WolframLang: Map Function to List

Apply a function to each element, at specific level or range of levels, specified by levelSpec.

Example: Map to a tree.

(* example of using levelspec in map *)

xx = {a, {{b,c}, d}, e};

(* map to 1st level *)
Map[ f, xx, {1} ] ===
{f[a], f[{{b, c}, d}], f[e]}

(* map to 2nd level *)
Map[ f, xx, {2} ] ===
{a, {f[{b, c}], f[d]}, e}

(* map to 3rd level *)
Map[ f, xx, {3} ] ===
{a, {{f[b], f[c]}, d}, e}

(* map to leafs *)
Map[ f, xx, {-1} ] ===
{f[a], {{f[b], f[c]}, f[d]}, f[e]}

Map a function to different levels of a rectangular array:

(xx = Table[{i, j}, {i, 2}, {j, 2}]) ===
{{{1, 1}, {1, 2}}, {{2, 1}, {2, 2}}}

(* map to 1st level, as in flat map *)
Map[ f, xx, {1} ] ===
{f[{{1, 1}, {1, 2}}], f[{{2, 1}, {2, 2}}]}

(* map to 2nd level *)
Map[ f, xx, {2} ] ===
{{f[{1, 1}], f[{1, 2}]}, {f[{2, 1}], f[{2, 2}]}}

(* map to 3rd level *)
Map[ f, xx, {3} ] ===
{{{f[1], f[1]}, {f[1], f[2]}}, {{f[2], f[1]}, {f[2], f[2]}}}

(* map to deepest level, the leafs. in this case, same as 3rd level *)
Map[ f, xx, {-1} ] ===
{{{f[1], f[1]}, {f[1], f[2]}}, {{f[2], f[1]}, {f[2], f[2]}}}

Scan

Like Map, but also feed the index to the function.

💡 TIP: Useful when you want to “iterate” over array but also need the index.

The function receive 2 args, first is value, second is the Position spec of the value.

MapIndexed

MapIndexed[ f, {a,b,c} ] ===
{f[a, {1}], f[b, {2}], f[c, {3}]}

Like Map, but for functions that take 2 args (or more).

MapThread

xx = {{1, 2, 3} , {a, b, c} };
MapThread[ f, xx ] ===
{f[1, a], f[2, b], f[3, c]}

xx = {{1, 2, 3}, {a, b, c}, {x, y, z} };
MapThread[f, xx] === {f[1, a, x], f[2, b, y], f[3, c, z]}