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( 0L )
Linear Supertypes
NormedVectorSpace[SA, A], MetricSpace[SA, A], SeqVectorSpace[A, SA], VectorSpace[SA, A], SeqModule[A, SA], Module[SA, A], AdditiveCommutativeGroup[SA], AdditiveCommutativeMonoid[SA], AdditiveCommutativeSemigroup[SA], AdditiveGroup[SA], AdditiveMonoid[SA], AdditiveSemigroup[SA], Serializable, Serializable, AnyRef, Any
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Inherited
  1. SeqLpNormedVectorSpace
  2. NormedVectorSpace
  3. MetricSpace
  4. SeqVectorSpace
  5. VectorSpace
  6. SeqModule
  7. Module
  8. AdditiveCommutativeGroup
  9. AdditiveCommutativeMonoid
  10. AdditiveCommutativeSemigroup
  11. AdditiveGroup
  12. AdditiveMonoid
  13. AdditiveSemigroup
  14. Serializable
  15. Serializable
  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: 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: CommutativeGroup[SA]

    Definition Classes
    AdditiveCommutativeGroup → AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → 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( classOf[java.lang.Throwable] )

  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 isZero(a: SA)(implicit ev: Eq[SA]): Boolean

    Definition Classes
    AdditiveMonoid

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

    Definition Classes
    SeqModule → AdditiveGroup

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

    Definition Classes
    AnyRef

  20. def negate(sa: SA): SA

    Definition Classes
    SeqModule → AdditiveGroup

  21. def norm(v: SA): A

    Definition Classes
    SeqLpNormedVectorSpace → NormedVectorSpace

  22. def normalize(v: SA): SA

    Definition Classes
    NormedVectorSpace

  23. final def notify(): Unit

    Definition Classes
    AnyRef

  24. final def notifyAll(): Unit

    Definition Classes
    AnyRef

  25. val p: Int

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

    Definition Classes
    SeqModule → AdditiveSemigroup

  27. def positiveSumN(a: SA, n: Int): SA

    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

  28. implicit val scalar: Field[A]

    Definition Classes
    SeqVectorSpace → VectorSpace → SeqModule → Module

  29. def sum(as: TraversableOnce[SA]): SA

    Definition Classes
    AdditiveMonoid

  30. def sumN(a: SA, n: Int): SA

    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

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

    Definition Classes
    AnyRef

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

    Definition Classes
    SeqModule → Module

  33. def timesr(v: SA, r: A): SA

    Definition Classes
    Module

  34. def toString(): String

    Definition Classes
    AnyRef → Any

  35. def trySum(as: TraversableOnce[SA]): Option[SA]

    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

  36. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  39. 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 AdditiveCommutativeGroup[SA]

Inherited from AdditiveCommutativeMonoid[SA]

Inherited from AdditiveCommutativeSemigroup[SA]

Inherited from AdditiveGroup[SA]

Inherited from AdditiveMonoid[SA]

Inherited from AdditiveSemigroup[SA]

Inherited from Serializable

Inherited from Serializable

Inherited from AnyRef

Inherited from Any

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