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MapThread[f,{{a1,a2,…},{b1,b2,…},…}]

gives {f[a1,b1,…],f[a2,b2,…],…}.

MapThread[f,{expr1,expr2,…},n]

applies f to the parts of the expri at level n.

MapThread[f]

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

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Scope  
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MapThread

MapThread[f,{{a1,a2,…},{b1,b2,…},…}]

gives {f[a1,b1,…],f[a2,b2,…],…}.

MapThread[f,{expr1,expr2,…},n]

applies f to the parts of the expri at level n.

MapThread[f]

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

Details

Examples

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Basic Examples  (4)

Apply f to corresponding pairs of elements:

Wolfram Language code: MapThread[f, {{a, b, c}, {x, y, z}}]

Apply f to elements of a matrix:

Wolfram Language code: MapThread[f, {{{a, b}, {c, d}}, {{u, v}, {s, t}}}, 2]

Apply f to corresponding values of associations:

Wolfram Language code: MapThread[f, {<|a -> 1|>, <|a -> 2|>}]

Use the operator form of MapThread:

Wolfram Language code: MapThread[f][{{a, b, c, d}, {1, 2, 3, 4}}]

Scope  (2)

By default, MapThread threads over level 1 of the arguments:

Wolfram Language code: MapThread[f, {{{a, b}, {c, d}}, {{u, v}, {w, x}}}]

Thread over level 2:

Wolfram Language code: MapThread[f, {{{a, b}, {c, d}}, {{u, v}, {w, x}}}, 2]

MapThread works with any number of expressions:

Wolfram Language code: MapThread[f, {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}}]

Applications  (3)

Set up an outer totalistic cellular automaton:

Wolfram Language code: t = RandomInteger[1, 10]
Wolfram Language code: MapThread[f, {t, RotateLeft[t] + RotateRight[t]}]

Divide eigenvectors by their corresponding eigenvalues:

Wolfram Language code: Eigensystem[{{1, 3}, {2, 7}}]
Wolfram Language code: MapThread[#2 / #1&, %]//FullSimplify

Apply the functions in a list to corresponding arguments:

Wolfram Language code: MapThread[#1@#2&, {{f, g, h}, {x, y, z}}]

Properties & Relations  (6)

Add columns of elements in a matrix:

Wolfram Language code: MapThread[Plus, {{a, b, c}, {u, v, w}, {x, y, z}}]
Wolfram Language code: Total[{{a, b, c}, {u, v, w}, {x, y, z}}]

Get lists of elements in columns of a matrix:

Wolfram Language code: MapThread[List, {{a, b, c}, {u, v, w}, {x, y, z}}]
Wolfram Language code: Transpose[{{a, b, c}, {u, v, w}, {x, y, z}}]

MapThread works like Thread, but takes the function and arguments separately:

Wolfram Language code: MapThread[f, {{a, b, c}, {x, y, z}}]
Wolfram Language code: Thread[f[{a, b, c}, {x, y, z}]]

Thread evaluates the whole expression before threading:

Wolfram Language code: Thread[D[{x, x y, x z}, {x, y, z}]]

MapThread takes the function and its arguments separately:

Wolfram Language code: MapThread[D, {{x, x y, x z}, {x, y, z}}]

MapThread is a generalization of Map to functions of several variables:

Wolfram Language code: Map[f, {a, b, c}]
Wolfram Language code: MapThread[f, {{a, b, c}}]
Wolfram Language code: MapThread[f, {{a, b, c}, {x, y, z}}]

Compute MapThread in parallel:

Wolfram Language code: Parallelize[MapThread[f, {{a, b, c}, {u, v, w}}]]

Possible Issues  (2)

All arguments must be lists of the same length:

Wolfram Language code: MapThread[f, {{a, b, c}, t, {u, v, w}}]

Thread repeats nonlist arguments as needed:

Wolfram Language code: Thread[f[{a, b, c}, t, {u, v, w}]]

MapThread combines associations in a list:

Wolfram Language code: MapThread[f, {<|a -> 1|>, <|a -> 2|>}]

Use Apply to combine values of an association:

Wolfram Language code: Apply[f, <|a -> {1, 2}, b -> {3, 4}|>, {1}]
Wolfram Research (1991), MapThread, Wolfram Language function, https://reference.wolfram.com/language/ref/MapThread.html (updated 2017).

Text

Wolfram Research (1991), MapThread, Wolfram Language function, https://reference.wolfram.com/language/ref/MapThread.html (updated 2017).

CMS

Wolfram Language. 1991. "MapThread." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/MapThread.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_mapthread, author="Wolfram Research", title="{MapThread}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/MapThread.html}", note=[Accessed: 15-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_mapthread, organization={Wolfram Research}, title={MapThread}, year={2017}, url={https://reference.wolfram.com/language/ref/MapThread.html}, note=[Accessed: 15-June-2026]}