Norm - Maple Help

SignalProcessing

 Norm
 compute the norm of an array of samples
 NormDifference
 compute the norm of the difference of arrays of samples

 Calling Sequence Norm(A, p) NormDifference(A, B, p)

Parameters

 A, B - Arrays of real or complex numeric values; signals p - (optional) infinity, 1 or 2; type of norm

Description

 • 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.

$\sqrt{{\sum }_{k=1}^{N}{\left|{a}_{k}\right|}^{2}}$

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$
 > $a≔\mathrm{Array}\left(\left[1,2,3,4,5\right],'\mathrm{datatype}'='\mathrm{float}'\left[8\right]\right)$
 ${a}{≔}\left[\begin{array}{ccccc}{1.}& {2.}& {3.}& {4.}& {5.}\end{array}\right]$ (1)
 > $\mathrm{Norm}\left(a\right)$
 ${5.}$ (2)
 > $\mathrm{Norm}\left(a,\mathrm{\infty }\right)$
 ${5.}$ (3)
 > $\mathrm{Norm}\left(a,1\right)$
 ${15.}$ (4)
 > $\mathrm{Norm}\left(a,2\right)$
 ${7.41619848709566298}$ (5)
 > $b≔\mathrm{Array}\left(\left[5,4,3,2,1\right],'\mathrm{datatype}'='\mathrm{float}'\left[8\right]\right)$
 ${b}{≔}\left[\begin{array}{ccccc}{5.}& {4.}& {3.}& {2.}& {1.}\end{array}\right]$ (6)
 > $a-b$
 $\left[\begin{array}{ccccc}{-4.}& {-2.}& {0.}& {2.}& {4.}\end{array}\right]$ (7)
 > $\mathrm{NormDifference}\left(a,b\right)$
 ${4.}$ (8)
 > $\mathrm{NormDifference}\left(a,b,\mathrm{\infty }\right)$
 ${4.}$ (9)
 > $\mathrm{NormDifference}\left(a,b,1\right)$
 ${12.}$ (10)
 > $\mathrm{NormDifference}\left(a,b,2\right)$
 ${6.32455532033675905}$ (11)

Compatibility

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