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MapIndexed
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MapIndexed

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MapIndexed[f,expr]

applies f to the elements of expr, giving the part specification of each element as a second argument to f.

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MapIndexed[f,expr,levelspec]

applies f to all parts of expr on levels specified by levelspec.

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

Details and Options

  • MapIndexed uses standard level specifications:
  • nlevels 1 through n
    Infinitylevels 1 through Infinity
    {n}level n only
    {n1,n2}levels n1 through n2
  • The default value for levelspec in MapIndexed 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 Heads->True, MapIndexed also applies to heads of expressions and their parts.
  • MapIndexed always effectively constructs a complete new expression and then evaluates it.
  • MapIndexed works on SparseArray objects, effectively by applying Normal to them.
  • MapIndexed works on Association objects, giving part specifications in the form Key[k].
  • MapIndexed[f][expr] is equivalent to MapIndexed[f,expr].
  • Parallelize[MapIndexed[f,expr]] computes MapIndexed[f,expr] in parallel on all subkernels. »

Examples

open allclose all

Basic Examples  (6)Summary of the most common use cases

In[1]:=1
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https://wolfram.com/xid/09belp27i-d6p
Out[1]=1

#2 gives the indices of each part:

In[1]:=1
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https://wolfram.com/xid/09belp27i-fhq
Out[1]=1
In[1]:=1
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https://wolfram.com/xid/09belp27i-bxu
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09belp27i-ynf
Out[2]=2

Map over an association:

In[1]:=1
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https://wolfram.com/xid/09belp27i-gwknyf
Out[1]=1

Map over nested associations:

In[1]:=1
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https://wolfram.com/xid/09belp27i-f1s871
Out[1]=1

Use the operator form of MapIndexed:

In[1]:=1
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https://wolfram.com/xid/09belp27i-dlfrce
Out[1]=1

Scope  (6)Survey of the scope of standard use cases

Level Specifications  (6)

Map at level 1 (default):

In[1]:=1
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https://wolfram.com/xid/09belp27i-m34
Out[1]=1

Map down to level 2:

In[2]:=2
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https://wolfram.com/xid/09belp27i-n3o
Out[2]=2

Map at level 2:

In[3]:=3
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https://wolfram.com/xid/09belp27i-vzc
Out[3]=3

Map down to level 3:

In[4]:=4
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https://wolfram.com/xid/09belp27i-jva
Out[4]=4

Map onto all elements of an expression:

In[1]:=1
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https://wolfram.com/xid/09belp27i-mgx
Out[1]=1

Map only onto the "leaves" of the expression:

In[1]:=1
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https://wolfram.com/xid/09belp27i-xyv
Out[1]=1

Negative levels:

In[1]:=1
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https://wolfram.com/xid/09belp27i-knq
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09belp27i-lg9
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/09belp27i-n1h
Out[3]=3

Different heads at each level:

In[1]:=1
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https://wolfram.com/xid/09belp27i-jn
Out[1]=1

Map on levels 0 through 1; the head has index {}:

In[1]:=1
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https://wolfram.com/xid/09belp27i-jdn
Out[1]=1

Generalizations & Extensions  (3)Generalized and extended use cases

MapIndexed can be used on expressions with any head:

In[1]:=1
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https://wolfram.com/xid/09belp27i-r7z
Out[1]=1

The function can be mapped onto the heads as well:

In[1]:=1
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https://wolfram.com/xid/09belp27i-j2f
Out[1]=1

MapIndexed works on sparse arrays:

In[1]:=1
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https://wolfram.com/xid/09belp27i-u0b
Out[1]=1

Options  (2)Common values & functionality for each option

Heads  (2)

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

In[1]:=1
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https://wolfram.com/xid/09belp27i-q1cg93
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09belp27i-hlt
Out[2]=2

Map onto the heads at all levels:

In[1]:=1
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https://wolfram.com/xid/09belp27i-v0k
Out[1]=1

Applications  (5)Sample problems that can be solved with this function

Label parts by position:

In[1]:=1
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https://wolfram.com/xid/09belp27i-xkm
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09belp27i-cnf
Out[2]=2

Use tooltips to show part numbers of subexpressions:

In[1]:=1
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https://wolfram.com/xid/09belp27i-jzo
Out[1]=1

Convert a list to a polynomial:

In[1]:=1
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https://wolfram.com/xid/09belp27i-dud
Out[1]=1

Rotate lists based on position:

In[1]:=1
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https://wolfram.com/xid/09belp27i-xex
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09belp27i-tds

Obtain a list of all parts in an expression:

In[1]:=1
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https://wolfram.com/xid/09belp27i-n04nq4
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09belp27i-dusheg
Out[2]=2

Properties & Relations  (3)Properties of the function, and connections to other functions

Using only the first argument is equivalent to using Map:

In[1]:=1
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https://wolfram.com/xid/09belp27i-62y4d0
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09belp27i-ghbs08
Out[2]=2

The result of MapIndexed on an association is closely related to the result of KeyValueMap:

In[1]:=1
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https://wolfram.com/xid/09belp27i-opegmy
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09belp27i-151daf
Out[2]=2

Use a combination of Values and Part to obtain the same result:

In[3]:=3
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https://wolfram.com/xid/09belp27i-kb0z49
Out[3]=3

Compute MapIndexed in parallel:

In[1]:=1
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https://wolfram.com/xid/09belp27i-ci4udx
Out[1]=1
Wolfram Research (1991), MapIndexed, Wolfram Language function, https://reference.wolfram.com/language/ref/MapIndexed.html (updated 2014).
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Wolfram Research (1991), MapIndexed, Wolfram Language function, https://reference.wolfram.com/language/ref/MapIndexed.html (updated 2014).

Text

Wolfram Research (1991), MapIndexed, Wolfram Language function, https://reference.wolfram.com/language/ref/MapIndexed.html (updated 2014).

✖
Wolfram Research (1991), MapIndexed, Wolfram Language function, https://reference.wolfram.com/language/ref/MapIndexed.html (updated 2014).

CMS

Wolfram Language. 1991. "MapIndexed." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/MapIndexed.html.

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Wolfram Language. 1991. "MapIndexed." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/MapIndexed.html.

APA

Wolfram Language. (1991). MapIndexed. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MapIndexed.html

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Wolfram Language. (1991). MapIndexed. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MapIndexed.html

BibTeX

@misc{reference.wolfram_2025_mapindexed, author="Wolfram Research", title="{MapIndexed}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/MapIndexed.html}", note=[Accessed: 19-May-2025 ]}

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@misc{reference.wolfram_2025_mapindexed, author="Wolfram Research", title="{MapIndexed}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/MapIndexed.html}", note=[Accessed: 19-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_mapindexed, organization={Wolfram Research}, title={MapIndexed}, year={2014}, url={https://reference.wolfram.com/language/ref/MapIndexed.html}, note=[Accessed: 19-May-2025 ]}

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@online{reference.wolfram_2025_mapindexed, organization={Wolfram Research}, title={MapIndexed}, year={2014}, url={https://reference.wolfram.com/language/ref/MapIndexed.html}, note=[Accessed: 19-May-2025 ]}