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Re: Map

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  • Subject: [mg130918] Re: Map
  • From: Szabolcs HorvÃt <szhorvat at>
  • Date: Sat, 25 May 2013 05:39:59 -0400 (EDT)
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  • References: <knnboj$qqi$>

On 2013-05-24 09:26:43 +0000, Jon Morris said:

> I'm new to Mathematica and I've been given some code to help me analyse 
> some data. I'm trying to understand what the Map function does, 
> specifically what the {2,2} means?
>    qbarlist = Map[(# - bragg) &, hkllist,{2, 2}];
> hklist is a 3 column list, bragg is a three element vector.
> When I try the same line with {2} or {1} I seem to get the same answer. 
> The online explanation of this term does not make that much sense to 
> me. I'd be very grateful if someone could explain the purpose of the 
> last term of the Map syntax.

Hello Jon,

Did you take a look at the examples in the documentation?  Those will 
make it much clearer how this works. Choose an undefined function so 
you get back the result in the form f[x].
I assume you understand what Map does without a level specification.

Now let's take an example from the docs and try different valus of the 
levels specification:

In[26]:= Map[f, {{a, b}, {c, d, e}}, {0}]
Out[26]= f[{{a, b}, {c, d, e}}]

In[27]:= Map[f, {{a, b}, {c, d, e}}, {1}]
Out[27]= {f[{a, b}], f[{c, d, e}]}

In[28]:= Map[f, {{a, b}, {c, d, e}}, {2}]
Out[28]= {{f[a], f[b]}, {f[c], f[d], f[e]}}

Notice how the function f goes deeper and deeper into the expression as 
you incerase the level.

In[29]:= Map[f, {{a, b}, {c, d, e}}, {3}]
Out[29]= {{a, b}, {c, d, e}}

There's no level 3 in the expression {{a, b}, {c, d, e}} so this last 
one does nothing.

{2,2} is exactly the same as {2}.

This will insert f into levels 0 through 2, i.e. all levels of this expression:

In[30]:= Map[f, {{a, b}, {c, d, e}}, {0, 2}]
Out[30]= f[{f[{f[a], f[b]}], f[{f[c], f[d], f[e]}]}]

A naive way to think of level n of a nested list is this: move to 
deeper and deeper lists until you have passed exactly n braces.  (But 
note that Map works on any expression, not just lists.)

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