SeqLpNormedVectorSpace

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

Instance Constructors

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

Value Members

final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def ##(): Int

Definition Classes
AnyRef → Any
final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def additive: AbGroup[SA]

Definition Classes
AdditiveAbGroup → AdditiveCMonoid → AdditiveCSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
final def asInstanceOf[T0]: T0

Definition Classes
Any
def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
def distance(v: SA, w: SA): A

Definition Classes
NormedVectorSpace → MetricSpace
def divr(v: SA, f: A): SA

Definition Classes
VectorSpace
final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
final def getClass(): Class[_]

Definition Classes
AnyRef → Any
def hashCode(): Int

Definition Classes
AnyRef → Any
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def isZero(a: SA)(implicit ev: Eq[SA]): Boolean

Tests if a is zero.
Tests if a is zero.

Definition Classes
AdditiveMonoid
def minus(x: SA, y: SA): SA

Definition Classes
SeqModule → AdditiveGroup
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def negate(sa: SA): SA

Definition Classes
SeqModule → AdditiveGroup
def norm(v: SA): A

Definition Classes
SeqLpNormedVectorSpace → NormedVectorSpace
def normalize(v: SA): SA

Definition Classes
NormedVectorSpace
final def notify(): Unit

Definition Classes
AnyRef
final def notifyAll(): Unit

Definition Classes
AnyRef
val p: Int
def plus(x: SA, y: SA): SA

Definition Classes
SeqModule → AdditiveSemigroup
implicit val scalar: Field[A]

Definition Classes
SeqVectorSpace → VectorSpace → SeqModule → Module
def sum(as: TraversableOnce[SA]): SA

Given a sequence of as, sum them using the monoid and return the total.
Given a sequence of as, sum them using the monoid and return the total.

Definition Classes
AdditiveMonoid
def sumOption(as: TraversableOnce[SA]): Option[SA]

Given a sequence of as, sum them using the semigroup and return the total.
Given a sequence of as, sum them using the semigroup and return the total.
If the sequence is empty, returns None. Otherwise, returns Some(total).

Definition Classes
AdditiveSemigroup
def sumn(a: SA, n: Int): SA

Return a added with itself n times.
Return a added with itself n times.

Definition Classes
AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
def sumnAboveOne(a: SA, n: Int): SA

Attributes
protected
Definition Classes
AdditiveSemigroup
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def timesl(r: A, sa: SA): SA

Definition Classes
SeqModule → Module
def timesr(v: SA, r: A): SA

Definition Classes
Module
def toString(): String

Definition Classes
AnyRef → Any
final def wait(): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
def zero: SA

Definition Classes
SeqModule → AdditiveMonoid

Related Doc: package std

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

Instance Constructors

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

Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

def additive: AbGroup[SA]

final def asInstanceOf[T0]: T0

def clone(): AnyRef

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

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

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def finalize(): Unit

final def getClass(): Class[_]

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

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

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

final def ne(arg0: AnyRef): Boolean

def negate(sa: SA): SA

def norm(v: SA): A

def normalize(v: SA): SA

final def notify(): Unit

final def notifyAll(): Unit

val p: Int

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

implicit val scalar: Field[A]

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

def sumOption(as: TraversableOnce[SA]): Option[SA]

def sumn(a: SA, n: Int): SA

def sumnAboveOne(a: SA, n: Int): SA

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

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

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

def toString(): String

final def wait(): Unit

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

final def wait(arg0: Long): Unit

def zero: SA

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

Ungrouped