MapAt


Name:
MapAt - applies a function to some of the elements of its argument
Synopsis:
array1 proc array2 MapAt -> array3  
Examples:
 

[3 4 5 6 7] {dup mul} -2 MapAt
-> [3 4 5 36 7]
[3 [-9 -12] 5 6 7] {dup mul} [2 2] MapAt
-> [3 [-9 144] 5 6 7]
[3 4 5 6 7] {dup mul} [[1] [3]] MapAt
-> [9 4 25 6 7]
[[3 9] 4 [5 -11] 6 7] {dup mul} [[1 2] [3 1]] MapAt
-> [[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
-> [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) <- 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: Source:
/home/graber/work-nest/nest-git/nest-simulator/lib/sli/mathematica.sli