spire.std

SeqLpNormedVectorSpace

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

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.

Annotations
@SerialVersionUID()
Linear Supertypes
NormedVectorSpace[SA, A], MetricSpace[SA, A], SeqVectorSpace[A, SA], VectorSpace[SA, A], SeqModule[A, SA], Serializable, Serializable, Module[SA, A], AdditiveAbGroup[SA], AdditiveCMonoid[SA], AdditiveCSemigroup[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. Serializable
  8. Serializable
  9. Module
  10. AdditiveAbGroup
  11. AdditiveCMonoid
  12. AdditiveCSemigroup
  13. AdditiveGroup
  14. AdditiveMonoid
  15. AdditiveSemigroup
  16. AnyRef
  17. Any
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Visibility
  1. Public
  2. All

Instance Constructors

  1. new SeqLpNormedVectorSpace(p: Int)(implicit arg0: Field[A], arg1: NRoot[A], arg2: Signed[A], cbf: CanBuildFrom[SA, A, SA])

Value Members

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

    Definition Classes
    AnyRef → Any

  2. final def ##(): Int

    Definition Classes
    AnyRef → Any

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

    Definition Classes
    AnyRef → Any

  4. def additive: AbGroup[SA]

    Definition Classes
    AdditiveAbGroup → AdditiveCMonoid → AdditiveCSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  5. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  6. def clone(): AnyRef

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

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

    Definition Classes
    NormedVectorSpace → MetricSpace

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

    Definition Classes
    VectorSpace

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

    Definition Classes
    AnyRef

  10. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

  11. def finalize(): Unit

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

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

    Definition Classes
    AnyRef → Any

  13. def hashCode(): Int

    Definition Classes
    AnyRef → Any

  14. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

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

    Definition Classes
    SeqModule → AdditiveGroup

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

    Definition Classes
    AnyRef

  17. def negate(sa: SA): SA

    Definition Classes
    SeqModule → AdditiveGroup

  18. def norm(v: SA): A

    Definition Classes
    SeqLpNormedVectorSpace → NormedVectorSpace

  19. def normalize(v: SA): SA

    Definition Classes
    NormedVectorSpace

  20. final def notify(): Unit

    Definition Classes
    AnyRef

  21. final def notifyAll(): Unit

    Definition Classes
    AnyRef

  22. val p: Int

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

    Definition Classes
    SeqModule → AdditiveSemigroup

  24. implicit val scalar: Field[A]

    Definition Classes
    SeqVectorSpace → VectorSpace → SeqModule → Module

  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 timesr(v: SA, r: A): SA

    Definition Classes
    Module

  28. def toString(): String

    Definition Classes
    AnyRef → Any

  29. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  32. 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 Serializable

Inherited from Serializable

Inherited from Module[SA, A]

Inherited from AdditiveAbGroup[SA]

Inherited from AdditiveCMonoid[SA]

Inherited from AdditiveCSemigroup[SA]

Inherited from AdditiveGroup[SA]

Inherited from AdditiveMonoid[SA]

Inherited from AdditiveSemigroup[SA]

Inherited from AnyRef

Inherited from Any

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