Сгенерированные методы для полиномиальной оценки

Question

Сгенерированные методы для полиномиальной оценки

Никогда. Когда-либо. Если у Вас есть переменное затенение, Ваши соглашения о присвоении имен находятся на трещине. Я не имею в виду, действительно, именования различения для членских переменных? Фейспалм

5

c# linq math expression-trees algebra

задан Sam Harwell 27 October 2009 в 14:54

1 ответ

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c# linq math expression-trees algebra

`Symbolic`

public static class Symbolic
{
    public static Expression Expand(Expression expression)
    {
        return new ExpandVisitor().Visit(expression);
    }

    public static Expression Simplify(Expression expression)
    {
        return new SimplifyVisitor().Visit(expression);
    }

    public static Expression PartialDerivative(Expression expression, ParameterExpression parameter)
    {
        bool totalDerivative = false;
        return new DerivativeVisitor(parameter, totalDerivative).Visit(expression);
    }

    public static string ToString(Expression expression)
    {
        ConstantExpression result = (ConstantExpression)new ListPrintVisitor().Visit(expression);
        return result.Value.ToString();
    }
}

Расширение выражений с помощью `ExpandVisitor`

internal class ExpandVisitor : ExpressionVisitor
{
    protected override Expression VisitBinary(BinaryExpression node)
    {
        var left = Visit(node.Left);
        var right = Visit(node.Right);

        if (node.NodeType == ExpressionType.Multiply)
        {
            Expression[] leftNodes = GetAddedNodes(left).ToArray();
            Expression[] rightNodes = GetAddedNodes(right).ToArray();
            var result =
                leftNodes
                .SelectMany(x => rightNodes.Select(y => Expression.Multiply(x, y)))
                .Aggregate((sum, term) => Expression.Add(sum, term));

            return result;
        }

        if (node.Left == left && node.Right == right)
            return node;

        return Expression.MakeBinary(node.NodeType, left, right, node.IsLiftedToNull, node.Method, node.Conversion);
    }

    /// <summary>
    /// Treats the <paramref name="node"/> as the sum (or difference) of one or more child nodes and returns the
    /// the individual addends in the sum.
    /// </summary>
    private static IEnumerable<Expression> GetAddedNodes(Expression node)
    {
        BinaryExpression binary = node as BinaryExpression;
        if (binary != null)
        {
            switch (binary.NodeType)
            {
            case ExpressionType.Add:
                foreach (var n in GetAddedNodes(binary.Left))
                    yield return n;

                foreach (var n in GetAddedNodes(binary.Right))
                    yield return n;

                yield break;

            case ExpressionType.Subtract:
                foreach (var n in GetAddedNodes(binary.Left))
                    yield return n;

                foreach (var n in GetAddedNodes(binary.Right))
                    yield return Expression.Negate(n);

                yield break;

            default:
                break;
            }
        }

        yield return node;
    }
}

Получение производной с помощью `DerivativeVisitor`

internal class DerivativeVisitor : ExpressionVisitor
{
    private ParameterExpression _parameter;
    private bool _totalDerivative;

    public DerivativeVisitor(ParameterExpression parameter, bool totalDerivative)
    {
        if (_totalDerivative)
            throw new NotImplementedException();

        _parameter = parameter;
        _totalDerivative = totalDerivative;
    }

    protected override Expression VisitBinary(BinaryExpression node)
    {
        switch (node.NodeType)
        {
        case ExpressionType.Add:
        case ExpressionType.Subtract:
            return Expression.MakeBinary(node.NodeType, Visit(node.Left), Visit(node.Right));

        case ExpressionType.Multiply:
            return Expression.Add(Expression.Multiply(node.Left, Visit(node.Right)), Expression.Multiply(Visit(node.Left), node.Right));

        case ExpressionType.Divide:
            return Expression.Divide(Expression.Subtract(Expression.Multiply(Visit(node.Left), node.Right), Expression.Multiply(node.Left, Visit(node.Right))), Expression.Power(node.Right, Expression.Constant(2)));

        case ExpressionType.Power:
            if (node.Right is ConstantExpression)
            {
                return Expression.Multiply(node.Right, Expression.Multiply(Visit(node.Left), Expression.Subtract(node.Right, Expression.Constant(1))));
            }
            else if (node.Left is ConstantExpression)
            {
                return Expression.Multiply(node, MathExpressions.Log(node.Left));
            }
            else
            {
                return Expression.Multiply(node, Expression.Add(
                    Expression.Multiply(Visit(node.Left), Expression.Divide(node.Right, node.Left)),
                    Expression.Multiply(Visit(node.Right), MathExpressions.Log(node.Left))
                    ));
            }

        default:
            throw new NotImplementedException();
        }
    }

    protected override Expression VisitConstant(ConstantExpression node)
    {
        return MathExpressions.Zero;
    }

    protected override Expression VisitInvocation(InvocationExpression node)
    {
        MemberExpression memberExpression = node.Expression as MemberExpression;
        if (memberExpression != null)
        {
            var member = memberExpression.Member;
            if (member.DeclaringType != typeof(Math))
                throw new NotImplementedException();

            switch (member.Name)
            {
            case "Log":
                return Expression.Divide(Visit(node.Expression), node.Expression);

            case "Log10":
                return Expression.Divide(Visit(node.Expression), Expression.Multiply(Expression.Constant(Math.Log(10)), node.Expression));

            case "Exp":
            case "Sin":
            case "Cos":
            default:
                throw new NotImplementedException();
            }
        }

        throw new NotImplementedException();
    }

    protected override Expression VisitParameter(ParameterExpression node)
    {
        if (node == _parameter)
            return MathExpressions.One;

        return MathExpressions.Zero;
    }
}

Упрощение выражений с помощью `SimplifyVisitor`

internal class SimplifyVisitor : ExpressionVisitor
{
    protected override Expression VisitBinary(BinaryExpression node)
    {
        var left = Visit(node.Left);
        var right = Visit(node.Right);

        ConstantExpression leftConstant = left as ConstantExpression;
        ConstantExpression rightConstant = right as ConstantExpression;
        if (leftConstant != null && rightConstant != null
            && (leftConstant.Value is double) && (rightConstant.Value is double))
        {
            double leftValue = (double)leftConstant.Value;
            double rightValue = (double)rightConstant.Value;

            switch (node.NodeType)
            {
            case ExpressionType.Add:
                return Expression.Constant(leftValue + rightValue);
            case ExpressionType.Subtract:
                return Expression.Constant(leftValue - rightValue);
            case ExpressionType.Multiply:
                return Expression.Constant(leftValue * rightValue);
            case ExpressionType.Divide:
                return Expression.Constant(leftValue / rightValue);
            default:
                throw new NotImplementedException();
            }
        }

        switch (node.NodeType)
        {
        case ExpressionType.Add:
            if (IsZero(left))
                return right;
            if (IsZero(right))
                return left;
            break;

        case ExpressionType.Subtract:
            if (IsZero(left))
                return Expression.Negate(right);
            if (IsZero(right))
                return left;
            break;

        case ExpressionType.Multiply:
            if (IsZero(left) || IsZero(right))
                return MathExpressions.Zero;
            if (IsOne(left))
                return right;
            if (IsOne(right))
                return left;
            break;

        case ExpressionType.Divide:
            if (IsZero(right))
                throw new DivideByZeroException();
            if (IsZero(left))
                return MathExpressions.Zero;
            if (IsOne(right))
                return left;
            break;

        default:
            throw new NotImplementedException();
        }

        return Expression.MakeBinary(node.NodeType, left, right);
    }

    protected override Expression VisitUnary(UnaryExpression node)
    {
        var operand = Visit(node.Operand);

        ConstantExpression operandConstant = operand as ConstantExpression;
        if (operandConstant != null && (operandConstant.Value is double))
        {
            double operandValue = (double)operandConstant.Value;

            switch (node.NodeType)
            {
            case ExpressionType.Negate:
                if (operandValue == 0.0)
                    return MathExpressions.Zero;

                return Expression.Constant(-operandValue);

            default:
                throw new NotImplementedException();
            }
        }

        switch (node.NodeType)
        {
        case ExpressionType.Negate:
            if (operand.NodeType == ExpressionType.Negate)
            {
                return ((UnaryExpression)operand).Operand;
            }

            break;

        default:
            throw new NotImplementedException();
        }

        return Expression.MakeUnary(node.NodeType, operand, node.Type);
    }

    private static bool IsZero(Expression expression)
    {
        ConstantExpression constant = expression as ConstantExpression;
        if (constant != null)
        {
            if (constant.Value.Equals(0.0))
                return true;
        }

        return false;
    }

    private static bool IsOne(Expression expression)
    {
        ConstantExpression constant = expression as ConstantExpression;
        if (constant != null)
        {
            if (constant.Value.Equals(1.0))
                return true;
        }

        return false;
    }
}

Форматирование выражений для отображения с помощью `ListPrintVisitor`

internal class ListPrintVisitor : ExpressionVisitor
{
    protected override Expression VisitBinary(BinaryExpression node)
    {
        string op = null;

        switch (node.NodeType)
        {
        case ExpressionType.Add:
            op = "+";
            break;
        case ExpressionType.Subtract:
            op = "-";
            break;
        case ExpressionType.Multiply:
            op = "*";
            break;
        case ExpressionType.Divide:
            op = "/";
            break;
        default:
            throw new NotImplementedException();
        }

        var left = Visit(node.Left);
        var right = Visit(node.Right);
        string result = string.Format("({0} {1} {2})", op, ((ConstantExpression)left).Value, ((ConstantExpression)right).Value);
        return Expression.Constant(result);
    }

    protected override Expression VisitConstant(ConstantExpression node)
    {
        if (node.Value is string)
            return node;

        return Expression.Constant(node.Value.ToString());
    }

    protected override Expression VisitParameter(ParameterExpression node)
    {
        return Expression.Constant(node.Name);
    }
}

Проверка результатов

[TestMethod]
public void BasicSymbolicTest()
{
    ParameterExpression x = Expression.Parameter(typeof(double), "x");
    Expression linear = Expression.Add(Expression.Constant(3.0), x);
    Assert.AreEqual("(+ 3 x)", Symbolic.ToString(linear));

    Expression quadratic = Expression.Multiply(linear, Expression.Add(Expression.Constant(2.0), x));
    Assert.AreEqual("(* (+ 3 x) (+ 2 x))", Symbolic.ToString(quadratic));

    Expression expanded = Symbolic.Expand(quadratic);
    Assert.AreEqual("(+ (+ (+ (* 3 2) (* 3 x)) (* x 2)) (* x x))", Symbolic.ToString(expanded));
    Assert.AreEqual("(+ (+ (+ 6 (* 3 x)) (* x 2)) (* x x))", Symbolic.ToString(Symbolic.Simplify(expanded)));

    Expression derivative = Symbolic.PartialDerivative(expanded, x);
    Assert.AreEqual("(+ (+ (+ (+ (* 3 0) (* 0 2)) (+ (* 3 1) (* 0 x))) (+ (* x 0) (* 1 2))) (+ (* x 1) (* 1 x)))", Symbolic.ToString(derivative));

    Expression simplified = Symbolic.Simplify(derivative);
    Assert.AreEqual("(+ 5 (+ x x))", Symbolic.ToString(simplified));
}

Сгенерированные методы для полиномиальной оценки

1 ответ

Symbolic

Расширение выражений с помощью ExpandVisitor

Получение производной с помощью DerivativeVisitor

Упрощение выражений с помощью SimplifyVisitor

Форматирование выражений для отображения с помощью ListPrintVisitor

Проверка результатов

Похожие вопросы:

`Symbolic`

Расширение выражений с помощью `ExpandVisitor`

Получение производной с помощью `DerivativeVisitor`

Упрощение выражений с помощью `SimplifyVisitor`

Форматирование выражений для отображения с помощью `ListPrintVisitor`