Dev #280
@ -24,7 +24,6 @@ import space.kscience.kmath.misc.UnstableKMathAPI
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*/
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@UnstableKMathAPI
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public interface DoubleDomain : Domain<Double> {
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/**
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* Global lower edge
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* @param num axis number
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@ -3,7 +3,10 @@ package space.kscience.kmath.linear
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import space.kscience.kmath.nd.as1D
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/**
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* A group of methods to resolve equation A dot X = B, where A and B are matrices or vectors
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* A group of methods to solve for *X* in equation *X = A <sup>-1</sup> · B*, where *A* and *B* are matrices or
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* vectors.
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*
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* @param T the type of items.
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*/
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public interface LinearSolver<T : Any> {
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/**
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@ -23,7 +26,7 @@ public interface LinearSolver<T : Any> {
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}
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/**
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* Convert matrix to vector if it is possible
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* Convert matrix to vector if it is possible.
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*/
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public fun <T : Any> Matrix<T>.asVector(): Point<T> =
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if (this.colNum == 1)
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@ -31,4 +34,11 @@ public fun <T : Any> Matrix<T>.asVector(): Point<T> =
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else
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error("Can't convert matrix with more than one column to vector")
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/**
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* Creates an n × 1 [VirtualMatrix], where n is the size of the given buffer.
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*
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* @param T the type of elements contained in the buffer.
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* @receiver a buffer.
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* @return the new matrix.
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*/
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public fun <T : Any> Point<T>.asMatrix(): VirtualMatrix<T> = VirtualMatrix(size, 1) { i, _ -> get(i) }
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@ -17,6 +17,8 @@ public typealias Matrix<T> = Structure2D<T>
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/**
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* Alias or using [Buffer] as a point/vector in a many-dimensional space.
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*
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* @param T the type of elements contained in the buffer.
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*/
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public typealias Point<T> = Buffer<T>
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@ -100,8 +100,8 @@ public fun <T : Any> Algebra<T>.bindSymbol(symbol: Symbol): T = bindSymbol(symbo
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public inline operator fun <A : Algebra<*>, R> A.invoke(block: A.() -> R): R = run(block)
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/**
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* Represents linear space without neutral element, i.e. algebraic structure with associative, binary operation [add]
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* and scalar multiplication [multiply].
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* Represents group without neutral element (also known as inverse semigroup), i.e. algebraic structure with
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* associative, binary operation [add].
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*
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* @param T the type of element of this semispace.
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*/
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@ -177,7 +177,7 @@ public interface GroupOperations<T> : Algebra<T> {
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}
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/**
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* Represents linear space with neutral element, i.e. algebraic structure with associative, binary operation [add].
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* Represents group, i.e. algebraic structure with associative, binary operation [add].
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*
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* @param T the type of element of this semispace.
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*/
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@ -189,8 +189,8 @@ public interface Group<T> : GroupOperations<T> {
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}
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/**
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* Represents rng, i.e. algebraic structure with associative, binary, commutative operation [add] and associative,
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* operation [multiply] distributive over [add].
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* Represents ring without multiplicative and additive identities, i.e. algebraic structure with
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* associative, binary, commutative operation [add] and associative, operation [multiply] distributive over [add].
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*
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* @param T the type of element of this semiring.
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*/
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@ -238,7 +238,7 @@ public interface Ring<T> : Group<T>, RingOperations<T> {
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}
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/**
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* Represents field without identity elements, i.e. algebraic structure with associative, binary, commutative operations
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* Represents field without without multiplicative and additive identities, i.e. algebraic structure with associative, binary, commutative operations
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* [add] and [multiply]; binary operation [divide] as multiplication of left operand by reciprocal of right one.
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*
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* @param T the type of element of this semifield.
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@ -276,10 +276,11 @@ public interface FieldOperations<T> : RingOperations<T> {
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}
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/**
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* Represents field, i.e. algebraic structure with three operations: associative "addition" and "multiplication",
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* and "division" and their neutral elements.
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* Represents field, i.e. algebraic structure with three operations: associative, commutative addition and
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* multiplication, and division. **This interface differs from the eponymous mathematical definition: fields in KMath
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* also support associative multiplication by scalar.**
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*
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* @param T the type of element of this semifield.
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* @param T the type of element of this field.
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*/
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public interface Field<T> : Ring<T>, FieldOperations<T>, ScaleOperations<T>, NumericAlgebra<T> {
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override fun number(value: Number): T = scale(one, value.toDouble())
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@ -12,8 +12,8 @@ import kotlin.math.max
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import kotlin.math.min
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import kotlin.math.sign
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public typealias Magnitude = UIntArray
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public typealias TBase = ULong
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private typealias Magnitude = UIntArray
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private typealias TBase = ULong
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/**
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* Kotlin Multiplatform implementation of Big Integer numbers (KBigInteger).
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@ -358,6 +358,9 @@ private fun stripLeadingZeros(mag: Magnitude): Magnitude {
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return mag.sliceArray(IntRange(0, resSize))
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}
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/**
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* Returns the absolute value of the given value [x].
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*/
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public fun abs(x: BigInt): BigInt = x.abs()
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/**
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@ -2,14 +2,28 @@ package space.kscience.kmath.functions
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import space.kscience.kmath.operations.Ring
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/**
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* Represents piecewise-defined function.
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*
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* @param T the piece key type.
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* @param R the sub-function type.
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*/
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public fun interface Piecewise<T, R> {
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/**
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* Returns the appropriate sub-function for given piece key.
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*/
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public fun findPiece(arg: T): R?
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}
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/**
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* Represents piecewise-defined function where all the sub-functions are polynomials.
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*/
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public fun interface PiecewisePolynomial<T : Any> : Piecewise<T, Polynomial<T>>
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/**
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* Ordered list of pieces in piecewise function
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* Basic [Piecewise] implementation where all the pieces are ordered by the [Comparable] type instances.
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*
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* @param T the comparable piece key type.
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*/
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public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) :
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PiecewisePolynomial<T> {
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@ -17,8 +31,10 @@ public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) :
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private val pieces: MutableList<Polynomial<T>> = arrayListOf()
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/**
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* Dynamically add a piece to the "right" side (beyond maximum argument value of previous piece)
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* @param right new rightmost position. If is less then current rightmost position, a error is thrown.
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* Dynamically adds a piece to the right side (beyond maximum argument value of previous piece)
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*
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* @param right new rightmost position. If is less then current rightmost position, an error is thrown.
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* @param piece the sub-function.
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*/
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public fun putRight(right: T, piece: Polynomial<T>) {
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require(right > delimiters.last()) { "New delimiter should be to the right of old one" }
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@ -26,13 +42,19 @@ public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) :
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pieces.add(piece)
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}
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/**
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* Dynamically adds a piece to the left side (beyond maximum argument value of previous piece)
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*
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* @param left the new leftmost position. If is less then current rightmost position, an error is thrown.
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* @param piece the sub-function.
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*/
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public fun putLeft(left: T, piece: Polynomial<T>) {
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require(left < delimiters.first()) { "New delimiter should be to the left of old one" }
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delimiters.add(0, left)
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pieces.add(0, piece)
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}
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override fun findPiece(arg: T): Polynomial<T>? {
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public override fun findPiece(arg: T): Polynomial<T>? {
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if (arg < delimiters.first() || arg >= delimiters.last())
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return null
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else {
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@ -46,7 +68,8 @@ public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) :
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}
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/**
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* Return a value of polynomial function with given [ring] an given [arg] or null if argument is outside of piecewise definition.
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* Return a value of polynomial function with given [ring] an given [arg] or null if argument is outside of piecewise
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* definition.
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*/
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public fun <T : Comparable<T>, C : Ring<T>> PiecewisePolynomial<T>.value(ring: C, arg: T): T? =
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findPiece(arg)?.value(ring, arg)
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@ -10,16 +10,26 @@ import kotlin.math.max
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import kotlin.math.pow
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/**
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* Polynomial coefficients without fixation on specific context they are applied to
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* @param coefficients constant is the leftmost coefficient
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* Polynomial coefficients model without fixation on specific context they are applied to.
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*
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* @param coefficients constant is the leftmost coefficient.
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*/
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public inline class Polynomial<T : Any>(public val coefficients: List<T>)
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/**
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* Returns a [Polynomial] instance with given [coefficients].
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*/
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@Suppress("FunctionName")
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public fun <T : Any> Polynomial(vararg coefficients: T): Polynomial<T> = Polynomial(coefficients.toList())
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/**
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* Evaluates the value of the given double polynomial for given double argument.
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*/
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public fun Polynomial<Double>.value(): Double = coefficients.reduceIndexed { index, acc, d -> acc + d.pow(index) }
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/**
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* Evaluates the value of the given polynomial for given argument.
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*/
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public fun <T : Any, C : Ring<T>> Polynomial<T>.value(ring: C, arg: T): T = ring {
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if (coefficients.isEmpty()) return@ring zero
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var res = coefficients.first()
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@ -35,19 +45,23 @@ public fun <T : Any, C : Ring<T>> Polynomial<T>.value(ring: C, arg: T): T = ring
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}
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/**
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* Represent the polynomial as a regular context-less function
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* Represent the polynomial as a regular context-less function.
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*/
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public fun <T : Any, C : Ring<T>> Polynomial<T>.asFunction(ring: C): (T) -> T = { value(ring, it) }
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/**
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* An algebra for polynomials
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* Space of polynomials.
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*
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* @param T the type of operated polynomials.
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* @param C the intersection of [Ring] of [T] and [ScaleOperations] of [T].
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* @param ring the [C] instance.
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*/
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public class PolynomialSpace<T : Any, C>(
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private val ring: C,
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) : Group<Polynomial<T>>, ScaleOperations<Polynomial<T>> where C : Ring<T>, C : ScaleOperations<T> {
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public override val zero: Polynomial<T> = Polynomial(emptyList())
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override fun Polynomial<T>.unaryMinus(): Polynomial<T> = with(ring) {
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override fun Polynomial<T>.unaryMinus(): Polynomial<T> = ring {
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Polynomial(coefficients.map { -it })
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}
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@ -64,6 +78,9 @@ public class PolynomialSpace<T : Any, C>(
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public override fun scale(a: Polynomial<T>, value: Double): Polynomial<T> =
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ring { Polynomial(List(a.coefficients.size) { index -> a.coefficients[index] * value }) }
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/**
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* Evaluates the polynomial for the given value [arg].
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*/
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public operator fun Polynomial<T>.invoke(arg: T): T = value(ring, arg)
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}
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@ -1,11 +1,11 @@
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package space.kscience.kmath.integration
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/**
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* A general interface for all integrators
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* A general interface for all integrators.
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*/
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public interface Integrator<I : Integrand> {
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/**
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* Run one integration pass and return a new [Integrand] with a new set of features
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* Runs one integration pass and return a new [Integrand] with a new set of features.
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*/
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public fun integrate(integrand: I): I
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}
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@ -8,8 +8,11 @@ import space.kscience.kmath.operations.invoke
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import space.kscience.kmath.structures.MutableBufferFactory
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/**
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* Generic spline interpolator. Not recommended for performance critical places, use platform-specific and type specific ones.
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* Based on https://github.com/apache/commons-math/blob/eb57d6d457002a0bb5336d789a3381a24599affe/src/main/java/org/apache/commons/math4/analysis/interpolation/SplineInterpolator.java
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* Generic spline interpolator. Not recommended for performance critical places, use platform-specific and type
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* specific ones.
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*
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* Based on
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* https://github.com/apache/commons-math/blob/eb57d6d457002a0bb5336d789a3381a24599affe/src/main/java/org/apache/commons/math4/analysis/interpolation/SplineInterpolator.java
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*/
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public class SplineInterpolator<T : Comparable<T>>(
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public override val algebra: Field<T>,
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@ -3,13 +3,40 @@ package space.kscience.kmath.interpolation
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import space.kscience.kmath.nd.Structure2D
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import space.kscience.kmath.structures.Buffer
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/**
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* Pair of associated buffers for X and Y axes values.
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*
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* @param X the type of X values.
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* @param Y the type of Y values.
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*/
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public interface XYPointSet<X, Y> {
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/**
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* The size of all the involved buffers.
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*/
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public val size: Int
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/**
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* The buffer of X values.
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*/
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public val x: Buffer<X>
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/**
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* The buffer of Y values.
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*/
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public val y: Buffer<Y>
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}
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/**
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* Triple of associated buffers for X, Y, and Z axes values.
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*
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* @param X the type of X values.
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* @param Y the type of Y values.
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* @param Z the type of Z values.
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*/
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public interface XYZPointSet<X, Y, Z> : XYPointSet<X, Y> {
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/**
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* The buffer of Z values.
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*/
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public val z: Buffer<Z>
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}
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Reference in New Issue
Block a user