# Map

Map[f,expr] or f/@expr

applies f to each element on the first level in expr.

Map[f,expr,levelspec]

applies f to parts of expr specified by levelspec.

Map[f]

represents an operator form of Map that can be applied to an expression.

# Details and Options

• Map uses standard level specifications:
•  n levels 1 through n Infinity levels 1 through Infinity {n} level n only {n1,n2} levels n1 through n2
• The default value for levelspec in Map is {1}.
• 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 , Map includes heads of expressions and their parts.
• Map always effectively constructs a complete new expression and then evaluates it.
• If expr is an Association object, Map[f,expr] applies f to the values in the association. »
• If expr is a SparseArray object or structured array, Map[f,expr] applies f to the values or subarrays that appear in expr. »
• Map[f][expr] is equivalent to Map[f,expr].
• Parallelize[Map[f,expr]] or ParallelMap[f,expr] computes Map[f,expr] in parallel on all subkernels. »

# Examples

open allclose all

## Basic Examples(5)

Evaluate f on each element of a list:

Use the short input form:

Use explicit pure functions:

Map at top level:

Map at level 2:

Map at levels 1 and 2:

Use a map operator:

Map a function over values in Association:

## Scope(11)

### Level Specifications(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:

Include heads in the levels specified:

### Types of Expressions(5)

Map can be used on expressions with any head:

Map can be used on sparse arrays:

Use Map with structured arrays, such as SymmetrizedArray:

Use Map to apply a function to the elements of a structured array of type QuantityArray:

Map at the second level of a nested Association:

Map at several levels in an Association:

## Options(1)

By default, the function is not mapped onto the heads:

## Applications(4)

Reverse all sublists:

Add the same vector to every vector in a list:

Frame integers that are prime:

Supply additional constant arguments by using a pure function:

## Properties & Relations(7)

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:

Functions with attribute Listable are mapped automatically:

ParallelMap computes Map in parallel:

Map can be parallelized automatically, effectively using ParallelMap:

Map wraps an expression around parts of another expression:

Comap wraps parts of an expression around another expression:

## 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:

Wolfram Research (1988), Map, Wolfram Language function, https://reference.wolfram.com/language/ref/Map.html (updated 2014).

#### Text

Wolfram Research (1988), Map, Wolfram Language function, https://reference.wolfram.com/language/ref/Map.html (updated 2014).

#### CMS

Wolfram Language. 1988. "Map." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/Map.html.

#### APA

Wolfram Language. (1988). Map. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Map.html

#### BibTeX

@misc{reference.wolfram_2024_map, author="Wolfram Research", title="{Map}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/Map.html}", note=[Accessed: 18-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_map, organization={Wolfram Research}, title={Map}, year={2014}, url={https://reference.wolfram.com/language/ref/Map.html}, note=[Accessed: 18-July-2024 ]}