spire.algebra

SeqLpNormedVectorSpace

trait SeqLpNormedVectorSpace[A, SA <: SeqLike[A, SA]] extends SeqVectorSpace[A, SA] with NormedVectorSpace[SA, A]

The L_p norm is equal to the p-th root of the sum of each element to the power p. For instance, if p = 1 we have the Manhattan distance. If you'd like the Euclidean norm (p = 2), then you'd probably be best to use an InnerProductSpace instead.

Linear Supertypes
NormedVectorSpace[SA, A], MetricSpace[SA, A], SeqVectorSpace[A, SA], VectorSpace[SA, A], SeqModule[A, SA], Module[SA, A], AdditiveAbGroup[SA], AdditiveGroup[SA], AdditiveMonoid[SA], AdditiveSemigroup[SA], AnyRef, Any
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Inherited
  1. SeqLpNormedVectorSpace
  2. NormedVectorSpace
  3. MetricSpace
  4. SeqVectorSpace
  5. VectorSpace
  6. SeqModule
  7. Module
  8. AdditiveAbGroup
  9. AdditiveGroup
  10. AdditiveMonoid
  11. AdditiveSemigroup
  12. AnyRef
  13. Any
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Abstract Value Members

  1. implicit abstract def cbf: CanBuildFrom[SA, A, SA]

    Definition Classes
    SeqModule

  2. abstract def nroot: NRoot[A]

  3. abstract def p: Int

  4. implicit abstract def scalar: Field[A]

    Definition Classes
    VectorSpace → Module

  5. abstract def signed: Signed[A]

Concrete Value Members

  1. final def !=(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  2. final def !=(arg0: Any): Boolean

    Definition Classes
    Any

  3. final def ##(): Int

    Definition Classes
    AnyRef → Any

  4. final def ==(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  5. final def ==(arg0: Any): Boolean

    Definition Classes
    Any

  6. def additive: AbGroup[SA]

    Definition Classes
    AdditiveAbGroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  7. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  8. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws()

  9. def distance(v: SA, w: SA): A

    Definition Classes
    NormedVectorSpace → MetricSpace

  10. def divr(v: SA, f: A): SA

    Definition Classes
    VectorSpace

  11. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  12. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

  13. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws()

  14. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any

  15. def hashCode(): Int

    Definition Classes
    AnyRef → Any

  16. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

  17. def minus(x: SA, y: SA): SA

    Definition Classes
    SeqModule → AdditiveGroup

  18. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  19. def negate(sa: SA): SA

    Definition Classes
    SeqModule → AdditiveGroup

  20. def norm(v: SA): A

    Definition Classes
    SeqLpNormedVectorSpace → NormedVectorSpace

  21. def normalize(v: SA): SA

    Definition Classes
    NormedVectorSpace

  22. final def notify(): Unit

    Definition Classes
    AnyRef

  23. final def notifyAll(): Unit

    Definition Classes
    AnyRef

  24. def plus(x: SA, y: SA): SA

    Definition Classes
    SeqModule → AdditiveSemigroup

  25. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef

  26. def timesl(r: A, sa: SA): SA

    Definition Classes
    SeqModule → Module

  27. def toString(): String

    Definition Classes
    AnyRef → Any

  28. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws()

  29. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws()

  30. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws()

  31. def zero: SA

    Definition Classes
    SeqModule → AdditiveMonoid

Inherited from NormedVectorSpace[SA, A]

Inherited from MetricSpace[SA, A]

Inherited from SeqVectorSpace[A, SA]

Inherited from VectorSpace[SA, A]

Inherited from SeqModule[A, SA]

Inherited from Module[SA, A]

Inherited from AdditiveAbGroup[SA]

Inherited from AdditiveGroup[SA]

Inherited from AdditiveMonoid[SA]

Inherited from AdditiveSemigroup[SA]

Inherited from AnyRef

Inherited from Any

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