//The original combination ("Combination" class), generated in the combinatorics part, requires from quite a few actions to become a valid combination, that is:
//a dependent variable in one of the output fits. This method performs this conversion
public ValidCombination createValidComb(Combination curCombination, List<Input> inputs, CombValues xVals, CombValues yVals, Config curConfig, bool checkModify)
{
ValidCombination curValidComb = createValidComb2(curCombination, inputs, xVals, yVals, curConfig);
if (curValidComb != null)
{
if(checkModify) curValidComb = modifyFit(curValidComb, inputs, yVals, curConfig);
if(curValidComb != null) curValidComb = assessComb(curValidComb, curConfig);
}
return curValidComb;
}
//This function forms also part of the redundant-variable-removal process: the removal of the given variable (or group of variables) has been confirmed to be fine and thus
//this function will update the corresponding ValidCombination variable
private ValidCombination validCombWithIgnoredItems(ValidCombination curValidComb, List<int> itemsToIgnore, List<Input> inputs, CombValues yVals, Config curConfig, bool isMulti)
{
//At least one of the variables in the original combination is redundant and thus the corresponding ValidCombination variable has to be re-calculated
for (int i = curValidComb.dependentVars.items.Count - 1; i >= 0; i--)
{
if (itemsToIgnore.Contains(i)) curValidComb.dependentVars.items.RemoveAt(i);
}
if (curValidComb.dependentVars.items.Count < 1)
{
curValidComb = null;
}
else
{
CombValues xVals = Common.getCombinationListVals(curValidComb.dependentVars, inputs);
curValidComb = createValidComb(curValidComb.dependentVars, inputs, xVals, yVals, curConfig, !isMulti); //Rechecking for redundant variables only after single removals to avoid potential infinite loops
}
return curValidComb;
}
//Looking at the weights variable to determine whether there are single variables (e.g., var1 + var2) which should better be removed
private ValidCombination removeSingleRedundant(ValidCombination curValidComb, List<Input> inputs, CombValues yVals, Config curConfig)
{
//Addition of the weights of all the variables in each row. This is a simplistic way to determine whether one of the variables
//forming the given combination is much more relevant than all the other ones
List<double> allWeights = new List<double>();
for (int i = 0; i < curValidComb.dependentVars.items.Count; i++)
{
//i2 avoids the warning "Using the iteration variable in a lambda expression is..."
//which, curiously, is only shown in VB.NET (even with Option Strict Off!), but not in C# (even though this "problem" is common to both)
int i2 = i;
allWeights.Add(curValidComb.calcVals.Average(x => x.weights[i2]));
}
double curMaxWeight = curConfig.limitVals.tooRelevantWeight;
bool goAhead = allWeights.FirstOrDefault(x => x >= curConfig.limitVals.tooRelevantWeight) >= curConfig.limitVals.tooRelevantWeight;
goAhead = goAhead ? goAhead : allWeights.FirstOrDefault(x => x <= curConfig.limitVals.maxErrorToIgnoreVar) <= curConfig.limitVals.maxErrorToIgnoreVar;
if (!goAhead && curValidComb.dependentVars.items.Count > 2)
{
curMaxWeight = curConfig.limitVals.tooRelevantWeight2;
goAhead = allWeights.FirstOrDefault(x => x >= curConfig.limitVals.tooRelevantWeight2) >= curConfig.limitVals.tooRelevantWeight2;
}
if (goAhead)
{
//One of the variables contributes in a much more relevant way (to the final calculated value) than all the other ones in the combination
List<int> itemsToIgnore = new List<int>();
for (int i = curValidComb.dependentVars.items.Count - 1; i >= 0; i--)
{
if (allWeights[i] < curMaxWeight)
{
bool canBeRemoved = (i == curValidComb.dependentVars.items.Count - 1 || curValidComb.dependentVars.items[i].operation != Operation.Multiplication);
canBeRemoved = canBeRemoved ? (i == 0 || curValidComb.dependentVars.items[i - 1].operation != Operation.Multiplication) : false;
if (canBeRemoved)
{
//The current variable might be irrelevant. The analysis performed in the following lines consists basically in removing this variable and comparing the resulting errors (with vs. without)
Combination tempDependent = new Combination();
tempDependent.items = new List<CombinationItem>(curValidComb.dependentVars.items);
tempDependent.items.RemoveAt(i);
if (ignoreItem(tempDependent, curValidComb, inputs, yVals, curConfig))
{
itemsToIgnore.Add(i);
}
}
}
}
if (itemsToIgnore.Count > 0)
{
curValidComb = validCombWithIgnoredItems(curValidComb, itemsToIgnore, inputs, yVals, curConfig, false);
}
}
return curValidComb;
}
//Method determining whether all the variables forming the corresponding combinations are actually required
private ValidCombination removeRedundantVars(ValidCombination curValidComb, List<Input> inputs, CombValues yVals, Config curConfig)
{
if (curValidComb.dependentVars.items.Count > 1)
{
if (curValidComb.calcVals.FirstOrDefault(x => x.weights2.Count > 0) != null)
{
//Removal of redundant groups of variables (i.e., products of 2 or more variables)
curValidComb = removeMultiRedundant(curValidComb, inputs, yVals, curConfig);
}
if(curValidComb != null) curValidComb = removeSingleRedundant(curValidComb, inputs, yVals, curConfig);
}
return curValidComb;
}
//Looking at the weights2 variable to determine whether there are group of factors (e.g., var1*var2) which should better be removed
private ValidCombination removeMultiRedundant(ValidCombination curValidComb, List<Input> inputs, CombValues yVals, Config curConfig)
{
List<Weight2> allWeights2 = new List<Weight2>();
for (int i = 0; i < curValidComb.calcVals[0].weights2.Count; i++)
{
//i2 avoids the warning "Using the iteration variable in a lambda expression is..."
//which, curiously, is only shown in VB.NET (even with Option Strict Off!), but not in C# (even though this "problem" is common to both)
int i2 = i;
Weight2 curWeight2 = new Weight2();
curWeight2.combWeight = curValidComb.calcVals.Average(x => x.weights2[i2].combWeight);
curWeight2.combItems = new List<CombinationItem>(curValidComb.calcVals[0].weights2[i].combItems);
allWeights2.Add(curWeight2);
}
bool goAhead = allWeights2.FirstOrDefault(x => x.combWeight >= curConfig.limitVals.tooRelevantWeight) != null;
goAhead = goAhead ? goAhead : allWeights2.FirstOrDefault(x => x.combWeight <= 0.5 * curConfig.limitVals.maxErrorToIgnoreVar) != null;
if (goAhead)
{
//One of the variables contributes in a much more relevant way (to the final calculated value) than all the other ones in the combination
List<int> itemsToIgnore = new List<int>();
for (int i = 0; i < allWeights2.Count; i++)
{
if (allWeights2[i].combWeight < curConfig.limitVals.tooRelevantWeight)
{
//The current variable might be irrelevant. The analysis performed in the following lines consists basically in removing this variable and comparing the resulting errors (with vs. without it)
Combination tempDependent = new Combination();
tempDependent.items = curValidComb.dependentVars.items.Except(allWeights2[i].combItems).ToList();
if (ignoreItem(tempDependent, curValidComb, inputs, yVals, curConfig))
{
itemsToIgnore.AddRange(allWeights2[i].combItems.Select(x => x.variable.index));
}
}
}
if (itemsToIgnore.Count > 0)
{
curValidComb = validCombWithIgnoredItems(curValidComb, itemsToIgnore, inputs, yVals, curConfig, true);
}
}
return curValidComb;
}
//Method called to add the assessing factors to the corresponding Assessment variable
private Assessment addFactor(int curCount, Assessment curAssessment, ValidCombination curValidComb, Config curConfig)
{
AssessmentFactor curFactor = new AssessmentFactor();
if (curCount == 0)
{
curFactor.name = "In-sample accuracy";
curFactor.weight = 10.0;
if (curValidComb.averError <= curConfig.limitVals.valueIsZero) //Zero cannot be considered because the (floating-point) double type might provoke errors
{
//Too perfect to continue
curFactor.rating = 10.0;
curAssessment.factors.Add(curFactor);
curAssessment.totWeight = 10.0;
curAssessment.globalRating = 10.0;
return curAssessment;
}
if (curValidComb.averError <= curConfig.fitConfig.globalAver * 0.05)
{
double curMinPercBelow = (double)curValidComb.lowErrorCount / (double)curValidComb.errors.Count;
if (curMinPercBelow >= 0.99) curFactor.rating = 9.0;
else if (curMinPercBelow >= 0.95) curFactor.rating = 8.0;
}
else
{
curFactor.rating = 8.0 * (curConfig.fitConfig.globalAver - curValidComb.averError) / (0.95 * curConfig.fitConfig.globalAver);
}
}
else if (curCount == 1 || curCount == 2)
{
curFactor.name = "Quality of independent variable";
double averRatingVars = curValidComb.independentVar.input.preAnalysis.rating;
if (curCount == 1)
{
curFactor.name = "Quality of dependent variable(s)";
averRatingVars = curValidComb.dependentVars.items.Count == 0 ? 10 : curValidComb.dependentVars.items.Average(x => x.variable.input.preAnalysis.rating);
}
curFactor.weight = 8.0;
if (curValidComb.errors.Count >= curConfig.fitConfig.minNoCases)
{
curFactor.rating = 8.0;
if (curValidComb.errors.Count >= 1.25 * curConfig.fitConfig.minNoCases) curFactor.rating = 10.0;
else if (curValidComb.errors.Count >= 1.1 * curConfig.fitConfig.minNoCases) curFactor.rating = 9.0;
}
curFactor.rating = Math.Round(0.5 * (double)curFactor.rating + 0.5 * averRatingVars, 0);
}
else if (curCount == 3)
{
curFactor.name = "Solution tunability";
curFactor.weight = 6.0;
curFactor.rating = ratingTunability(curValidComb);
}
else if (curCount == 4)
{
curFactor.name = "Complexity of polynomial fit";
curFactor.weight = 5.0;
curFactor.rating = ratingFitComplexity(curValidComb);
}
if (curFactor.rating < 0.0) curFactor.rating = 0.0;
curAssessment.totWeight = curAssessment.totWeight + curFactor.weight;
curAssessment.factors.Add(curFactor);
return curAssessment;
}
//After a new ValidCombination has been created (and thus the preliminary thresholds have been met), further analysis are required to determine whether it is actually right
private ValidCombination modifyFit(ValidCombination curValidComb, List<Input> inputs, CombValues yVals, Config curConfig)
{
if (fitIsConstant(curValidComb, curConfig))
{
//y = A represents accurately the current fit; no further information needs to be accounted for
if (curValidComb.averError >= curConfig.limitVals.maxErrorConstant)
{
//Having a too big error for a constant fit might indicate an "understanding error". Example: 10001, 9999, 10000... modelled with y = 10000
curValidComb = null;
}
else
{
curValidComb.dependentVars = new Combination();
curValidComb.coeffs.B = 0;
curValidComb.coeffs.C = 0;
}
}
else
{
//The current fit is certainly not constant, but some of the variables might not be required. Example: y = x1 + 0.00000000000001 * x2
curValidComb = removeRedundantVars(curValidComb, inputs, yVals, curConfig);
}
return curValidComb;
}
//Method performing all the required actions to create the combinations under the most difficult conditions (i.e., more than one variable), that is: perform all the
//combinations among variables, exponents and operations; call the methods in charge of creating the corresponding "ValidCombination"; and, eventually, add the new
//instance to the list of all the valid combinations so far
//NOTA DEL CREADOR: modestia aparte, esta función es una puta obra de arte (en Spanish porque suena mejor :))
private List<ValidCombination> addMulti(List<Input> inputs, List<int> indices, Config curConfig, List<ValidCombination> allCombinations, Variable indepVar)
{
int[] curExps = new int[indices.Count];
int[] curOpers = new int[indices.Count];
//The code below these lines is fairly complicated as far as it has to deal with many variations (i.e., all the possible combinations among exponents, operations and variables).
//In any case, it should be noted that a relevant "combinatorics effort" has already been done before calling this function, that is: setting all the possible combinations of variables.
//The combinations are created as shown in the following example (vars: var1, var2, var3; exps: 1, 2; operations: *, +):
// var1^1 * var2^1 * var3^1
// var1^1 * var2^1 + var3^1
// var1^1 * var2^1 * var3^2
// var1^1 * var2^1 + var3^2
// var1^1 + var2^1 * var3^1
// var1^1 + var2^1 + var3^1
// var1^1 + var2^1 * var3^2
//etc.
ExpRelUpdate obj1 = new ExpRelUpdate(indices.Count - 2, curConfig.exponents.Count - 1, indices.Count, curExps);
curExps[obj1.index] = -1;
while (!obj1.completed)
{
obj1 = updateObjs13(obj1, true);
if (obj1.completed) break;
ExpRelUpdate obj2 = new ExpRelUpdate(indices.Count - 2, curConfig.exponents.Count - 1, indices.Count, curExps);
while (!obj2.completed)
{
for (int i = 0; i < indices.Count; i++)
{
curOpers[i] = 0;
}
ExpRelUpdate obj3 = new ExpRelUpdate(indices.Count - 2, curConfig.operations.Count - 1, indices.Count, curOpers);
curOpers[obj3.index] = -1;
while (!obj3.completed)
{
obj3 = updateObjs13(obj3, false);
if (obj3.completed) break;
for (int exp = 0; exp < curConfig.exponents.Count; exp++)
{
if (cancelSim) break;
curExps[indices.Count - 1] = exp;
allCombinations = internalLoop(curOpers, curExps, allCombinations, curConfig, indices, inputs, indepVar);
}
}
obj2 = updateObj2(obj2);
if (obj2.otherProp)
{
obj1.completed = true;
break;
}
}
}
return allCombinations;
}
//Method determining whether the current fit (as stored in a ValidCombination variable) can be considered as constant (i.e., y = A)
private bool fitIsConstant(ValidCombination curValidComb, Config curConfig)
{
bool fitIsConstant = false;
if (Math.Abs(curValidComb.coeffs.B) <= curConfig.limitVals.valueIsZero && Math.Abs(curValidComb.coeffs.C) <= curConfig.limitVals.valueIsZero)
{
fitIsConstant = true;
}
else
{
double averError = 0;
foreach (var val in curValidComb.realVals)
{
averError = averError + 100 * Math.Abs((val - curValidComb.coeffs.A) / curValidComb.coeffs.A);
}
if (averError <= 0.01)
{
fitIsConstant = true;
}
}
return fitIsConstant;
}
//Method in charge of performing the initial actions to convert a "Combination" variable into a ValidCombination one, that is: regression and first crosscheck of the
//calculated values against the applicable error thresholds
private ValidCombination createValidComb2(Combination curCombination, List<Input> inputs, CombValues xVals, CombValues yVals, Config curConfig)
{
ValidCombination curValidComb = new ValidCombination();
//Performing the corresponding regression to determine the polynomial fit matching the input conditions
CurveFitting curFitting = new CurveFitting();
PolCurve curCurve = curFitting.performPolRegress(xVals, yVals);
List<double> errors = new List<double>();
curValidComb.dependentVars.items = new List<CombinationItem>(curCombination.items);
curValidComb.independentVar = curCurve.yValues.combination.items[0].variable;
curValidComb.coeffs = curCurve.coeffs;
//Loop applying the newly-created fit to all the input values and calculating the associated variables
for (int i = 0; i < xVals.values.Count; i++)
{
double realVal = yVals.values[i].value;
curValidComb.realVals.Add(realVal);
RowVal curCalcVal = new RowVal();
curCalcVal.value = Common.valueFromPol(curCurve.coeffs, xVals.values[i].value);
curCalcVal.weights = xVals.values[i].weights;
curCalcVal.weights2 = xVals.values[i].weights2;
curValidComb.calcVals.Add(curCalcVal);
double curError = Common.errorCalcs(realVal, curCalcVal.value);
curValidComb.errors.Add(curError);
if (curError <= curConfig.fitConfig.averLimit) curValidComb.lowErrorCount = curValidComb.lowErrorCount + 1;
}
curValidComb.averError = curValidComb.errors.Average(x => x);
bool isOK = false;
if (curValidComb.averError <= curConfig.fitConfig.globalAver)
{
if ((double)curValidComb.lowErrorCount / (double)curValidComb.errors.Count >= curConfig.fitConfig.minPercBelowLimit)
{
isOK = true;
}
}
if (!isOK) curValidComb = null;
return curValidComb;
}
//Method actually creating a new ValidCombination variable and performing preliminary validity checks
private ValidCombination newCombination(Combination curCombination, Variable yVar, List<Input> inputs, List<ValidCombination> allValidCombinations, Config curConfig)
{
//Performing the regression and the corresponding analysis to determine whether this specific combination should be stored or not
CombValues xVals = Common.getCombinationListVals(curCombination, inputs);
CombValues yVals = new CombValues();
yVals.combination = new Combination();
int maxDec = inputs[yVar.index].vals.Max(x => x <= Int32.MaxValue ? ((decimal)x - Convert.ToInt32((decimal)x)).ToString().Length - 2 : 0);
if (maxDec < 0) maxDec = 0;
Variable curVariable = new Variable() { index = yVar.index, input = inputs[yVar.index], noDec = maxDec };
CombinationItem curItem = new CombinationItem() { variable = curVariable, operation = new Operation(), exponent = 1.0 };
yVals.combination.items.Add(curItem);
for (int row = 0; row < inputs[yVar.index].vals.Count; row++)
{
RowVal curRowVal = new RowVal();
curRowVal.value = inputs[yVar.index].vals[row];
curRowVal.weights.Add(1.0);
yVals.values.Add(curRowVal);
}
Analysis curAnalysis = new Analysis();
ValidCombination curValidCombination = curAnalysis.createValidComb(curCombination, inputs, xVals, yVals, curConfig, true);
if (curValidCombination != null && allValidCombinations.Count > 0)
{
if (alreadyStored(curValidCombination, allValidCombinations))
{
curValidCombination = null;
}
}
return curValidCombination;
}
//Method called from the main combinatorics loops for multivariate cases above (addMulti). Its whole purpose is reducing the size of the loops.
//It includes the "more internal loops", the ones creating the corresponding ValidCombination and adding it to the list of all the combinations so far
private List<ValidCombination> internalLoop(int[] curOpers, int[] curExps, List<ValidCombination> allCombinations, Config curConfig, List<int> indices, List<Input> inputs, Variable indepVar)
{
for (int rel = 0; rel < curConfig.operations.Count; rel++)
{
if (cancelSim) return allCombinations;
Combination curCombination = new Combination();
curOpers[indices.Count - 2] = rel;
for (int i = 0; i < indices.Count; i++)
{
int genIndex = indices[i];
//The cast to decimal type is included in order to avoid problems with the double floating point (e.g., without casting to decimal, 10.55 wouldn't be found)
int maxDec = inputs[genIndex].vals.Max(x => x <= Int32.MaxValue ? ((decimal)x - Convert.ToInt32((decimal)x)).ToString().Length - 2 : 0);
if (maxDec < 0) maxDec = 0;
Variable curVariable = new Variable { index = genIndex, input = inputs[genIndex], noDec = maxDec };
CombinationItem curItem = new CombinationItem() { variable = curVariable, exponent = curConfig.exponents[curExps[i]], operation = curConfig.operations[curOpers[i]] };
curCombination.items.Add(curItem);
}
allCombinations = addToAllCombinations(curCombination, inputs, curConfig, allCombinations, indepVar);
}
return allCombinations;
}
//Method starting the creation of the corresponding "ValidCombination" and, eventually, storing it in the list including all the ones so far
private List<ValidCombination> addToAllCombinations(Combination curCombination, List<Input> inputs, Config curConfig, List<ValidCombination> allCombinations, Variable indepVar)
{
ValidCombination curValid = newCombination(curCombination, indepVar, inputs, allCombinations, curConfig);
if (curValid != null)
{
if (allCombinations.Count >= curConfig.maxNoCombs)
{
allCombinations = allCombinations.OrderByDescending(x => x.assessment.globalRating).ToList();
if (curValid.assessment.globalRating > allCombinations[allCombinations.Count - 1].assessment.globalRating)
{
allCombinations.RemoveAt(allCombinations.Count - 1);
}
else
{
curValid = null;
}
}
if (curValid != null)
{
if (curValid.dependentVars.items.Count < 1)
{
if (curValid.coeffs.B != 0.0 || curValid.coeffs.C != 0.0) curValid = null;
}
}
}
if(curValid != null) allCombinations.Add(curValid);
return allCombinations;
}
//After a ValidCombination has been formed, it is necessary to assess its suitability/rating; this is what this method takes care of.
private ValidCombination assessComb(ValidCombination curValidComb, Config curConfig)
{
curValidComb.assessment = new Assessment();
//The assessment of the given fit results from different factors, which account for different aspects of the input data, the predicted results, etc.
//In-sample accuracy
int curCount = 0;
curValidComb.assessment = addFactor(curCount, curValidComb.assessment, curValidComb, curConfig);
if (curValidComb.assessment.globalRating == 10.0)
{
//Perfect situation
curValidComb.assessment.factors[0].weight = 100.0;
curValidComb.averError = 0.0;
return curValidComb;
}
//Quality of dependent variable(s)
curCount = curCount + 1;
curValidComb.assessment = addFactor(curCount, curValidComb.assessment, curValidComb, curConfig);
//Quality of independent variable
curCount = curCount + 1;
curValidComb.assessment = addFactor(curCount, curValidComb.assessment, curValidComb, curConfig);
//Tunability
curCount = curCount + 1;
curValidComb.assessment = addFactor(curCount, curValidComb.assessment, curValidComb, curConfig);
//Complexity of polynomial fit
curCount = curCount + 1;
curValidComb.assessment = addFactor(curCount, curValidComb.assessment, curValidComb, curConfig);
foreach (AssessmentFactor factor in curValidComb.assessment.factors)
{
factor.weight = factor.weight * 100 / curValidComb.assessment.totWeight; //Converting the partial weights into a 0-100 scale
curValidComb.assessment.globalRating = curValidComb.assessment.globalRating + (factor.rating * factor.weight / 100);
}
return curValidComb;
}
//This function is part of the redundant-variable-removal process: after the given variable (or group of variables) has been (temporarily) removed, this
//function checks whether the resulting combination is still valid or not (and thus the removal process can go further)
private bool ignoreItem(Combination tempDependent, ValidCombination curValidComb, List<Input> inputs, CombValues yVals, Config curConfig)
{
bool ignoreIt = false;
CombValues xVals = Common.getCombinationListVals(tempDependent, inputs);
ValidCombination tempValid = createValidComb(tempDependent, inputs, xVals, yVals, curConfig, false);
if (tempValid != null)
{
ignoreIt = tempValid.averError < curValidComb.averError || (tempValid.averError <= curConfig.limitVals.maxErrorToIgnoreVar && curValidComb.averError <= curConfig.limitVals.maxErrorToIgnoreVar);
ignoreIt = ignoreIt ? ignoreIt : Common.valsAreEquivalent(tempValid.averError, curValidComb.averError, curConfig.limitVals.similarity.medium);
}
return ignoreIt;
}
public Results()
{
config = new Config();
allInputs = new List<Input>();
combinations = new List<ValidCombination>();
}
//Method in charge of putting together all the inputs for the given combination (i.e., variables, exponents and operations) and bring together all the remaining factors (e.g., suitability of the fit)
//to form the associated ValidCombination and add it to the list of valid combinations created so far
private List<ValidCombination> addCombination(List<Input> inputs, List<int> indices, Config curConfig, List<ValidCombination> allCombinations, Variable indepVar)
{
if (indices.Count == 1)
{
//Only one variable is accounted for and thus the whole combinatorial process will consist in accounting for the different exponents
int genIndex = indices[0];
for (int i = 0; i < curConfig.exponents.Count; i++)
{
if (cancelSim) break;
Combination curCombination = new Combination();
//The cast to decimal type is included in order to avoid problems from the double floating point (e.g., 10.55)
int maxDec = inputs[genIndex].vals.Max(x => x <= Int32.MaxValue ? ((decimal)x - Convert.ToInt32((decimal)x)).ToString().Length - 2 : 0);
if (maxDec < 0) maxDec = 0;
Variable curVariable = new Variable { index = genIndex, input = inputs[genIndex], noDec = maxDec };
CombinationItem curItem = new CombinationItem() { variable = curVariable, exponent = curConfig.exponents[i], operation = curConfig.operations[0] };
curCombination.items.Add(curItem);
allCombinations = addToAllCombinations(curCombination, inputs, curConfig, allCombinations, indepVar);
}
}
else
{
//Various variables are accounted for and thus everything (i.e., variables, exponents & operations) have to be brought into picture
allCombinations = addMulti(inputs, indices, curConfig, allCombinations, indepVar);
}
return allCombinations;
}