kmath-ast/build.gradle.kts

@@ -0,0 +1,27 @@
+plugins {
+    id("scientifik.mpp")
+}
+
+repositories{
+    maven("https://dl.bintray.com/hotkeytlt/maven")
+}
+
+kotlin.sourceSets {
+    commonMain {
+        dependencies {
+            api(project(":kmath-core"))
+            implementation("com.github.h0tk3y.betterParse:better-parse-multiplatform:0.4.0-alpha-3")
+            implementation("com.github.h0tk3y.betterParse:better-parse-multiplatform-metadata:0.4.0-alpha-3")
+        }
+    }
+    jvmMain{
+        dependencies{
+            implementation("com.github.h0tk3y.betterParse:better-parse-jvm:0.4.0-alpha-3")
+        }
+    }
+    jsMain{
+        dependencies{
+            implementation("com.github.h0tk3y.betterParse:better-parse-js:0.4.0-alpha-3")
+        }
+    }
+}

kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MST.kt

@@ -0,0 +1,62 @@
+package scientifik.kmath.ast
+
+import scientifik.kmath.operations.NumericAlgebra
+import scientifik.kmath.operations.RealField
+
+/**
+ * A Mathematical Syntax Tree node for mathematical expressions
+ */
+sealed class MST {
+
+    /**
+     * A node containing unparsed string
+     */
+    data class Singular(val value: String) : MST()
+
+    /**
+     * A node containing a number
+     */
+    data class Numeric(val value: Number) : MST()
+
+    /**
+     * A node containing an unary operation
+     */
+    data class Unary(val operation: String, val value: MST) : MST() {
+        companion object {
+            const val ABS_OPERATION = "abs"
+            //TODO add operations
+        }
+    }
+
+    /**
+     * A node containing binary operation
+     */
+    data class Binary(val operation: String, val left: MST, val right: MST) : MST() {
+        companion object
+    }
+}
+
+//TODO add a function with positional arguments
+
+//TODO add a function with named arguments
+
+fun <T> NumericAlgebra<T>.evaluate(node: MST): T {
+    return when (node) {
+        is MST.Numeric -> number(node.value)
+        is MST.Singular -> symbol(node.value)
+        is MST.Unary -> unaryOperation(node.operation, evaluate(node.value))
+        is MST.Binary -> when {
+            node.left is MST.Numeric && node.right is MST.Numeric -> {
+                val number = RealField.binaryOperation(
+                    node.operation,
+                    node.left.value.toDouble(),
+                    node.right.value.toDouble()
+                )
+                number(number)
+            }
+            node.left is MST.Numeric -> leftSideNumberOperation(node.operation, node.left.value, evaluate(node.right))
+            node.right is MST.Numeric -> rightSideNumberOperation(node.operation, evaluate(node.left), node.right.value)
+            else -> binaryOperation(node.operation, evaluate(node.left), evaluate(node.right))
+        }
+    }
+}

kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/MSTExpression.kt

@@ -0,0 +1,19 @@
+package scientifik.kmath.ast
+
+import scientifik.kmath.expressions.Expression
+import scientifik.kmath.operations.NumericAlgebra
+
+/**
+ * The expression evaluates MST on-flight. Should be much faster than functional expression, but slower than ASM-generated expressions.
+ */
+class MSTExpression<T>(val algebra: NumericAlgebra<T>, val mst: MST) : Expression<T> {
+
+    /**
+     * Substitute algebra raw value
+     */
+    private inner class InnerAlgebra(val arguments: Map<String, T>) : NumericAlgebra<T> by algebra {
+        override fun symbol(value: String): T = arguments[value] ?: super.symbol(value)
+    }
+
+    override fun invoke(arguments: Map<String, T>): T = InnerAlgebra(arguments).evaluate(mst)
+}

kmath-ast/src/commonMain/kotlin/scientifik/kmath/ast/parser.kt

@@ -0,0 +1,59 @@
+package scientifik.kmath.ast
+
+import com.github.h0tk3y.betterParse.combinators.*
+import com.github.h0tk3y.betterParse.grammar.Grammar
+import com.github.h0tk3y.betterParse.grammar.parseToEnd
+import com.github.h0tk3y.betterParse.grammar.parser
+import com.github.h0tk3y.betterParse.grammar.tryParseToEnd
+import com.github.h0tk3y.betterParse.parser.ParseResult
+import com.github.h0tk3y.betterParse.parser.Parser
+import scientifik.kmath.operations.FieldOperations
+import scientifik.kmath.operations.PowerOperations
+import scientifik.kmath.operations.RingOperations
+import scientifik.kmath.operations.SpaceOperations
+
+/**
+ * TODO move to common
+ */
+private object ArithmeticsEvaluator : Grammar<MST>() {
+    val num by token("-?[\\d.]+(?:[eE]-?\\d+)?")
+    val lpar by token("\\(")
+    val rpar by token("\\)")
+    val mul by token("\\*")
+    val pow by token("\\^")
+    val div by token("/")
+    val minus by token("-")
+    val plus by token("\\+")
+    val ws by token("\\s+", ignore = true)
+
+    val number: Parser<MST> by num use { MST.Numeric(text.toDouble()) }
+
+    val term: Parser<MST> by number or
+            (skip(minus) and parser(this::term) map { MST.Unary(SpaceOperations.MINUS_OPERATION, it) }) or
+            (skip(lpar) and parser(this::rootParser) and skip(rpar))
+
+    val powChain by leftAssociative(term, pow) { a, _, b ->
+        MST.Binary(PowerOperations.POW_OPERATION, a, b)
+    }
+
+    val divMulChain: Parser<MST> by leftAssociative(powChain, div or mul use { type }) { a, op, b ->
+        if (op == div) {
+            MST.Binary(FieldOperations.DIV_OPERATION, a, b)
+        } else {
+            MST.Binary(RingOperations.TIMES_OPERATION, a, b)
+        }
+    }
+
+    val subSumChain: Parser<MST> by leftAssociative(divMulChain, plus or minus use { type }) { a, op, b ->
+        if (op == plus) {
+            MST.Binary(SpaceOperations.PLUS_OPERATION, a, b)
+        } else {
+            MST.Binary(SpaceOperations.MINUS_OPERATION, a, b)
+        }
+    }
+
+    override val rootParser: Parser<MST> by subSumChain
+}
+
+fun String.tryParseMath(): ParseResult<MST> = ArithmeticsEvaluator.tryParseToEnd(this)
+fun String.parseMath(): MST = ArithmeticsEvaluator.parseToEnd(this)

kmath-ast/src/jvmMain/kotlin/scientifik/kmath/ast/asm.kt

@@ -0,0 +1,23 @@
+package scientifik.kmath.ast
+
+import scientifik.kmath.expressions.Expression
+import scientifik.kmath.operations.Algebra
+import scientifik.kmath.operations.NumericAlgebra
+
+//TODO stubs for asm generation
+
+interface AsmExpression<T>
+
+interface AsmExpressionAlgebra<T, A : Algebra<T>> : NumericAlgebra<AsmExpression<T>> {
+    val algebra: A
+}
+
+fun <T> AsmExpression<T>.compile(): Expression<T> = TODO()
+
+//TODO add converter for functional expressions
+
+inline fun <reified T : Any, A : Algebra<T>> A.asm(
+    block: AsmExpressionAlgebra<T, A>.() -> AsmExpression<T>
+): Expression<T> = TODO()
+
+inline fun <reified T : Any, A : Algebra<T>> A.asm(ast: MST): Expression<T> = asm { evaluate(ast) }

kmath-ast/src/jvmTest/kotlin/scietifik/kmath/ast/ParserTest.kt

@@ -0,0 +1,17 @@
+package scietifik.kmath.ast
+
+import org.junit.jupiter.api.Assertions.assertEquals
+import org.junit.jupiter.api.Test
+import scientifik.kmath.ast.evaluate
+import scientifik.kmath.ast.parseMath
+import scientifik.kmath.operations.Complex
+import scientifik.kmath.operations.ComplexField
+
+internal class ParserTest{
+    @Test
+    fun parsedExpression(){
+        val mst = "2+2*(2+2)".parseMath()
+        val res = ComplexField.evaluate(mst)
+        assertEquals(Complex(10.0,0.0), res)
+    }
+}

kmath-commons/src/main/kotlin/scientifik/kmath/commons/expressions/DiffExpression.kt

@@ -2,7 +2,7 @@ package scientifik.kmath.commons.expressions
 
 import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
 import scientifik.kmath.expressions.Expression
-import scientifik.kmath.expressions.ExpressionContext
+import scientifik.kmath.expressions.ExpressionAlgebra
 import scientifik.kmath.operations.ExtendedField
 import scientifik.kmath.operations.Field
 import kotlin.properties.ReadOnlyProperty
@@ -115,7 +115,7 @@ fun DiffExpression.derivative(name: String) = derivative(name to 1)
 /**
  * A context for [DiffExpression] (not to be confused with [DerivativeStructure])
  */
-object DiffExpressionContext : ExpressionContext<Double, DiffExpression>, Field<DiffExpression> {
+object DiffExpressionAlgebra : ExpressionAlgebra<Double, DiffExpression>, Field<DiffExpression> {
     override fun variable(name: String, default: Double?) =
         DiffExpression { variable(name, default?.const()) }
 

kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt

@@ -7,6 +7,12 @@ import scientifik.kmath.operations.Algebra
  */
 interface Expression<T> {
     operator fun invoke(arguments: Map<String, T>): T
+
+    companion object {
+        operator fun <T> invoke(block: (Map<String, T>) -> T): Expression<T> = object : Expression<T> {
+            override fun invoke(arguments: Map<String, T>): T = block(arguments)
+        }
+    }
 }
 
 operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T = invoke(mapOf(*pairs))
@@ -14,7 +20,7 @@ operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T = invoke
 /**
  * A context for expression construction
  */
-interface ExpressionContext<T, E> : Algebra<E> {
+interface ExpressionAlgebra<T, E> : Algebra<E> {
     /**
      * Introduce a variable into expression context
      */

kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/SyntaxTreeNode.kt

@@ -1,52 +0,0 @@
-package scientifik.kmath.expressions
-
-import scientifik.kmath.operations.NumericAlgebra
-
-/**
- * A syntax tree node for mathematical expressions
- */
-sealed class SyntaxTreeNode
-
-/**
- * A node containing unparsed string
- */
-data class SingularNode(val value: String) : SyntaxTreeNode()
-
-/**
- * A node containing a number
- */
-data class NumberNode(val value: Number) : SyntaxTreeNode()
-
-/**
- * A node containing an unary operation
- */
-data class UnaryNode(val operation: String, val value: SyntaxTreeNode) : SyntaxTreeNode() {
-    companion object {
-        const val ABS_OPERATION = "abs"
-        const val SIN_OPERATION = "sin"
-        const val COS_OPERATION = "cos"
-        const val EXP_OPERATION = "exp"
-        const val LN_OPERATION = "ln"
-        //TODO add operations
-    }
-}
-
-/**
- * A node containing binary operation
- */
-data class BinaryNode(val operation: String, val left: SyntaxTreeNode, val right: SyntaxTreeNode) : SyntaxTreeNode() {
-    companion object
-}
-
-//TODO add a function with positional arguments
-
-//TODO add a function with named arguments
-
-fun <T> NumericAlgebra<T>.compile(node: SyntaxTreeNode): T{
-    return when (node) {
-        is NumberNode -> number(node.value)
-        is SingularNode -> raw(node.value)
-        is UnaryNode -> unaryOperation(node.operation, compile(node.value))
-        is BinaryNode -> binaryOperation(node.operation, compile(node.left), compile(node.right))
-    }
-}

kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/functionalExpressions.kt

@@ -21,8 +21,11 @@ internal class SumExpression<T>(
     override fun invoke(arguments: Map<String, T>): T = context.add(first.invoke(arguments), second.invoke(arguments))
 }
 
-internal class ProductExpression<T>(val context: Ring<T>, val first: Expression<T>, val second: Expression<T>) :
-    Expression<T> {
+internal class ProductExpression<T>(
+    val context: Ring<T>,
+    val first: Expression<T>,
+    val second: Expression<T>
+) : Expression<T> {
     override fun invoke(arguments: Map<String, T>): T =
         context.multiply(first.invoke(arguments), second.invoke(arguments))
 }
@@ -39,7 +42,7 @@ internal class DivExpession<T>(val context: Field<T>, val expr: Expression<T>, v
 
 open class FunctionalExpressionSpace<T>(
     val space: Space<T>
-) : Space<Expression<T>>, ExpressionContext<T,Expression<T>> {
+) : Space<Expression<T>>, ExpressionAlgebra<T, Expression<T>> {
 
     override val zero: Expression<T> = ConstantExpression(space.zero)
 
@@ -61,10 +64,9 @@ open class FunctionalExpressionSpace<T>(
 
 open class FunctionalExpressionField<T>(
     val field: Field<T>
-) :  Field<Expression<T>>, ExpressionContext<T,Expression<T>>, FunctionalExpressionSpace<T>(field) {
+) : Field<Expression<T>>, ExpressionAlgebra<T, Expression<T>>, FunctionalExpressionSpace<T>(field) {
 
-    override val one: Expression<T>
-        get() = const(this.field.one)
+    override val one: Expression<T> = ConstantExpression(this.field.one)
 
     fun const(value: Double): Expression<T> = const(field.run { one * value })
 
@@ -78,3 +80,15 @@ open class FunctionalExpressionField<T>(
     operator fun T.times(arg: Expression<T>) = arg * this
     operator fun T.div(arg: Expression<T>) = arg / this
 }
+
+/**
+ * Create a functional expression on this [Space]
+ */
+fun <T> Space<T>.buildExpression(block: FunctionalExpressionSpace<T>.() -> Expression<T>): Expression<T> =
+    FunctionalExpressionSpace(this).run(block)
+
+/**
+ * Create a functional expression on this [Field]
+ */
+fun <T> Field<T>.buildExpression(block: FunctionalExpressionField<T>.() -> Expression<T>): Expression<T> =
+    FunctionalExpressionField(this).run(block)

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

@@ -128,14 +128,14 @@ fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
                     luRow[col] = sum
 
                     // maintain best permutation choice
-                    if (abs(sum) > largest) {
-                        largest = abs(sum)
+                    if (this@lup.abs(sum) > largest) {
+                        largest = this@lup.abs(sum)
                         max = row
                     }
                 }
 
                 // Singularity check
-                if (checkSingular(abs(lu[max, col]))) {
+                if (checkSingular(this@lup.abs(lu[max, col]))) {
                     error("The matrix is singular")
                 }
 

kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/Grids.kt

@@ -1,5 +1,7 @@
 package scientifik.kmath.misc
 
+import kotlin.math.abs
+
 /**
  * Convert double range to sequence.
  *
@@ -8,8 +10,7 @@ package scientifik.kmath.misc
  *
  * If step is negative, the same goes from upper boundary downwards
  */
-fun ClosedFloatingPointRange<Double>.toSequence(step: Double): Sequence<Double> =
-        when {
+fun ClosedFloatingPointRange<Double>.toSequenceWithStep(step: Double): Sequence<Double> = when {
     step == 0.0 -> error("Zero step in double progression")
     step > 0 -> sequence {
         var current = start
@@ -27,9 +28,18 @@ fun ClosedFloatingPointRange<Double>.toSequence(step: Double): Sequence<Double>
     }
 }
 
+/**
+ * Convert double range to sequence with the fixed number of points
+ */
+fun ClosedFloatingPointRange<Double>.toSequenceWithPoints(numPoints: Int): Sequence<Double> {
+    require(numPoints > 1) { "The number of points should be more than 2" }
+    return toSequenceWithStep(abs(endInclusive - start) / (numPoints - 1))
+}
+
 /**
  * Convert double range to array of evenly spaced doubles, where the size of array equals [numPoints]
  */
+@Deprecated("Replace by 'toSequenceWithPoints'")
 fun ClosedFloatingPointRange<Double>.toGrid(numPoints: Int): DoubleArray {
     if (numPoints < 2) error("Can't create generic grid with less than two points")
     return DoubleArray(numPoints) { i -> start + (endInclusive - start) / (numPoints - 1) * i }

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

@@ -10,7 +10,10 @@ interface Algebra<T> {
     /**
      * Wrap raw string or variable
      */
-    fun raw(value: String): T = error("Wrapping of '$value' is not supported in $this")
+    fun symbol(value: String): T = error("Wrapping of '$value' is not supported in $this")
+
+    @Deprecated("Symbol is more concise",replaceWith = ReplaceWith("symbol"))
+    fun raw(value: String): T = symbol(value)
 
     /**
      * Dynamic call of unary operation with name [operation] on [arg]
@@ -31,6 +34,12 @@ interface NumericAlgebra<T> : Algebra<T> {
      * Wrap a number
      */
     fun number(value: Number): T
+
+    fun leftSideNumberOperation(operation: String, left: Number, right: T): T =
+        binaryOperation(operation, number(left), right)
+
+    fun rightSideNumberOperation(operation: String, left: T, right: Number): T =
+        leftSideNumberOperation(operation, right, left)
 }
 
 /**
@@ -128,7 +137,13 @@ interface Ring<T> : Space<T>, RingOperations<T>, NumericAlgebra<T> {
 
     override fun number(value: Number): T = one * value.toDouble()
 
-    // those operators are blocked by type conflict in RealField
+    override fun leftSideNumberOperation(operation: String, left: Number, right: T): T = when (operation) {
+        RingOperations.TIMES_OPERATION -> left * right
+        else -> super.leftSideNumberOperation(operation, left, right)
+    }
+
+    //TODO those operators are blocked by type conflict in RealField
+
 //    operator fun T.plus(b: Number) = this.plus(b * one)
 //    operator fun Number.plus(b: T) = b + this
 //

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

@@ -13,7 +13,7 @@ private val PI_DIV_2 = Complex(PI / 2, 0)
 /**
  * A field for complex numbers
  */
-object ComplexField : ExtendedFieldOperations<Complex>, Field<Complex> {
+object ComplexField : ExtendedField<Complex> {
     override val zero: Complex = Complex(0.0, 0.0)
 
     override val one: Complex = Complex(1.0, 0.0)
@@ -54,6 +54,12 @@ object ComplexField : ExtendedFieldOperations<Complex>, Field<Complex> {
     operator fun Complex.minus(d: Double) = add(this, -d.toComplex())
 
     operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)
+
+    override fun symbol(value: String): Complex = if (value == "i") {
+        i
+    } else {
+        super.symbol(value)
+    }
 }
 
 /**

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

@@ -10,10 +10,30 @@ interface ExtendedFieldOperations<T> :
     FieldOperations<T>,
     InverseTrigonometricOperations<T>,
     PowerOperations<T>,
-    ExponentialOperations<T>
+    ExponentialOperations<T> {
 
-interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T>
+    override fun tan(arg: T): T = sin(arg) / cos(arg)
 
+    override fun unaryOperation(operation: String, arg: T): T = when (operation) {
+        TrigonometricOperations.COS_OPERATION -> cos(arg)
+        TrigonometricOperations.SIN_OPERATION -> sin(arg)
+        PowerOperations.SQRT_OPERATION -> sqrt(arg)
+        ExponentialOperations.EXP_OPERATION -> exp(arg)
+        ExponentialOperations.LN_OPERATION -> ln(arg)
+        else -> super.unaryOperation(operation, arg)
+    }
+
+}
+
+interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T> {
+    override fun rightSideNumberOperation(operation: String, left: T, right: Number): T {
+        return when (operation) {
+            PowerOperations.POW_OPERATION -> power(left, right)
+            else -> super.rightSideNumberOperation(operation, left, right)
+        }
+
+    }
+}
 /**
  * Real field element wrapping double.
  *

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

@@ -49,9 +49,11 @@ fun <T : MathElement<out InverseTrigonometricOperations<T>>> atan(arg: T): T = a
 interface PowerOperations<T> : Algebra<T> {
     fun power(arg: T, pow: Number): T
     fun sqrt(arg: T) = power(arg, 0.5)
+
     infix fun T.pow(pow: Number) = power(this, pow)
 
     companion object {
+        const val POW_OPERATION = "pow"
         const val SQRT_OPERATION = "sqrt"
     }
 }
@@ -65,6 +67,11 @@ fun <T : MathElement<out PowerOperations<T>>> sqr(arg: T): T = arg pow 2.0
 interface ExponentialOperations<T>: Algebra<T> {
     fun exp(arg: T): T
     fun ln(arg: T): T
+
+    companion object {
+        const val EXP_OPERATION = "exp"
+        const val LN_OPERATION = "ln"
+    }
 }
 
 fun <T : MathElement<out ExponentialOperations<T>>> exp(arg: T): T = arg.context.exp(arg)

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

@@ -1,13 +1,8 @@
 package scientifik.kmath.structures
 
-import scientifik.kmath.operations.*
+import scientifik.kmath.operations.ExtendedField
 
-interface ExtendedNDField<T : Any, F, N : NDStructure<T>> :
-    NDField<T, F, N>,
-    InverseTrigonometricOperations<N>,
-    PowerOperations<N>,
-    ExponentialOperations<N>
-        where F : ExtendedFieldOperations<T>, F : Field<T>
+interface ExtendedNDField<T : Any, F : ExtendedField<T>, N : NDStructure<T>> : NDField<T, F, N>, ExtendedField<N>
 
 
 ///**

kmath-core/src/jvmMain/kotlin/scientifik/kmath/operations/bigNumbers.kt

@@ -1,10 +1,12 @@
 package scientifik.kmath.operations
 
-import scientifik.kmath.structures.*
 import java.math.BigDecimal
 import java.math.BigInteger
 import java.math.MathContext
 
+/**
+ * A field wrapper for Java [BigInteger]
+ */
 object JBigIntegerField : Field<BigInteger> {
     override val zero: BigInteger = BigInteger.ZERO
     override val one: BigInteger = BigInteger.ONE
@@ -18,6 +20,9 @@ object JBigIntegerField : Field<BigInteger> {
     override fun divide(a: BigInteger, b: BigInteger): BigInteger = a.div(b)
 }
 
+/**
+ * A Field wrapper for Java [BigDecimal]
+ */
 class JBigDecimalField(val mathContext: MathContext = MathContext.DECIMAL64) : Field<BigDecimal> {
     override val zero: BigDecimal = BigDecimal.ZERO
     override val one: BigDecimal = BigDecimal.ONE

settings.gradle.kts

@@ -44,5 +44,6 @@ include(
     ":kmath-dimensions",
     ":kmath-for-real",
     ":kmath-geometry",
+    ":kmath-ast",
     ":examples"
 )