Wolfram: Map Function to List

🔸 SHORT SYNTAX: f /@ list

Apply a function to each element, return the result list.

Map

(* Map a function to list *)

Map[ f, {3,4,5} ]
(* {f[3], f[4], f[5]} *)

(* short syntax *)
f /@ {3,4,5}

(* Map a user-defined function to list *)

Map[
Function[x, x+1 ],
{1, 2, 3}
]

(* {2, 3, 4} *)

Apply a function to each element, at Level Spec .

💡 TIP: one great use is map to leafs of a tree by using {-1} for levelSpec.

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

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

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

(* map to leafs *)
Map[ f, {1, {2, {3}}}, {-1} ]
(* {f[1], {f[2], {f[3]}}} *)

• MapIndexed[ f, list ]
• MapIndexed[ f, list, levelSpec ] → map at Level Spec

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

💡 TIP: Useful when you want to go over a list 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}]} *)

(* map at level 2 *)
MapIndexed[ f, {{a}, {b}}, {2} ]
(* {{f[a, {1, 1}]}, {f[b, {2, 1}]}} *)

(* map at level -1 *)
MapIndexed[ f, {{a}, {b}, c}, {-1} ]
(* {{f[a, {1, 1}]}, {f[b, {2, 1}]}, f[c, {3}]} *)

• MapThread[ f, {list1 , list2, etc} ]
• MapThread[ f, {list1 , list2, etc}, n ] → map at Level n

Like Map, but for functions that take 2 args (or more). The function is given args from each list.

MapThread

MapThread[ f, {{1, 2, 3} , {a, b, c}} ]
(* {f[1, a], f[2, b], f[3, c]} *)

MapThread[f, {{1, 2, 3}, {a, b, c}, {x, y, z}}]
(* {f[1, a, x], f[2, b, y], f[3, c, z]} *)

(* map to level 2 *)
MapThread[ f, {{{1}, {2}} , {{a}, {b}}} , 2 ]
(* {{f[1, a]}, {f[2, b]}} *)