Explore the latest version of An Elementary Introduction to the Wolfram Language »
45Datasets
Create a simple dataset that can be viewed as having 2 rows and 3 columns:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
You can first extract the whole b row, then get the z element of the result:
In[3]:=
Click for copyable input
Out[3]=
You can also just get the whole b row of the dataset. The result is a new dataset, which for ease of reading happens to be displayed in this case as a column.
Generate a new dataset from the b row of the original dataset:
In[4]:=
Click for copyable input
Out[4]=
Here is the dataset that corresponds to the z column for all rows.
Generate a dataset consisting of the z column for all rows:
In[5]:=
Click for copyable input
Out[5]=
Get totals for each row by applying Total to all columns for all the rows:
In[6]:=
Click for copyable input
Out[6]=
If we use f instead of Total, we can see whats going on: the function is being applied to each of the row associations.
Apply the function f to each row:
In[7]:=
Click for copyable input
Out[7]=
Apply a function that adds the x and z elements of each association:
In[8]:=
Click for copyable input
Out[8]=
In[9]:=
Click for copyable input
Out[9]=
You can give a function to apply to all rows too.
This extracts the value of each z column, then applies f to the association of results:
In[10]:=
Click for copyable input
Out[10]=
Apply f to the totals of all columns:
In[11]:=
Click for copyable input
Out[11]=
In[12]:=
Click for copyable input
Out[12]=
Find totals for all rows, then pick out the total for the b row:
In[13]:=
Click for copyable input
Out[13]=
Its equivalent to this:
In[14]:=
Click for copyable input
Out[14]=
In[15]:=
Click for copyable input
Out[15]=
In[16]:=
Click for copyable input
Out[16]=
The operator form of Select is a function which can be applied to actually perform the Select operation.
Make a dataset by selecting only rows whose z column is greater than 5:
In[17]:=
Click for copyable input
Out[17]=
For each row, select columns whose values are greater than 5, leaving a ragged structure:
In[18]:=
Click for copyable input
Out[18]=
Normal turns the dataset into an ordinary association of associations:
In[19]:=
Click for copyable input
Out[19]=
Many Wolfram Language functions have operator forms.
In[20]:=
Click for copyable input
Out[20]=
SortBy has an operator form:
In[21]:=
Click for copyable input
Out[21]=
Sort rows according to the value of the difference of the x and y columns:
In[22]:=
Click for copyable input
Out[22]=
Sort the rows, and find the total of all columns:
In[23]:=
Click for copyable input
Out[23]=
Sometimes you want to apply a function to each element in the dataset.
Apply f to each element in the dataset:
In[24]:=
Click for copyable input
Out[24]=
Sort the rows before totaling the squares of their elements:
In[25]:=
Click for copyable input
Out[25]=
A dataset formed from a list of associations:
In[26]:=
Click for copyable input
Out[26]=
In[27]:=
Click for copyable input
Out[27]=
In[28]:=
Click for copyable input
Out[28]=
In[29]:=
Click for copyable input
Out[29]=
In[30]:=
Click for copyable input
Out[30]=
If we ask about the moons of Mars, we get a dataset, which we can then query further.
Get a dataset about the moons of Mars:
In[31]:=
Click for copyable input
Out[31]=
Drill down to make a table of radii of all the moons of Mars:
In[32]:=
Click for copyable input
Out[32]=
Make a dataset of the number of moons listed for each planet:
In[33]:=
Click for copyable input
Out[33]=
Find the total mass of all moons for each planet:
In[34]:=
Click for copyable input
Out[34]=
Get the same result, but only for planets with more than 10 moons:
In[35]:=
Click for copyable input
Out[35]=
In[36]:=
Click for copyable input
Out[36]=
Get a dataset with moons that are more than 1% of the mass of the Earth.
For all moons, select ones whose mass is greater than 0.01 times the mass of the Earth:
In[37]:=
Click for copyable input
Out[37]=
Get the list of keys (i.e. moon names) in the resulting association for each planet:
In[38]:=
Click for copyable input
Out[38]=
In[39]:=
Click for copyable input
Out[39]=
In[40]:=
Click for copyable input
Out[40]=
Heres the whole computation in one line:
In[41]:=
Click for copyable input
Out[41]=
Make number line plots of the logarithms of masses for moons of each planet:
In[42]:=
Click for copyable input
Out[42]=
Heres how to make a word cloud of names of moons, sized according to the masses of the moons. To do this, we need a single association that associates the name of each moon with its mass.
When given an association, WordCloud determines sizes from values in the association:
In[43]:=
Click for copyable input
Out[43]=
The function Association combines associations:
In[44]:=
Click for copyable input
Out[44]=
In[45]:=
Click for copyable input
Out[45]=
Weve seen before that we can write something like f[g[x]] as f@g@x or x//g//f. We can also write it f[g[#]]&[x]. But what about f[g[#]]&? Is there a short way to write this? The answer is that there is, in terms of the function composition operators @* and /*.
f@*g@*h represents a composition of functions to be applied right-to-left:
In[46]:=
Click for copyable input
Out[46]=
h/*g/*f represents a composition of functions to be applied left-to-right:
In[47]:=
Click for copyable input
Out[47]=
Heres the previous code rewritten using composition @*:
In[48]:=
Click for copyable input
Out[48]=
In[49]:=
Click for copyable input
Out[49]=
As a final example, lets look at another datasetthis time coming straight from the Wolfram Data Repository. Heres a webpage (about big meteors) from the repository:
To get the main dataset thats mentioned here, just use ResourceData.
Get the dataset just by giving its name to ResourceData:
In[50]:=
Click for copyable input
Out[50]=
Extract the coordinates entry from each row, and plot the results:
In[51]:=
Click for copyable input
Out[51]=
Make a histogram of the altitudes:
In[52]:=
Click for copyable input
Out[52]=
Dataset[data] a dataset
Normal[dataset] convert a dataset to normal lists and associations
Catenate[{assoc1, ...}] catenate associations, combining their elements
f@*g composition of functions (f[g[x]] when applied to x)
f/*g right composition (g[f[x]] when applied to x)
Note: These exercises use the dataset planets=CloudGet["http://wolfr.am/7FxLgPm5"].
45.1Make a word cloud of the planets, with weights determined by their number of moons. »
Sample expected output:
Out[]=
45.2Make a bar chart of the number of moons for each planet. »
Sample expected output:
Out[]=
45.3Make a dataset of the masses of the planets, sorted by their number of moons. »
Sample expected output:
Out[]=
45.4Make a dataset of planets and the mass of each ones most massive moon. »
Sample expected output:
Out[]=
45.5Make a dataset of masses of planets, where the planets are sorted by the largest mass of their moons. »
Sample expected output:
Out[]=
45.6Make a dataset of the median mass of all moons for each planet. »
Sample expected output:
Out[]=
Sample expected output:
Out[]=
45.8Make a word cloud of countries in Central America, with the names of countries proportional to the lengths of the Wikipedia article about them. »
Sample expected output:
Out[]=
45.9Find the maximum observed altitude in the Fireballs & Bolides dataset. »
Expected output:
Out[]=
45.10Find a dataset of the 5 largest observed altitudes in the Fireballs & Bolides dataset. »
Expected output:
Out[]=
45.11Make a histogram of the differences in successive peak brightness times in the Fireballs & Bolides dataset. »
Expected output:
Out[]=
45.12Plot the nearest cities for the first 10 entries in the Fireballs & Bolides dataset, labeling each city. »
Expected output:
Out[]=
45.13Plot the nearest cities for the 10 entries with largest altitudes in the Fireballs & Bolides dataset, labeling each city. »
Expected output:
Out[]=
What kinds of data can datasets contain?
Any kinds. Not just numbers and text but also images, graphs and lots more. Theres no need for all elements of a particular row or column to be the same type.
Yes. SemanticImport is often a good way to do it.
What are databases and how do they relate to Dataset?
Databases are a traditional way to store structured data in a computer system. Databases are often set up to allow both reading and writing of data. Dataset is a way to represent data that might be stored in a database so that its easy to manipulate with the Wolfram Language.
How does data in Dataset compare to data in an SQL (relational) database?
SQL databases are strictly based on tables of data arranged in rows and columns of particular types, with additional data linked in through foreign keys. Dataset can have any mixture of types of data, with any number of levels of nesting, and any hierarchical structure, somewhat more analogous to a NoSQL database, but with additional operations made possible by the symbolic nature of the language.
 
Download Notebook Version
es