The Norm(A, p) command returns the norm of the array V.

The default value of p is infinity. In this case, the maximum of the absolute values of the elements of A is returned.

If p is 1, then the $L^1$ norm of A, defined as the sum of the absolute values of the elements of A, is returned.

If p is 2, then the $L^2$ norm of A is returned. This is defined by the following formula, with $N$ being the number of elements in A.

The NormDifference(A, B, p) command returns the norm of the difference of the arrays A and B, with p defined as above. A and B must have the same number of elements.

Before the code performing the computation runs, Maple converts each input Array to a hardware datatype, first attempting float[8] and subsequently complex[8], unless it already has one of these datatypes. For this reason, it is most efficient the input Arrays have one of these datatypes beforehand.

The SignalProcessing[Norm] and SignalProcessing[NormDifference] commands are thread-safe as of Maple 17.

For more information on thread safety, see index/threadsafe.

$\mathrm{with}\left(\mathrm{SignalProcessing}\right)\:$

$a≔\mathrm{Array}\left(\left[1\,2\,3\,4\,5\right]\,'\mathrm{datatype}'='\mathrm{float}'\left[8\right]\right)$

$a≔\left[\begin{array}{ccccc}1.& 2.& 3.& 4.& 5.\end{array}\right]$

$\mathrm{Norm}\left(a\right)$

$5.$

$\mathrm{Norm}\left(a\,\mathrm{\infty }\right)$

$5.$

$\mathrm{Norm}\left(a\,1\right)$

$15.$

$\mathrm{Norm}\left(a\,2\right)$

$7.41619848709566298$

$b≔\mathrm{Array}\left(\left[5\,4\,3\,2\,1\right]\,'\mathrm{datatype}'='\mathrm{float}'\left[8\right]\right)$

$b≔\left[\begin{array}{ccccc}5.& 4.& 3.& 2.& 1.\end{array}\right]$

$a-b$

$\left[\begin{array}{ccccc}\mathrm{-4.}& \mathrm{-2.}& 0.& 2.& 4.\end{array}\right]$

$\mathrm{NormDifference}\left(a\,b\right)$

$4.$

$\mathrm{NormDifference}\left(a\,b\,\mathrm{\infty }\right)$

$4.$

$\mathrm{NormDifference}\left(a\,b\,1\right)$

$12.$

$\mathrm{NormDifference}\left(a\,b\,2\right)$

$6.32455532033675905$

The SignalProcessing[Norm] and SignalProcessing[NormDifference] commands were introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.