DefaultDifferentiation.cs

using System.Threading.Tasks;
using Waher.Script.Abstraction.Elements;
using Waher.Script.Exceptions;
using Waher.Script.Model;
using Waher.Script.Objects;
 
namespace Waher.Script.Operators.Calculus
{
    public class DefaultDifferentiation : NullCheckUnaryOperator
    {
        private readonly int nrDifferentiations;
 
        public DefaultDifferentiation(ScriptNode Operand, int NrDifferentiations, bool NullCheck, int Start, int Length, Expression Expression)
            : base(Operand, NullCheck, Start, Length, Expression)
        {
            this.nrDifferentiations = NrDifferentiations;
        }
 
        public int NrDifferentiations => this.nrDifferentiations;
 
        public override IElement Evaluate(Variables Variables)
        {
            ScriptNode Node = this.op;
            IElement Result = null;
            int i;
 
            for (i = 0; i < this.nrDifferentiations; i++)
            {
                if (Node is null)
                    return DoubleNumber.ZeroElement;
 
                Result = this.DifferentiateOnce(Node, Variables);
                Node = Result as ScriptNode;
            }
            
            return Result;
        }
 
        public override Task<IElement> EvaluateAsync(Variables Variables)
        {
            return Task.FromResult<IElement>(this.Evaluate(Variables));
        }
 
        public override IElement Evaluate(IElement Operand, Variables Variables)
        {
            return ObjectValue.Null;    // Node not evaluated directly.
        }
 
        private IElement DifferentiateOnce(ScriptNode Node, Variables Variables)
        {
            if (Node is VariableReference VariableReference)
            {
                if (Variables.TryGetVariable(VariableReference.VariableName, out Variable v))
                {
                    if (v.ValueObject is IDifferentiable Differentiable)
                        return this.DifferentiateOnce(Differentiable, Variables);
                    else if (v.ValueObject is ILambdaExpression)
                        throw new ScriptRuntimeException(VariableReference.VariableName + " not differentiable.", this);
                    else
                        return DoubleNumber.ZeroElement;
                }
                else
                {
                    IElement f = Expression.GetFunctionLambdaDefinition(VariableReference.VariableName, this.Start, this.Length, this.Expression);
                    if (!(f is null))
                    {
                        if (f is IDifferentiable Differentiable)
                            return this.DifferentiateOnce(Differentiable, Variables);
                        else
                            throw new ScriptRuntimeException(VariableReference.VariableName + " not differentiable.", this);
                    }
                    else if (this.nullCheck)
                        return ObjectValue.Null;
                    else
                        throw new ScriptRuntimeException(VariableReference.VariableName + " not defined.", this);
                }
            }
            else if (Node is IDifferentiable Differentiable)
                return this.DifferentiateOnce(Differentiable, Variables);
            else
                throw new ScriptRuntimeException("Not differentiable.", this);
        }
 
        private IElement DifferentiateOnce(IDifferentiable Differentiable, Variables Variables)
        {
            string VariableName = Differentiable.DefaultVariableName;
            if (string.IsNullOrEmpty(VariableName))
                throw new ScriptRuntimeException("No default variable available.", this);
 
            ScriptNode Result = Differentiable.Differentiate(VariableName, Variables);
            if (Result is IElement Element)
                return Element;
 
            return new LambdaDefinition(new string[] { VariableName }, new ArgumentType[] { ArgumentType.Normal },
                Result, this.Start, this.Length, this.Expression);
        }
 
    }
}