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Matrix revision

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Alexander Nozik 2019-01-16 14:52:27 +03:00
parent 037735c210
commit 7e83b080ad
9 changed files with 345 additions and 274 deletions
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258
kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LUDecomposition.kt
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@ -2,31 +2,39 @@ package scientifik.kmath.linear
import scientifik.kmath.operations.Field import scientifik.kmath.operations.Field
import scientifik.kmath.operations.RealField import scientifik.kmath.operations.RealField
import scientifik.kmath.operations.Ring
import scientifik.kmath.structures.*
import scientifik.kmath.structures.MutableBuffer.Companion.boxing import scientifik.kmath.structures.MutableBuffer.Companion.boxing
import scientifik.kmath.structures.MutableNDStructure
import scientifik.kmath.structures.NDStructure
import scientifik.kmath.structures.get
import scientifik.kmath.structures.mutableNdStructure
import kotlin.math.absoluteValue
/** /**
* Implementation based on Apache common-maths LU-decomposition * Matrix LUP decomposition
*/ */
abstract class LUDecomposition<T : Comparable<T>, F : Field<T>>(val matrix: Matrix<T, F>) { interface LUPDecompositionFeature<T : Any> : DeterminantFeature<T> {
/**
* A reference to L-matrix
*/
val l: Matrix<T>
/**
* A reference to u-matrix
*/
val u: Matrix<T>
/**
* Pivoting points for each row
*/
val pivot: IntArray
/**
* Permutation matrix based on [pivot]
*/
val p: Matrix<T>
}
private val field get() = matrix.context.ring
/** Entries of LU decomposition. */
internal val lu: NDStructure<T>
/** Pivot permutation associated with LU decomposition. */
internal val pivot: IntArray
/** Parity of the permutation associated with the LU decomposition. */
private var even: Boolean = false
init { private class LUPDecomposition<T : Comparable<T>, R : Ring<T>>(
val pair = calculateLU() val context: R,
lu = pair.first val lu: NDStructure<T>,
pivot = pair.second override val pivot: IntArray,
} private val even: Boolean
) : LUPDecompositionFeature<T> {
/** /**
* Returns the matrix L of the decomposition. * Returns the matrix L of the decomposition.
@ -34,13 +42,11 @@ abstract class LUDecomposition<T : Comparable<T>, F : Field<T>>(val matrix: Matr
* L is a lower-triangular matrix * L is a lower-triangular matrix
* @return the L matrix (or null if decomposed matrix is singular) * @return the L matrix (or null if decomposed matrix is singular)
*/ */
val l: Matrix<out T, F> by lazy { override val l: Matrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1]) { i, j ->
matrix.context.produce(matrix.numRows, matrix.numCols) { i, j -> when {
when { j < i -> lu[i, j]
j < i -> lu[i, j] j == i -> context.one
j == i -> matrix.context.ring.one else -> context.zero
else -> matrix.context.ring.zero
}
} }
} }
@ -51,12 +57,11 @@ abstract class LUDecomposition<T : Comparable<T>, F : Field<T>>(val matrix: Matr
* U is an upper-triangular matrix * U is an upper-triangular matrix
* @return the U matrix (or null if decomposed matrix is singular) * @return the U matrix (or null if decomposed matrix is singular)
*/ */
val u: Matrix<out T, F> by lazy { override val u: Matrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1]) { i, j ->
matrix.context.produce(matrix.numRows, matrix.numCols) { i, j -> if (j >= i) lu[i, j] else context.zero
if (j >= i) lu[i, j] else field.zero
}
} }
/** /**
* Returns the P rows permutation matrix. * Returns the P rows permutation matrix.
* *
@ -67,59 +72,64 @@ abstract class LUDecomposition<T : Comparable<T>, F : Field<T>>(val matrix: Matr
* @return the P rows permutation matrix (or null if decomposed matrix is singular) * @return the P rows permutation matrix (or null if decomposed matrix is singular)
* @see .getPivot * @see .getPivot
*/ */
val p: Matrix<out T, F> by lazy { override val p: Matrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1]) { i, j ->
matrix.context.produce(matrix.numRows, matrix.numCols) { i, j -> if (j == pivot[i]) context.one else context.zero
//TODO ineffective. Need sparse matrix for that
if (j == pivot[i]) field.one else field.zero
}
} }
/** /**
* Return the determinant of the matrix * Return the determinant of the matrix
* @return determinant of the matrix * @return determinant of the matrix
*/ */
val determinant: T override val determinant: T by lazy {
get() { with(context) {
with(matrix.context.ring) { (0 until lu.shape[0]).fold(if (even) one else -one) { value, i -> value * lu[i, i] }
var determinant = if (even) one else -one
for (i in 0 until matrix.numRows) {
determinant *= lu[i, i]
}
return determinant
}
} }
}
}
/**
* Implementation based on Apache common-maths LU-decomposition
*/
class LUPDecompositionBuilder<T : Comparable<T>, F : Field<T>>(val context: F, val bufferFactory: MutableBufferFactory<T> = ::boxing, val singularityCheck: (T) -> Boolean) {
/** /**
* In-place transformation for [MutableNDStructure], using given transformation for each element * In-place transformation for [MutableNDStructure], using given transformation for each element
*/ */
operator fun <T> MutableNDStructure<T>.set(i: Int, j: Int, value: T) { private operator fun <T> MutableNDStructure<T>.set(i: Int, j: Int, value: T) {
this[intArrayOf(i, j)] = value this[intArrayOf(i, j)] = value
} }
abstract fun isSingular(value: T): Boolean private fun abs(value: T) = if (value > context.zero) value else with(context) { -value }
private fun abs(value: T) = if (value > matrix.context.ring.zero) value else with(matrix.context.ring) { -value } fun decompose(matrix: Matrix<T>): LUPDecompositionFeature<T> {
// Use existing decomposition if it is provided by matrix
matrix.features.find { it is LUPDecompositionFeature<*> }?.let {
@Suppress("UNCHECKED_CAST")
return it as LUPDecompositionFeature<T>
}
private fun calculateLU(): Pair<NDStructure<T>, IntArray> { if (matrix.rowNum != matrix.colNum) {
if (matrix.numRows != matrix.numCols) {
error("LU decomposition supports only square matrices") error("LU decomposition supports only square matrices")
} }
val m = matrix.numCols val m = matrix.colNum
val pivot = IntArray(matrix.numRows) val pivot = IntArray(matrix.rowNum)
//TODO fix performance //TODO replace by custom optimized 2d structure
val lu: MutableNDStructure<T> = mutableNdStructure( val lu: MutableNDStructure<T> = mutableNdStructure(
intArrayOf(matrix.numRows, matrix.numCols), intArrayOf(matrix.rowNum, matrix.colNum),
::boxing bufferFactory
) { index: IntArray -> matrix[index[0], index[1]] } ) { index: IntArray -> matrix[index[0], index[1]] }
with(matrix.context.ring) { with(context) {
// Initialize permutation array and parity // Initialize permutation array and parity
for (row in 0 until m) { for (row in 0 until m) {
pivot[row] = row pivot[row] = row
} }
even = true var even = true
// Loop over columns // Loop over columns
for (col in 0 until m) { for (col in 0 until m) {
@ -139,22 +149,18 @@ abstract class LUDecomposition<T : Comparable<T>, F : Field<T>>(val matrix: Matr
for (i in 0 until col) { for (i in 0 until col) {
sum -= lu[row, i] * lu[i, col] sum -= lu[row, i] * lu[i, col]
} }
//luRow[col] = sum
lu[row, col] = sum lu[row, col] = sum
abs(sum) abs(sum)
} ?: col } ?: col
// Singularity check // Singularity check
if (isSingular(lu[max, col])) { if (singularityCheck(lu[max, col])) {
error("Singular matrix") error("Singular matrix")
} }
// Pivot if necessary // Pivot if necessary
if (max != col) { if (max != col) {
//var tmp = zero
//val luMax = lu[max]
//val luCol = lu[col]
for (i in 0 until m) { for (i in 0 until m) {
lu[max, i] = lu[col, i] lu[max, i] = lu[col, i]
lu[col, i] = lu[max, i] lu[col, i] = lu[max, i]
@ -169,86 +175,70 @@ abstract class LUDecomposition<T : Comparable<T>, F : Field<T>>(val matrix: Matr
val luDiag = lu[col, col] val luDiag = lu[col, col]
for (row in col + 1 until m) { for (row in col + 1 until m) {
lu[row, col] = lu[row, col] / luDiag lu[row, col] = lu[row, col] / luDiag
// lu[row, col] /= luDiag
} }
} }
return LUPDecomposition(context, lu, pivot, even)
} }
return Pair(lu, pivot)
}
/**
* Returns the pivot permutation vector.
* @return the pivot permutation vector
* @see .getP
*/
fun getPivot(): IntArray = pivot.copyOf()
}
class RealLUDecomposition(matrix: RealMatrix, private val singularityThreshold: Double = DEFAULT_TOO_SMALL) :
LUDecomposition<Double, RealField>(matrix) {
override fun isSingular(value: Double): Boolean {
return value.absoluteValue < singularityThreshold
} }
companion object { companion object {
/** Default bound to determine effective singularity in LU decomposition. */ val real: LUPDecompositionBuilder<Double, RealField> = LUPDecompositionBuilder(RealField) { it < 1e-11 }
private const val DEFAULT_TOO_SMALL = 1e-11
} }
} }
/** Specialized solver. */ //class LUSolver<T : Comparable<T>, F : Field<T>>(val singularityCheck: (T) -> Boolean) : LinearSolver<T, F> {
object RealLUSolver : LinearSolver<Double, RealField> { //
//
fun decompose(mat: Matrix<Double, RealField>, threshold: Double = 1e-11): RealLUDecomposition = // override fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T> {
RealLUDecomposition(mat, threshold) // val decomposition = LUPDecompositionBuilder(ring, singularityCheck).decompose(a)
//
override fun solve(a: RealMatrix, b: RealMatrix): RealMatrix { // if (b.rowNum != a.colNum) {
val decomposition = decompose(a, a.context.ring.zero) // error("Matrix dimension mismatch expected ${a.rowNum}, but got ${b.colNum}")
// }
if (b.numRows != a.numCols) { //
error("Matrix dimension mismatch expected ${a.numRows}, but got ${b.numCols}") //
} //// val bp = Array(a.rowNum) { Array<T>(b.colNum){ring.zero} }
//// for (row in 0 until a.rowNum) {
// Apply permutations to b //// val bpRow = bp[row]
val bp = Array(a.numRows) { DoubleArray(b.numCols) } //// val pRow = decomposition.pivot[row]
for (row in 0 until a.numRows) { //// for (col in 0 until b.colNum) {
val bpRow = bp[row] //// bpRow[col] = b[pRow, col]
val pRow = decomposition.pivot[row] //// }
for (col in 0 until b.numCols) { //// }
bpRow[col] = b[pRow, col] //
} // // Apply permutations to b
} // val bp = produce(a.rowNum, a.colNum) { i, j -> b[decomposition.pivot[i], j] }
//
// Solve LY = b // // Solve LY = b
for (col in 0 until a.numRows) { // for (col in 0 until a.rowNum) {
val bpCol = bp[col] // val bpCol = bp[col]
for (i in col + 1 until a.numRows) { // for (i in col + 1 until a.rowNum) {
val bpI = bp[i] // val bpI = bp[i]
val luICol = decomposition.lu[i, col] // val luICol = decomposition.lu[i, col]
for (j in 0 until b.numCols) { // for (j in 0 until b.colNum) {
bpI[j] -= bpCol[j] * luICol // bpI[j] -= bpCol[j] * luICol
} // }
} // }
} // }
//
// Solve UX = Y // // Solve UX = Y
for (col in a.numRows - 1 downTo 0) { // for (col in a.rowNum - 1 downTo 0) {
val bpCol = bp[col] // val bpCol = bp[col]
val luDiag = decomposition.lu[col, col] // val luDiag = decomposition.lu[col, col]
for (j in 0 until b.numCols) { // for (j in 0 until b.colNum) {
bpCol[j] /= luDiag // bpCol[j] /= luDiag
} // }
for (i in 0 until col) { // for (i in 0 until col) {
val bpI = bp[i] // val bpI = bp[i]
val luICol = decomposition.lu[i, col] // val luICol = decomposition.lu[i, col]
for (j in 0 until b.numCols) { // for (j in 0 until b.colNum) {
bpI[j] -= bpCol[j] * luICol // bpI[j] -= bpCol[j] * luICol
} // }
} // }
} // }
//
return a.context.produce(a.numRows, a.numCols) { i, j -> bp[i][j] } // return produce(a.rowNum, a.colNum) { i, j -> bp[i][j] }
} // }
} //}

57
kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgrebra.kt
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@ -4,18 +4,26 @@ import scientifik.kmath.operations.Field
import scientifik.kmath.operations.Norm import scientifik.kmath.operations.Norm
import scientifik.kmath.operations.RealField import scientifik.kmath.operations.RealField
import scientifik.kmath.operations.Ring import scientifik.kmath.operations.Ring
import scientifik.kmath.structures.Buffer.Companion.boxing
import scientifik.kmath.structures.asSequence import scientifik.kmath.structures.asSequence
/** /**
* A group of methods to resolve equation A dot X = B, where A and B are matrices or vectors * A group of methods to resolve equation A dot X = B, where A and B are matrices or vectors
*/ */
interface LinearSolver<T : Any, F : Field<T>> { interface LinearSolver<T : Any, R : Ring<T>> : MatrixContext<T, R> {
fun solve(a: Matrix<T, F>, b: Matrix<T, F>): Matrix<T, F> /**
fun solve(a: Matrix<T, F>, b: Vector<T, F>): Vector<T, F> = solve(a, b.toMatrix()).toVector() * Convert matrix to vector if it is possible
fun inverse(a: Matrix<T, F>): Matrix<T, F> = solve(a, a.context.one) */
fun Matrix<T>.toVector(): Point<T> =
if (this.colNum == 1) {
point(rowNum){ get(it, 0) }
} else error("Can't convert matrix with more than one column to vector")
fun Point<T>.toMatrix(): Matrix<T> = produce(size, 1) { i, _ -> get(i) }
fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T>
fun solve(a: Matrix<T>, b: Point<T>): Point<T> = solve(a, b.toMatrix()).toVector()
fun inverse(a: Matrix<T>): Matrix<T> = solve(a, one(a.rowNum, a.colNum))
} }
/** /**
@ -26,39 +34,10 @@ fun <T : Any> Array<T>.toVector(field: Field<T>) = Vector.generic(size, field) {
fun DoubleArray.toVector() = Vector.real(this.size) { this[it] } fun DoubleArray.toVector() = Vector.real(this.size) { this[it] }
fun List<Double>.toVector() = Vector.real(this.size) { this[it] } fun List<Double>.toVector() = Vector.real(this.size) { this[it] }
/** object VectorL2Norm : Norm<Point<out Number>, Double> {
* Convert matrix to vector if it is possible override fun norm(arg: Point<out Number>): Double =
*/ kotlin.math.sqrt(arg.asSequence().sumByDouble { it.toDouble() })
fun <T : Any, F : Ring<T>> Matrix<T, F>.toVector(): Vector<T, F> =
if (this.numCols == 1) {
// if (this is ArrayMatrix) {
// //Reuse existing underlying array
// ArrayVector(ArrayVectorSpace(rows, context.field, context.ndFactory), array)
// } else {
// //Generic vector
// vector(rows, context.field) { get(it, 0) }
// }
Vector.generic(numRows, context.ring) { get(it, 0) }
} else error("Can't convert matrix with more than one column to vector")
fun <T : Any, R : Ring<T>> Vector<T, R>.toMatrix(): Matrix<T, R> {
// val context = StructureMatrixContext(size, 1, context.space)
//
// return if (this is ArrayVector) {
// //Reuse existing underlying array
// StructureMatrix(context,this.buffer)
// } else {
// //Generic vector
// matrix(size, 1, context.field) { i, j -> get(i) }
// }
//return Matrix.of(size, 1, context.space) { i, _ -> get(i) }
return StructureMatrixSpace(size, 1, context.space, ::boxing).produce { i, _ -> get(i) }
}
object VectorL2Norm : Norm<Vector<out Number, *>, Double> {
override fun norm(arg: Vector<out Number, *>): Double =
kotlin.math.sqrt(arg.asSequence().sumByDouble { it.toDouble() })
} }
typealias RealVector = Vector<Double, RealField> typealias RealVector = Vector<Double, RealField>
typealias RealMatrix = Matrix<Double, RealField> typealias RealMatrix = Matrix<Double>

217
kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/Matrix.kt
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@ -2,64 +2,91 @@ package scientifik.kmath.linear
import scientifik.kmath.operations.RealField import scientifik.kmath.operations.RealField
import scientifik.kmath.operations.Ring import scientifik.kmath.operations.Ring
import scientifik.kmath.operations.Space
import scientifik.kmath.operations.SpaceElement
import scientifik.kmath.structures.* import scientifik.kmath.structures.*
import scientifik.kmath.structures.Buffer.Companion.DoubleBufferFactory import scientifik.kmath.structures.Buffer.Companion.DoubleBufferFactory
import scientifik.kmath.structures.Buffer.Companion.boxing import scientifik.kmath.structures.Buffer.Companion.boxing
interface MatrixSpace<T : Any, R : Ring<T>> : Space<Matrix<T, R>> { interface MatrixContext<T : Any, R : Ring<T>> {
/** /**
* The ring context for matrix elements * The ring context for matrix elements
*/ */
val ring: R val ring: R
val rowNum: Int
val colNum: Int
/** /**
* Produce a matrix with this context and given dimensions * Produce a matrix with this context and given dimensions
*/ */
fun produce(rows: Int = rowNum, columns: Int = colNum, initializer: (i: Int, j: Int) -> T): Matrix<T, R> fun produce(rows: Int, columns: Int, initializer: (i: Int, j: Int) -> T): Matrix<T>
/** /**
* Produce a point compatible with matrix space * Produce a point compatible with matrix space
*/ */
fun point(size: Int, initializer: (Int) -> T): Point<T> fun point(size: Int, initializer: (Int) -> T): Point<T>
override val zero: Matrix<T, R> get() = produce { _, _ -> ring.zero } fun scale(a: Matrix<T>, k: Number): Matrix<T> {
//TODO create a special wrapper class for scaled matrices
return produce(a.rowNum, a.colNum) { i, j -> ring.run { a[i, j] * k } }
}
val one get() = produce { i, j -> if (i == j) ring.one else ring.zero } infix fun Matrix<T>.dot(other: Matrix<T>): Matrix<T> {
//TODO add typed error
if (this.colNum != other.rowNum) error("Matrix dot operation dimension mismatch: ($rowNum, $colNum) x (${other.rowNum}, ${other.colNum})")
return produce(rowNum, other.colNum) { i, j ->
val row = rows[i]
val column = other.columns[j]
with(ring) {
row.asSequence().zip(column.asSequence(), ::multiply).sum()
}
}
}
override fun add(a: Matrix<T, R>, b: Matrix<T, R>): Matrix<T, R> = infix fun Matrix<T>.dot(vector: Point<T>): Point<T> {
produce(rowNum, colNum) { i, j -> ring.run { a[i, j] + b[i, j] } } //TODO add typed error
if (this.colNum != vector.size) error("Matrix dot vector operation dimension mismatch: ($rowNum, $colNum) x (${vector.size})")
return point(rowNum) { i ->
val row = rows[i]
with(ring) {
row.asSequence().zip(vector.asSequence(), ::multiply).sum()
}
}
}
operator fun Matrix<T>.unaryMinus() =
produce(rowNum, colNum) { i, j -> ring.run { -get(i, j) } }
operator fun Matrix<T>.plus(b: Matrix<T>): Matrix<T> {
if (rowNum != b.rowNum || colNum != b.colNum) error("Matrix operation dimension mismatch. [$rowNum,$colNum] + [${b.rowNum},${b.colNum}]")
return produce(rowNum, colNum) { i, j -> ring.run { get(i, j) + b[i, j] } }
}
operator fun Matrix<T>.minus(b: Matrix<T>): Matrix<T> {
if (rowNum != b.rowNum || colNum != b.colNum) error("Matrix operation dimension mismatch. [$rowNum,$colNum] - [${b.rowNum},${b.colNum}]")
return produce(rowNum, colNum) { i, j -> ring.run { get(i, j) + b[i, j] } }
}
operator fun Matrix<T>.times(number: Number): Matrix<T> =
produce(rowNum, colNum) { i, j -> ring.run { get(i, j) * number } }
operator fun Number.times(m: Matrix<T>): Matrix<T> = m * this
override fun multiply(a: Matrix<T, R>, k: Number): Matrix<T, R> =
produce(rowNum, colNum) { i, j -> ring.run { a[i, j] * k } }
companion object { companion object {
/** /**
* Non-boxing double matrix * Non-boxing double matrix
*/ */
fun real(rows: Int, columns: Int): MatrixSpace<Double, RealField> = val real: MatrixContext<Double, RealField> = StructureMatrixContext(RealField, DoubleBufferFactory)
StructureMatrixSpace(rows, columns, RealField, DoubleBufferFactory)
/** /**
* A structured matrix with custom buffer * A structured matrix with custom buffer
*/ */
fun <T : Any, R : Ring<T>> buffered( fun <T : Any, R : Ring<T>> buffered(ring: R, bufferFactory: BufferFactory<T> = ::boxing): MatrixContext<T, R> =
rows: Int, StructureMatrixContext(ring, bufferFactory)
columns: Int,
ring: R,
bufferFactory: BufferFactory<T> = ::boxing
): MatrixSpace<T, R> = StructureMatrixSpace(rows, columns, ring, bufferFactory)
/** /**
* Automatic buffered matrix, unboxed if it is possible * Automatic buffered matrix, unboxed if it is possible
*/ */
inline fun <reified T : Any, R : Ring<T>> auto(rows: Int, columns: Int, ring: R): MatrixSpace<T, R> = inline fun <reified T : Any, R : Ring<T>> auto(ring: R): MatrixContext<T, R> =
buffered(rows, columns, ring, Buffer.Companion::auto) buffered(ring, Buffer.Companion::auto)
} }
} }
@ -69,108 +96,102 @@ interface MatrixSpace<T : Any, R : Ring<T>> : Space<Matrix<T, R>> {
*/ */
interface MatrixFeature interface MatrixFeature
object DiagonalFeature : MatrixFeature
object ZeroFeature : MatrixFeature
object UnitFeature : MatrixFeature
interface InverseMatrixFeature<T : Any> : MatrixFeature {
val inverse: Matrix<T>
}
interface DeterminantFeature<T : Any> : MatrixFeature {
val determinant: T
}
/** /**
* Specialized 2-d structure * Specialized 2-d structure
*/ */
interface Matrix<T : Any, R : Ring<T>> : NDStructure<T>, SpaceElement<Matrix<T, R>, Matrix<T, R>, MatrixSpace<T, R>> { interface Matrix<T : Any> : NDStructure<T> {
val rowNum: Int
val colNum: Int
val features: Set<MatrixFeature>
operator fun get(i: Int, j: Int): T operator fun get(i: Int, j: Int): T
override fun get(index: IntArray): T = get(index[0], index[1]) override fun get(index: IntArray): T = get(index[0], index[1])
val numRows get() = context.rowNum override val shape: IntArray get() = intArrayOf(rowNum, colNum)
val numCols get() = context.colNum
//TODO replace by lazy buffers
val rows: Point<Point<T>> val rows: Point<Point<T>>
get() = ListBuffer((0 until numRows).map { i -> get() = VirtualBuffer(rowNum) { i ->
context.point(numCols) { j -> get(i, j) } VirtualBuffer(colNum) { j -> get(i, j) }
}) }
val columns: Point<Point<T>> val columns: Point<Point<T>>
get() = ListBuffer((0 until numCols).map { j -> get() = VirtualBuffer(colNum) { j ->
context.point(numRows) { i -> get(i, j) } VirtualBuffer(rowNum) { i -> get(i, j) }
}) }
val features: Set<MatrixFeature> override fun elements(): Sequence<Pair<IntArray, T>> = sequence {
for (i in (0 until rowNum)) {
for (j in (0 until colNum)) {
yield(intArrayOf(i, j) to get(i, j))
}
}
}
companion object { companion object {
fun real(rows: Int, columns: Int, initializer: (Int, Int) -> Double) = fun real(rows: Int, columns: Int, initializer: (Int, Int) -> Double) =
MatrixSpace.real(rows, columns).produce(rows, columns, initializer) MatrixContext.real.produce(rows, columns, initializer)
} }
} }
infix fun <T : Any, R : Ring<T>> Matrix<T, R>.dot(other: Matrix<T, R>): Matrix<T, R> { /**
//TODO add typed error * Diagonal matrix of ones. The matrix is virtual no actual matrix is created
if (this.numCols != other.numRows) error("Matrix dot operation dimension mismatch: ($numRows, $numCols) x (${other.numRows}, ${other.numCols})") */
return context.produce(numRows, other.numCols) { i, j -> fun <T : Any, R : Ring<T>> MatrixContext<T, R>.one(rows: Int, columns: Int): Matrix<T> {
val row = rows[i] return object : Matrix<T> {
val column = other.columns[j] override val rowNum: Int get() = rows
with(context.ring) { override val colNum: Int get() = columns
row.asSequence().zip(column.asSequence(), ::multiply).sum() override val features: Set<MatrixFeature> get() = setOf(DiagonalFeature, UnitFeature)
} override fun get(i: Int, j: Int): T = if (i == j) ring.one else ring.zero
} }
} }
infix fun <T : Any, R : Ring<T>> Matrix<T, R>.dot(vector: Point<T>): Point<T> { /**
//TODO add typed error * A virtual matrix of zeroes
if (this.numCols != vector.size) error("Matrix dot vector operation dimension mismatch: ($numRows, $numCols) x (${vector.size})") */
return context.point(numRows) { i -> fun <T : Any, R : Ring<T>> MatrixContext<T, R>.zero(rows: Int, columns: Int): Matrix<T> {
val row = rows[i] return object : Matrix<T> {
with(context.ring) { override val rowNum: Int get() = rows
row.asSequence().zip(vector.asSequence(), ::multiply).sum() override val colNum: Int get() = columns
} override val features: Set<MatrixFeature> get() = setOf(ZeroFeature)
override fun get(i: Int, j: Int): T = ring.zero
} }
} }
data class StructureMatrixSpace<T : Any, R : Ring<T>>(
override val rowNum: Int,
override val colNum: Int,
override val ring: R,
private val bufferFactory: BufferFactory<T>
) : MatrixSpace<T, R> {
val shape: IntArray = intArrayOf(rowNum, colNum) inline class TransposedMatrix<T : Any>(val original: Matrix<T>) : Matrix<T> {
override val rowNum: Int get() = original.colNum
override val colNum: Int get() = original.rowNum
override val features: Set<MatrixFeature> get() = emptySet() //TODO retain some features
private val strides = DefaultStrides(shape) override fun get(i: Int, j: Int): T = original[j, i]
override fun produce(rows: Int, columns: Int, initializer: (i: Int, j: Int) -> T): Matrix<T, R> { override fun elements(): Sequence<Pair<IntArray, T>> =
return if (rows == rowNum && columns == colNum) { original.elements().map { (key, value) -> intArrayOf(key[1], key[0]) to value }
val structure = ndStructure(strides, bufferFactory) { initializer(it[0], it[1]) }
StructureMatrix(this, structure)
} else {
val context = StructureMatrixSpace(rows, columns, ring, bufferFactory)
val structure = ndStructure(context.strides, bufferFactory) { initializer(it[0], it[1]) }
StructureMatrix(context, structure)
}
}
override fun point(size: Int, initializer: (Int) -> T): Point<T> = bufferFactory(size, initializer)
} }
data class StructureMatrix<T : Any, R : Ring<T>>( /**
override val context: StructureMatrixSpace<T, R>, * Create a virtual transposed matrix without copying anything. `A.transpose().transpose() === A`
val structure: NDStructure<T>, */
override val features: Set<MatrixFeature> = emptySet() fun <T : Any, R : Ring<T>> Matrix<T>.transpose(): Matrix<T> {
) : Matrix<T, R> { return if (this is TransposedMatrix) {
init { original
if (structure.shape.size != 2 || structure.shape[0] != context.rowNum || structure.shape[1] != context.colNum) { } else {
error("Dimension mismatch for structure, (${context.rowNum}, ${context.colNum}) expected, but ${structure.shape} found") TransposedMatrix(this)
}
} }
}
override fun unwrap(): Matrix<T, R> = this
override fun Matrix<T, R>.wrap(): Matrix<T, R> = this
override val shape: IntArray get() = structure.shape
override fun get(index: IntArray): T = structure[index]
override fun get(i: Int, j: Int): T = structure[i, j]
override fun elements(): Sequence<Pair<IntArray, T>> = structure.elements()
}
//TODO produce transposed matrix via reference without creating new space and structure
fun <T : Any, R : Ring<T>> Matrix<T, R>.transpose(): Matrix<T, R> =
context.produce(numCols, numRows) { i, j -> get(j, i) }

50
kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/StructureMatrix.kt Normal file
View File

@ -0,0 +1,50 @@
package scientifik.kmath.linear
import scientifik.kmath.operations.Ring
import scientifik.kmath.structures.BufferFactory
import scientifik.kmath.structures.NDStructure
import scientifik.kmath.structures.get
import scientifik.kmath.structures.ndStructure
/**
* Basic implementation of Matrix space based on [NDStructure]
*/
class StructureMatrixContext<T : Any, R : Ring<T>>(
override val ring: R,
private val bufferFactory: BufferFactory<T>
) : MatrixContext<T, R> {
override fun produce(rows: Int, columns: Int, initializer: (i: Int, j: Int) -> T): Matrix<T> {
val structure =
ndStructure(intArrayOf(rows, columns), bufferFactory) { index -> initializer(index[0], index[1]) }
return StructureMatrix(structure)
}
override fun point(size: Int, initializer: (Int) -> T): Point<T> = bufferFactory(size, initializer)
}
data class StructureMatrix<T : Any>(
val structure: NDStructure<T>,
override val features: Set<MatrixFeature> = emptySet()
) : Matrix<T> {
init {
if (structure.shape.size != 2) {
error("Dimension mismatch for matrix structure")
}
}
override val rowNum: Int
get() = structure.shape[0]
override val colNum: Int
get() = structure.shape[1]
override val shape: IntArray get() = structure.shape
override fun get(index: IntArray): T = structure[index]
override fun get(i: Int, j: Int): T = structure[i, j]
override fun elements(): Sequence<Pair<IntArray, T>> = structure.elements()
}

10
kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/VirtualMatrix.kt Normal file
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@ -0,0 +1,10 @@
package scientifik.kmath.linear
class VirtualMatrix<T : Any>(
override val rowNum: Int,
override val colNum: Int,
override val features: Set<MatrixFeature> = emptySet(),
val generator: (i: Int, j: Int) -> T
) : Matrix<T> {
override fun get(i: Int, j: Int): T = generator(i, j)
}

2
kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt
View File

@ -33,8 +33,8 @@ interface Space<T> {
operator fun T.times(k: Number) = multiply(this, k.toDouble()) operator fun T.times(k: Number) = multiply(this, k.toDouble())
operator fun T.div(k: Number) = multiply(this, 1.0 / k.toDouble()) operator fun T.div(k: Number) = multiply(this, 1.0 / k.toDouble())
operator fun Number.times(b: T) = b * this operator fun Number.times(b: T) = b * this
fun Iterable<T>.sum(): T = fold(zero) { left, right -> add(left,right) }
fun Iterable<T>.sum(): T = fold(zero) { left, right -> add(left,right) }
fun Sequence<T>.sum(): T = fold(zero) { left, right -> add(left, right) } fun Sequence<T>.sum(): T = fold(zero) { left, right -> add(left, right) }
} }

21
kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
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@ -95,6 +95,8 @@ inline class ListBuffer<T>(private val list: List<T>) : Buffer<T> {
override fun iterator(): Iterator<T> = list.iterator() override fun iterator(): Iterator<T> = list.iterator()
} }
fun <T> List<T>.asBuffer() = ListBuffer(this)
inline class MutableListBuffer<T>(private val list: MutableList<T>) : MutableBuffer<T> { inline class MutableListBuffer<T>(private val list: MutableList<T>) : MutableBuffer<T> {
override val size: Int override val size: Int
@ -191,6 +193,25 @@ inline class ReadOnlyBuffer<T>(private val buffer: MutableBuffer<T>) : Buffer<T>
override fun iterator(): Iterator<T> = buffer.iterator() override fun iterator(): Iterator<T> = buffer.iterator()
} }
/**
* A buffer with content calculated on-demand. The calculated contect is not stored, so it is recalculated on each call.
* Useful when one needs single element from the buffer.
*/
class VirtualBuffer<T>(override val size: Int, private val generator: (Int) -> T) : Buffer<T> {
override fun get(index: Int): T = generator(index)
override fun iterator(): Iterator<T> = (0 until size).asSequence().map(generator).iterator()
override fun contentEquals(other: Buffer<*>): Boolean {
return if (other is VirtualBuffer) {
this.size == other.size && this.generator == other.generator
} else {
super.contentEquals(other)
}
}
}
/** /**
* Convert this buffer to read-only buffer * Convert this buffer to read-only buffer
*/ */

2
kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/MatrixTest.kt
View File

@ -22,7 +22,7 @@ class MatrixTest {
@Test @Test
fun testTranspose() { fun testTranspose() {
val matrix = MatrixSpace.real(3, 3).one val matrix = MatrixContext.real(3, 3).one
val transposed = matrix.transpose() val transposed = matrix.transpose()
assertEquals(matrix.context, transposed.context) assertEquals(matrix.context, transposed.context)
assertEquals((matrix as StructureMatrix).structure, (transposed as StructureMatrix).structure) assertEquals((matrix as StructureMatrix).structure, (transposed as StructureMatrix).structure)

2
kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt
View File

@ -6,7 +6,7 @@ import kotlin.test.assertEquals
class RealLUSolverTest { class RealLUSolverTest {
@Test @Test
fun testInvertOne() { fun testInvertOne() {
val matrix = MatrixSpace.real(2, 2).one val matrix = MatrixContext.real(2, 2).one
val inverted = RealLUSolver.inverse(matrix) val inverted = RealLUSolver.inverse(matrix)
assertEquals(matrix, inverted) assertEquals(matrix, inverted)
} }