Expressions!

README.md

@@ -11,16 +11,16 @@ and `scipy` it is modular and has a lightweight core.
 * **Array-like structures** Full support of numpy-like ndarray including mixed arithmetic operations and function operations
 on arrays and numbers just like it works in python (with benefit of static type checking).
 
+* **Expressions** Expressions are one of the ultimate goals of kmath. It is planned to be able to write some mathematical
+expression once an then apply it to different types of objects by providing different context. Exception could be used
+for a wide variety of purposes from high performance calculations to code generation.
+
 ## Planned features
 
 * **Common mathematics** It is planned to gradually wrap most parts of [Apache commons-math](http://commons.apache.org/proper/commons-math/) 
 library in kotlin code and maybe rewrite some parts to better suite kotlin programming paradigm. There is no fixed priority list for that. Feel free
 to submit a future request if you want something to be done first.
 
-* **Expressions** Expressions are one of the ultimate goals of kmath. It is planned to be able to write some mathematical
-expression once an then apply it to different types of objects by providing different context. Exception could be used
-for a wide variety of purposes from high performance calculations to code generation.
-
 * **Messaging** A mathematical notation to support multilanguage and multinod communication for mathematical tasks.
 
 ## Multi-platform support

kmath-common/src/main/kotlin/scientifik/kmath/expressions/Expression.kt

@@ -0,0 +1,62 @@
+package scientifik.kmath.expressions
+
+import scientifik.kmath.operations.Field
+import scientifik.kmath.operations.Space
+
+
+interface Expression<T> {
+    operator fun invoke(arguments: Map<String, T>): T
+}
+
+operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T = invoke(mapOf(*pairs))
+
+interface ExpressionContext<T> {
+    fun variable(name: String, default: T? = null): Expression<T>
+
+    fun const(value: T): Expression<T>
+}
+
+internal class VariableExpression<T>(val name: String, val default: T? = null) : Expression<T> {
+    override fun invoke(arguments: Map<String, T>): T {
+        return arguments[name] ?: default ?: error("The parameter not found: $name")
+    }
+}
+
+internal class ConstantExpression<T>(val value: T) : Expression<T> {
+    override fun invoke(arguments: Map<String, T>): T = value
+}
+
+internal class SumExpression<T>(val context: Space<T>, val first: Expression<T>, val second: Expression<T>) : Expression<T> {
+    override fun invoke(arguments: Map<String, T>): T = context.add(first.invoke(arguments), second.invoke(arguments))
+}
+
+internal class ProductExpression<T>(val context: Field<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))
+}
+
+internal class ConstProductExpession<T>(val context: Field<T>, val expr: Expression<T>, val const: Double) : Expression<T> {
+    override fun invoke(arguments: Map<String, T>): T = context.multiply(expr.invoke(arguments), const)
+}
+
+internal class DivExpession<T>(val context: Field<T>, val expr: Expression<T>, val second: Expression<T>) : Expression<T> {
+    override fun invoke(arguments: Map<String, T>): T = context.divide(expr.invoke(arguments), second.invoke(arguments))
+}
+
+class FieldExpressionContext<T>(val field: Field<T>) : Field<Expression<T>>, ExpressionContext<T> {
+
+    override val zero: Expression<T> = ConstantExpression(field.zero)
+
+    override val one: Expression<T> = ConstantExpression(field.one)
+
+    override fun const(value: T): Expression<T> = ConstantExpression(value)
+
+    override fun variable(name: String, default: T?): Expression<T> = VariableExpression(name, default)
+
+    override fun add(a: Expression<T>, b: Expression<T>): Expression<T> = SumExpression(field, a, b)
+
+    override fun multiply(a: Expression<T>, k: Double): Expression<T> = ConstProductExpession(field, a, k)
+
+    override fun multiply(a: Expression<T>, b: Expression<T>): Expression<T> = ProductExpression(field, a, b)
+
+    override fun divide(a: Expression<T>, b: Expression<T>): Expression<T> = DivExpession(field, a, b)
+}

kmath-common/src/main/kotlin/scientifik/kmath/operations/Fields.kt

@@ -29,7 +29,7 @@ object RealField : Field<Real>, TrigonometricOperations<Real>, PowerOperations<R
  *
  * TODO could be replaced by inline class in kotlin 1.3 if it would allow to avoid boxing
  */
-class Real(val value: Double) : Number(), FieldElement<Real, RealField> {
+data class Real(val value: Double) : Number(), FieldElement<Real, RealField> {
     /*
      * The class uses composition instead of inheritance since Double is final
      */
@@ -94,10 +94,19 @@ data class Complex(val re: Double, val im: Double) : FieldElement<Complex, Compl
 /**
  * A field for double without boxing. Does not produce appropriate field element
  */
-object DoubleField : Field<Double> {
+object DoubleField : Field<Double>, TrigonometricOperations<Double>, PowerOperations<Double>, ExponentialOperations<Double> {
     override val zero: Double = 0.0
     override fun add(a: Double, b: Double): Double = a + b
     override fun multiply(a: Double, @Suppress("PARAMETER_NAME_CHANGED_ON_OVERRIDE") b: Double): Double = a * b
     override val one: Double = 1.0
     override fun divide(a: Double, b: Double): Double = a / b
+
+    override fun sin(arg: Double): Double  = kotlin.math.sin(arg)
+    override fun cos(arg: Double): Double = kotlin.math.cos(arg)
+
+    override fun power(arg: Double, pow: Double): Double  = arg.pow(pow)
+
+    override fun exp(arg: Double): Double  =kotlin.math.exp(arg)
+
+    override fun ln(arg: Double): Double  = kotlin.math.ln(arg)
 }

kmath-common/src/test/kotlin/scientifik/kmath/expressions/FieldExpressionContextTest.kt

@@ -0,0 +1,18 @@
+package scientifik.kmath.expressions
+
+import scientifik.kmath.operations.DoubleField
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+class FieldExpressionContextTest {
+    @Test
+    fun testExpression() {
+        val context = FieldExpressionContext(DoubleField)
+        val expression = with(context) {
+            val x = variable("x", 2.0)
+            x * x + 2 * x + 1.0 * one
+        }
+        assertEquals(expression("x" to 1.0), 4.0)
+        assertEquals(expression(), 9.0)
+    }
+}