# Data: Pivoting Data#

Purpose: Data is easiest to use when it is tidy. In fact, grama is specifically designed to use tidy data. But not all data we’ll encounter is tidy! To that end, in this exercise we’ll learn how to tidy our data by pivoting.

As a result of learning how to quickly tidy data, you’ll vastly expand the set of datasets you can analyze. Rather than fighting with data, you’ll be able to quickly wrangle and extract insights.

## Setup#

import grama as gr
DF = gr.Intention()
%matplotlib inline

# For assertion
from pandas.api.types import is_integer_dtype


# Tidy Data#

Tidy Data is a very simple—but very powerful—concept for structuring a dataset.

Artwork by @allison_horst

## Tidy Data: Definition#

A tidy dataset has three properties:

• each variable forms a column

• each observation forms a row

• each cell is a single measurement

As an example, the following dataset is tidy:

from grama.data import df_stang

thick alloy E mu ang
0 0.022 al_24st 10600 0.321 0
1 0.022 al_24st 10600 0.323 0
2 0.032 al_24st 10400 0.329 0
3 0.032 al_24st 10300 0.319 0
4 0.064 al_24st 10500 0.323 0

The observations are all measured material properties taken at a particular angle (with respect to the direction in which the specimens were rolled). Each column reports values for just one variable, each row corresponds to a single observation, and every cell reports just one measurement.

However, the following form of the same dataset is not tidy:

from grama.data import df_stang_wide
df_stang_wide

thick E_00 mu_00 E_45 mu_45 E_90 mu_90 alloy
0 0.022 10600 0.321 10700 0.329 10500 0.310 al_24st
1 0.022 10600 0.323 10500 0.331 10700 0.323 al_24st
2 0.032 10400 0.329 10400 0.318 10300 0.322 al_24st
3 0.032 10300 0.319 10500 0.326 10400 0.330 al_24st
4 0.064 10500 0.323 10400 0.331 10400 0.327 al_24st
5 0.064 10700 0.328 10500 0.328 10500 0.320 al_24st
6 0.081 10000 0.315 10000 0.320 9900 0.314 al_24st
7 0.081 10100 0.312 9900 0.312 10000 0.316 al_24st
8 0.081 10000 0.311 -1 -1.000 9900 0.314 al_24st

This dataset is not tidy: The angle of each measurement 00, 45, 90 is a variable, but these numerical values are expressed as column names. Put differently, some of the values are not in cells, but rather in the column names.

## Why tidy data?#

Tidy data makes analysis easier. Putting our data in tidy form means we can use a consistent set of tools to work with any dataset.

Artwork by @allison_horst

Note that untidy data is not bad data; untidy data are simply harder to work with when doing data analysis. Data often come in untidy form when they are reported, say in a paper or a presentation. For instance, the wide form of the Stang et al. dataset can easily fit on one page:

df_stang_wide

thick E_00 mu_00 E_45 mu_45 E_90 mu_90 alloy
0 0.022 10600 0.321 10700 0.329 10500 0.310 al_24st
1 0.022 10600 0.323 10500 0.331 10700 0.323 al_24st
2 0.032 10400 0.329 10400 0.318 10300 0.322 al_24st
3 0.032 10300 0.319 10500 0.326 10400 0.330 al_24st
4 0.064 10500 0.323 10400 0.331 10400 0.327 al_24st
5 0.064 10700 0.328 10500 0.328 10500 0.320 al_24st
6 0.081 10000 0.315 10000 0.320 9900 0.314 al_24st
7 0.081 10100 0.312 9900 0.312 10000 0.316 al_24st
8 0.081 10000 0.311 -1 -1.000 9900 0.314 al_24st

However, the tidy form of the same dataset is far less compact:

df_stang

thick alloy E mu ang
0 0.022 al_24st 10600 0.321 0
1 0.022 al_24st 10600 0.323 0
2 0.032 al_24st 10400 0.329 0
3 0.032 al_24st 10300 0.319 0
4 0.064 al_24st 10500 0.323 0
... ... ... ... ... ...
71 0.064 al_24st 10400 0.327 90
72 0.064 al_24st 10500 0.320 90
73 0.081 al_24st 9900 0.314 90
74 0.081 al_24st 10000 0.316 90
75 0.081 al_24st 9900 0.314 90

76 rows × 5 columns

## Exercises#

Let’s practice identifying tidy and untidy data.

### q1 Identify#

Inspect the following dataset; answer the questions under observations below.

## TASK: No need to edit; run and inspect
df_cases = gr.df_make(
country=["FR", "DE", "US"],
year2011=[7000, 5800, 15000],
year2012=[6900, 6000, 14000],
year2013=[7000, 6200, 13000],
)
df_cases

country year2011 year2012 year2013
0 FR 7000 6900 7000
1 DE 5800 6000 6200
2 US 15000 14000 13000

Observations

• What are the variables in this dataset?

• Country, year, and some unknown quantity (n, count, etc.)

• Is this dataset tidy? Why or why not?

• No; the year values are in the column names.

### q2 Identify#

Inspect the following dataset; answer the questions under observations below.

## TASK: No need to edit; run and inspect
df_alloys1 = gr.df_make(
thick=[0.022, 0.022, 0.032, 0.032],
E_00=[10600, 10600, 10400, 10300],
mu_00=[0.321, 0.323, 0.329, 0.319],
E_45=[10700, 10500, 10400, 10500],
mu_45=[0.329, 0.331, 0.318, 0.326],
rep=[1, 2, 1, 2],
)
df_alloys1

thick E_00 mu_00 E_45 mu_45 rep
0 0.022 10600 0.321 10700 0.329 1
1 0.022 10600 0.323 10500 0.331 2
2 0.032 10400 0.329 10400 0.318 1
3 0.032 10300 0.319 10500 0.326 2

Observations

• What are the variables in this dataset?

• Thickness thick, elasticity E, poisson’s ratio mu, angle (in column names), replication rep

• Is this dataset tidy? Why or why not?

• No; the angle values are in the column names.

### q3 Identify#

Inspect the following dataset; answer the questions under observations below.

## TASK: No need to edit; run and inspect
df_alloys2 = gr.df_make(
thick=[0.022, 0.022, 0.032, 0.032],
var=["E", "mu", "E", "mu"],
value=[10700, 0.321, 10500, 0.323],
rep=[1, 1, 2, 2],
angle=[0, 0, 0, 0],
)
df_alloys2

thick var value rep angle
0 0.022 E 10700.000 1 0
1 0.022 mu 0.321 1 0
2 0.032 E 10500.000 2 0
3 0.032 mu 0.323 2 0

Observations

• What are the variables in this dataset?

• Thickness thick, elasticity E, poisson’s ratio mu, angle, replication rep

• Is this dataset tidy? Why or why not?

• No; the column value contains values of two different variables E and mu.

# Pivoting Data#

The untidy datasets above fail to be tidy because they have the wrong shape; we can tidy these datasets by pivoting the data. There are just two pivots we need to learn about: tf_pivot_longer() and tf_pivot_wider().

## Pivot Longer#

Let’s take another look at the df_cases example dataset:

## NOTE: No need to edit
df_cases

country year2011 year2012 year2013
0 FR 7000 6900 7000
1 DE 5800 6000 6200
2 US 15000 14000 13000

This dataset is too wide; the column names year2011,year2012,year2013 should really be numbers inside a single year column. We can pivot longer to move from a wide structure to a longer one:

## NOTE: No need to edit
(
df_cases
>> gr.tf_pivot_longer(
columns=["year2011", "year2012", "year2013"],
names_to="year",
values_to="count",
)
)

country year count
0 FR year2011 7000
1 DE year2011 5800
2 US year2011 15000
3 FR year2012 6900
4 DE year2012 6000
5 US year2012 14000
6 FR year2013 7000
7 DE year2013 6200
8 US year2013 13000

Note what we had to provide as arguments to gr.tf_pivot_longer():

• columns specifies the columns to involve in the pivoting

• names_to specifies what new column will contain the previous column names

• value_to specifies what new column will contain the previous cell values

Often, a pivot alone is not enough to fully clean a dataset; for instance, we would still need to remove the year string from each cell entry. However, we can do this much more easily once the data are pivoted into a longer format:

## NOTE: No need to edit
(
df_cases
>> gr.tf_pivot_longer(
columns=["year2011", "year2012", "year2013"],
names_to="year",
values_to="count",
)
>> gr.tf_mutate(year=gr.str_replace(DF.year, "year", ""))
)

country year count
0 FR 2011 7000
1 DE 2011 5800
2 US 2011 15000
3 FR 2012 6900
4 DE 2012 6000
5 US 2012 14000
6 FR 2013 7000
7 DE 2013 6200
8 US 2013 13000

### q4 Pivot the data#

Pivot the dataset df_alloys1 to place each of E_00, mu_00, E_45, mu_45 as values in a new variable column, and move the original values to a new value column. Answer the questions under observations below.

## TASK: Tidy the data, make sure to provide variable and value columns
df_res1 = (
df_alloys1

>> gr.tf_pivot_longer(
columns=["E_00", "mu_00", "E_45", "mu_45"],
names_to="variable",
values_to="value",
)
)

## NOTE: Use this to check your work
print(df_res1)

assert \
{"thick", "rep", "variable", "value"} == set(df_res1.columns), \
'columns of df_res1 are not ["thick", "rep", "variable", "value"]'

assert \
{"E_00", "mu_00", "E_45", "mu_45"} == set(df_res1.variable), \
'Entries in df_res1.variable are incorrect'

    thick  rep variable      value
0   0.022    1     E_00  10600.000
1   0.022    2     E_00  10600.000
2   0.032    1     E_00  10400.000
3   0.032    2     E_00  10300.000
4   0.022    1    mu_00      0.321
5   0.022    2    mu_00      0.323
6   0.032    1    mu_00      0.329
7   0.032    2    mu_00      0.319
8   0.022    1     E_45  10700.000
9   0.022    2     E_45  10500.000
10  0.032    1     E_45  10400.000
11  0.032    2     E_45  10500.000
12  0.022    1    mu_45      0.329
13  0.022    2    mu_45      0.331
14  0.032    1    mu_45      0.318
15  0.032    2    mu_45      0.326


Observations

• Is this dataset tidy? Why or why not?

• This dataset is not tidy; the entries in the value column include values of E and mu (two different variables). Also, the variable column contains both variable names and angle values.

### Using selection helpers#

One useful feature of gr.tf_pivot_longer() is that we can use selection helpers to choose which columns to use in a pivot. This can save us a lot of typing, and allows us to write code that can react to multiple different datasets. Let’s practice using selection helpers by re-doing the previous task.

### q5 Simplify with selection helpers#

Use a single selection helper to simplify the columns argument to gr.tf_pivot_longer().

Hint: There are multiple ways to do this: The string "E|mu" will match the strings "E" or "mu". The string "\\d+" will match any string of consecutive digits.

## TASK: Replace the columns argument with a selection helper
df_simplified = (
df_alloys1
>> gr.tf_pivot_longer(

columns=gr.matches("E|mu"),
names_to="variable",
values_to="value",
)
)

## NOTE: Use this to check your work
print(df_simplified)

assert \
{"thick", "rep", "variable", "value"} == set(df_simplified.columns), \
'columns of df_res1 are not ["thick", "rep", "variable", "value"]'

assert \
{"E_00", "mu_00", "E_45", "mu_45"} == set(df_simplified.variable), \
'Entries in df_res1.variable are incorrect'

    thick  rep variable      value
0   0.022    1     E_00  10600.000
1   0.022    2     E_00  10600.000
2   0.032    1     E_00  10400.000
3   0.032    2     E_00  10300.000
4   0.022    1    mu_00      0.321
5   0.022    2    mu_00      0.323
6   0.032    1    mu_00      0.329
7   0.032    2    mu_00      0.319
8   0.022    1     E_45  10700.000
9   0.022    2     E_45  10500.000
10  0.032    1     E_45  10400.000
11  0.032    2     E_45  10500.000
12  0.022    1    mu_45      0.329
13  0.022    2    mu_45      0.331
14  0.032    1    mu_45      0.318
15  0.032    2    mu_45      0.326


## Pivot Wider#

Just as a dataset can be “too wide”, it can also be “too long.” In this case, we can use gr.tf_pivot_wider(). Let’s look at an illustrative example:

## NOTE: No need to edit
df_long = gr.df_make(
variable=["x", "y", "f", "x", "y", "f"],
value=[0, 0, 1, 0, 1, 0],
observation=[0, 0, 0, 1, 1, 1],
)
df_long

variable value observation
0 x 0 0
1 y 0 0
2 f 1 0
3 x 0 1
4 y 1 1
5 f 0 1

Here, the value column has mixed variables; values of x, y, and f comingle in the value column. Really we should have the columns x, y, and f: In this sense the data is too long. Let’s pivot wider to tidy the data.

## NOTE: No need to edit
(
df_long
>> gr.tf_pivot_wider(
names_from="variable",
values_from="value",
)
)

observation f x y
0 0 1 0 0
1 1 0 0 1

Note that we had to provide just two inputs to gr.tf_pivot_wider():

• names_from specifies which column will provide the new column names

• value_from specifies which column will provide the new column values

Let’s get some practice!

### q6 Pivot the data#

Pivot the dataset df_alloys2 to provide E and mu as columns in df_res2. Answer the questions under observations below.

## TASK: Pivot the dataset wider
df_res2 = (
df_alloys2
>> gr.tf_pivot_wider(
names_from="var",
values_from="value",
)
)

## NOTE: Use the following to check your work
print(df_res2)

assert \
{"thick", "rep", "angle", "E", "mu"} == set(df_res2.columns), \
'df_res2 does not have the columns ["thick", "rep", "angle", "E", "mu"]'

   thick  rep  angle        E     mu
0  0.022    1      0  10700.0  0.321
1  0.032    2      0  10500.0  0.323


Observations

• Is this dataset tidy? Why or why not?

• This dataset is tidy! Every column is one variable, every row is one observation, and every cell contains one value.

### Warning: No observation identifier#

While the arguments to gr.tf_pivot_wider() only target two columns, we do need to think carefully about what other columns are in the dataset. It is important that the other columns help identify which values are associated with the same observation—the easiest way to do this is with some sort of observation identifier column.

Let’s take a look at what happens when we do not have a way to associate values with the same observation:

## NOTE: No need to edit
(
gr.df_make(
variable=["x", "y", "f", "x", "y", "f"],
value=[0, 0, 1, 0, 1, 0],
# observation=[0, 0, 0, 1, 1, 1], # Remove the observation identifier
)
>> gr.tf_pivot_wider(
names_from="variable",
values_from="value",
)
)

f x y
0 NaN 0.0 NaN
1 NaN NaN 0.0
2 1.0 NaN NaN
3 NaN 0.0 NaN
4 NaN NaN 1.0
5 0.0 NaN NaN

Note that gr.tf_pivot_wider() placed all of the values in the “correct” column, but filled all over column values with NaNs. If you get strange behavior with gr.tf_pivot_wider(), you should think about whether you are providing the information necessary to associate common values with the same observation. We’ll learn more about this in the next exercise.