algebra

Type Members

trait Aggregatable[F, A, B] extends AnyRef

Annotations
@implicitNotFound( ... )
type AggregatableK1[M[_], A, B] = Aggregatable[M[A], A, B]
trait ArrayFrom[C, A] extends AnyRef

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@implicitNotFound( ... )
trait Bijection[A, B] extends (A) ⇒ B

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@implicitNotFound( ... )
case class BijectiveIdentity[N]() extends Bijection[N, N] with Product with Serializable
trait DirectedGraph[DG, V, E] extends AnyRef

Annotations
@implicitNotFound( ... )
case class DistanceMatrix[T, F, M](vectors: F)(implicit space: MetricSpace[T, Double], la: LinearAlgebra[M, Int, Int, Double], index: Indexed[F, Int, T], finite: Finite[F, Int]) extends Product with Serializable
trait Endofunctor[E, T] extends AnyRef

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@implicitNotFound( ... )
trait Finite[C, S] extends AnyRef

Annotations
@implicitNotFound( ... )
type FiniteK1[M[_], N, I] = Finite[M[N], I]
trait FoldLeft[F[_]] extends AnyRef

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@implicitNotFound( ... )
trait FromStream[S, A] extends AnyRef
trait FunctionPair[A, B] extends AnyRef

A FunctionPair is not necessarily a bijection, but it could be.
A FunctionPair is not necessarily a bijection, but it could be.

Annotations
@implicitNotFound( ... )
trait Functor[F, A, B, G] extends AnyRef

Annotations
@implicitNotFound( ... )
type FunctorK1[M[_], A, B] = Functor[M[A], A, B, M[B]]
case class GeoCoordinates[N](latitude: UnittedQuantity[Angle, N], longitude: UnittedQuantity[Angle, N]) extends Product with Serializable
trait Indexed[C, I, A] extends AnyRef

Annotations
@implicitNotFound( ... )
type IndexedK1[M[_], I, N] = Indexed[M[N], I, N]
trait LengthSpace[V, R, P] extends MetricSpace[V, R]

http://en.wikipedia.org/wiki/Intrinsic_metric
http://en.wikipedia.org/wiki/Intrinsic_metric

Annotations
@implicitNotFound( ... )
trait LinearAlgebra[M, R, C, T] extends AnyRef

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@implicitNotFound( ... )
trait MapFrom[C, K, V] extends AnyRef

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@implicitNotFound( ... )
trait MapReducible[M, A, B, K, G] extends AnyRef

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@implicitNotFound( ... )
trait Plottable[T] extends AnyRef

Annotations
@implicitNotFound( ... )
trait Position3D[X, Y, Z, P] extends AnyRef
trait Position3DSpace[N, P] extends Position3D[UnittedQuantity[Distance, N], UnittedQuantity[Distance, N], UnittedQuantity[Distance, N], P]
trait Reducible[R, A] extends AnyRef

Annotations
@implicitNotFound( ... )
case class Scale[N, M](factor: M)(implicit evidence$1: Field[M], module: Module[N, M]) extends Bijection[N, N] with Product with Serializable
case class Scale10s[N](exp: Int)(implicit evidence$2: Field[N]) extends Bijection[N, N] with Product with Serializable
case class Scale2s[N](exp: Int)(implicit evidence$3: Field[N]) extends Bijection[N, N] with Product with Serializable
trait Scanner[S, A, B, T] extends AnyRef

Annotations
@implicitNotFound( ... )
trait SetFrom[C, A] extends AnyRef

Annotations
@implicitNotFound( ... )
case class SphericalVector[N](ρ: UnittedQuantity[Distance, N], θ: UnittedQuantity[Angle, N], φ: UnittedQuantity[Angle, N]) extends Product with Serializable

Uses the physics conventions instead of mathematical conventions.
Uses the physics conventions instead of mathematical conventions.
http://en.wikipedia.org/wiki/Spherical_coordinate_system
trait Talliable[F, A, N] extends AnyRef

Annotations
@implicitNotFound( ... )
trait Tics[T] extends AnyRef

Annotations
@implicitNotFound( "Witness not found for Tics[${T}]" )
case class Transform[N](u: N)(implicit group: AbGroup[N]) extends Bijection[N, N] with Product with Serializable
trait UndirectedGraph[UG, V, E] extends AnyRef

Annotations
@implicitNotFound( ... )
trait Vec[V[_]] extends AnyRef

Vec is the Vector typeclass
Vec is the Vector typeclass

Annotations
@implicitNotFound( "Witness not found for Vec[${V}]" )
trait Zero[T] extends AnyRef

Zero
Zero
∅

Annotations
@implicitNotFound( "Witness not found for Zero[${T}]" )
trait Zipper[X, A, Y, B, Z] extends AnyRef
type ZipperK1[M[_], A, B] = Zipper[M[A], A, M[B], B, M[(A, B)]]

Value Members

object Aggregatable
object ArrayFrom
object Bijection
object DirectedGraph
object Endofunctor
object Finite
object FoldLeft
object FromStream
object FunctionPair
object Functor
object GeoCoordinates extends Serializable
object Indexed
object LengthSpace
object LinearAlgebra
object MapFrom
object MapReducible
object Plottable
object Position3DSpace
object Reducible
object Scanner
object SetFrom
object Talliable
object Tics
object UndirectedGraph
object Vec
object Zero
object Zipper
def argmax[R, K, N, S](ks: R, f: (K) ⇒ N)(implicit arg0: Order[N], functorRknS: Functor[R, K, (K, N), S], redicibleS: Reducible[S, (K, N)]): Option[K]
def arithmeticMean[N, F](ns: F)(implicit field: Field[N], aggregatable: Aggregatable[F, N, N], finite: Finite[F, N]): N
implicit val doubleDoubleMetricSpace: MetricSpace[Double, Double]
def generalizedFMean[N, F](f: Bijection[N, N], ns: F)(implicit field: Field[N], functorFaaF: Functor[F, N, N, F], agg: Aggregatable[F, N, N], fin: Finite[F, N]): N

Generalized f-Mean
Generalized f-Mean
https://en.wikipedia.org/wiki/Generalized_mean#Generalized_f-mean
https://en.wikipedia.org/wiki/Quasi-arithmetic_mean
TODO f need only be injective
def generalizedMean[N, F](p: N, ns: F)(implicit field: Field[N], functorFaaF: Functor[F, N, N, F], agg: Aggregatable[F, N, N], fin: Finite[F, N], nroot: NRoot[N]): N

Generalized mean
Generalized mean
https://en.wikipedia.org/wiki/Generalized_mean
TODO could be special-cased for p = -∞ or ∞
def geometricMean[N, F](ns: F)(implicit ev: MultiplicativeMonoid[N], agg: Aggregatable[F, N, N], fin: Finite[F, Int], nroot: NRoot[N]): N
def harmonicMean[N, F](ns: F)(implicit field: Field[N], functorFaaF: Functor[F, N, N, F], agg: Aggregatable[F, N, N], fin: Finite[F, N]): N
package laws
def mean[N, F](ns: F)(implicit field: Field[N], aggregatable: Aggregatable[F, N, N], finite: Finite[F, N]): N

arithmetic, geometric, and harmonic means are "Pythagorean"
arithmetic, geometric, and harmonic means are "Pythagorean"
https://en.wikipedia.org/wiki/Pythagorean_means
object modules
def movingArithmeticMean[F, I, N, G](xs: F, size: I)(implicit convert: (I) ⇒ N, indexed: Indexed[F, I, N], fin: Finite[F, N], field: Field[N], zipper: Zipper[F, N, F, N, G], agg: Aggregatable[F, N, N], scanner: Scanner[G, (N, N), N, F], functor: Functor[F, N, N, F]): F
def movingGeneralizedFMean[F, I, N, G](f: Bijection[N, N], xs: F, size: I)(implicit convert: (I) ⇒ N, indexed: Indexed[F, I, N], field: Field[N], zipper: Zipper[F, N, F, N, G], agg: Aggregatable[F, N, N], scanner: Scanner[G, (N, N), N, F], functor: Functor[F, N, N, F], fin: Finite[F, N]): F
def movingGeneralizedMean[F, I, N, G](p: N, xs: F, size: I)(implicit convert: (I) ⇒ N, indexed: Indexed[F, I, N], field: Field[N], zipper: Zipper[F, N, F, N, G], agg: Aggregatable[F, N, N], scanner: Scanner[G, (N, N), N, F], functor: Functor[F, N, N, F], fin: Finite[F, N], nroot: NRoot[N]): F
def movingGeometricMean[F, I, N, G](xs: F, size: I)(implicit convert: (I) ⇒ Int, indexed: Indexed[F, I, N], field: Field[N], zipper: Zipper[F, N, F, N, G], agg: Aggregatable[F, N, N], scanner: Scanner[G, (N, N), N, F], functor: Functor[F, N, N, F], fin: Finite[F, Int], nroot: NRoot[N]): F
def movingHarmonicMean[F, I, N, G](xs: F, size: I)(implicit convert: (I) ⇒ N, indexed: Indexed[F, I, N], field: Field[N], zipper: Zipper[F, N, F, N, G], agg: Aggregatable[F, N, N], scanner: Scanner[G, (N, N), N, F], functor: Functor[F, N, N, F], fin: Finite[F, N]): F
def product[A, F](fa: F)(implicit ev: MultiplicativeMonoid[A], agg: Aggregatable[F, A, A]): A
implicit val rationalDoubleMetricSpace: MetricSpace[Rational, Double]
implicit val realDoubleMetricSpace: MetricSpace[Real, Double]
def sum[A, F](fa: F)(implicit ev: AdditiveMonoid[A], agg: Aggregatable[F, A, A]): A
implicit def wrappedStringSpace[N](implicit iscSpace: MetricSpace[IndexedSeq[Char], N]): MetricSpace[String, N]
def Π[A, F](fa: F)(implicit ev: MultiplicativeMonoid[A], agg: Aggregatable[F, A, A]): A
def Σ[A, F](fa: F)(implicit ev: AdditiveMonoid[A], agg: Aggregatable[F, A, A]): A

package algebra

Type Members

trait Aggregatable[F, A, B] extends AnyRef

type AggregatableK1[M[_], A, B] = Aggregatable[M[A], A, B]

trait ArrayFrom[C, A] extends AnyRef

trait Bijection[A, B] extends (A) ⇒ B

case class BijectiveIdentity[N]() extends Bijection[N, N] with Product with Serializable

trait DirectedGraph[DG, V, E] extends AnyRef

case class DistanceMatrix[T, F, M](vectors: F)(implicit space: MetricSpace[T, Double], la: LinearAlgebra[M, Int, Int, Double], index: Indexed[F, Int, T], finite: Finite[F, Int]) extends Product with Serializable

trait Endofunctor[E, T] extends AnyRef

trait Finite[C, S] extends AnyRef

type FiniteK1[M[_], N, I] = Finite[M[N], I]

trait FoldLeft[F[_]] extends AnyRef

trait FromStream[S, A] extends AnyRef

trait FunctionPair[A, B] extends AnyRef

trait Functor[F, A, B, G] extends AnyRef

type FunctorK1[M[_], A, B] = Functor[M[A], A, B, M[B]]

case class GeoCoordinates[N](latitude: UnittedQuantity[Angle, N], longitude: UnittedQuantity[Angle, N]) extends Product with Serializable

trait Indexed[C, I, A] extends AnyRef

type IndexedK1[M[_], I, N] = Indexed[M[N], I, N]

trait LengthSpace[V, R, P] extends MetricSpace[V, R]

trait LinearAlgebra[M, R, C, T] extends AnyRef

trait MapFrom[C, K, V] extends AnyRef

trait MapReducible[M, A, B, K, G] extends AnyRef

trait Plottable[T] extends AnyRef

trait Position3D[X, Y, Z, P] extends AnyRef

trait Position3DSpace[N, P] extends Position3D[UnittedQuantity[Distance, N], UnittedQuantity[Distance, N], UnittedQuantity[Distance, N], P]

trait Reducible[R, A] extends AnyRef

case class Scale[N, M](factor: M)(implicit evidence$1: Field[M], module: Module[N, M]) extends Bijection[N, N] with Product with Serializable

case class Scale10s[N](exp: Int)(implicit evidence$2: Field[N]) extends Bijection[N, N] with Product with Serializable

case class Scale2s[N](exp: Int)(implicit evidence$3: Field[N]) extends Bijection[N, N] with Product with Serializable

trait Scanner[S, A, B, T] extends AnyRef

trait SetFrom[C, A] extends AnyRef

case class SphericalVector[N](ρ: UnittedQuantity[Distance, N], θ: UnittedQuantity[Angle, N], φ: UnittedQuantity[Angle, N]) extends Product with Serializable

trait Talliable[F, A, N] extends AnyRef

trait Tics[T] extends AnyRef

case class Transform[N](u: N)(implicit group: AbGroup[N]) extends Bijection[N, N] with Product with Serializable

trait UndirectedGraph[UG, V, E] extends AnyRef

trait Vec[V[_]] extends AnyRef

trait Zero[T] extends AnyRef

trait Zipper[X, A, Y, B, Z] extends AnyRef

type ZipperK1[M[_], A, B] = Zipper[M[A], A, M[B], B, M[(A, B)]]

Value Members

object Aggregatable

object ArrayFrom

object Bijection

object DirectedGraph

object Endofunctor

object Finite

object FoldLeft

object FromStream

object FunctionPair

object Functor

object GeoCoordinates extends Serializable

object Indexed

object LengthSpace

object LinearAlgebra

object MapFrom

object MapReducible

object Plottable

object Position3DSpace

object Reducible

object Scanner

object SetFrom

object Talliable

object Tics

object UndirectedGraph

object Vec

object Zero

object Zipper

def argmax[R, K, N, S](ks: R, f: (K) ⇒ N)(implicit arg0: Order[N], functorRknS: Functor[R, K, (K, N), S], redicibleS: Reducible[S, (K, N)]): Option[K]

def arithmeticMean[N, F](ns: F)(implicit field: Field[N], aggregatable: Aggregatable[F, N, N], finite: Finite[F, N]): N

implicit val doubleDoubleMetricSpace: MetricSpace[Double, Double]

def generalizedFMean[N, F](f: Bijection[N, N], ns: F)(implicit field: Field[N], functorFaaF: Functor[F, N, N, F], agg: Aggregatable[F, N, N], fin: Finite[F, N]): N

def generalizedMean[N, F](p: N, ns: F)(implicit field: Field[N], functorFaaF: Functor[F, N, N, F], agg: Aggregatable[F, N, N], fin: Finite[F, N], nroot: NRoot[N]): N

def geometricMean[N, F](ns: F)(implicit ev: MultiplicativeMonoid[N], agg: Aggregatable[F, N, N], fin: Finite[F, Int], nroot: NRoot[N]): N

def harmonicMean[N, F](ns: F)(implicit field: Field[N], functorFaaF: Functor[F, N, N, F], agg: Aggregatable[F, N, N], fin: Finite[F, N]): N

package laws

def mean[N, F](ns: F)(implicit field: Field[N], aggregatable: Aggregatable[F, N, N], finite: Finite[F, N]): N