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

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.

Warning: You cannot see the full API documentation of this class since the access to the DatMelt documentation for third-party Java classes is denied. Guests can only view jhplot Java API. To view the complete description of this class and its methods, please request the full DataMelt membership.

If you are already a full member, please login to the DataMelt member area before visiting this documentation.