Documentation API of the 'org.ejml.ops.NormOps' Java class

Class NormOps

  • public class NormOpsextends Object

    Norms are a measure of the size of a vector or a matrix. One typical application is in error analysis.

    Vector norms have the following properties:

    1. ||x|| > 0 if x ≠ 0 and ||0|| = 0
    2. ||αx|| = |α| ||x||
    3. ||x+y|| ≤ ||x|| + ||y||

    Matrix norms have the following properties:

    1. ||A|| > 0 if A ≠ 0 where A ∈ ℜ m × n
    2. || α A || = |α| ||A|| where A ∈ ℜ m × n
    3. ||A+B|| ≤ ||A|| + ||B|| where A and B are ∈ ℜ m × n
    4. ||AB|| ≤ ||A|| ||B|| where A and B are ∈ ℜ m × m
    Note that the last item in the list only applies to square matrices.

    Matrix norms can be induced from vector norms as is shown below:

    ||A||M = maxx≠0||Ax||v/||x||v

    where ||.||M is the induced matrix norm for the vector norm ||.||v.

    By default implementations that try to mitigate overflow/underflow are used. If the word fast is found before a function's name that means it does not mitigate those issues, but runs a bit faster.

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