/// <summary>
/// Checks whether the given <see cref="MathProgram" /> computes a value that is consistently equivalent to that
/// computed
/// by another program according to some margin. The method works by substituting the variables in both programs'
/// expressions by random values for a certain number of trials. In each trial, the difference between the values
/// computed by both programs is calculated. If the difference is less than a given margin for all the trials, then the
/// programs are considered to be value-equivalent.
/// </summary>
/// <param name="program">The first program that we want to test.</param>
/// <param name="other">The second program that we want to test.</param>
/// <param name="margin">
/// The margin used to compare against the difference of values computed by both expressions in each
/// trial.
/// </param>
/// <param name="numTrials">The number of trials used to discern whether the given programs are equivalent.</param>
/// <returns><c>True</c> if the given programs are considered to be value-equivalent, <c>False</c> otherwise.</returns>
public static bool IsValueEquivalent(
this ITreeProgram <double> program, ITreeProgram <double> other, double margin = DEFAULT_MARGIN,
uint numTrials = DEFAULT_NUM_TRIALS)
{
// checks null
if (program == null || other == null)
{
return(false);
}
// checks equivalence
if (program.Equals(other))
{
return(true);
}
// checks expression or constant equivalence after simplification
program = program.Simplify();
other = other.Simplify();
if (program.Equals(other) ||
program.IsConstant() && other.IsConstant() && Math.Abs(program.Compute() - other.Compute()) < margin)
{
return(true);
}
// gets RMSE by replacing the values of the variables in some number of trials
return(program.GetValueRmsd(other, numTrials) <= margin);
}
/// <summary>
/// Gets the root-mean-square deviation (RMSD) between the values computed for the given programs. The method works by
/// substituting the variables in both programs' expressions by random values for a certain number of trials. In each
/// trial, the square of the difference between the values computed by both programs is calculated.
/// </summary>
/// <param name="program">The first program that we want to test.</param>
/// <param name="other">The second program that we want to test.</param>
/// <param name="numTrials">The number of trials used to compute the squared difference.</param>
/// <returns>The RMSD between the several values computed for the given programs.</returns>
public static double GetValueRmsd(
this ITreeProgram <double> program, ITreeProgram <double> other, uint numTrials = DEFAULT_NUM_TRIALS)
{
// checks null
if (program == null || other == null)
{
return(double.MaxValue);
}
// checks expression or constant equivalence after simplification
program = program.Simplify();
other = other.Simplify();
if (program.Equals(other) || program.IsConstant() && other.IsConstant())
{
return(Math.Abs(program.Compute() - other.Compute()));
}
// replaces variables of each expression by custom variables
var customVariables = new Dictionary <Variable, Variable>();
program = ReplaceVariables(program, customVariables);
other = ReplaceVariables(other, customVariables);
if (customVariables.Count == 0)
{
return(double.MaxValue);
}
// gets random values for each variable
var customVariablesValues = customVariables.Values.ToDictionary(
variable => variable,
variable => GetTrialRandomNumbers(numTrials, variable.Range));
// runs a batch of trials
var squareDiffSum = 0d;
for (var i = 0; i < numTrials; i++)
{
// replaces the value of each variable by a random number
foreach (var customVariablesValue in customVariablesValues)
{
customVariablesValue.Key.Value = customVariablesValue.Value[i];
}
// computes difference of the resulting values of the expressions
var prog1Value = program.Compute();
var prog2Value = other.Compute();
var diff = prog1Value.Equals(prog2Value) ? 0 : prog1Value - prog2Value;
squareDiffSum += diff * diff;
}
// returns RMSD
return(Math.Sqrt(squareDiffSum / numTrials));
}
