg Wilson's avatar
Greg Wilson committed
472
~~~
473
{: .output}
474

475
476
477
Arrays also know how to perform common mathematical operations on their values.  The simplest
operations with data are arithmetic: addition, subtraction, multiplication, and division.  When you
do such operations on arrays, the operation is done element-by-element.  Thus:
478

479
~~~
Greg Wilson's avatar
Greg Wilson committed
480
481
doubledata = data * 2.0
~~~
482
{: .language-python}
483

Greg Wilson's avatar
Greg Wilson committed
484
will create a new array `doubledata`
Brian Jackson's avatar
Brian Jackson committed
485
each elements of which is twice the value of the corresponding element in `data`:
486

487
~~~
488
489
490
491
print('original:')
print(data[:3, 36:])
print('doubledata:')
print(doubledata[:3, 36:])
Greg Wilson's avatar
Greg Wilson committed
492
~~~
493
{: .language-python}
494
495

~~~
Greg Wilson's avatar
Greg Wilson committed
496
original:
497
498
499
500
501
502
503
[[ 2.  3.  0.  0.]
 [ 1.  1.  0.  1.]
 [ 2.  2.  1.  1.]]
doubledata:
[[ 4.  6.  0.  0.]
 [ 2.  2.  0.  2.]
 [ 4.  4.  2.  2.]]
Greg Wilson's avatar
Greg Wilson committed
504
~~~
505
{: .output}
506

507
508
509
If, instead of taking an array and doing arithmetic with a single value (as above), you did the
arithmetic operation with another array of the same shape, the operation will be done on
corresponding elements of the two arrays.  Thus:
510

511
~~~
Greg Wilson's avatar
Greg Wilson committed
512
513
tripledata = doubledata + data
~~~
514
{: .language-python}
515

516
517
518
will give you an array where `tripledata[0,0]` will equal `doubledata[0,0]` plus `data[0,0]`,
and so on for all other elements of the arrays.

519
~~~
520
521
print('tripledata:')
print(tripledata[:3, 36:])
Greg Wilson's avatar
Greg Wilson committed
522
~~~
523
{: .language-python}
524
525

~~~
Greg Wilson's avatar
Greg Wilson committed
526
tripledata:
527
528
529
[[ 6.  9.  0.  0.]
 [ 3.  3.  0.  3.]
 [ 6.  6.  3.  3.]]
Greg Wilson's avatar
Greg Wilson committed
530
~~~
531
{: .output}
532

533
534
535
Often, we want to do more than add, subtract, multiply, and divide array elements.  NumPy knows how
to do more complex operations, too.  If we want to find the average inflammation for all patients on
all days, for example, we can ask NumPy to compute `data`'s mean value:
536

537
~~~
538
print(numpy.mean(data))
Greg Wilson's avatar
Greg Wilson committed
539
~~~
540
{: .language-python}
541
542

~~~
Greg Wilson's avatar
Greg Wilson committed
543
544
6.14875
~~~
545
{: .output}
546

547
548
`mean` is a [function]({{ page.root }}/reference/#function) that takes
an array as an [argument]({{ page.root }}/reference/#argument).
549

550
> ## Not All Functions Have Input
551
552
553
>
> Generally, a function uses inputs to produce outputs.
> However, some functions produce outputs without
554
555
> needing any input. For example, checking the current time
> doesn't require any input.
556
>
557
> ~~~
558
559
> import time
> print(time.ctime())
560
> ~~~
561
> {: .language-python}
562
563
>
> ~~~
564
> 'Sat Mar 26 13:07:33 2016'
565
> ~~~
566
> {: .output}
567
568
569
570
>
> For functions that don't take in any arguments,
> we still need parentheses (`()`)
> to tell Python to go and do something for us.
571
{: .callout}
572
573
574

NumPy has lots of useful functions that take an array as input.
Let's use three of those functions to get some descriptive values about the dataset.
575
576
We'll also use multiple assignment,
a convenient Python feature that will enable us to do this all in one line.
577

578
~~~
579
maxval, minval, stdval = numpy.max(data), numpy.min(data), numpy.std(data)
580

Alistair Walsh's avatar
Alistair Walsh committed
581
582
583
print('maximum inflammation:', maxval)
print('minimum inflammation:', minval)
print('standard deviation:', stdval)
Greg Wilson's avatar
Greg Wilson committed
584
~~~
585
{: .language-python}
586
587
588
589

Here we've assigned the return value from `numpy.max(data)` to the variable `maxval`, the value
from `numpy.min(data)` to `minval`, and so on.

590
~~~
Greg Wilson's avatar
Greg Wilson committed
591
maximum inflammation: 20.0
592
593
minimum inflammation: 0.0
standard deviation: 4.61383319712
Greg Wilson's avatar
Greg Wilson committed
594
~~~
595
{: .output}
596

597
> ## Mystery Functions in IPython
598
>
599
> How did we know what functions NumPy has and how to use them?
Brian Jackson's avatar
Brian Jackson committed
600
> If you are working in the IPython/Jupyter Notebook, there is an easy way to find out.
Dustin Lang's avatar
Dustin Lang committed
601
> If you type the name of something followed by a dot, then you can use tab completion
602
> (e.g. type `numpy.` and then press tab)
Brian Jackson's avatar
Brian Jackson committed
603
604
> to see a list of all functions and attributes that you can use. After selecting one, you
> can also add a question mark (e.g. `numpy.cumprod?`), and IPython will return an
605
> explanation of the method! This is the same as doing `help(numpy.cumprod)`.
606
{: .callout}
607
608

When analyzing data, though,
Brian Jackson's avatar
Brian Jackson committed
609
610
611
we often want to look at variations in statistical values,
such as the maximum inflammation per patient
or the average inflammation per day.
612
One way to do this is to create a new temporary array of the data we want,
613
then ask it to do the calculation:
614

615
~~~
Dustin Lang's avatar
Dustin Lang committed
616
patient_0 = data[0, :] # 0 on the first axis (rows), everything on the second (columns)
617
print('maximum inflammation for patient 0:', patient_0.max())
Greg Wilson's avatar
Greg Wilson committed
618
~~~
619
{: .language-python}
620
621

~~~
Greg Wilson's avatar
Greg Wilson committed
622
623
maximum inflammation for patient 0: 18.0
~~~
624
{: .output}
625

626
Everything in a line of code following the '#' symbol is a
627
[comment]({{ page.root }}/reference/#comment) that is ignored by Python.
628
Comments allow programmers to leave explanatory notes for other
jstapleton's avatar
jstapleton committed
629
630
programmers or their future selves.

631
We don't actually need to store the row in a variable of its own.
632
Instead, we can combine the selection and the function call:
633

634
~~~
635
print('maximum inflammation for patient 2:', numpy.max(data[2, :]))
Greg Wilson's avatar
Greg Wilson committed
636
~~~
637
{: .language-python}
638
639

~~~
Greg Wilson's avatar
Greg Wilson committed
640
641
maximum inflammation for patient 2: 19.0
~~~
642
{: .output}
643

644
What if we need the maximum inflammation for each patient over all days (as in the
Brian Jackson's avatar
Brian Jackson committed
645
next diagram on the left) or the average for each day (as in the
646
647
diagram on the right)? As the diagram below shows, we want to perform the
operation across an axis:
648

649
![Operations Across Axes](../fig/python-operations-across-axes.png)
650

Brian Jackson's avatar
Brian Jackson committed
651
To support this functionality,
652
most array functions allow us to specify the axis we want to work on.
653
If we ask for the average across axis 0 (rows in our 2D example),
654
we get:
655

656
~~~
657
print(numpy.mean(data, axis=0))
Greg Wilson's avatar
Greg Wilson committed
658
~~~
659
{: .language-python}
660
661

~~~
Greg Wilson's avatar
Greg Wilson committed
662
[  0.           0.45         1.11666667   1.75         2.43333333   3.15
663
664
665
666
667
668
669
   3.8          3.88333333   5.23333333   5.51666667   5.95         5.9
   8.35         7.73333333   8.36666667   9.5          9.58333333
  10.63333333  11.56666667  12.35        13.25        11.96666667
  11.03333333  10.16666667  10.           8.66666667   9.15         7.25
   7.33333333   6.58333333   6.06666667   5.95         5.11666667   3.6
   3.3          3.56666667   2.48333333   1.5          1.13333333
   0.56666667]
Greg Wilson's avatar
Greg Wilson committed
670
~~~
671
{: .output}
672

673
674
As a quick check,
we can ask this array what its shape is:
675

676
~~~
677
print(numpy.mean(data, axis=0).shape)
Greg Wilson's avatar
Greg Wilson committed
678
~~~
679
{: .language-python}
680
681

~~~
Greg Wilson's avatar
Greg Wilson committed
682
683
(40,)
~~~
684
{: .output}
685

Greg Wilson's avatar
Greg Wilson committed
686
The expression `(40,)` tells us we have an N×1 vector,
687
so this is the average inflammation per day for all patients.
688
If we average across axis 1 (columns in our 2D example), we get:
689

690
~~~
691
print(numpy.mean(data, axis=1))
Greg Wilson's avatar
Greg Wilson committed
692
~~~
693
{: .language-python}
694
695

~~~
Greg Wilson's avatar
Greg Wilson committed
696
[ 5.45   5.425  6.1    5.9    5.55   6.225  5.975  6.65   6.625  6.525
697
698
699
700
701
  6.775  5.8    6.225  5.75   5.225  6.3    6.55   5.7    5.85   6.55
  5.775  5.825  6.175  6.1    5.8    6.425  6.05   6.025  6.175  6.55
  6.175  6.35   6.725  6.125  7.075  5.725  5.925  6.15   6.075  5.75
  5.975  5.725  6.3    5.9    6.75   5.925  7.225  6.15   5.95   6.275  5.7
  6.1    6.825  5.975  6.725  5.7    6.25   6.4    7.05   5.9  ]
Greg Wilson's avatar
Greg Wilson committed
702
~~~
703
{: .output}
704

705
706
which is the average inflammation per patient across all days.

707
708
709
710
711
712
713
## Visualizing data
The mathematician Richard Hamming once said, "The purpose of computing is insight, not numbers," and
the best way to develop insight is often to visualize data.  Visualization deserves an entire
lecture of its own, but we can explore a few features of Python's `matplotlib` library here.  While
there is no official plotting library, `matplotlib` is the _de facto_ the standard.  First, we will
import the `pyplot` module from `matplotlib` and use two of its functions to create and display a
heat map of our data:
714

715
~~~
716
import matplotlib.pyplot
717
image = matplotlib.pyplot.imshow(data)
718
matplotlib.pyplot.show()
Greg Wilson's avatar
Greg Wilson committed
719
~~~
720
{: .language-python}
721

722
![Heatmap of the Data](../fig/01-numpy_71_0.png)
723

724
725
Blue pixels in this heat map represent low values, while yellow pixels represent high values.  As we
can see, inflammation rises and falls over a 40-day period.
726

727
> ## Some IPython Magic
728
729
730
731
>
> If you're using an IPython / Jupyter notebook,
> you'll need to execute the following command
> in order for your matplotlib images to appear
Damien Irving's avatar
Damien Irving committed
732
> in the notebook when `show()` is called:
Damien Irving's avatar
Damien Irving committed
733
>
734
> ~~~
735
> %matplotlib inline
Damien Irving's avatar
Damien Irving committed
736
> ~~~
737
> {: .language-python}
738
>
739
740
> The `%` indicates an IPython magic function -
> a function that is only valid within the notebook environment.
741
> Note that you only have to execute this function once per notebook.
742
{: .callout}
743

744
Let's take a look at the average inflammation over time:
745

746
~~~
747
ave_inflammation = numpy.mean(data, axis=0)
748
ave_plot = matplotlib.pyplot.plot(ave_inflammation)
749
matplotlib.pyplot.show()
Greg Wilson's avatar
Greg Wilson committed
750
~~~
751
{: .language-python}
752

753
![Average Inflammation Over Time](../fig/01-numpy_73_0.png)
754

755
756
757
758
Here, we have put the average per day across all patients in the variable `ave_inflammation`, then
asked `matplotlib.pyplot` to create and display a line graph of those values.  The result is a
roughly linear rise and fall, which is suspicious: we might instead expect a sharper rise and slower
fall.  Let's have a look at two other statistics:
759

760
~~~
761
max_plot = matplotlib.pyplot.plot(numpy.max(data, axis=0))
762
matplotlib.pyplot.show()
Greg Wilson's avatar
Greg Wilson committed
763
~~~
764
{: .language-python}
765

766
![Maximum Value Along The First Axis](../fig/01-numpy_75_1.png)
Greg Wilson's avatar
Greg Wilson committed
767

768
~~~
769
min_plot = matplotlib.pyplot.plot(numpy.min(data, axis=0))
770
matplotlib.pyplot.show()
Greg Wilson's avatar
Greg Wilson committed
771
~~~
772
{: .language-python}
773

774
![Minimum Value Along The First Axis](../fig/01-numpy_75_3.png)
775

776
777
778
779
The maximum value rises and falls smoothly, while the minimum seems to be a step function.  Neither
trend seems particularly likely, so either there's a mistake in our calculations or something is
wrong with our data.  This insight would have been difficult to reach by examining the numbers
themselves without visualization tools.
780

781
### Grouping plots
782
You can group similar plots in a single figure using subplots.
783
This script below uses a number of new commands. The function `matplotlib.pyplot.figure()`
784
creates a space into which we will place all of our plots. The parameter `figsize`
785
tells Python how big to make this space. Each subplot is placed into the figure using
786
787
788
its `add_subplot` [method]({{ page.root }}/reference/#method). The `add_subplot` method takes 3
parameters. The first denotes how many total rows of subplots there are, the second parameter
refers to the total number of subplot columns, and the final parameter denotes which subplot
789
790
791
your variable is referencing (left-to-right, top-to-bottom). Each subplot is stored in a
different variable (`axes1`, `axes2`, `axes3`). Once a subplot is created, the axes can
be titled using the `set_xlabel()` command (or `set_ylabel()`).
792
Here are our three plots side by side:
793

794
~~~
795
796
import numpy
import matplotlib.pyplot
797

798
data = numpy.loadtxt(fname='inflammation-01.csv', delimiter=',')
799

800
fig = matplotlib.pyplot.figure(figsize=(10.0, 3.0))
801

802
803
804
axes1 = fig.add_subplot(1, 3, 1)
axes2 = fig.add_subplot(1, 3, 2)
axes3 = fig.add_subplot(1, 3, 3)