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Map

Map or
applies f to each element on the first level in expr.
Map
applies f to parts of expr specified by levelspec.
MORE INFORMATION
  • Map uses standard level specifications:
nlevels 1 through n
Infinitylevels 1 through Infinity
{n}level n only
{n1,n2}levels through
  • The default value for levelspec in Map is .
  • A positive level n consists of all parts of expr specified by n indices.
  • A negative level -n consists of all parts of expr with depth n.
  • Level -1 consists of numbers, symbols, and other objects that do not have subparts.
  • Level 0 corresponds to the whole expression.
  • With the option setting Heads->True, Map includes heads of expressions and their parts.
  • Map always effectively constructs a complete new expression and then evaluates it.
  • If expr is a SparseArray object, Map applies f to the values or subarrays that appear in expr.
EXAMPLESCLOSE ALL
Basic Examples   (4)
Alternative input form:
Use explicit pure functions:
Map at top level:
Map at level 2:
Map at levels 1 and 2:
In[1]:=
Click for copyable input
Out[1]=
 
Alternative input form:
In[1]:=
Click for copyable input
Out[1]=
 
Use explicit pure functions:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Map at top level:
In[1]:=
Click for copyable input
Out[1]=
Map at level 2:
In[2]:=
Click for copyable input
Out[2]=
Map at levels 1 and 2:
In[3]:=
Click for copyable input
Out[3]=
Scope   (6)
Map at level 1 (default):
Map down to level 2:
Map at level 2:
Map on levels 0 through 2:
Map down to level 3:
Map on all levels, starting at level 1:
Map also at level 0:
Negative levels:
Positive and negative levels can be mixed:
Different heads at each level:
Include heads in the levels specified:
Generalizations & Extensions   (4)
Map can be used on expressions with any head:
The function can be mapped onto the heads as well:
Functions with attribute Listable are mapped automatically:
Map can be used on sparse arrays:
Options   (1)
By default, the function is not mapped onto the heads:
Applications   (3)
Reverse all sublists:
Add the same vector to every vector in a list:
Frame integers that are prime:
Properties & Relations   (5)
Leaves are visited before roots:
A function of several arguments can be mapped with MapThread:
MapIndexed passes the index of an element to the mapped function:
MapAll is equivalent to a specific level specification in Map:
Scan does the same as Map, but without returning a result:
Possible Issues   (1)
Map by default starts at level 1, so does not apply the function to the whole expression:
Neat Examples   (1)
Show nesting structure of an expression:
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