How to | Work with Nested Lists
Nested lists are lists within a list; they are the principal structure for data in
Mathematica 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:
| Out[1]= |  |
Matrices in
Mathematica are represented as nested lists. Note that each row corresponds to a sublist in the nested list:
Out[2]//MatrixForm= |
| |  |
Use
, the short form of the
Part function, to get the second row:
| Out[3]= |  |
From row 2, get element 3:
| Out[2]= |  |
Get element 3 from each row:
| Out[3]= |  |
Use
Flatten to remove the nesting:
| Out[4]= |  |
Display the flattened data as a column:
Out[7]//MatrixForm= |
| |  |
For comparison, to display the flattened data as a row, add
:
Out[8]//MatrixForm= |
| |  |
You can operate on the individual sublists of a nested list or on the nested list as a whole.
| Out[9]= |  |
Out[10]//MatrixForm= |
| |  |
Most functions map over each sublist within a nested list.
Create four plots from the rows in the dataset:
| Out[11]= |  |
Most descriptive statistics functions operate by columns.
| Out[12]= |  |
Get the mean of all the numbers by flattening the list:
| Out[13]= |  |
Create a doubly nested list:
Out[15]//MatrixForm= |
| |  |
Mean now lists the means by each individual nested sublist:
Out[16]//MatrixForm= |
| |  |
Use
Flatten to obtain the mean of the entire dataset:
| Out[17]= |  |
