DOTPOWER Elementwise Power Operator
Section: Mathematical Operators
Usage
Raises one numerical array to another array (elementwise). There are three operators all with the same general syntax:y = a .^ b
The result y
depends on which of the following three situations applies to the arguments a
and b
:

a
is a scalar,b
is an arbitraryn
dimensional numerical array, in which case the output isa
raised to the power of each element ofb
, and the output is the same size asb
. 
a
is ann
dimensional numerical array, andb
is a scalar, then the output is the same size asa
, and is defined by each element ofa
raised to the powerb
. 
a
andb
are bothn
dimensional numerical arrays of \emph{the same size}. In this case, each element of the output is the corresponding element ofa
raised to the power defined by the corresponding element ofb
.
typerules
for more details.
Function Internals
There are three formulae for this operator. For the first form
and the second form
and in the third form
Examples
We demonstrate the three forms of the dotpower operator using some simple examples. First, the case of a scalar raised to a series of values.> a = 2 a = 2 > b = 1:4 b = 1 2 3 4 > c = a.^b c = 2 4 8 16
The second case shows a vector raised to a scalar.
> c = b.^a c = 1 4 9 16
The third case shows the most general use of the dotpower operator.
> A = [1,2;3,2] A = 1 2 3 2 > B = [2,1.5;0.5,0.6] B = 2.0000 1.5000 0.5000 0.6000 > C = A.^B C = 1.0000 2.8284 1.7321 1.5157