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Relationship between "Apply" and "Map"

John Willett, Retired
Posted 5 years ago
POSTED BY: John Willett
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The use of "applies" in the documentation for Map is misleading. Map does not Apply. A better description might be "Map evaluates f for each element of the first level in expr".<

Rohit -- This seems to be the crux of my problem. I wish Wolfram would fix it, as I think it's tripped me up in the past. If I had written my f like this:

radiusOperator = (Sqrt[#2^2 + #4^2] &) @@ # &

with two layers of slots to replace the heads of the list-of-list elements, it would have worked as originally used in Map. Nevertheless

Apply[radiusOperator, solidWorksData, 1]

with the old definition f is simpler and more direct.

Thanks much for your (and Yehuda's) help! -- John Willett
POSTED BY: John Willett
Rohit Namjoshi
Rohit Namjoshi
Posted 5 years ago

Hi John,

The use of "applies" in the documentation for Map is misleading. Map does not Apply. A better description might be "Map evaluates f for each element of the first level in expr". The following examples should help you understand the difference.

ClearAll@f;
list = {266138, 106.75, 73.533, -85.006, -0.00230909, -0.000852509, 0.00228309, 0.00335725};

(* Head of list is List *)
list // Head
(* List *)

(* Head of f applied to list is f *)
f @@ list // Head
(* f *)

(* f applied to list passes each element of list as an argument to f *)
f @@ list
(* f[266138, 106.75, 73.533, -85.006, -0.00230909, -0.000852509, 0.00228309, 0.00335725] *)

(* f mapped over list *)
f /@ list
(* {f[266138], f[106.75], f[73.533], f[-85.006], f[-0.00230909], f[-0.000852509], f[0.00228309], f[0.00335725]} *)

(* Define f that returns a list of the second and fourth arguments passed to it *)
f = {#2, #4} &

(* Apply f to list *)
f @@ list
(* {106.75, -85.006} *)

(* Since f expects 4 arguments Map fails because only one argument is passed *)
f /@ list
(* "Slot number 2 in {#2,#4}& cannot be filled from ({#2,#4}&)[266138]" *)

(* This also fails since a single argument is passed to f *)
f[list]
(* "Slot number 2 in {#2,#4}& cannot be filled from 
({#2,#4}&)[{266138,106.75,73.533,-85.006,-0.00230909,-0.000852509,0.
00228309,0.00335725}]" *)

(* To make it work, change the Head of list to Sequence *)
f[Sequence @@ list]
(* {106.75, -85.006} *)
POSTED BY: Rohit Namjoshi

You function should be called as

radiusOperator[arg1,arg2,arg3,...]

And this happened when you use Apply, since you replace the head List with a head which is your function radiusOperator

When you used Map the way you called it, the function accepts (in each call) a single argument which is a list. So, it cannot find the second and forth arguments, since there is only one argument

From the result of calling solidWorksData [[1]] it seems that solidWorksData is a matrix (or a list of lists). So, all you have to do, it to use Apply at level one

Apply[radiusOperator, solidWorksData, 1]

or just

radiusOperator@@@ solidWorksData
POSTED BY: Yehuda Ben-Shimol

UPDATE, NOT ANSWER: This works, the levelspec = 1 being required:

In[58]:= temp = Apply[radiusOperator, solidWorksData, 1];

In[59]:= temp[[1]]

Out[59]= 136.461

But I still don't understand why Map does not work, with or without levelspec = 1. -- John Willett
POSTED BY: John Willett
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