I'm trying to come up with an elegant way to handle some generated polynomials. Here's the situation we'll focus on (exclusively) for this question:
order is a parameter in generating an nth order polynomial, where n:=order + 1.
i is an integer parameter in the range 0..n
The polynomial has zeros at x_j, where j = 1..n and j ≠ i (it should be clear at this point that StackOverflow needs a new feature or it's present and I don't know it)
The polynomial evaluates to 1 at x_i.
Since this particular code example generates x_1 .. x_n, I'll explain how they're found in the code. The points are evenly spaced x_j = j * elementSize / order apart, where n = order + 1.
I generate a Func<double, double> to evaluate this polynomial¹.
private static Func<double, double> GeneratePsi(double elementSize, int order, int i)
{
if (order < 1)
throw new ArgumentOutOfRangeException("order", "order must be greater than 0.");
if (i < 0)
throw new ArgumentOutOfRangeException("i", "i cannot be less than zero.");
if (i > order)
throw new ArgumentException("i", "i cannot be greater than order");
ParameterExpression xp = Expression.Parameter(typeof(double), "x");
// generate the terms of the factored polynomial in form (x_j - x)
List<Expression> factors = new List<Expression>();
for (int j = 0; j <= order; j++)
{
if (j == i)
continue;
double p = j * elementSize / order;
factors.Add(Expression.Subtract(Expression.Constant(p), xp));
}
// evaluate the result at the point x_i to get scaleInv=1.0/scale.
double xi = i * elementSize / order;
double scaleInv = Enumerable.Range(0, order + 1).Aggregate(0.0, (product, j) => product * (j == i ? 1.0 : (j * elementSize / order - xi)));
/* generate an expression to evaluate
* (x_0 - x) * (x_1 - x) .. (x_n - x) / (x_i - x)
* obviously the term (x_i - x) is cancelled in this result, but included here to make the result clear
*/
Expression expr = factors.Skip(1).Aggregate(factors[0], Expression.Multiply);
// multiplying by scale forces the condition f(x_i)=1
expr = Expression.Multiply(Expression.Constant(1.0 / scaleInv), expr);
Expression<Func<double, double>> lambdaMethod = Expression.Lambda<Func<double, double>>(expr, xp);
return lambdaMethod.Compile();
}
The problem: I also need to evaluate ψ′=dψ/dx. To do this, I can rewrite ψ=scale×(x_0 - x)(x_1 - x)×..×(x_n - x)/(x_i - x) in the form ψ=α_n×x^n + α_n×x^(n-1) + .. + α_1×x + α_0. This gives ψ′=n×α_n×x^(n-1) + (n-1)×α_n×x^(n-2) + .. + 1×α_1.
For computational reasons, we can rewrite the final answer without calls to Math.Pow by writing ψ′=x×(x×(x×(..) - β_2) - β_1) - β_0.
To do all this "trickery" (all very basic algebra), I need a clean way to:
Expand a factored Expression containing ConstantExpression and ParameterExpression leaves and basic mathematical operations (end up either BinaryExpression with the NodeType set to the operation) - the result here can include InvocationExpression elements to the MethodInfo for Math.Pow which we'll handle in a special manner throughout.
Then I take the derivative with respect to some specified ParameterExpression. Terms in the result where the right hand side parameter to an invocation of Math.Pow was the constant 2 are replaced by the ConstantExpression(2) multiplied by what was the left hand side (the invocation of Math.Pow(x,1) is removed). Terms in the result that become zero because they were constant with respect to x are removed.
Then factor out the instances of some specific ParameterExpression where they occur as the left hand side parameter to an invocation of Math.Pow. When the right hand side of the invocation becomes a ConstantExpression with the value 1, we replace the invocation with just the ParameterExpression itself.
¹ In the future, I'd like the method to take a ParameterExpression and return an Expression that evaluates based on that parameter. That way I can aggregate generated functions. I'm not there yet.
² In the future, I hope to release a general library for working with LINQ Expressions as symbolic math.
I wrote the basics of several symbolic math features using the ExpressionVisitor type in .NET 4. It's not perfect, but it looks like the foundation of a viable solution.
Symbolic is a public static class exposing methods like Expand, Simplify, and PartialDerivative
ExpandVisitor is an internal helper type that expands expressions
SimplifyVisitor is an internal helper type that simplifies expressions
DerivativeVisitor is an internal helper type that takes the derivative of an expression
ListPrintVisitor is an internal helper type that converts an Expression to a prefix notation with a Lisp syntax
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();
}
}
Expanding expressions with 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;
}
}
Taking a derivative with 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;
}
}
Simplifying expressions with 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;
}
}
Formatting expressions for display with 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);
}
}
Testing the results
[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));
}
Related
I have been trying to construct an expression tree that will evaluate math expressions in RPN.
I have got an exception when trying to call my MakeBinary expression to calculate numbers in the tree.
The exception is the following "System.InvalidOperationException: 'The binary operator Add is not defined for the types 'System.Char' and 'System.Char'.'"
Here is my code:
public static bool isOp(char checkIt)
{
bool verify;
if(checkIt== '+'|| checkIt== '-'||checkIt== '*' || checkIt== '/'||checkIt== '^')
{
return verify= true;
}
else
{
return verify= false;
}
return verify;
}
public static BinaryExpression myMakeBiniray(char ops,Expression leftOp, Expression rightOp)
{
switch (ops)
{
case '+':
Expression left = leftOp;
Expression right = rightOp;
return Expression.MakeBinary(ExpressionType.Add, left, right);
// return Expression.MakeBinary(ExpressionType.Add, Expression.Constant(2), Expression.Constant(4));
case '-':
return Expression.MakeBinary(ExpressionType.Subtract, Expression.Constant(leftOp), Expression.Constant(rightOp));
case '*':
return Expression.MakeBinary(ExpressionType.Multiply, Expression.Constant(leftOp), Expression.Constant(rightOp));
case '/':
return Expression.MakeBinary(ExpressionType.Divide, Expression.Constant(leftOp), Expression.Constant(rightOp));
case '^':
return Expression.MakeBinary(ExpressionType.Power, Expression.Constant(leftOp), Expression.Constant(rightOp));
default:
return null;
}
}
static void Main(string[] args)
{
Console.WriteLine("Enter mathematical expression : ");
string input = "12+";
Stack<Expression> ex = new Stack<Expression>();
for (int i = 0; i < input.Length; i++)
{
var d = input[i];
if (!isOp(d))
{
Expression constacntNumberExpression = Expression.Constant(d);
ex.Push(constacntNumberExpression);
}
else
{
Expression popLeft = ex.Pop();
Expression popRight = ex.Pop();
BinaryExpression node= myMakeBiniray(d, popLeft, popRight);
ex.Push(node);
}
}
I am struggling to understand the source of the problem,
any help would be greatly appreciated!
You need to convert the input from char to int when you're adding number expressions into the stack.
Change this part of Main:
var d = input[i];
if (!isOp(d))
{
Expression constacntNumberExpression = Expression.Constant(d);
ex.Push(constacntNumberExpression);
}
To:
var d = input[i];
if (!isOp(d) && Char.IsNumber(d))
{
var constantNumber = Char.GetNumericValue(d);
Expression constacntNumberExpression = Expression.Constant(constantNumber);
ex.Push(constacntNumberExpression);
}
I have been trying to create a expression tree filter for Linq that take 2 dates and a string of possible values { "lessthan", "equals", "morethan" }. I wish to format the call to be something like Query.Where(CompareDates(x => x.left, right, "less than"));
I have the code:
public static IQueryable<TSource> CompareDates<TSource>(
this IQueryable<TSource> source,
Expression<Func<TSource, DateTime?>> left,
DateTime? right,
string equality)
{
if (right == null || string.IsNullOrWhiteSpace(equality))
return source;
var p = left.Parameters.Single();
Expression member = p;
Expression leftExpression = Expression.Property(member, "left");
Expression rightParameter = Expression.Constant(right, typeof(DateTime));
BinaryExpression BExpression = null;
switch (equality)
{
case "lessthan":
BExpression = Expression.LessThan(leftExpression, rightParameter);
break;
case "equal":
BExpression = Expression.Equal(leftExpression, rightParameter);
break;
case "morethan":
BExpression = Expression.GreaterThan(leftExpression, rightParameter);
break;
default:
throw new Exception(String.Format("Equality {0} not recognised.", equality));
}
return source.Where(Expression.Lambda<Func<TSource, bool>>(BExpression, p));
}
Unfortunately it is producing an error of "System.ArgumentException: Instance property 'left' is not defined for type 'Model' at System.Linq.Expressions.Expression.Property(Expression expression, String propertyName) at SARRestAPI.Extensions.Expressions.CompareDates[TSource](IQueryable1 source, Expression1 src, DateTime supplied, String equality)"
Anyone have an ideas why this is happening?
Here we go; what you want to do is use the .Body of the incoming selector, not look for .left. Meaning, given an input selector of x => x.Foo.Bar.Blap, a constant, and a comparison, you want to construct something like x => x.Foo.Bar.Blap < someValue, by reusing both the x (the parameter, which you're already doing) and the body (x.Foo.Bar.Blap).
In code (note this works for any TValue, not just DateTime):
public enum Comparison
{
Equal,
NotEqual,
LessThan,
LessThanOrEqual,
GreaterThan,
GreaterThanOrEqual
}
public static IQueryable<TSource> Compare<TSource, TValue>(
this IQueryable<TSource> source,
Expression<Func<TSource, TValue>> selector,
TValue value,
Comparison comparison)
{
Expression left = selector.Body;
Expression right = Expression.Constant(value, typeof(TValue));
BinaryExpression body;
switch (comparison)
{
case Comparison.LessThan:
body = Expression.LessThan(left, right);
break;
case Comparison.LessThanOrEqual:
body = Expression.LessThanOrEqual(left, right);
break;
case Comparison.Equal:
body = Expression.Equal(left, right);
break;
case Comparison.NotEqual:
body = Expression.NotEqual(left, right);
break;
case Comparison.GreaterThan:
body = Expression.GreaterThan(left, right);
break;
case Comparison.GreaterThanOrEqual:
body = Expression.GreaterThanOrEqual(left, right);
break;
default:
throw new ArgumentOutOfRangeException(nameof(comparison));
}
return source.Where(Expression.Lambda<Func<TSource, bool>>(body, selector.Parameters));
}
Example usage (here using LINQ-to-Objects, but it should work for other LINQ backends, too):
var arr = new[] { new { X = 11 }, new { X = 12 }, new { X = 13 }, new { X = 14 } };
var source = arr.AsQueryable();
var filtered = source.Compare(x => x.X, 12, Comparison.GreaterThan);
foreach (var item in filtered)
{
Console.WriteLine(item.X); // 13 and 14
}
Note that with C# vCurrent you can do:
var body = comparison switch
{
Comparison.LessThan => Expression.LessThan(left, right),
Comparison.LessThanOrEqual => Expression.LessThanOrEqual(left, right),
Comparison.Equal => Expression.Equal(left, right),
Comparison.NotEqual => Expression.NotEqual(left, right),
Comparison.GreaterThan => Expression.GreaterThan(left, right),
Comparison.GreaterThanOrEqual => Expression.GreaterThanOrEqual(left, right),
_ => throw new ArgumentOutOfRangeException(nameof(comparison)),
};
return source.Where(Expression.Lambda<Func<TSource, bool>>(body, selector.Parameters));
which you might fine preferable.
So, for those who have not been involved in my earlier question on this topic, I have some C# types to represent Sequences, like in math, and I store a formula for generating the nth-term as
Func NTerm;
Now, I would like to compare one Sequence's nth-term formula to another for mathematical equality. I have determined that practically, this requires a limitation to five simple binary operators: +,-,/,*,%.
With tremendous help from Scott Chamberlain on the OP, I've managed to get here. I'm envisioning some kind of recursive solution, but I'm not quite sure where to proceed. Will keep chugging away. Currently, this handles single binary expressions like x + 5 or 7 * c, well, but doesn't deal with other cases. I think the idea is to start from the end of the List, since I think it parses with last operations at the top of the syntax tree and first ones at the bottom. I haven't yet done extensive testing for this method.
UPDATE
public sealed class LambdaParser : ExpressionVisitor
{
public List<BinaryExpression> Expressions { get; } = new List<BinaryExpression> ();
protected override Expression VisitBinary (BinaryExpression node)
{
Expressions.Add (node);
return base.VisitBinary (node);
}
public bool MathEquals (LambdaParser g)
{
try
{
return MathEquals (Expressions, g.Expressions);
} catch (Exception e)
{
throw new Exception ("MathEquals", e);
}
}
public static bool MathEquals (List<BinaryExpression> f, List<BinaryExpression> g)
{
//handle simple cases
if (ReferenceEquals (f, g))
return true;
if (f == null || g == null)
return false;
if (f.Count == 0 || g.Count == 0)
return false;
try
{
//handle single one element cases
if (f.Count == 1 && g.Count == 1)
{
return MathEquals (f[0], g[0]);
}
} catch (Exception e)
{
throw new Exception ("MathEquals", e);
}
throw new NotImplementedException ("Math Equals");
}
static bool MathEquals (BinaryExpression f, BinaryExpression g)
{
if (ReferenceEquals (f, g))
return true;
if (f == null || g == null)
return false;
if (f.NodeType != g.NodeType)
return false;
try
{
switch (f.NodeType)
{
case ExpressionType.Add:
case ExpressionType.Multiply:
return CompareCommutative (f, g);
case ExpressionType.Subtract:
case ExpressionType.Divide:
case ExpressionType.Modulo:
return CompareNonCommutative (f, g);
default:
throw new NotImplementedException ($"Math Equals {nameof(f)}: {f.NodeType}, {nameof(g)}: {g.NodeType}");
}
} catch (Exception e)
{
throw new Exception ($"MathEquals {nameof(f)}: {f.NodeType}, {nameof(g)}: {g.NodeType}", e);
}
}
static bool IsParam (Expression f)
{
return f.NodeType == ExpressionType.Parameter;
}
static bool IsConstant (Expression f)
{
return f.NodeType == ExpressionType.Constant;
}
static bool CompareCommutative (BinaryExpression f, BinaryExpression g)
{
bool left, right;
try
{
//parse left f to left g and right g
left = CompareParamOrConstant (f.Left, g.Left) || CompareParamOrConstant (f.Left, g.Right);
//parse right f to left g and right g
right = CompareParamOrConstant (f.Right, g.Left) || CompareParamOrConstant (f.Right, g.Right);
return left && right;
} catch (Exception e)
{
throw new Exception ($"CompareCommutative {nameof(f)}: {f.NodeType}, {nameof(g)}: {g.NodeType}", e);
}
}
static bool CompareNonCommutative (BinaryExpression f, BinaryExpression g)
{
bool left, right;
try
{
//compare f left to g left
left = CompareParamOrConstant (f.Left, g.Left);
//compare f right to f right
right = CompareParamOrConstant (f.Right, g.Right);
} catch (Exception e)
{
throw new Exception ($"CompareNonCommutative {nameof(f)}: {f.NodeType}, {nameof(g)}: {g.NodeType}", e);
}
return left && right;
}
static bool CompareParamOrConstant (Expression f, Expression g)
{
var ParamF = IsParam (f);
var ConstantF = IsConstant (f);
if (!(ParamF || ConstantF))
{
throw new ArgumentException ($"{nameof(f)} is neither a param or a constant", $"{nameof(f)}");
}
var ParamG = IsParam (g);
var ConstantG = IsConstant (g);
if (!(ParamG || ConstantG))
{
throw new ArgumentException ($"{nameof(g)} is neither a param or a constant", $"{nameof(g)}");
}
if (ParamF)
{
return ParamG;
}
if (ConstantF)
{
return ConstantG && (f as ConstantExpression).Value.Equals ((g as ConstantExpression).Value);
}
}
}
END_UPDATE
I updated the above code to reflect the changes made (mostly refactoring, but also a slightly different approach) after comments reminded me that I'd ignored the non-commutability of some operators.
How do I extend it for expressions with multiple operators of the five defined above? Instead of just 5 * x, something like 2 * x % 3 - x / 5.
I have some fun with Expressions and a question appears: it throws an exception that I didn't suppose.
I have an input - simple math formula, for example 2*x+3, and I want to create an expression tree for it. So I write this code
using System;
using System.Linq.Expressions;
namespace ConsoleApplication50
{
class Program
{
static void Main()
{
string s = "3*x^2+2/5*x+4";
Expression<Func<double, double>> expr = MathExpressionGenerator.GetExpression(s);
Console.WriteLine(expr);
var del = expr.Compile();
Console.WriteLine(del(10));
}
}
static class MathExpressionGenerator
{
public const string SupportedOps = "+-*/^";
private static readonly ParameterExpression Parameter = Expression.Parameter(typeof(double), "x");
public static Expression<Func<double, double>> GetExpression(string s)
{
ParameterExpression parameterExpression = Expression.Parameter(typeof(double), "x");
Expression result = GetExpressionInternal(s);
return Expression.Lambda<Func<double, double>>(result, parameterExpression);
}
private static Expression GetExpressionInternal(string s)
{
double constant;
if (s == "x")
return Parameter;
if (double.TryParse(s, out constant))
return Expression.Constant(constant, typeof(double));
foreach (char op in SupportedOps)
{
var split = s.Split(new[] { op }, StringSplitOptions.RemoveEmptyEntries);
if (split.Length > 1)
{
var expression = GetExpressionInternal(split[0]);
for (int i = 1; i < split.Length; i++)
{
expression = RunOp(expression, GetExpressionInternal(split[i]), op);
}
return expression;
}
}
throw new NotImplementedException("never throws");
}
private static Expression RunOp(Expression a, Expression b, char op)
{
switch (op)
{
case '+':
return Expression.Add(a, b);
case '-':
return Expression.Subtract(a, b);
case '/':
return Expression.Divide(a, b);
case '*':
return Expression.Multiply(a, b);
case '^':
return Expression.Power(a, b);
}
throw new NotSupportedException();
}
}
}
but I get an error:
Unhandled Exception: System.InvalidOperationException: variable 'x' of
type 'Sys tem.Double' referenced from scope '', but it is not defined
at
System.Linq.Expressions.Compiler.VariableBinder.Reference(ParameterExpress
ion node, VariableStorageKind storage) at
System.Linq.Expressions.Compiler.VariableBinder.VisitParameter(ParameterEx
pression node) at
System.Linq.Expressions.ParameterExpression.Accept(ExpressionVisitor
visit or) at ... and so on
Please, advice, how can it be fixed? Here I have a single global parameter and referencing it so I have no idea, why it says this stuff.
Problem with your code is that you have two instances of x parameter. One of them is private static field that is used across expression generation, and second one is that you create and use in Lambda creation.
If you have ParameterExpression, then you should use the same instance in expression and pass the same instance into Lambda generation, otherwise it will fail like in your example.
it will work fine if you remove parameterExpression and will use private Parameter field like this:
public static Expression<Func<double, double>> GetExpression(string s)
{
Expression result = GetExpressionInternal(s);
return Expression.Lambda<Func<double, double>>(result, Parameter);
}
Working example in .NetFiddle - https://dotnetfiddle.net/Onw0Hy
static void Main(string[] args)
{
var str = #"3*x^2+2/5*x+4";
str = Transform(str);
var param = Expression.Parameter(typeof (double), "x");
var expression = System.Linq.Dynamic.DynamicExpression.ParseLambda(new[] {param}, null, str);
var exp10 = expression.Compile().DynamicInvoke(10);
Console.WriteLine(exp10);
}
public const string SupportedOps = "+-*/";//separators without ^
private static string Transform(string expression)
{
//replace x^y with Math.Pow(x,y)
var toBeReplaced = expression.Split(SupportedOps.ToCharArray()).Where(s => s.Contains("^"));
var result = expression;
return toBeReplaced.Aggregate(expression, (current, str) => current.Replace(str, string.Format("Math.Pow({0})", str.Replace('^', ','))));
//OR
//foreach (var str in toBeReplaced)
//{
// result =result.Replace(str, string.Format("Math.Pow({0})", str.Replace('^', ',')));
//}
//return result;
}
Basically I've wrote my own parser and I'm parsing a string into and expression and then compiling and storing to be reused later on.
For (an odd) example the type of string I'm parsing is this:-
if #name == 'max' and #legs > 5 and #ears > 5 then shoot()
The hash parts in the string are telling my parser to look at the properties on the object of type T that I pass in, if not found to look in a Dictionary that also gets passed in as extra.
I parse up the string into parts create an expression and join the expressions using methods from the PredicateBuilder.
I get the left value from where ever it may be and then the right value and turn it into an int32 or a string based on if it's wrapped in single quotes.. for now, then pass both into Expression.Equals/Expression.GreaterThan etc. dependant on the operator.
So far this works fine for equals and strings but take for example #ears which isn't a property on the object but is in the dictionary I end up with "does string equal int32" and it throws an exception.
I need to be able to parse the string from the dictionary into and int32 and then try the equal/greater/less than method.
Hopefully someone could shed some light on this as I haven't found anything yet that will do it and its driving me mad.
Here is the CreateExpression method I'm using to create an expression from the string.
private Expression<Func<T, IDictionary<string, string>, bool>> CreateExpression<T>(string condition)
{
string[] parts = condition.Split(new char[] { ' ' }, 3, StringSplitOptions.RemoveEmptyEntries);
if (parts.Length == 3)
{
var typeCache = _cache[typeof(T).FullName];
var param = Expression.Parameter(typeCache.T, "o");
var param2 = Expression.Parameter(typeof(IDictionary<string, string>), "d");
/* Convert right hand side into correct value type
*/
Expression right = null;
if (parts[2][0] == '\'' && parts[2][parts[2].Length - 1] == '\'')
right = Expression.Constant(parts[2].Trim(new char[] { '\'' }), typeof(string));
else
{
int x = 0;
right = (int.TryParse(parts[2].Trim(), out x))
? Expression.Constant(x)
: Expression.Constant(parts[2].Trim(new char[] { '\'' }), typeof(string));
}
/* Get the left hand side value from object T or IDictionary and then attempt to convert it
* into the right hand side value type
*/
Expression left = null;
var key = (parts[0][0] == '#') ? parts[0].TrimStart('#') : parts[0];
if (_cache[typeCache.T.FullName].Properties.Find(key, true) == null)
{
var m = typeof(ExpressionExtensions).GetMethod("GetValue");
left = Expression.Call(null, m, new Expression[] { param2, Expression.Constant(key) });
}
else
left = Expression.PropertyOrField(param, key);
/* Find the operator and return the correct expression
*/
if (parts[1] == "==")
{
return Expression.Lambda<Func<T, IDictionary<string, string>, bool>>(
Expression.Equal(left, right), new ParameterExpression[] { param, param2 });
}
else if (parts[1] == ">")
{
return Expression.Lambda<Func<T, IDictionary<string, string>, bool>>(
Expression.GreaterThan(left, right), new ParameterExpression[] { param, param2 });
}
}
return null;
}
And here is the method to parse the whole string into parts and build up the expression.
public Func<T, IDictionary<string, string>, bool> Parse<T>(string rule)
{
var type = typeof(T);
if (!_cache.ContainsKey(type.FullName))
_cache[type.FullName] = new TypeCacheItem()
{
T = type,
Properties = TypeDescriptor.GetProperties(type)
};
Expression<Func<T, IDictionary<string, string>, bool>> exp = null;
var actionIndex = rule.IndexOf("then");
if (rule.IndexOf("if") == 0 && actionIndex > 0)
{
var conditionStatement = rule.Substring(2, actionIndex - 2).Trim();
var actionStatement = rule.Substring(actionIndex + 4).Trim();
var startIndex = 0;
var endIndex = 0;
var conditionalOperator = "";
var lastConditionalOperator = "";
do
{
endIndex = FindConditionalOperator(conditionStatement, out conditionalOperator, startIndex);
var condition = (endIndex == -1) ? conditionStatement.Substring(startIndex) : conditionStatement.Substring(startIndex, endIndex - startIndex);
var x = CreateExpression<T>(condition.Trim());
if (x != null)
{
if (exp != null)
{
switch (lastConditionalOperator)
{
case "or":
exp = exp.Or<T>(x);
break;
case "and":
exp = exp.And<T>(x);
break;
default:
exp = x;
break;
}
}
else
exp = x;
}
lastConditionalOperator = conditionalOperator;
startIndex = endIndex + conditionalOperator.Length;
} while (endIndex > -1);
}
else
throw new ArgumentException("Rule must start with 'if' and contain 'then'.");
return (exp == null) ? null : exp.Compile();
}
My eyes are open to suggestions or advice on this but the idea of parsing that string as is to return true or false has to be,
EDIT:
I've now alter my method that retrieves the value from the dictionary to a generic one as Fahad suggested to this:-
public static T GetValue<T>(this IDictionary<string, string> dictionary, string key)
{
string x = string.Empty;
dictionary.TryGetValue(key, out x);
if (typeof(T) == typeof(int))
{
int i = 0;
if (int.TryParse(x, out i))
return (T)(i as object);
}
return default(T);
//throw new ArgumentException("Failed to convert dictionary value to type.");
}
And this works fine but I would rather return null than a default value for the type i've tried using Nullable ... where T : struct and returning null when not found or can't convert but I don't know how to use the null result in my expression.
I think you should redo your problem analysis and try another way. One way I would propose is to have a generic method that would give you the value from a IDictionary or IList etc., and use this method to wrap around your Expression's. The Expression would only want the "Type" of the object to be satisfied, if that is done correctly, then you could easily do it. If you know the "Type" then you can implement it with generic methods, otherwise, you could still use reflection and do generics.
So all you have to think is how to get the value from the dictionary or any other list through expressions.
Hope that helps.
-Fahad
You could use Expression.Call(null, typeof(int), "Parse", Type.EmptyTypes, yourTextExpression)