private static string[] CalculateRange(string rawEquation, string variables)
{
int success = Consolidate.ConvertAndCheckInputs(rawEquation, variables, Solver.GetValidOperators(), Solver.GetValidTerminators(), Input.GetLineDelimiter(), Input.GetFieldDelimiter());
string[] results = null;
if (success == 0)
{
EquationStruct eq = Consolidate.GetEquationStruct();
IntervalStruct[] intervals = Consolidate.GetIntervalStructList();
IntervalStruct range = Solver.FindRange(eq, intervals);
if (range != null)
{
results = new string[] { Output.PrintInterval(range, false), Output.PrintEquationTree(eq) };
frm_Main.UpdateLog("Range calculated successfully." + System.Environment.NewLine);
hasRun = true;
}
}
else
{
successCode = success;
}
return(results);
}
/* CONVERSION FUNCTION */
private static IntervalStruct MakeInterval(string varName, string min, string max)
{
IntervalStruct iv = null;
bool proceed = true;
double cMin = 0;
double cMax = 0;
// Check that a non-empty variable name was provided
if (CheckVarName(varName) && CheckBoundExistence(min, max))
{
// Try to convert the min to a string
try
{
if (min == "")
{
frm_Main.UpdateLog("Warning: No minimum interval bound given. Setting it to the same value as the maximum bound." + System.Environment.NewLine);
min = max;
}
cMin = System.Convert.ToDouble(min);
}
catch (System.FormatException)
{
frm_Main.UpdateLog("Error: The string provided for the minimum bound cannot be converted to a real number." + System.Environment.NewLine);
proceed = false;
}
// Try to convert the max to a string
try
{
if (max == "")
{
frm_Main.UpdateLog("Warning: No maximum interval bound given. Setting it to the same value as the minimum bound." + System.Environment.NewLine);
max = min;
}
cMax = System.Convert.ToDouble(max);
}
catch (System.FormatException)
{
frm_Main.UpdateLog("Error: The string provided for the maximum bound cannot be converted to a real number." + System.Environment.NewLine);
proceed = false;
}
// If you have reached this point, all the inputs are available to create an IntervalStruct object
if (proceed)
{
iv = new IntervalStruct(varName, cMin, cMax, true, true);
}
}
return(iv);
}
private static IntervalStruct IntervalAsExponent(double b, IntervalStruct x)
{
IntervalStruct exp = null;
if (b > 1)
{
exp = new IntervalStruct("", System.Math.Pow(b, x.GetMinBound()), System.Math.Pow(b, x.GetMaxBound()), true, true);
}
else
{
frm_Main.UpdateLog("Error: An unsupported operation was encountered while solving for the range of the equation (Exponent base <= 1)." + System.Environment.NewLine);
}
return(exp);
}
/* CALCULATION */
public static IntervalStruct FindRange(EquationStruct eqRoot, IntervalStruct[] intervals)
{
string[] varNames = GetVariableNamesFromIntervals(intervals);
IntervalStruct range = null;
if (eqRoot != null)
{
range = CalculateRange(eqRoot, intervals, varNames);
}
else
{
throw new System.ArgumentException("Error: No information was provided for the equation.");
}
return(range);
}
/* CALCULATION -- MULTIPLICATION */
private static IntervalStruct IntervalMultiplication(IntervalStruct x, IntervalStruct y)
{
// Comparing a1 * a2 and a1 * b2
double min = System.Math.Min(x.GetMinBound() * y.GetMinBound(), x.GetMinBound() * y.GetMaxBound());
double max = System.Math.Max(x.GetMinBound() * y.GetMinBound(), x.GetMinBound() * y.GetMaxBound());
// Comparing the previous results to b1 * a2
min = System.Math.Min(min, x.GetMaxBound() * y.GetMinBound());
max = System.Math.Max(max, x.GetMaxBound() * y.GetMinBound());
// Comparing the previous results to b1 * b2
min = System.Math.Min(min, x.GetMaxBound() * y.GetMaxBound());
max = System.Math.Max(max, x.GetMaxBound() * y.GetMaxBound());
return(new IntervalStruct("", min, max, true, true));
}
private static IntervalStruct[] RemoveInterval(IntervalStruct[] nameList, int index)
{
IntervalStruct[] newIvList = new IntervalStruct[nameList.Length - 1];
int i = 0;
int j = 0;
while (i < nameList.Length)
{
if (i != index)
{
newIvList[j] = nameList[i];
j++;
}
i++;
}
return(newIvList);
}
/* CALCULATION -- EXPONENTS */
private static IntervalStruct IntervalExponents(IntervalStruct x, IntervalStruct y)
{
IntervalStruct exp = null;
if (x.GetMinBound() == x.GetMaxBound())
{
exp = IntervalAsExponent(x.GetMinBound(), y);
}
else if (y.GetMinBound() == y.GetMaxBound())
{
exp = IntervalAsBase(x, y.GetMinBound());
}
else
{
frm_Main.UpdateLog("Error: An unsupported operation was encountered while solving for the range of the equation (Exponents)." + System.Environment.NewLine);
}
return(exp);
}
/* CALCULATION -- DIVISION */
private static IntervalStruct IntervalDivision(IntervalStruct x, IntervalStruct y)
{
IntervalStruct divInterval = null;
// 0 < a2 <= b2
if (y.GetMinBound() > 0)
{
divInterval = IntervalDivisionPositiveDivisor(x, y);
}
// a2 <= b2 < 0
else if (y.GetMaxBound() < 0)
{
divInterval = IntervalDivisionNegativeDivisor(x, y);
}
// a2 = 0 v b2 = 0
else
{
frm_Main.UpdateLog("Error: An unsupported operation was encountered while solving for the range of the equation (Mixed interval division)." + System.Environment.NewLine);
}
return(divInterval);
}
private static IntervalStruct IntervalDivisionNegativeDivisor(IntervalStruct x, IntervalStruct y)
{
double min = 0;
double max = 0;
// 0 < a1 <= b1
if (x.GetMinBound() > 0)
{
min = x.GetMaxBound() / y.GetMaxBound();
max = x.GetMinBound() / y.GetMinBound();
}
// a1 = 0, a1 <= b1
else if (x.GetMinBound() == 0)
{
min = x.GetMaxBound() / y.GetMaxBound();
max = 0;
}
// a1 < 0 < b1
else if (x.GetMaxBound() > 0)
{
min = x.GetMaxBound() / y.GetMaxBound();
max = x.GetMinBound() / y.GetMaxBound();
}
// b1 = 0, a1 <= b1
else if (x.GetMaxBound() == 0)
{
min = 0;
max = x.GetMinBound() / y.GetMaxBound();
}
//a1 <= b1 < 0
else if (x.GetMaxBound() < 0)
{
min = x.GetMaxBound() / y.GetMinBound();
max = x.GetMinBound() / y.GetMaxBound();
}
return(new IntervalStruct("", min, max, true, true));
}
private static IntervalStruct IntervalAsBase(IntervalStruct x, double n)
{
IntervalStruct exp = null;
double roundedN = System.Math.Round(n);
if (n >= 0)
{
if (n != roundedN)
{
frm_Main.UpdateLog("Warning: The value provided for the exponent" + System.Convert.ToString(n) + "is not a natural number. It has been rounded to " + System.Convert.ToString(roundedN) + System.Environment.NewLine);
}
if (roundedN % 2 != 0)
{
exp = new IntervalStruct("", System.Math.Pow(x.GetMinBound(), roundedN), System.Math.Pow(x.GetMaxBound(), roundedN), true, true);
}
else if (x.GetMinBound() >= 0)
{
exp = new IntervalStruct("", System.Math.Pow(x.GetMinBound(), roundedN), System.Math.Pow(x.GetMaxBound(), roundedN), true, true);
}
else if (x.GetMaxBound() < 0)
{
exp = new IntervalStruct("", System.Math.Pow(x.GetMaxBound(), roundedN), System.Math.Pow(x.GetMinBound(), roundedN), true, true);
}
else
{
exp = new IntervalStruct("", 0, System.Math.Max(System.Math.Pow(x.GetMinBound(), roundedN), System.Math.Pow(x.GetMaxBound(), roundedN)), true, true);
}
}
else
{
frm_Main.UpdateLog("Error: An unsupported operation was encountered while solving for the range of the equation (Exponent < 0)." + System.Environment.NewLine);
}
return(exp);
}
private static IntervalStruct CalculateRange(EquationStruct eqTree, IntervalStruct[] intervals, string[] intervalNames)
{
IntervalStruct range = null;
IntervalStruct leftResult = null;
IntervalStruct rightResult = null;
double constant = 0;
int varIndex = -1;
// This is either a variable or a constant
if (eqTree.GetLeftOperand() == null && eqTree.GetRightOperand() == null)
{
try
{
constant = System.Convert.ToDouble(eqTree.GetVariableName());
range = new IntervalStruct("", constant, constant, true, true);
}
catch (System.FormatException)
{
varIndex = System.Array.IndexOf(intervalNames, eqTree.GetVariableName());
if (varIndex > -1)
{
range = intervals[varIndex];
}
else
{
frm_Main.UpdateLog("Error: Could not find an associated interval for variable " + eqTree.GetVariableName() + System.Environment.NewLine);
}
}
}
// This is an equation, so calculate the result
else if (eqTree.GetOperator() == "+")
{
leftResult = CalculateRange(eqTree.GetLeftOperand(), intervals, intervalNames);
rightResult = CalculateRange(eqTree.GetRightOperand(), intervals, intervalNames);
if (leftResult != null && rightResult != null)
{
range = IntervalAddition(leftResult, rightResult);
}
}
else if (eqTree.GetOperator() == "-")
{
leftResult = CalculateRange(eqTree.GetLeftOperand(), intervals, intervalNames);
rightResult = CalculateRange(eqTree.GetRightOperand(), intervals, intervalNames);
if (leftResult != null && rightResult != null)
{
range = IntervalSubtraction(leftResult, rightResult);
}
}
else if (eqTree.GetOperator() == "*")
{
leftResult = CalculateRange(eqTree.GetLeftOperand(), intervals, intervalNames);
rightResult = CalculateRange(eqTree.GetRightOperand(), intervals, intervalNames);
if (leftResult != null && rightResult != null)
{
range = IntervalMultiplication(leftResult, rightResult);
}
}
else if (eqTree.GetOperator() == "/")
{
leftResult = CalculateRange(eqTree.GetLeftOperand(), intervals, intervalNames);
rightResult = CalculateRange(eqTree.GetRightOperand(), intervals, intervalNames);
if (leftResult != null && rightResult != null)
{
range = IntervalDivision(leftResult, rightResult);
}
}
else if (eqTree.GetOperator() == "^")
{
leftResult = CalculateRange(eqTree.GetLeftOperand(), intervals, intervalNames);
rightResult = CalculateRange(eqTree.GetRightOperand(), intervals, intervalNames);
if (leftResult != null && rightResult != null)
{
range = IntervalExponents(leftResult, rightResult);
}
}
else if (eqTree.GetOperator() == "()")
{
range = CalculateRange(eqTree.GetLeftOperand(), intervals, intervalNames);
}
else
{
frm_Main.UpdateLog("Error: An unsupported operation was encountered while solving for the range of the equation (Unknown operator)." + System.Environment.NewLine);
}
return(range);
}
/* CALCULATION -- SUBTRACTION */
private static IntervalStruct IntervalSubtraction(IntervalStruct x, IntervalStruct y)
{
return(new IntervalStruct("", x.GetMinBound() - y.GetMinBound(), x.GetMaxBound() - y.GetMaxBound(), true, true));
}
