LUDecomposition finished. Not tested

build.gradle.kts

@@ -1,5 +1,5 @@
 buildscript {
-    extra["kotlinVersion"] = "1.3.20-eap-52"
+    extra["kotlinVersion"] = "1.3.20-eap-100"
     extra["ioVersion"] = "0.1.2"
     extra["coroutinesVersion"] = "1.1.0"
 

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

@@ -57,7 +57,7 @@ private class LUPDecomposition<T : Comparable<T>, R : Ring<T>>(
      * U is an upper-triangular matrix
      * @return the U matrix (or null if decomposed matrix is singular)
      */
-    override val u: Matrix<T> = VirtualMatrix(lu.shape[0],  lu.shape[1]) { i, j ->
+    override val u: Matrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1]) { i, j ->
         if (j >= i) lu[i, j] else context.zero
     }
 
@@ -93,7 +93,11 @@ private class LUPDecomposition<T : Comparable<T>, R : Ring<T>>(
 /**
  * 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) {
+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
@@ -105,23 +109,16 @@ class LUPDecompositionBuilder<T : Comparable<T>, F : Field<T>>(val context: F, v
     private fun abs(value: T) = if (value > context.zero) value else with(context) { -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>
-        }
-
         if (matrix.rowNum != matrix.colNum) {
             error("LU decomposition supports only square matrices")
         }
 
         val m = matrix.colNum
         val pivot = IntArray(matrix.rowNum)
-        //TODO replace by custom optimized 2d structure
+
-        val lu: MutableNDStructure<T> = mutableNdStructure(
+        val lu = Mutable2DStructure.create(matrix.rowNum, matrix.colNum, bufferFactory) { i, j ->
-            intArrayOf(matrix.rowNum, matrix.colNum),
+            matrix[i, j]
-            bufferFactory
+        }
-        ) { index: IntArray -> matrix[index[0], index[1]] }
 
 
         with(context) {
@@ -188,57 +185,56 @@ class LUPDecompositionBuilder<T : Comparable<T>, F : Field<T>>(val context: F, v
 }
 
 
-class LUSolver<T : Comparable<T>, F : Field<T>>(val singularityCheck: (T) -> Boolean) : LinearSolver<T, F> {
+class LUSolver<T : Comparable<T>, F : Field<T>>(
+    override val context: MatrixContext<T, F>,
+    val bufferFactory: MutableBufferFactory<T> = ::boxing,
+    val singularityCheck: (T) -> Boolean
+) : LinearSolver<T, F> {
 
 
     override fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T> {
-        val decomposition = LUPDecompositionBuilder(ring, singularityCheck).decompose(a)
-
         if (b.rowNum != a.colNum) {
             error("Matrix dimension mismatch expected ${a.rowNum}, but got ${b.colNum}")
         }
 
+        // Use existing decomposition if it is provided by matrix
+        @Suppress("UNCHECKED_CAST")
+        val decomposition = a.features.find { it is LUPDecompositionFeature<*> }?.let {
+            it as LUPDecompositionFeature<T>
+        } ?: LUPDecompositionBuilder(context.elementContext, bufferFactory, singularityCheck).decompose(a)
 
-//        val bp = Array(a.rowNum) { Array<T>(b.colNum){ring.zero} }
+        with(decomposition) {
-//        for (row in 0 until a.rowNum) {
+            with(context.elementContext) {
-//            val bpRow = bp[row]
+                // Apply permutations to b
-//            val pRow = decomposition.pivot[row]
+                val bp = Mutable2DStructure.create(a.rowNum, a.colNum, bufferFactory) { i, j ->
-//            for (col in 0 until b.colNum) {
+                    b[pivot[i], j]
-//                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
-        for (col in 0 until a.rowNum) {
-            val bpCol = bp[col]
-            for (i in col + 1 until a.rowNum) {
-                val bpI = bp[i]
-                val luICol = decomposition.lu[i, col]
-                for (j in 0 until b.colNum) {
-                    bpI[j] -= bpCol[j] * luICol
                 }
+
+                // Solve LY = b
+                for (col in 0 until a.rowNum) {
+                    for (i in col + 1 until a.rowNum) {
+                        for (j in 0 until b.colNum) {
+                            bp[i, j] -= bp[col, j] * l[i, col]
+                        }
+                    }
+                }
+
+
+                // Solve UX = Y
+                for (col in a.rowNum - 1 downTo 0) {
+                    for (i in 0 until col) {
+                        for (j in 0 until b.colNum) {
+                            bp[i, j] -= bp[col, j] / u[col, col] * u[i, col]
+                        }
+                    }
+                }
+
+                return context.produce(a.rowNum, a.colNum) { i, j -> bp[i, j] }
             }
         }
+    }
 
-        // Solve UX = Y
+    companion object {
-        for (col in a.rowNum - 1 downTo 0) {
+        val real = LUSolver(MatrixContext.real, MutableBuffer.Companion::auto) { it < 1e-11 }
-            val bpCol = bp[col]
-            val luDiag = decomposition.lu[col, col]
-            for (j in 0 until b.colNum) {
-                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.colNum) {
-                    bpI[j] -= bpCol[j] * luICol
-                }
-            }
-        }
-
-        return produce(a.rowNum, a.colNum) { i, j -> bp[i][j] }
     }
 }

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

@@ -4,26 +4,20 @@ import scientifik.kmath.operations.Field
 import scientifik.kmath.operations.Norm
 import scientifik.kmath.operations.RealField
 import scientifik.kmath.operations.Ring
+import scientifik.kmath.structures.VirtualBuffer
 import scientifik.kmath.structures.asSequence
 
 
 /**
  * A group of methods to resolve equation A dot X = B, where A and B are matrices or vectors
  */
-interface LinearSolver<T : Any, R : Ring<T>> : MatrixContext<T, R> {
+interface LinearSolver<T : Any, R : Ring<T>>  {
-    /**
+    val context: MatrixContext<T,R>
-     * Convert matrix to vector if it is possible
-     */
-    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))
+    fun inverse(a: Matrix<T>): Matrix<T> = solve(a, context.one(a.rowNum, a.colNum))
 }
 
 /**
@@ -41,3 +35,15 @@ object VectorL2Norm : Norm<Point<out Number>, Double> {
 
 typealias RealVector = Vector<Double, RealField>
 typealias RealMatrix = Matrix<Double>
+
+
+
+/**
+ * Convert matrix to vector if it is possible
+ */
+fun <T: Any> Matrix<T>.toVector(): Point<T> =
+    if (this.colNum == 1) {
+        VirtualBuffer(rowNum){ get(it, 0) }
+    } else error("Can't convert matrix with more than one column to vector")
+
+fun <T: Any> Point<T>.toMatrix(): Matrix<T> = VirtualMatrix(size, 1) { i, _ -> get(i) }

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

@@ -11,7 +11,7 @@ interface MatrixContext<T : Any, R : Ring<T>> {
     /**
      * The ring context for matrix elements
      */
-    val ring: R
+    val elementContext: R
 
     /**
      * Produce a matrix with this context and given dimensions
@@ -25,7 +25,7 @@ interface MatrixContext<T : Any, R : Ring<T>> {
 
     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 } }
+        return produce(a.rowNum, a.colNum) { i, j -> elementContext.run { a[i, j] * k } }
     }
 
     infix fun Matrix<T>.dot(other: Matrix<T>): Matrix<T> {
@@ -34,7 +34,7 @@ interface MatrixContext<T : Any, R : Ring<T>> {
         return produce(rowNum, other.colNum) { i, j ->
             val row = rows[i]
             val column = other.columns[j]
-            with(ring) {
+            with(elementContext) {
                 row.asSequence().zip(column.asSequence(), ::multiply).sum()
             }
         }
@@ -45,27 +45,27 @@ interface MatrixContext<T : Any, R : Ring<T>> {
         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) {
+            with(elementContext) {
                 row.asSequence().zip(vector.asSequence(), ::multiply).sum()
             }
         }
     }
 
     operator fun Matrix<T>.unaryMinus() =
-        produce(rowNum, colNum) { i, j -> ring.run { -get(i, j) } }
+        produce(rowNum, colNum) { i, j -> elementContext.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] } }
+        return produce(rowNum, colNum) { i, j -> elementContext.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] } }
+        return produce(rowNum, colNum) { i, j -> elementContext.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 } }
+        produce(rowNum, colNum) { i, j -> elementContext.run { get(i, j) * number } }
 
     operator fun Number.times(m: Matrix<T>): Matrix<T> = m * this
 
@@ -157,7 +157,7 @@ fun <T : Any, R : Ring<T>> MatrixContext<T, R>.one(rows: Int, columns: Int): Mat
         override val rowNum: Int get() = rows
         override val colNum: Int get() = columns
         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
+        override fun get(i: Int, j: Int): T = if (i == j) elementContext.one else elementContext.zero
     }
 }
 
@@ -169,7 +169,7 @@ fun <T : Any, R : Ring<T>> MatrixContext<T, R>.zero(rows: Int, columns: Int): Ma
         override val rowNum: Int get() = rows
         override val colNum: Int get() = columns
         override val features: Set<MatrixFeature> get() = setOf(ZeroFeature)
-        override fun get(i: Int, j: Int): T = ring.zero
+        override fun get(i: Int, j: Int): T = elementContext.zero
     }
 }
 

kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/Mutable2DStructure.kt

@@ -0,0 +1,40 @@
+package scientifik.kmath.linear
+
+import scientifik.kmath.structures.MutableBuffer
+import scientifik.kmath.structures.MutableBufferFactory
+import scientifik.kmath.structures.MutableNDStructure
+
+class Mutable2DStructure<T>(val rowNum: Int, val colNum: Int, val buffer: MutableBuffer<T>) : MutableNDStructure<T> {
+    override val shape: IntArray
+        get() = intArrayOf(rowNum, colNum)
+
+    operator fun get(i: Int, j: Int): T = buffer[i * colNum + j]
+
+    override fun get(index: IntArray): T = get(index[0], index[1])
+
+    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))
+            }
+        }
+    }
+
+    operator fun set(i: Int, j: Int, value: T) {
+        buffer[i * colNum + j] = value
+    }
+
+    override fun set(index: IntArray, value: T) = set(index[0], index[1], value)
+
+    companion object {
+        fun <T> create(
+            rowNum: Int,
+            colNum: Int,
+            bufferFactory: MutableBufferFactory<T>,
+            init: (i: Int, j: Int) -> T
+        ): Mutable2DStructure<T> {
+            val buffer = bufferFactory(rowNum * colNum) { offset -> init(offset / colNum, offset % colNum) }
+            return Mutable2DStructure(rowNum, colNum, buffer)
+        }
+    }
+}

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

@@ -10,7 +10,7 @@ import scientifik.kmath.structures.ndStructure
  * Basic implementation of Matrix space based on [NDStructure]
  */
 class StructureMatrixContext<T : Any, R : Ring<T>>(
-    override val ring: R,
+    override val elementContext: R,
     private val bufferFactory: BufferFactory<T>
 ) : MatrixContext<T, R> {
 

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

@@ -124,8 +124,6 @@ inline class MutableListBuffer<T>(private val list: MutableList<T>) : MutableBuf
     override fun copy(): MutableBuffer<T> = MutableListBuffer(ArrayList(list))
 }
 
-fun <T> MutableList<T>.asBuffer() = MutableListBuffer(this)
-
 class ArrayBuffer<T>(private val array: Array<T>) : MutableBuffer<T> {
     //Can't inline because array is invariant
     override val size: Int

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

@@ -22,9 +22,8 @@ class MatrixTest {
 
     @Test
     fun testTranspose() {
-        val matrix = MatrixContext.real(3, 3).one
+        val matrix = MatrixContext.real.one(3, 3)
         val transposed = matrix.transpose()
-        assertEquals(matrix.context, transposed.context)
         assertEquals((matrix as StructureMatrix).structure, (transposed as StructureMatrix).structure)
         assertEquals(matrix, transposed)
     }
@@ -37,7 +36,7 @@ class MatrixTest {
 
         val matrix1 = vector1.toMatrix()
         val matrix2 = vector2.toMatrix().transpose()
-        val product = matrix1 dot matrix2
+        val product = MatrixContext.real.run { matrix1 dot matrix2 }
 
 
         assertEquals(5.0, product[1, 0])

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

@@ -6,8 +6,8 @@ import kotlin.test.assertEquals
 class RealLUSolverTest {
     @Test
     fun testInvertOne() {
-        val matrix = MatrixContext.real(2, 2).one
+        val matrix = MatrixContext.real.one(2, 2)
-        val inverted = RealLUSolver.inverse(matrix)
+        val inverted = LUSolver.real.inverse(matrix)
         assertEquals(matrix, inverted)
     }