/// <summary>
/// Subtract derivatives.
/// </summary>
/// <param name="b">The other operand.</param>
/// <returns>
/// The difference.
/// </returns>
public override Derivatives <Expression> Subtract(Derivatives <Expression> b)
{
var size = Math.Max(Count, b.Count);
var result = new ExpressionTreeDerivatives(size);
for (var i = 0; i < size; i++)
{
if (this[i] == null)
{
if (b[i] == null)
{
result[i] = null;
}
else
{
result[i] = Expression.Negate(b[i]);
}
}
else
{
if (b[i] == null)
{
result[i] = this[i];
}
else
{
result[i] = Expression.Subtract(this[i], b[i]);
}
}
}
return(result);
}
/// <summary>
/// Push a double value.
/// </summary>
/// <param name="value">The value.</param>
protected override void PushValue(double value)
{
var d = new ExpressionTreeDerivatives();
d[0] = Expression.Constant(value);
_stack.Push(d);
}
/// <summary>
/// Check for inequality.
/// </summary>
/// <param name="b">The other operand.</param>
/// <returns>
/// A value representing true if not equal.
/// </returns>
public override Derivatives <Expression> NotEqual(Derivatives <Expression> b)
{
var result = new ExpressionTreeDerivatives();
result[0] = Expression.Condition(Expression.NotEqual(this[0], b[0]), One, Zero);
return(result);
}
/// <summary>
/// And the derivatives.
/// </summary>
/// <param name="b">The other operand.</param>
/// <returns>
/// The derivatives.
/// </returns>
public override Derivatives <Expression> And(Derivatives <Expression> b)
{
var result = new ExpressionTreeDerivatives();
result[0] = Expression.Condition(
Expression.Or(
Expression.Equal(this[0], Zero),
Expression.Equal(b[0], Zero)), Zero, One);
return(result);
}
/// <summary>
/// Divide derivatives.
/// </summary>
/// <param name="b">The other operand.</param>
/// <returns>
/// The divided result.
/// </returns>
public override Derivatives <Expression> Divide(Derivatives <Expression> b)
{
var size = Math.Max(Count, b.Count);
var result = new ExpressionTreeDerivatives(size);
Expression a0 = this[0], b0 = b[0];
if (a0 == null)
{
return(null);
}
if (b0 == null)
{
throw new DivideByZeroException();
}
result[0] = Expression.Call(Division, a0, b0);
for (var i = 1; i < size; i++)
{
if (this[i] == null)
{
if (b[i] == null)
{
result[i] = null;
}
else
{
// (a/gx)' = -a/gx^2*g'x
result[i] = Expression.Call(Division,
Expression.Negate(Expression.Multiply(a0, b[i])),
Expression.Call(SquareInfo, b0));
}
}
else
{
if (b[i] == null)
{
// (fx/b)' = f'x/b
result[i] = Expression.Call(Division, this[i], b0);
}
else
{
// (fx/gx)' = (f'x*gx-fx*g'x)/gx^2
result[i] = Expression.Call(Division,
Expression.Subtract(
Expression.Multiply(this[i], b0),
Expression.Multiply(a0, b[i])),
Expression.Call(SquareInfo, b0));
}
}
}
return(result);
}
/// <summary>
/// Check greater or equal.
/// </summary>
/// <param name="b">The operand.</param>
/// <returns>
/// A value representing true if this is greater or equal.
/// </returns>
public override Derivatives <Expression> GreaterOrEqual(Derivatives <Expression> b)
{
var result = new ExpressionTreeDerivatives();
Expression a0 = this[0], b0 = b[0];
if (a0 == null && b0 == null)
{
return(result);
}
a0 = a0 ?? Zero;
b0 = b0 ?? Zero;
result[0] = Expression.Condition(Expression.GreaterThanOrEqual(a0, b0), One, Zero); return(result);
}
/// <summary>
/// Negate the derivatives.
/// </summary>
/// <returns>
/// The derivatives.
/// </returns>
public override Derivatives <Expression> Negate()
{
var result = new ExpressionTreeDerivatives(Count);
for (var i = 0; i < Count; i++)
{
if (this[i] != null)
{
result[i] = Expression.Negate(this[i]);
}
}
return(result);
}
/// <summary>
/// Not (binary) the derivatives.
/// </summary>
/// <returns>
/// The derivatives.
/// </returns>
public override Derivatives <Expression> Not()
{
var result = new ExpressionTreeDerivatives(Count);
if (this[0] != null)
{
result[0] = Expression.Condition(Expression.Equal(this[0], Zero), One, Zero);
}
else
{
result[0] = One;
}
return(result);
}
/// <summary>
/// Modulo operation on derivatives.
/// </summary>
/// <param name="b">The other operand.</param>
/// <returns>
/// The remainder of the division.
/// </returns>
public override Derivatives <Expression> Modulo(Derivatives <Expression> b)
{
var result = new ExpressionTreeDerivatives();
if (this[0] == null)
{
return(result);
}
if (b[0] == null)
{
throw new Exception("Modulo by 0");
}
result[0] = Expression.Modulo(this[0], b[0]);
return(result);
}
/// <summary>
/// Raises the derivatives to a power.
/// </summary>
/// <param name="exponent">The exponent.</param>
/// <returns>
/// The raised power.
/// </returns>
public override Derivatives <Expression> Pow(Derivatives <Expression> exponent)
{
var size = Math.Max(Count, exponent.Count);
var result = new ExpressionTreeDerivatives(size);
Expression a0 = this[0], b0 = exponent[0];
if (a0 == null && b0 == null)
{
// This doesn't make much sense (0^0 is invalid) but Math.Pow does it like that so we will too
result[0] = One;
return(result);
}
if (a0 == null)
{
a0 = Zero;
}
if (b0 == null)
{
// (fx)^0 = 1
result[0] = One;
return(result);
}
result[0] = Expression.Call(PowInfo, a0, b0);
if (a0 != One && a0 != Zero)
{
a0 = Expression.Call(AbsInfo, a0);
}
for (var i = 1; i < size; i++)
{
// (fx^b)' = b * fx^(b-1) * f'x
if (this[i] != null)
{
result[i] = Expression.Multiply(b0, Expression.Multiply(this[i],
Expression.Call(PowInfo, a0, Expression.Subtract(b0, One))));
}
// (fx^gx)' = (e^(gx*ln(fx)))'
// = fx^(gx-1)*f'x + fx^gx*ln(fx)*g'x
if (exponent[i] != null)
{
var contribution = Expression.Multiply(Expression.Call(PowInfo, a0, b0),
Expression.Multiply(Expression.Call(LogInfo, a0), exponent[i]));
result[i] = result[i] == null ? contribution :
Expression.Add(result[i], contribution);
}
}
return(result);
}
/// <summary>
/// Multiply derivatives.
/// </summary>
/// <param name="b">The other operand.</param>
/// <returns>
/// The multiplied result.
/// </returns>
public override Derivatives <Expression> Multiply(Derivatives <Expression> b)
{
var size = Math.Max(Count, b.Count);
var result = new ExpressionTreeDerivatives(size);
Expression a0 = this[0], b0 = b[0];
if (a0 == null || b0 == null)
{
return(result); // x*0 = 0 and so is all its derivatives
}
else
{
result[0] = Expression.Multiply(a0, b0);
}
for (var i = 1; i < size; i++)
{
if (this[i] == null)
{
if (b[i] == null)
{
result[i] = null;
}
else
{
// (a*gx)' = a*g'x
result[i] = Expression.Multiply(a0, b[i]);
}
}
else
{
if (b[i] == null)
{
// (fx*b)' = f'x*b
result[i] = Expression.Multiply(this[i], b0);
}
else
{
// (fx*gx)' = fx*g'x + f'x*gx
result[i] = Expression.Add(
Expression.Multiply(a0, b[i]),
Expression.Multiply(this[i], b0));
}
}
}
return(result);
}
/// <summary>
/// Apply a derivative.
/// </summary>
/// <param name="value"></param>
/// <param name="index"></param>
/// <param name="derivative"></param>
public override void Apply(Func <double> value, int index, double derivative)
{
var result = new ExpressionTreeDerivatives();
// Specify the actual value
if (value != null)
{
result[0] = Expression.Call(Expression.Constant(value), InvokeMethod);
}
// Specify the derivative
if (index > 0)
{
result[index] = Expression.Constant(derivative);
}
Result = result;
}
/// <summary>
/// Conditional derivatives.
/// </summary>
/// <param name="iftrue">Argument if true.</param>
/// <param name="iffalse">Argument if false.</param>
/// <returns>
/// The derivatives.
/// </returns>
public override Derivatives <Expression> IfThenElse(Derivatives <Expression> iftrue, Derivatives <Expression> iffalse)
{
if (this[0] == null)
{
return(iffalse);
}
var size = Math.Max(iftrue.Count, iffalse.Count);
var result = new ExpressionTreeDerivatives(size);
var notcondition = Expression.Equal(this[0], Zero);
for (var i = 0; i < size; i++)
{
var iftruei = iftrue[i];
var iffalsei = iffalse[i];
if (iftruei == null && iffalsei == null)
{
continue;
}
result[i] = Expression.Condition(notcondition, iffalsei ?? Zero, iftruei ?? Zero);
}
return(result);
}
/// <summary>
/// Constructor
/// </summary>
/// <param name="property">The property.</param>
public ExpressionTreeDerivativePropertyEventArgs(SpiceProperty property)
: base(property)
{
Result = null;
}