Package space.kscience.kmath.linear

Types

BufferedLinearSpace

common

class BufferedLinearSpace<T : Any, A : Ring<T>>(elementAlgebra: A, bufferFactory: BufferFactory<T>) : LinearSpace<T, A>

CholeskyDecompositionFeature

common

interface CholeskyDecompositionFeature<T : Any> : MatrixFeature

Matrices with this feature support Cholesky factorization: a = l · l^H where a is the owning matrix.

DeterminantFeature

common

interface DeterminantFeature<T : Any> : MatrixFeature

Matrices with this feature can compute their determinant.

DiagonalFeature

common

interface DiagonalFeature : MatrixFeature

Matrices with this feature are considered to have only diagonal non-null elements.

InverseMatrixFeature

common

interface InverseMatrixFeature<T : Any> : MatrixFeature

Matrices with this feature can be inverted: inverse = a^-1 where a is the owning matrix.

LFeature

common

object LFeature : MatrixFeature

Matrices with this feature are lower triangular ones.

LinearSolver

common

interface LinearSolver<T : Any>

A group of methods to solve for X in equation X = A ^-1 · B, where A and B are matrices or vectors.

LinearSpace

common

interface LinearSpace<T : Any, out A : Ring<T>>

Basic operations on matrices and vectors.

LupDecomposition

common

class LupDecomposition<T : Any>(context: LinearSpace<T, *>, elementContext: Field<T>, lu: Matrix<T>, pivot: IntArray, even: Boolean) : LupDecompositionFeature<T> , DeterminantFeature<T>

Common implementation of LupDecompositionFeature.

LupDecompositionFeature

common

interface LupDecompositionFeature<T : Any> : MatrixFeature

Matrices with this feature support LU factorization with partial pivoting: p · a = l · u where a is the owning matrix.

Matrix

common

typealias Matrix<T> = Structure2D<T>

Alias for Structure2D with more familiar name.

MatrixBuilder

common

class MatrixBuilder<T : Any, A : Ring<T>>(linearSpace: LinearSpace<T, A>, rows: Int, columns: Int)

MatrixFeature

common

interface MatrixFeature : StructureFeature

A marker interface representing some properties of matrices or additional transformations of them.

MatrixWrapper

common

class MatrixWrapper<T : Any> : Structure2D<T>

A Matrix that holds MatrixFeature objects.

MutableMatrix

common

typealias MutableMatrix<T> = MutableStructure2D<T>

OrthogonalFeature

common

object OrthogonalFeature : MatrixFeature

Matrices with this feature are orthogonal ones: a · a^T = u where a is the owning matrix, u is the unit matrix (UnitFeature).

Point

common

typealias Point<T> = Buffer<T>

Alias or using Buffer as a point/vector in a many-dimensional space.

QRDecompositionFeature

common

interface QRDecompositionFeature<T : Any> : MatrixFeature

Matrices with this feature support QR factorization: a = q · r where a is the owning matrix.

SingularValueDecompositionFeature

common

interface SingularValueDecompositionFeature<T : Any> : MatrixFeature

Matrices with this feature support SVD: a = u · s · v^H where a is the owning matrix.

TransposedFeature

common

class TransposedFeature<T : Any>(original: Matrix<T>) : MatrixFeature

UFeature

common

object UFeature : MatrixFeature

Matrices with this feature are upper triangular ones.

UnitFeature

common

object UnitFeature : DiagonalFeature

Matrices with this feature have unit elements on diagonal and zero elements in all other places.

VirtualMatrix

common

class VirtualMatrix<T : Any>(rowNum: Int, colNum: Int, generator: (i: Int, j: Int) -> T) : Structure2D<T>

The matrix where each element is evaluated each time when is being accessed.

ZeroFeature

common

object ZeroFeature : DiagonalFeature

Matrices with this feature have all zero elements.

Functions

asMatrix

common

fun <T : Any> Point<T>.asMatrix(): VirtualMatrix<T>

Creates an n × 1 VirtualMatrix, where n is the size of the given buffer.

asVector

common

fun <T : Any> Matrix<T>.asVector(): Point<T>

Convert matrix to vector if it is possible.

column

common

fun <T : Any> LinearSpace<T, Ring<T>>.column(vararg values: T): Matrix<T>

inline fun <T : Any> LinearSpace<T, Ring<T>>.column(size: Int, crossinline builder: (Int) -> T): Matrix<T>

DeterminantFeature

common

fun <T : Any> DeterminantFeature(determinant: T): DeterminantFeature<T>

Produces a DeterminantFeature where the DeterminantFeature.determinant is determinant.

getFeature

common

inline fun <T : Any, F : StructureFeature> LinearSpace<T, *>.getFeature(structure: Matrix<T>): F?

Get a feature of the structure in this scope.

inverseWithLup

common

fun LinearSpace<Double, DoubleField>.inverseWithLup(matrix: Matrix<Double>): Matrix<Double>

Inverses a square matrix using LUP decomposition.

inline fun <T : Comparable<T>> LinearSpace<T, Field<T>>.inverseWithLup(matrix: Matrix<T>, noinline bufferFactory: MutableBufferFactory<T> = MutableBuffer.Companion::auto, noinline checkSingular: (T) -> Boolean): Matrix<T>

invoke

common

operator fun <LS : LinearSpace<*, *>, R> LS.invoke(block: LS.() -> R): R

lup

common

fun LinearSpace<Double, DoubleField>.lup(matrix: Matrix<Double>): LupDecomposition<Double>

inline fun <T : Comparable<T>> LinearSpace<T, Field<T>>.lup(matrix: Matrix<T>, noinline checkSingular: (T) -> Boolean): LupDecomposition<T>

fun <T : Comparable<T>> LinearSpace<T, Field<T>>.lup(factory: MutableBufferFactory<T>, matrix: Matrix<T>, checkSingular: (T) -> Boolean): LupDecomposition<T>

Create a lup decomposition of generic matrix.

matrix

common

fun <T : Any, A : Ring<T>> LinearSpace<T, A>.matrix(rows: Int, columns: Int): MatrixBuilder<T, A>

Create a matrix builder with given number of rows and columns

one

common

fun <T : Any> LinearSpace<T, Ring<T>>.one(rows: Int, columns: Int): Matrix<T>

Diagonal matrix of ones.

plus

common

operator fun <T : Any> Matrix<T>.plus(newFeatures: Collection<MatrixFeature>): MatrixWrapper<T>

Add a collection of features to a Matrix

operator fun <T : Any> Matrix<T>.plus(newFeature: MatrixFeature): MatrixWrapper<T>

Add a single feature to a Matrix

row

common

fun <T : Any> LinearSpace<T, Ring<T>>.row(vararg values: T): Matrix<T>

inline fun <T : Any> LinearSpace<T, Ring<T>>.row(size: Int, crossinline builder: (Int) -> T): Matrix<T>

solveWithLup

common

inline fun <T : Any> LupDecomposition<T>.solveWithLup(matrix: Matrix<T>): Matrix<T>

fun LinearSpace<Double, DoubleField>.solveWithLup(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double>

fun <T : Any> LupDecomposition<T>.solveWithLup(factory: MutableBufferFactory<T>, matrix: Matrix<T>): Matrix<T>

inline fun <T : Comparable<T>> LinearSpace<T, Field<T>>.solveWithLup(a: Matrix<T>, b: Matrix<T>, noinline bufferFactory: MutableBufferFactory<T> = MutableBuffer.Companion::auto, noinline checkSingular: (T) -> Boolean): Matrix<T>

Solves a system of linear equations ax = b* using LUP decomposition.

transpose

common

fun <T : Any> Matrix<T>.transpose(): Matrix<T>

Create a virtual transposed matrix without copying anything.

vector

common

fun <T : Any> LinearSpace<T, Ring<T>>.vector(vararg elements: T): Point<T>

zero

common

fun <T : Any> LinearSpace<T, Ring<T>>.zero(rows: Int, columns: Int): Matrix<T>

A virtual matrix of zeroes

Properties

origin

common

val <T : Any> Matrix<T>.origin: Matrix<T>

Return the original matrix.