compute the norm of an array of samples - Maple Help

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SignalProcessing[Norm] - compute the norm of an array of samples

SignalProcessing[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 L1 norm of A, defined as the sum of the absolute values of the elements of A, is returned.

• 

If p is 2, then the L2 norm of A is returned. This is defined by the following formula, with N being the number of elements in A.

k=1Nak2

• 

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.

Thread Safety

• 

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

• 

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

Examples

withSignalProcessing:

a:=Array1,2,3,4,5,'datatype'='float'8

a:=1.2.3.4.5.

(1)

Norma

5.

(2)

Norma,∞

5.

(3)

Norma,1

15.

(4)

Norma,2

7.41619848709566298

(5)

b:=Array5,4,3,2,1,'datatype'='float'8

b:=5.4.3.2.1.

(6)

ab

4.2.0.2.4.

(7)

NormDifferencea,b

4.

(8)

NormDifferencea,b,∞

4.

(9)

NormDifferencea,b,1

12.

(10)

NormDifferencea,b,2

6.32455532033675905

(11)

See Also

Array, LinearAlgebra[VectorNorm], with


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