Class

spire.std

SeqLpNormedVectorSpace

Related Doc: package std

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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], 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])

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Value Members

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

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    Definition Classes
    AnyRef → Any

  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any

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

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    Definition Classes
    AnyRef → Any

  4. def additive: CommutativeGroup[SA]

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    Definition Classes
    AdditiveCommutativeGroup → AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  5. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any

  6. def clone(): AnyRef

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

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

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    Definition Classes
    NormedVectorSpace → MetricSpace

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

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    Definition Classes
    VectorSpace

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

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    Definition Classes
    AnyRef

  10. def equals(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any

  11. def finalize(): Unit

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

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

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    Definition Classes
    AnyRef → Any

  13. def hashCode(): Int

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    Definition Classes
    AnyRef → Any

  14. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any

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

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    Definition Classes
    AdditiveMonoid

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

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    Definition Classes
    SeqModule → AdditiveGroup

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

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    Definition Classes
    AnyRef

  18. def negate(sa: SA): SA

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    Definition Classes
    SeqModule → AdditiveGroup

  19. def norm(v: SA): A

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    Definition Classes
    SeqLpNormedVectorSpace → NormedVectorSpace

  20. def normalize(v: SA): SA

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    Definition Classes
    NormedVectorSpace

  21. final def notify(): Unit

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    Definition Classes
    AnyRef

  22. final def notifyAll(): Unit

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    Definition Classes
    AnyRef

  23. val p: Int

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

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    Definition Classes
    SeqModule → AdditiveSemigroup

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

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    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

  26. implicit val scalar: Field[A]

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    Definition Classes
    SeqVectorSpace → VectorSpace → SeqModule → Module

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

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    Definition Classes
    AdditiveMonoid

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

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    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

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

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    Definition Classes
    AnyRef

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

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    Definition Classes
    SeqModule → Module

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

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    Definition Classes
    Module

  32. def toString(): String

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    Definition Classes
    AnyRef → Any

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

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    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

  34. final def wait(): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  37. def zero: SA

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    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

Ungrouped