Name: MapAt - applies a function to some of the elements of its argument

Synopsis:

array1 proc array2 MapAt -&gt; array3


Examples:

[3 4 5 6 7] {dup mul} -2 MapAt 
-&gt; [3 4 5 36 7] 
[3 [-9 -12] 5 6 7] {dup mul} [2 2] MapAt 
-&gt; [3 [-9 144] 5 6 7] 
[3 4 5 6 7] {dup mul} [[1] [3]] MapAt 
-&gt; [9 4 25 6 7] 
[[3 9] 4 [5 -11] 6 7] {dup mul} [[1 2] [3 1]] MapAt 
-&gt; [[3 81] 4 [25 -11] 6 7] 
[0 0 0 0 0] {1 add} [2 4 5 2 3 2 2 5] 1 1 Partition MapAt 
-&gt; [0 4 1 1 2]


Description:

MapAt successively applies proc to the elements of array1 
specified by array2 and replaces the original values by the 
return value of proc. The return value array3 has exactly the 
same shape as the first argument array1. 
Compared to languages like Matlab MapAt constitutes an lhs 
assignment operator for constructs like a(i)=f(a(i)), where 
i may be an array of indices. However, unlike in Matlab no 
temporary object a(i) for the rhs expression is created. 
Consequently, if the index ii occurs in array i n times the 
final value of a(ii) returned by MapAt is the cumulative effect 
of f operating n times on the original value of a(ii): 
a(ii) &lt;- f(f(...f(a(ii))...)) 
n times 
In Matlab the result is f(a(ii)), independent of n. 
The behavior of MapAt is, for example, useful in counting 
processes like the construction of a histogram as shown in the 
last example of the examples section.


Parameters:

array1 is an arbitrarily shaped array. In particular 
it does not need to be rectangular. 
array2 specifies a multi-dimensional position [i, j,...] 
in array1 or a list of positions [ [i1,j1,...], [i2,j2,...], ...]. 
The same element may be specified multiple times in array2 at 
arbitrary positions. 
The first element on each level has index 1. Indices can also 
be specified counting from the end of the array, in this case the 
last element has index -1. Positive and negative indices can 
arbitrarily be intermixed.


Remarks:

This function is an implementation of Mathematica's MapAt function. 
Mathematica-style functions in SLI use Mathematica index notation.


References:

[1] The Mathematica Book V4.0 "Part"


Author:

Diesmann


FirstVersion:

2007.08.12


SeeAlso:

ReplacePart
Part
Map
Partition

Source:

/var/www/debian/nest/nest-simulator-2.20.0/lib/sli/mathematica.sli
