# MapAt

Command: MapAt

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.

Author
Diesmann
Synopsis
array1 proc array2 MapAt -> array3
References

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

File
lib/sli/mathematica.sli
Remarks

This function is an implementation of Mathematica's MapAt function.
Mathematica-style functions in SLI use Mathematica index notation.
FirstVersion
2007.08.12