Linear algebra in progress

build.gradle

@@ -1,5 +1,5 @@
 buildscript {
-    ext.kotlin_version = '1.3.0-rc-116'
+    ext.kotlin_version = '1.3.0-rc-146'
 
     repositories {
         jcenter()

kmath-commons/src/main/kotlin/scientifik/kmath/commons/CommonsMatrix.kt

@@ -0,0 +1,3 @@
+package scientifik.kmath.commons
+
+//val solver: DecompositionSolver

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LUDecomposition.kt

@@ -0,0 +1,321 @@
+package scientifik.kmath.linear
+
+import scientifik.kmath.operations.Field
+import scientifik.kmath.structures.MutableNDArray
+import scientifik.kmath.structures.NDArray
+import scientifik.kmath.structures.NDArrays
+
+/**
+ * Calculates the LUP-decomposition of a square matrix.
+ *
+ * The LUP-decomposition of a matrix A consists of three matrices L, U and
+ * P that satisfy: PA = LU. L is lower triangular (with unit
+ * diagonal terms), U is upper triangular and P is a permutation matrix. All
+ * matrices are mm.
+ *
+ * As shown by the presence of the P matrix, this decomposition is
+ * implemented using partial pivoting.
+ *
+ * This class is based on the class with similar name from the
+ * [JAMA](http://math.nist.gov/javanumerics/jama/) library.
+ *
+ *  * a [getP][.getP] method has been added,
+ *  * the `det` method has been renamed as [   getDeterminant][.getDeterminant],
+ *  * the `getDoublePivot` method has been removed (but the int based
+ * [getPivot][.getPivot] method has been kept),
+ *  * the `solve` and `isNonSingular` methods have been replaced
+ * by a [getSolver][.getSolver] method and the equivalent methods
+ * provided by the returned [DecompositionSolver].
+ *
+ *
+ * @see [MathWorld](http://mathworld.wolfram.com/LUDecomposition.html)
+ *
+ * @see [Wikipedia](http://en.wikipedia.org/wiki/LU_decomposition)
+ *
+ * @since 2.0 (changed to concrete class in 3.0)
+ *
+ * @param matrix The matrix to decompose.
+ * @param singularityThreshold threshold (based on partial row norm)
+ * under which a matrix is considered singular
+ * @throws NonSquareMatrixException if matrix is not square
+
+ */
+abstract class LUDecomposition<T : Comparable<T>>(val matrix: Matrix<T>) {
+
+    private val field get() = matrix.context.field
+    /** Entries of LU decomposition.  */
+    internal val lu: NDArray<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 {
+        val pair = matrix.context.field.calculateLU()
+        lu = pair.first
+        pivot = pair.second
+    }
+
+    /**
+     * Returns the matrix L of the decomposition.
+     *
+     * L is a lower-triangular matrix
+     * @return the L matrix (or null if decomposed matrix is singular)
+     */
+    val l: Matrix<out T> by lazy {
+        matrix.context.produce { i, j ->
+            when {
+                j < i -> lu[i, j]
+                j == i -> matrix.context.field.one
+                else -> matrix.context.field.zero
+            }
+        }
+    }
+
+
+    /**
+     * Returns the matrix U of the decomposition.
+     *
+     * U is an upper-triangular matrix
+     * @return the U matrix (or null if decomposed matrix is singular)
+     */
+    val u: Matrix<out T> by lazy {
+        matrix.context.produce { i, j ->
+            if (j >= i) lu[i, j] else field.zero
+        }
+    }
+
+    /**
+     * Returns the P rows permutation matrix.
+     *
+     * P is a sparse matrix with exactly one element set to 1.0 in
+     * each row and each column, all other elements being set to 0.0.
+     *
+     * The positions of the 1 elements are given by the [ pivot permutation vector][.getPivot].
+     * @return the P rows permutation matrix (or null if decomposed matrix is singular)
+     * @see .getPivot
+     */
+    val p: Matrix<out T> by lazy {
+        matrix.context.produce { i, j ->
+            //TODO ineffective. Need sparse matrix for that
+            if (j == pivot[i]) field.one else field.zero
+        }
+    }
+
+    /**
+     * Return the determinant of the matrix
+     * @return determinant of the matrix
+     */
+    val determinant: T
+        get() {
+            with(matrix.context.field) {
+                var determinant = if (even) one else -one
+                for (i in 0 until matrix.rows) {
+                    determinant *= lu[i, i]
+                }
+                return determinant
+            }
+        }
+
+//    /**
+//     * Get a solver for finding the A  X = B solution in exact linear
+//     * sense.
+//     * @return a solver
+//     */
+//    val solver: DecompositionSolver
+//        get() = Solver(lu, pivot, singular)
+
+    /**
+     * In-place transformation for [MutableNDArray], using given transformation for each element
+     */
+    operator fun <T> MutableNDArray<T>.set(i: Int, j: Int, value: T) {
+        this[listOf(i, j)] = value
+    }
+
+    abstract fun isSingular(value: T): Boolean
+
+    private fun Field<T>.calculateLU(): Pair<NDArray<T>, IntArray> {
+        if (matrix.rows != matrix.columns) {
+            error("LU decomposition supports only square matrices")
+        }
+
+        fun T.abs() = if (this > zero) this else -this
+
+        val m = matrix.columns
+        val pivot = IntArray(matrix.rows)
+        //TODO fix performance
+        val lu: MutableNDArray<T> = NDArrays.createMutable(matrix.context.field, listOf(matrix.rows, matrix.columns)) { index -> matrix[index[0], index[1]] }
+
+        // Initialize permutation array and parity
+        for (row in 0 until m) {
+            pivot[row] = row
+        }
+        even = true
+
+        // Loop over columns
+        for (col in 0 until m) {
+
+            // upper
+            for (row in 0 until col) {
+                var sum = lu[row, col]
+                for (i in 0 until row) {
+                    sum -= lu[row, i] * lu[i, col]
+                }
+                lu[row, col] = sum
+            }
+
+            // lower
+            val max = (col until m).maxBy { row ->
+                var sum = lu[row, col]
+                for (i in 0 until col) {
+                    sum -= lu[row, i] * lu[i, col]
+                }
+                //luRow[col] = sum
+                lu[row, col] = sum
+
+                sum.abs()
+            } ?: col
+
+            // Singularity check
+            if (isSingular(lu[max, col].abs())) {
+                error("Singular matrix")
+            }
+
+            // Pivot if necessary
+            if (max != col) {
+                //var tmp = zero
+                //val luMax = lu[max]
+                //val luCol = lu[col]
+                for (i in 0 until m) {
+                    lu[max, i] = lu[col, i]
+                    lu[col, i] = lu[max, i]
+                }
+                val temp = pivot[max]
+                pivot[max] = pivot[col]
+                pivot[col] = temp
+                even = !even
+            }
+
+            // Divide the lower elements by the "winning" diagonal elt.
+            val luDiag = lu[col, col]
+            for (row in col + 1 until m) {
+                lu[row, col] /= luDiag
+            }
+        }
+        return Pair(lu, pivot)
+    }
+
+    /**
+     * Returns the pivot permutation vector.
+     * @return the pivot permutation vector
+     * @see .getP
+     */
+    fun getPivot(): IntArray {
+        return pivot.copyOf()
+    }
+
+    companion object {
+        /** Default bound to determine effective singularity in LU decomposition.  */
+        private const val DEFAULT_TOO_SMALL = 1e-11
+    }
+}
+
+class RealLUDecomposition(matrix: Matrix<Double>, private val singularityThreshold: Double = 1e-11) : LUDecomposition<Double>(matrix) {
+    override fun isSingular(value: Double): Boolean {
+        return value < singularityThreshold
+    }
+}
+
+
+/** Specialized solver.  */
+class RealLUSolver : LinearSolver<Double> {
+
+//
+//    /** {@inheritDoc}  */
+//    override fun solve(b: RealVector): RealVector {
+//        val m = pivot.size
+//        if (b.getDimension() != m) {
+//            throw DimensionMismatchException(b.getDimension(), m)
+//        }
+//        if (singular) {
+//            throw SingularMatrixException()
+//        }
+//
+//        val bp = DoubleArray(m)
+//
+//        // Apply permutations to b
+//        for (row in 0 until m) {
+//            bp[row] = b.getEntry(pivot[row])
+//        }
+//
+//        // Solve LY = b
+//        for (col in 0 until m) {
+//            val bpCol = bp[col]
+//            for (i in col + 1 until m) {
+//                bp[i] -= bpCol * lu[i][col]
+//            }
+//        }
+//
+//        // Solve UX = Y
+//        for (col in m - 1 downTo 0) {
+//            bp[col] /= lu[col][col]
+//            val bpCol = bp[col]
+//            for (i in 0 until col) {
+//                bp[i] -= bpCol * lu[i][col]
+//            }
+//        }
+//
+//        return ArrayRealVector(bp, false)
+//    }
+
+
+    fun decompose(mat: Matrix<Double>, threshold: Double = 1e-11): RealLUDecomposition = RealLUDecomposition(mat, threshold)
+
+    override fun solve(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double> {
+        val decomposition = decompose(a, a.context.field.zero)
+
+        if (b.rows != a.rows) {
+            error("Matrix dimension mismatch expected ${a.rows}, but got ${b.rows}")
+        }
+
+        // Apply permutations to b
+        val bp = Array(a.rows) { DoubleArray(b.columns) }
+        for (row in 0 until a.rows) {
+            val bpRow = bp[row]
+            val pRow = decomposition.pivot[row]
+            for (col in 0 until b.columns) {
+                bpRow[col] = b[pRow, col]
+            }
+        }
+
+        // Solve LY = b
+        for (col in 0 until a.rows) {
+            val bpCol = bp[col]
+            for (i in col + 1 until a.rows) {
+                val bpI = bp[i]
+                val luICol = decomposition.lu[i, col]
+                for (j in 0 until b.columns) {
+                    bpI[j] -= bpCol[j] * luICol
+                }
+            }
+        }
+
+        // Solve UX = Y
+        for (col in a.rows - 1 downTo 0) {
+            val bpCol = bp[col]
+            val luDiag = decomposition.lu[col, col]
+            for (j in 0 until b.columns) {
+                bpCol[j] /= luDiag
+            }
+            for (i in 0 until col) {
+                val bpI = bp[i]
+                val luICol = decomposition.lu[i, col]
+                for (j in 0 until b.columns) {
+                    bpI[j] -= bpCol[j] * luICol
+                }
+            }
+        }
+
+        return a.context.produce { i, j -> bp[i][j] }
+    }
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgrebra.kt

@@ -0,0 +1,250 @@
+package scientifik.kmath.linear
+
+import scientifik.kmath.operations.DoubleField
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.Space
+import scientifik.kmath.operations.SpaceElement
+import scientifik.kmath.structures.NDArray
+import scientifik.kmath.structures.NDArrays.createFactory
+import scientifik.kmath.structures.NDFieldFactory
+import scientifik.kmath.structures.realNDFieldFactory
+
+/**
+ * The space for linear elements. Supports scalar product alongside with standard linear operations.
+ * @param T type of individual element of the vector or matrix
+ * @param V the type of vector space element
+ */
+abstract class LinearSpace<T : Any, V : Matrix<T>>(val rows: Int, val columns: Int, val field: Field<T>) : Space<V> {
+
+    /**
+     * Produce the element of this space
+     */
+    abstract fun produce(initializer: (Int, Int) -> T): V
+
+    /**
+     * Produce new linear space with given dimensions. The space produced could be raised from cache since [LinearSpace] does not have mutable elements
+     */
+    abstract fun produceSpace(rows: Int, columns: Int): LinearSpace<T, V>
+
+    override val zero: V by lazy {
+        produce { _, _ -> field.zero }
+    }
+
+    val one: V by lazy {
+        produce { i, j -> if (i == j) field.one else field.zero }
+    }
+
+    override fun add(a: V, b: V): V {
+        return produce { i, j -> with(field) { a[i, j] + b[i, j] } }
+    }
+
+    override fun multiply(a: V, k: Double): V {
+        //TODO it is possible to implement scalable linear elements which normed values and adjustable scale to save memory and processing poser
+        return produce { i, j -> with(field) { a[i, j] * k } }
+    }
+
+    /**
+     * Dot product. Throws exception on dimension mismatch
+     */
+    fun multiply(a: V, b: V): V {
+        if (a.rows != b.columns) {
+            //TODO replace by specific exception
+            error("Dimension mismatch in linear structure dot product: [${a.rows},${a.columns}]*[${b.rows},${b.columns}]")
+        }
+        return produceSpace(a.rows, b.columns).produce { i, j ->
+            (0..a.columns).asSequence().map { k -> field.multiply(a[i, k], b[k, j]) }.reduce { first, second -> field.add(first, second) }
+        }
+    }
+
+    infix fun V.dot(b: V): V = multiply(this, b)
+}
+
+/**
+ * A specialized [LinearSpace] which works with vectors
+ */
+abstract class VectorSpace<T : Any, V : Vector<T>>(size: Int, field: Field<T>) : LinearSpace<T, V>(size, 1, field)
+
+/**
+ * A matrix-like structure
+ */
+interface Matrix<T : Any> {
+    val context: LinearSpace<T, out Matrix<T>>
+    /**
+     * Number of rows
+     */
+    val rows: Int
+    /**
+     * Number of columns
+     */
+    val columns: Int
+
+    /**
+     * Get element in row [i] and column [j]. Throws error in case of call ounside structure dimensions
+     */
+    operator fun get(i: Int, j: Int): T
+
+    fun transpose(): Matrix<T> {
+        return object : Matrix<T> {
+            override val context: LinearSpace<T, out Matrix<T>> = this@Matrix.context
+            override val rows: Int = this@Matrix.columns
+            override val columns: Int = this@Matrix.rows
+            override fun get(i: Int, j: Int): T = this@Matrix[j, i]
+        }
+    }
+}
+
+interface Vector<T : Any> : Matrix<T> {
+    override val context: VectorSpace<T, Vector<T>>
+    override val columns: Int
+        get() = 1
+
+    operator fun get(i: Int) = get(i, 0)
+}
+
+
+/**
+ * NDArray-based implementation of vector space. By default uses slow [SimpleNDField], but could be overridden with custom [NDField] factory.
+ */
+class ArraySpace<T : Any>(
+        rows: Int,
+        columns: Int,
+        field: Field<T>,
+        val ndFactory: NDFieldFactory<T> = createFactory(field)
+) : LinearSpace<T, Matrix<T>>(rows, columns, field) {
+
+    val ndField by lazy {
+        ndFactory(listOf(rows, columns))
+    }
+
+    override fun produce(initializer: (Int, Int) -> T): Matrix<T> = ArrayMatrix(this, initializer)
+
+    override fun produceSpace(rows: Int, columns: Int): ArraySpace<T> {
+        return ArraySpace(rows, columns, field, ndFactory)
+    }
+}
+
+class ArrayVectorSpace<T : Any>(
+        size: Int,
+        field: Field<T>,
+        val ndFactory: NDFieldFactory<T> = createFactory(field)
+) : VectorSpace<T, Vector<T>>(size, field) {
+    val ndField by lazy {
+        ndFactory(listOf(size))
+    }
+
+    override fun produce(initializer: (Int, Int) -> T): Vector<T> = produceVector { i -> initializer(i, 0) }
+
+    fun produceVector(initializer: (Int) -> T): Vector<T> = ArrayVector(this, initializer)
+
+    override fun produceSpace(rows: Int, columns: Int): LinearSpace<T, Vector<T>> {
+        TODO("not implemented") //To change body of created functions use File | Settings | File Templates.
+    }
+}
+
+/**
+ * Member of [ArraySpace] which wraps 2-D array
+ */
+class ArrayMatrix<T : Any> internal constructor(override val context: ArraySpace<T>, val array: NDArray<T>) : Matrix<T>, SpaceElement<Matrix<T>, ArraySpace<T>> {
+
+    constructor(context: ArraySpace<T>, initializer: (Int, Int) -> T) : this(context, context.ndField.produce { list -> initializer(list[0], list[1]) })
+
+    override val rows: Int get() = context.rows
+
+    override val columns: Int get() = context.columns
+
+    override fun get(i: Int, j: Int): T {
+        return array[i, j]
+    }
+
+    override val self: ArrayMatrix<T> get() = this
+}
+
+
+class ArrayVector<T : Any> internal constructor(override val context: ArrayVectorSpace<T>, val array: NDArray<T>) : Vector<T>, SpaceElement<Vector<T>, ArrayVectorSpace<T>> {
+
+    constructor(context: ArrayVectorSpace<T>, initializer: (Int) -> T) : this(context, context.ndField.produce { list -> initializer(list[0]) })
+
+    init {
+        if (context.columns != 1) {
+            error("Vector must have single column")
+        }
+        if (context.rows != array.shape[0]) {
+            error("Array dimension mismatch")
+        }
+    }
+
+    //private val array = context.ndField.produce { list -> initializer(list[0]) }
+
+
+    override val rows: Int get() = context.rows
+
+    override val columns: Int = 1
+
+    override fun get(i: Int, j: Int): T {
+        return array[i]
+    }
+
+    override val self: ArrayVector<T> get() = this
+
+}
+
+/**
+ * A group of methods to resolve equation A dot X = B, where A and B are matrices or vectors
+ */
+interface LinearSolver<T : Any> {
+    fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T>
+    fun solve(a: Matrix<T>, b: Vector<T>): Vector<T> = solve(a, b as Matrix<T>).toVector()
+    fun inverse(a: Matrix<T>): Matrix<T> = solve(a, a.context.one)
+}
+
+/**
+ * Create vector with custom field
+ */
+fun <T : Any> vector(size: Int, field: Field<T>, initializer: (Int) -> T) =
+        ArrayVector(ArrayVectorSpace(size, field), initializer)
+
+/**
+ * Create vector of [Double]
+ */
+fun realVector(size: Int, initializer: (Int) -> Double) =
+        ArrayVector(ArrayVectorSpace(size, DoubleField, realNDFieldFactory), initializer)
+
+/**
+ * Convert vector to array (copying content of array)
+ */
+fun <T : Any> Array<T>.asVector(field: Field<T>) = vector(size, field) { this[it] }
+
+fun DoubleArray.asVector() = realVector(this.size) { this[it] }
+
+/**
+ * Create [ArrayMatrix] with custom field
+ */
+fun <T : Any> matrix(rows: Int, columns: Int, field: Field<T>, initializer: (Int, Int) -> T) =
+        ArrayMatrix(ArraySpace(rows, columns, field), initializer)
+
+/**
+ * Create [ArrayMatrix] of doubles.
+ */
+fun realMatrix(rows: Int, columns: Int, initializer: (Int, Int) -> Double) =
+        ArrayMatrix(ArraySpace(rows, columns, DoubleField, realNDFieldFactory), initializer)
+
+
+/**
+ * Convert matrix to vector if it is possible
+ */
+fun <T : Any> Matrix<T>.toVector(): Vector<T> {
+    return when {
+        this is Vector -> return this
+        this.columns == 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) }
+            }
+        }
+        else -> error("Can't convert matrix with more than one column to vector")
+    }
+}
+

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt

@@ -0,0 +1,41 @@
+package scientifik.kmath.operations
+
+/**
+ * A field for complex numbers
+ */
+object ComplexField : Field<Complex> {
+    override val zero: Complex = Complex(0.0, 0.0)
+
+    override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
+
+    override fun multiply(a: Complex, k: Double): Complex = Complex(a.re * k, a.im * k)
+
+    override val one: Complex = Complex(1.0, 0.0)
+
+    override fun multiply(a: Complex, b: Complex): Complex = Complex(a.re * b.re - a.im * b.im, a.re * b.im + a.im * b.re)
+
+    override fun divide(a: Complex, b: Complex): Complex = Complex(a.re * b.re + a.im * b.im, a.re * b.im - a.im * b.re) / b.square
+
+}
+
+/**
+ * Complex number class
+ */
+data class Complex(val re: Double, val im: Double) : FieldElement<Complex, ComplexField> {
+    override val self: Complex get() = this
+    override val context: ComplexField
+        get() = ComplexField
+
+    /**
+     * A complex conjugate
+     */
+    val conjugate: Complex
+        get() = Complex(re, -im)
+
+    val square: Double
+        get() = re * re + im * im
+
+    val abs: Double
+        get() = kotlin.math.sqrt(square)
+
+}

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Fields.kt

@@ -1,7 +1,6 @@
 package scientifik.kmath.operations
 
 import kotlin.math.pow
-import kotlin.math.sqrt
 
 /**
  * Field for real values
@@ -51,46 +50,6 @@ data class Real(val value: Double) : Number(), FieldElement<Real, RealField> {
 
 }
 
-/**
- * A field for complex numbers
- */
-object ComplexField : Field<Complex> {
-    override val zero: Complex = Complex(0.0, 0.0)
-
-    override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
-
-    override fun multiply(a: Complex, k: Double): Complex = Complex(a.re * k, a.im * k)
-
-    override val one: Complex = Complex(1.0, 0.0)
-
-    override fun multiply(a: Complex, b: Complex): Complex = Complex(a.re * b.re - a.im * b.im, a.re * b.im + a.im * b.re)
-
-    override fun divide(a: Complex, b: Complex): Complex = Complex(a.re * b.re + a.im * b.im, a.re * b.im - a.im * b.re) / b.square
-
-}
-
-/**
- * Complex number class
- */
-data class Complex(val re: Double, val im: Double) : FieldElement<Complex, ComplexField> {
-    override val self: Complex get() = this
-    override val context: ComplexField
-        get() = ComplexField
-
-    /**
-     * A complex conjugate
-     */
-    val conjugate: Complex
-        get() = Complex(re, -im)
-
-    val square: Double
-        get() = re * re + im * im
-
-    val module: Double
-        get() = sqrt(square)
-
-}
-
 /**
  * A field for double without boxing. Does not produce appropriate field element
  */

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferNDField.kt

@@ -9,6 +9,11 @@ import scientifik.kmath.operations.Field
 interface Buffer<T> {
     operator fun get(index: Int): T
     operator fun set(index: Int, value: T)
+
+    /**
+     * A shallow copy of the buffer
+     */
+    fun copy(): Buffer<T>
 }
 
 /**
@@ -63,8 +68,16 @@ abstract class BufferNDField<T>(shape: List<Int>, field: Field<T>) : NDField<T>(
         return BufferNDArray(this, buffer)
     }
 
+    /**
+     * Produce mutable NDArray instance
+     */
+    fun produceMutable(initializer: (List<Int>) -> T): MutableNDArray<T> {
+        val buffer = createBuffer(capacity) { initializer(index(it)) }
+        return MutableBufferedNDArray(this, buffer)
+    }
 
-    class BufferNDArray<T>(override val context: BufferNDField<T>, val data: Buffer<T>) : NDArray<T> {
+
+    private open class BufferNDArray<T>(override val context: BufferNDField<T>, val data: Buffer<T>) : NDArray<T> {
 
         override fun get(vararg index: Int): T {
             return data[context.offset(index.asList())]
@@ -88,6 +101,12 @@ abstract class BufferNDField<T>(shape: List<Int>, field: Field<T>) : NDField<T>(
 
         override val self: NDArray<T> get() = this
     }
+
+    private class MutableBufferedNDArray<T>(context: BufferNDField<T>, data: Buffer<T>): BufferNDArray<T>(context,data), MutableNDArray<T>{
+        override operator fun set(index: List<Int>, value: T){
+            data[context.offset(index)] = value
+        }
+    }
 }
 
 

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/LinearAlgrebra.kt

@@ -1,169 +0,0 @@
-package scientifik.kmath.structures
-
-import scientifik.kmath.operations.DoubleField
-import scientifik.kmath.operations.Field
-import scientifik.kmath.operations.Space
-import scientifik.kmath.operations.SpaceElement
-import scientifik.kmath.structures.NDArrays.createSimpleNDFieldFactory
-
-/**
- * The space for linear elements. Supports scalar product alongside with standard linear operations.
- * @param T type of individual element of the vector or matrix
- * @param V the type of vector space element
- */
-abstract class LinearSpace<T : Any, V : LinearStructure<out T>>(val rows: Int, val columns: Int, val field: Field<T>) : Space<V> {
-
-    /**
-     * Produce the element of this space
-     */
-    abstract fun produce(initializer: (Int, Int) -> T): V
-
-    /**
-     * Produce new linear space with given dimensions. The space produced could be raised from cache since [LinearSpace] does not have mutable elements
-     */
-    abstract fun produceSpace(rows: Int, columns: Int): LinearSpace<T, V>
-
-    override val zero: V by lazy {
-        produce { _, _ -> field.zero }
-    }
-
-    override fun add(a: V, b: V): V {
-        return produce { i, j -> with(field) { a[i, j] + b[i, j] } }
-    }
-
-    override fun multiply(a: V, k: Double): V {
-        //TODO it is possible to implement scalable linear elements which normed values and adjustable scale to save memory and processing poser
-        return produce { i, j -> with(field) { a[i, j] * k } }
-    }
-
-    /**
-     * Dot product. Throws exception on dimension mismatch
-     */
-    fun multiply(a: V, b: V): V {
-        if (a.rows != b.columns) {
-            //TODO replace by specific exception
-            error("Dimension mismatch in linear structure dot product: [${a.rows},${a.columns}]*[${b.rows},${b.columns}]")
-        }
-        return produceSpace(a.rows, b.columns).produce { i, j ->
-            (0..a.columns).asSequence().map { k -> field.multiply(a[i, k], b[k, j]) }.reduce { first, second -> field.add(first, second) }
-        }
-    }
-
-    infix fun V.dot(b: V): V = multiply(this, b)
-}
-
-/**
- * A matrix-like structure that is not dependent on specific space implementation
- */
-interface LinearStructure<T : Any> {
-    /**
-     * Number of rows
-     */
-    val rows: Int
-    /**
-     * Number of columns
-     */
-    val columns: Int
-
-    /**
-     * Get element in row [i] and column [j]. Throws error in case of call ounside structure dimensions
-     */
-    operator fun get(i: Int, j: Int): T
-
-    fun transpose(): LinearStructure<T> {
-        return object : LinearStructure<T> {
-            override val rows: Int = this@LinearStructure.columns
-            override val columns: Int = this@LinearStructure.rows
-            override fun get(i: Int, j: Int): T = this@LinearStructure[j, i]
-        }
-    }
-}
-
-interface Vector<T : Any> : LinearStructure<T> {
-    override val columns: Int
-        get() = 1
-
-    operator fun get(i: Int) = get(i, 0)
-}
-
-
-/**
- * NDArray-based implementation of vector space. By default uses slow [SimpleNDField], but could be overridden with custom [NDField] factory.
- */
-class ArraySpace<T : Any>(
-        rows: Int,
-        columns: Int,
-        field: Field<T>,
-        val ndFactory: NDFieldFactory<T> = createSimpleNDFieldFactory(field)
-) : LinearSpace<T, LinearStructure<out T>>(rows, columns, field) {
-
-    val ndField by lazy {
-        ndFactory(listOf(rows, columns))
-    }
-
-    override fun produce(initializer: (Int, Int) -> T): LinearStructure<T> = ArrayMatrix<T>(this, initializer)
-
-    override fun produceSpace(rows: Int, columns: Int): LinearSpace<T, LinearStructure<out T>> {
-        return ArraySpace(rows, columns, field, ndFactory)
-    }
-}
-
-/**
- * Member of [ArraySpace] which wraps 2-D array
- */
-class ArrayMatrix<T : Any>(override val context: ArraySpace<T>, initializer: (Int, Int) -> T) : LinearStructure<T>, SpaceElement<LinearStructure<out T>, ArraySpace<T>> {
-
-    private val array = context.ndField.produce { list -> initializer(list[0], list[1]) }
-
-    //val list: List<List<T>> = (0 until rows).map { i -> (0 until columns).map { j -> initializer(i, j) } }
-
-    override val rows: Int get() = context.rows
-
-    override val columns: Int get() = context.columns
-
-    override fun get(i: Int, j: Int): T {
-        return array[i, j]
-    }
-
-    override val self: ArrayMatrix<T> get() = this
-}
-
-
-class ArrayVector<T : Any>(override val context: ArraySpace<T>, initializer: (Int) -> T) : Vector<T>, SpaceElement<LinearStructure<out T>, ArraySpace<T>> {
-
-    init {
-        if (context.columns != 1) {
-            error("Vector must have single column")
-        }
-    }
-
-    private val array = context.ndField.produce { list -> initializer(list[0]) }
-
-
-    override val rows: Int get() = context.rows
-
-    override val columns: Int = 1
-
-    override fun get(i: Int, j: Int): T {
-        return array[i]
-    }
-
-    override val self: ArrayVector<T> get() = this
-
-}
-
-fun <T : Any> vector(size: Int, field: Field<T>, initializer: (Int) -> T) =
-        ArrayVector(ArraySpace(size, 1, field), initializer)
-
-fun realVector(size: Int, initializer: (Int) -> Double) =
-        ArrayVector(ArraySpace(size, 1, DoubleField, realNDFieldFactory), initializer)
-
-fun <T : Any> Array<T>.asVector(field: Field<T>) = vector(size, field) { this[it] }
-
-fun DoubleArray.asVector() = realVector(this.size) { this[it] }
-
-fun <T : Any> matrix(rows: Int, columns: Int, field: Field<T>, initializer: (Int, Int) -> T) =
-        ArrayMatrix(ArraySpace(rows, columns, field), initializer)
-
-fun realMatrix(rows: Int, columns: Int, initializer: (Int, Int) -> Double) =
-        ArrayMatrix(ArraySpace(rows, columns, DoubleField, realNDFieldFactory), initializer)

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDArray.kt

@@ -73,7 +73,9 @@ abstract class NDField<T>(val shape: List<Int>, val field: Field<T>) : Field<NDA
     }
 }
 
-
+/**
+ * Many-dimensional array
+ */
 interface NDArray<T> : FieldElement<NDArray<T>, NDField<T>> {
 
     /**
@@ -125,6 +127,22 @@ interface NDArray<T> : FieldElement<NDArray<T>, NDField<T>> {
     }
 }
 
+/**
+ * In-place mutable [NDArray]
+ */
+interface MutableNDArray<T> : NDArray<T> {
+    operator fun set(index: List<Int>, value: T)
+}
+
+/**
+ * In-place transformation for [MutableNDArray], using given transformation for each element
+ */
+fun <T> MutableNDArray<T>.transformInPlace(action: (List<Int>, T) -> T) {
+    for ((index, oldValue) in this) {
+        this[index] = action(index, oldValue)
+    }
+}
+
 /**
  * Element by element application of any operation on elements to the whole array. Just like in numpy
  */

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDArrays.kt

@@ -9,6 +9,28 @@ typealias NDFieldFactory<T> = (shape: List<Int>) -> NDField<T>
  */
 expect val realNDFieldFactory: NDFieldFactory<Double>
 
+
+class SimpleNDField<T : Any>(field: Field<T>, shape: List<Int>) : BufferNDField<T>(shape, field) {
+    override fun createBuffer(capacity: Int, initializer: (Int) -> T): Buffer<T> {
+        val array = ArrayList<T>(capacity)
+        (0 until capacity).forEach {
+            array.add(initializer(it))
+        }
+
+        return BufferOfObjects(array)
+    }
+
+    private class BufferOfObjects<T>(val array: ArrayList<T>) : Buffer<T> {
+        override fun get(index: Int): T = array[index]
+
+        override fun set(index: Int, value: T) {
+            array[index] = value
+        }
+
+        override fun copy(): Buffer<T> = BufferOfObjects(ArrayList(array))
+    }
+}
+
 object NDArrays {
     /**
      * Create a platform-optimized NDArray of doubles
@@ -29,26 +51,22 @@ object NDArrays {
         return realNDArray(listOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
     }
 
-    class SimpleNDField<T : Any>(field: Field<T>, shape: List<Int>) : BufferNDField<T>(shape, field) {
+    /**
-        override fun createBuffer(capacity: Int, initializer: (Int) -> T): Buffer<T> {
+     * Simple boxing NDField
-            val array = ArrayList<T>(capacity)
+     */
-            (0 until capacity).forEach {
+    fun <T : Any> createFactory(field: Field<T>): NDFieldFactory<T> = { shape -> SimpleNDField(field, shape) }
-                array.add(initializer(it))
-            }
 
-            return object : Buffer<T> {
+    /**
-                override fun get(index: Int): T = array[index]
+     * Simple boxing NDArray
-
+     */
-                override fun set(index: Int, value: T) {
+    fun <T : Any> create(field: Field<T>, shape: List<Int>, initializer: (List<Int>) -> T): NDArray<T> {
-                    array[index] = initializer(index)
-                }
-            }
-        }
-    }
-
-    fun <T : Any> createSimpleNDFieldFactory(field: Field<T>): NDFieldFactory<T> = { list -> SimpleNDField(field, list) }
-
-    fun <T : Any> simpleNDArray(field: Field<T>, shape: List<Int>, initializer: (List<Int>) -> T): NDArray<T> {
         return SimpleNDField(field, shape).produce { initializer(it) }
     }
+
+    /**
+     * Mutable boxing NDArray
+     */
+    fun <T : Any> createMutable(field: Field<T>, shape: List<Int>, initializer: (List<Int>) -> T): MutableNDArray<T> {
+        return SimpleNDField(field, shape).produceMutable { initializer(it) }
+    }
 }

kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/ArrayMatrixTest.kt

@@ -1,5 +1,6 @@
 package scientifik.kmath.structures
 
+import scientifik.kmath.linear.realVector
 import kotlin.test.Test
 import kotlin.test.assertEquals
 

kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/SimpleNDFieldTest.kt

@@ -1,7 +1,7 @@
 package scientifik.kmath.structures
 
 import scientifik.kmath.operations.DoubleField
-import scientifik.kmath.structures.NDArrays.simpleNDArray
+import scientifik.kmath.structures.NDArrays.create
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
@@ -9,7 +9,7 @@ import kotlin.test.assertEquals
 class SimpleNDFieldTest{
     @Test
     fun testStrides(){
-        val ndArray = simpleNDArray(DoubleField, listOf(10,10)){(it[0]+it[1]).toDouble()}
+        val ndArray = create(DoubleField, listOf(10,10)){(it[0]+it[1]).toDouble()}
         assertEquals(ndArray[5,5], 10.0)
     }
 

kmath-core/src/jsMain/kotlin/scientifik/kmath/structures/_NDArrays.kt

@@ -5,4 +5,4 @@ import scientifik.kmath.operations.DoubleField
 /**
  * Using boxing implementation for js
  */
-actual val realNDFieldFactory: NDFieldFactory<Double> = NDArrays.createSimpleNDFieldFactory(DoubleField)
+actual val realNDFieldFactory: NDFieldFactory<Double> = NDArrays.createFactory(DoubleField)

kmath-core/src/jvmMain/kotlin/scientifik/kmath/structures/_NDArrays.kt

@@ -7,12 +7,18 @@ private class RealNDField(shape: List<Int>) : BufferNDField<Double>(shape, Doubl
     override fun createBuffer(capacity: Int, initializer: (Int) -> Double): Buffer<Double> {
         val array = DoubleArray(capacity, initializer)
         val buffer = DoubleBuffer.wrap(array)
-        return object : Buffer<Double> {
+        return BufferOfDoubles(buffer)
-            override fun get(index: Int): Double = buffer.get(index)
+    }
 
-            override fun set(index: Int, value: Double) {
+    private class BufferOfDoubles(val buffer: DoubleBuffer): Buffer<Double>{
-                buffer.put(index, value)
+        override fun get(index: Int): Double = buffer.get(index)
-            }
+
+        override fun set(index: Int, value: Double) {
+            buffer.put(index, value)
+        }
+
+        override fun copy(): Buffer<Double> {
+            return BufferOfDoubles(buffer)
         }
     }
 }

settings.gradle

@@ -10,4 +10,5 @@ enableFeaturePreview('GRADLE_METADATA')
 
 rootProject.name = 'kmath'
 include ':kmath-core'
+include ':kmath-commons'