Optimizing inversion performance

benchmarks/src/main/kotlin/scientifik/kmath/linear/LinearAlgebraBenchmark.kt

@@ -15,19 +15,20 @@ fun main() {
 
     val n = 5000 // iterations
 
-    val solver = LUSolver.real
+    MatrixContext.real.run {
 
-    repeat(50) {
+        repeat(50) {
-        val res = solver.inverse(matrix)
+            val res = inverse(matrix)
-    }
-
-    val inverseTime = measureTimeMillis {
-        repeat(n) {
-            val res = solver.inverse(matrix)
         }
-    }
 
-    println("[kmath] Inversion of $n matrices $dim x $dim finished in $inverseTime millis")
+        val inverseTime = measureTimeMillis {
+            repeat(n) {
+                val res = inverse(matrix)
+            }
+        }
+
+        println("[kmath] Inversion of $n matrices $dim x $dim finished in $inverseTime millis")
+    }
 
     //commons-math
 

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

@@ -1,5 +1,6 @@
 package scientifik.kmath.linear
 
+import scientifik.kmath.operations.RealField
 import scientifik.kmath.operations.Ring
 import scientifik.kmath.structures.*
 
@@ -17,6 +18,10 @@ class BufferMatrixContext<T : Any, R : Ring<T>>(
     }
 
     override fun point(size: Int, initializer: (Int) -> T): Point<T> = bufferFactory(size, initializer)
+
+    companion object {
+
+    }
 }
 
 class BufferMatrix<T : Any>(

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

@@ -1,16 +1,17 @@
 package scientifik.kmath.linear
 
 import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.RealField
 import scientifik.kmath.operations.Ring
 import scientifik.kmath.structures.*
-import scientifik.kmath.structures.MutableBuffer.Companion.boxing
+import kotlin.reflect.KClass
 
 /**
  * Common implementation of [LUPDecompositionFeature]
  */
-class LUPDecomposition<T : Comparable<T>>(
+class LUPDecomposition<T : Any>(
     private val elementContext: Ring<T>,
-    internal val lu: NDStructure<T>,
+    val lu: Structure2D<T>,
     val pivot: IntArray,
     private val even: Boolean
 ) : LUPDecompositionFeature<T>, DeterminantFeature<T> {
@@ -62,146 +63,222 @@ class LUPDecomposition<T : Comparable<T>>(
 
 }
 
-/**
+open class BufferAccessor<T : Any>(val type: KClass<T>, val field: Field<T>, val rowNum: Int, val colNum: Int) {
- * Common implementation of LUP [LinearSolver] based on commons-math code
+    open operator fun MutableBuffer<T>.get(i: Int, j: Int) = get(i + colNum * j)
- */
+    open operator fun MutableBuffer<T>.set(i: Int, j: Int, value: T) {
-class LUSolver<T : Comparable<T>, F : Field<T>>(
+        set(i + colNum * j, value)
-    val context: GenericMatrixContext<T, F>,
-    val bufferFactory: MutableBufferFactory<T> = ::boxing,
-    val singularityCheck: (T) -> Boolean
-) : LinearSolver<T> {
-
-
-    private fun abs(value: T) =
-        if (value > context.elementContext.zero) value else with(context.elementContext) { -value }
-
-    fun buildDecomposition(matrix: Matrix<T>): LUPDecomposition<T> {
-        if (matrix.rowNum != matrix.colNum) {
-            error("LU decomposition supports only square matrices")
-        }
-
-        val m = matrix.colNum
-        val pivot = IntArray(matrix.rowNum)
-
-        val lu = Mutable2DStructure.create(matrix.rowNum, matrix.colNum, bufferFactory) { i, j ->
-            matrix[i, j]
-        }
-
-
-        with(context.elementContext) {
-            // Initialize permutation array and parity
-            for (row in 0 until m) {
-                pivot[row] = row
-            }
-            var 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]
-                    }
-                    lu[row, col] = sum
-
-                    abs(sum)
-                } ?: col
-
-                // Singularity check
-                if (singularityCheck(lu[max, col])) {
-                    error("Singular matrix")
-                }
-
-                // Pivot if necessary
-                if (max != 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] = lu[row, col] / luDiag
-                }
-            }
-            return LUPDecomposition(context.elementContext, lu, pivot, even)
-        }
     }
 
-    /**
+    fun create(init: (i: Int, j: Int) -> T) =
-     * Produce a matrix with added decomposition feature
+        MutableBuffer.auto(type, rowNum * colNum) { offset -> init(offset / colNum, offset % colNum) }
-     */
-    fun decompose(matrix: Matrix<T>): Matrix<T> {
-        if (matrix.hasFeature<LUPDecomposition<*>>()) {
-            return matrix
-        } else {
-            val decomposition = buildDecomposition(matrix)
-            return VirtualMatrix.wrap(matrix, decomposition)
-        }
-    }
 
+    fun create(mat: Structure2D<T>) = create { i, j -> mat[i, j] }
 
-    override fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T> {
+    //TODO optimize wrapper
-        if (b.rowNum != a.colNum) {
+    fun MutableBuffer<T>.collect(): Structure2D<T> =
-            error("Matrix dimension mismatch expected ${a.rowNum}, but got ${b.colNum}")
+        NDStructure.auto(type, rowNum, colNum) { (i, j) -> get(i, j) }.as2D()
-        }
 
-        // Use existing decomposition if it is provided by matrix
+    open fun MutableBuffer<T>.innerProduct(row: Int, col: Int, max: Int): T {
-        val decomposition = a.getFeature() ?: buildDecomposition(a)
+        var sum = field.zero
-
+        field.run {
-        with(decomposition) {
+            for (i in 0 until max) {
-            with(context.elementContext) {
+                sum += get(row, i) * get(i, col)
-                // Apply permutations to b
-                val bp = Mutable2DStructure.create(a.rowNum, a.colNum, bufferFactory) { i, j ->
-                    b[pivot[i], j]
-                }
-
-                // 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] * lu[i, col]
-                        }
-                    }
-                }
-
-                // Solve UX = Y
-                for (col in a.rowNum - 1 downTo 0) {
-                    for (j in 0 until b.colNum) {
-                        bp[col, j] /= lu[col, col]
-                    }
-                    for (i in 0 until col) {
-                        for (j in 0 until b.colNum) {
-                            bp[i, j] -= bp[col, j] * lu[i, col]
-                        }
-                    }
-                }
-
-                return context.produce(a.rowNum, a.colNum) { i, j -> bp[i, j] }
             }
         }
+        return sum
     }
 
-    override fun inverse(a: Matrix<T>): Matrix<T> = solve(a, context.one(a.rowNum, a.colNum))
+    open fun MutableBuffer<T>.divideInPlace(i: Int, j: Int, factor: T) {
+        field.run { set(i, j, get(i, j) / factor) }
+    }
 
-    companion object {
+    open fun MutableBuffer<T>.subtractInPlace(i: Int, j: Int, lu: MutableBuffer<T>, col: Int) {
-        val real = LUSolver(MatrixContext.real, MutableBuffer.Companion::auto) { it < 1e-11 }
+        field.run {
+            set(i, j, get(i, j) - get(col, j) * lu[i, col])
+        }
     }
 }
+
+/**
+ * Specialized LU operations for Doubles
+ */
+class RealBufferAccessor(rowNum: Int, colNum: Int) : BufferAccessor<Double>(Double::class, RealField, rowNum, colNum) {
+    override inline fun MutableBuffer<Double>.get(i: Int, j: Int) = (this as DoubleBuffer).array[i + colNum * j]
+    override inline fun MutableBuffer<Double>.set(i: Int, j: Int, value: Double) {
+        (this as DoubleBuffer).array[i + colNum * j] = value
+    }
+
+    override fun MutableBuffer<Double>.innerProduct(row: Int, col: Int, max: Int): Double {
+        var sum = 0.0
+        for (i in 0 until max) {
+            sum += get(row, i) * get(i, col)
+        }
+        return sum
+    }
+
+    override fun MutableBuffer<Double>.divideInPlace(i: Int, j: Int, factor: Double) {
+        set(i, j, get(i, j) / factor)
+    }
+
+    override fun MutableBuffer<Double>.subtractInPlace(i: Int, j: Int, lu: MutableBuffer<Double>, col: Int) {
+        set(i, j, get(i, j) - get(col, j) * lu[i, col])
+    }
+}
+
+fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.buildAccessor(
+    type:KClass<T>,
+    rowNum: Int,
+    colNum: Int
+): BufferAccessor<T> {
+    return if (elementContext == RealField) {
+        @Suppress("UNCHECKED_CAST")
+        RealBufferAccessor(rowNum, colNum) as BufferAccessor<T>
+    } else {
+        BufferAccessor(type, elementContext, rowNum, colNum)
+    }
+}
+
+fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.abs(value: T) =
+    if (value > elementContext.zero) value else with(elementContext) { -value }
+
+
+fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lupDecompose(
+    type: KClass<T>,
+    matrix: Matrix<T>,
+    checkSingular: (T) -> Boolean
+): LUPDecomposition<T> {
+    if (matrix.rowNum != matrix.colNum) {
+        error("LU decomposition supports only square matrices")
+    }
+
+
+    val m = matrix.colNum
+    val pivot = IntArray(matrix.rowNum)
+
+    buildAccessor(type, matrix.rowNum, matrix.colNum).run {
+
+        val lu = create(matrix)
+
+        // Initialize permutation array and parity
+        for (row in 0 until m) {
+            pivot[row] = row
+        }
+        var 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]
+//                }
+                val sum = lu.innerProduct(row, col, row)
+                lu[row, col] = field.run { 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]
+//                }
+//                lu[row, col] = sum
+                val sum = lu.innerProduct(row, col, col)
+                lu[row, col] = field.run { lu[row, col] - sum }
+                abs(sum)
+            } ?: col
+
+            // Singularity check
+            if (checkSingular(lu[max, col])) {
+                error("Singular matrix")
+            }
+
+            // Pivot if necessary
+            if (max != 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.divideInPlace(row, col, luDiag)
+                //lu[row, col] = lu[row, col] / luDiag
+            }
+        }
+        return scientifik.kmath.linear.LUPDecomposition(elementContext, lu.collect(), pivot, even)
+
+    }
+}
+
+/**
+ * Solve a linear equation **a*x = b**
+ */
+fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.solve(
+    type: KClass<T>,
+    a: Matrix<T>,
+    b: Matrix<T>,
+    checkSingular: (T) -> Boolean
+): Matrix<T> {
+    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
+    val decomposition = a.getFeature() ?: lupDecompose(type, a, checkSingular)
+
+    buildAccessor(type, a.rowNum, a.colNum).run {
+
+        val lu = create(decomposition.lu)
+
+        // Apply permutations to b
+        val bp = create { i, j ->
+            b[decomposition.pivot[i], j]
+        }
+
+        // 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.subtractInPlace(i, j, lu, col)
+                    //bp[i, j] -= bp[col, j] * lu[i, col]
+                }
+            }
+        }
+
+        // Solve UX = Y
+        for (col in a.rowNum - 1 downTo 0) {
+            val luDiag = lu[col, col]
+            for (j in 0 until b.colNum) {
+                bp.divideInPlace(col, j, luDiag)
+                //bp[col, j] /= lu[col, col]
+            }
+            for (i in 0 until col) {
+                for (j in 0 until b.colNum) {
+                    bp.subtractInPlace(i, j, lu, col)
+                    //bp[i, j] -= bp[col, j] * lu[i, col]
+                }
+            }
+        }
+
+        return produce(a.rowNum, a.colNum) { i, j -> bp[i, j] }
+    }
+
+}
+
+inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.inverse(
+    matrix: Matrix<T>,
+    noinline checkSingular: (T) -> Boolean
+) =
+    solve(T::class, matrix, one(matrix.rowNum, matrix.colNum), checkSingular)
+
+fun GenericMatrixContext<Double, RealField>.inverse(matrix: Matrix<Double>) =
+    inverse(matrix) { it < 1e-11 }

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

@@ -1,40 +0,0 @@
-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/structures/Buffers.kt

@@ -2,6 +2,7 @@ package scientifik.kmath.structures
 
 import scientifik.kmath.operations.Complex
 import scientifik.kmath.operations.complex
+import kotlin.reflect.KClass
 
 
 typealias BufferFactory<T> = (Int, (Int) -> T) -> Buffer<T>
@@ -41,13 +42,10 @@ interface Buffer<T> {
          */
         inline fun <T> boxing(size: Int, initializer: (Int) -> T): Buffer<T> = ListBuffer(List(size, initializer))
 
-        /**
-         * Create most appropriate immutable buffer for given type avoiding boxing wherever possible
-         */
         @Suppress("UNCHECKED_CAST")
-        inline fun <reified T : Any> auto(size: Int, crossinline initializer: (Int) -> T): Buffer<T> {
+        inline fun <T : Any> auto(type: KClass<T>, size: Int, crossinline initializer: (Int) -> T): Buffer<T> {
             //TODO add resolution based on Annotation or companion resolution
-            return when (T::class) {
+            return when (type) {
                 Double::class -> DoubleBuffer(DoubleArray(size) { initializer(it) as Double }) as Buffer<T>
                 Short::class -> ShortBuffer(ShortArray(size) { initializer(it) as Short }) as Buffer<T>
                 Int::class -> IntBuffer(IntArray(size) { initializer(it) as Int }) as Buffer<T>
@@ -56,6 +54,13 @@ interface Buffer<T> {
                 else -> boxing(size, initializer)
             }
         }
+
+        /**
+         * Create most appropriate immutable buffer for given type avoiding boxing wherever possible
+         */
+        @Suppress("UNCHECKED_CAST")
+        inline fun <reified T : Any> auto(size: Int, crossinline initializer: (Int) -> T): Buffer<T> =
+            auto(T::class, size, initializer)
     }
 }
 
@@ -78,12 +83,9 @@ interface MutableBuffer<T> : Buffer<T> {
         inline fun <T> boxing(size: Int, initializer: (Int) -> T): MutableBuffer<T> =
             MutableListBuffer(MutableList(size, initializer))
 
-        /**
-         * Create most appropriate mutable buffer for given type avoiding boxing wherever possible
-         */
         @Suppress("UNCHECKED_CAST")
-        inline fun <reified T : Any> auto(size: Int, initializer: (Int) -> T): MutableBuffer<T> {
+        inline fun <T : Any> auto(type: KClass<T>, size: Int, initializer: (Int) -> T): MutableBuffer<T> {
-            return when (T::class) {
+            return when (type) {
                 Double::class -> DoubleBuffer(DoubleArray(size) { initializer(it) as Double }) as MutableBuffer<T>
                 Short::class -> ShortBuffer(ShortArray(size) { initializer(it) as Short }) as MutableBuffer<T>
                 Int::class -> IntBuffer(IntArray(size) { initializer(it) as Int }) as MutableBuffer<T>
@@ -91,6 +93,17 @@ interface MutableBuffer<T> : Buffer<T> {
                 else -> boxing(size, initializer)
             }
         }
+
+        /**
+         * Create most appropriate mutable buffer for given type avoiding boxing wherever possible
+         */
+        @Suppress("UNCHECKED_CAST")
+        inline fun <reified T : Any> auto(size: Int, initializer: (Int) -> T): MutableBuffer<T> =
+            auto(T::class, size, initializer)
+
+        val real: MutableBufferFactory<Double> = { size: Int, initializer: (Int) -> Double ->
+            DoubleBuffer(DoubleArray(size) { initializer(it) })
+        }
     }
 }
 

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

@@ -1,5 +1,8 @@
 package scientifik.kmath.structures
 
+import kotlin.jvm.JvmName
+import kotlin.reflect.KClass
+
 
 interface NDStructure<T> {
 
@@ -40,6 +43,9 @@ interface NDStructure<T> {
         inline fun <reified T : Any> auto(strides: Strides, crossinline initializer: (IntArray) -> T) =
             BufferNDStructure(strides, Buffer.auto(strides.linearSize) { i -> initializer(strides.index(i)) })
 
+        inline fun <T : Any> auto(type: KClass<T>, strides: Strides, crossinline initializer: (IntArray) -> T) =
+            BufferNDStructure(strides, Buffer.auto(type, strides.linearSize) { i -> initializer(strides.index(i)) })
+
         fun <T> build(
             shape: IntArray,
             bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
@@ -48,6 +54,13 @@ interface NDStructure<T> {
 
         inline fun <reified T : Any> auto(shape: IntArray, crossinline initializer: (IntArray) -> T) =
             auto(DefaultStrides(shape), initializer)
+
+        @JvmName("autoVarArg")
+        inline fun <reified T : Any> auto(vararg shape: Int, crossinline initializer: (IntArray) -> T) =
+            auto(DefaultStrides(shape), initializer)
+
+        inline fun <T : Any> auto(type: KClass<T>, vararg shape: Int, crossinline initializer: (IntArray) -> T) =
+            auto(type, DefaultStrides(shape), initializer)
     }
 }
 
@@ -57,7 +70,7 @@ interface MutableNDStructure<T> : NDStructure<T> {
     operator fun set(index: IntArray, value: T)
 }
 
-fun <T> MutableNDStructure<T>.mapInPlace(action: (IntArray, T) -> T) {
+inline fun <T> MutableNDStructure<T>.mapInPlace(action: (IntArray, T) -> T) {
     elements().forEach { (index, oldValue) ->
         this[index] = action(index, oldValue)
     }