How to | Work with Nested Lists

Nested lists are lists within a list; they are the principal structure for data in the Wolfram Language and allow for high-dimension arrays and ragged datasets as well as common uses such as matrices.

Create a list of lists to work with:

Matrices in the Wolfram Language are represented as nested lists. Note that each row corresponds to a sublist in the nested list:

Use [[]], the short form of the Part function, to get the second row:

From row 2, get element 3:

Get element 3 from each row:

Use Flatten to remove the nesting:

Display the flattened data as a column:

For comparison, to display the flattened data as a row, add {}:

    

You can operate on the individual sublists of a nested list or on the nested list as a whole.

Set up a dataset:

Most functions map over each sublist within a nested list.

Create four plots from the rows in the dataset:

Most descriptive statistics functions operate by columns.

Take the mean by column:

Get the mean of all the numbers by flattening the list:

    

Create a doubly nested list:

Mean now lists the means by each individual nested sublist:

Use Flatten to obtain the mean of the entire dataset:

  • Combining Lists
  • Lists as Sets
  • Rearranging Lists
  • Nested Lists
  • Rearranging Nested Lists
  • How to: Work with Lists
  • List  Flatten  Partition  Level

  • Constructing Lists
  • "How to" Topics