Symbol Symbolicate(string formula, int begin, int end, Expression exp)
{
var symbols = new SymbolList();
int i = begin - 1;
int currentTermBegin = formula[begin] == '+' ? begin + 1 : begin;
int currentDepth = 0;
for (;;)
{
i++;
if (i == end || (currentDepth == 0 && i > begin && (formula[i - 1] != '*' && formula[i - 1] != '/') && (formula[i] == '+' || formula[i] == '-')))
{
symbols.Append(SymbolicateMonome(formula, currentTermBegin, i, exp));
if (i == end)
{
break;
}
else
{
// The sign of the term is included in the next monome only if its minus
currentTermBegin = (formula[i] == '-') ? i : i + 1;
symbols.Append(new Symbol(SymbolType.OperatorAdd));
}
}
else if (formula[i] == '(')
{
currentDepth++;
}
else if (formula[i] == ')')
{
currentDepth--;
}
else if (formula[i] == '^')
{
i = SolverTools.ParseUntilEndOfExponent(formula, i + 1, end) - 1;
}
}
// If at this point we only have one real number left, just return it as a simple value.
if (symbols.Length == 1 && symbols.first.type == SymbolType.RealValue)
{
return(symbols.first);
}
// We don't have that single expression, but:
// Now that we are here, we have symbol list which consists of only addition operators and value types. This is a great place to sum constant values together!
double constantSum = 0;
bool addedConstants = false;
for (int j = 0; j < symbols.Length; j++)
{
Symbol s = symbols.getSymbol(j);
if (s.IsImmutableConstant() && s.IsRealValueType())
{
constantSum += s.value;
addedConstants = true;
if (j == symbols.Length - 1)
{
// Destroy preceding +
symbols.symbols.RemoveAt(j);
break;
}
symbols.symbols.RemoveAt(j);
symbols.symbols.RemoveAt(j);
j--;
}
else
{
// Skip the following + symbol
j++;
}
}
if (addedConstants)
{
if (symbols.Length > 0 && symbols.getSymbol(symbols.Length - 1).IsRealValueType())
{
symbols.Append(new Symbol(SymbolType.OperatorAdd));
}
symbols.Append(new Symbol(constantSum));
}
// Finally, if the symbolicated sum is just a single real number, even varying, return just a simple symbol
if (symbols.Length == 1 && symbols.getSymbol(0).type == SymbolType.RealValue)
{
Symbol s = symbols.getSymbol(0);
return(s);
}
// Optimization: get rid of unnecessary jumps to subexpressions
for (int j = 0; j < symbols.Length; j++)
{
var s = symbols.getSymbol(j);
if (s.type == SymbolType.SubExpression)
{
var subExpression = s.subExpression;
int subExpressionLength = subExpression.Length;
s.CopyValuesFrom(subExpression.first);
for (int k = 1; k < subExpressionLength; k++)
{
symbols.InsertBefore(j + k, subExpression.getSymbol(k));
}
j += subExpressionLength;
}
}
// We have turned the formula into a subexpression symbol
Symbol returnSymbol = new Symbol(symbols);
returnSymbol.Simplify();
return(returnSymbol);
}
Symbol SymbolicateMonome(string formula, int begin, int end, Expression exp)
{
var symbols = new SymbolList();
int sign = 0;
int i = begin - 1;
int currentTermBegin = begin;
int numValues = 0;
int currentDepth = 0;
double constMultiplier = 1.0;
bool divideNext = false;
bool constMultiplierUsed = false;
for (;;)
{
i++;
if (i == end || (currentDepth == 0 && i > begin && (formula[i] == '*' || formula[i] == '/')))
{
numValues++;
// Unless we are dealing with a monome, symbolicate the term
Symbol newSymbol = SymbolicateValue(formula, formula[currentTermBegin] == '-' ? currentTermBegin + 1 : currentTermBegin, i, exp);
// Check if we can simplify the generated symbol
if (newSymbol.IsImmutableConstant() && newSymbol.IsRealValueType())
{
// Constants are multiplied/divided together
if (divideNext)
{
constMultiplier /= GetSymbolValue(newSymbol);
}
else
{
constMultiplier *= GetSymbolValue(newSymbol);
}
constMultiplierUsed = true;
}
else
{
if (divideNext)
{
symbols.Append(new Symbol(SymbolType.OperatorDivide));
}
newSymbol.Simplify();
symbols.Append(newSymbol);
}
if (i == end)
{
break;
}
divideNext = formula[i] == '/';
currentTermBegin = i + 1;
}
else if (formula[i] == '(')
{
currentDepth++;
}
else if (formula[i] == ')')
{
currentDepth--;
}
else if (formula[i] == '-' && currentDepth == 0 && !(i > begin && formula[i - 1] == '^'))
{
sign++;
}
}
// If the generated monome has negative number of minus signs, then we append *-1 to end of the list, or if the preceding symbol is constant real number that is part of a monome, we multiply it.
if (sign % 2 == 1)
{
constMultiplier = -constMultiplier;
}
if (constMultiplierUsed || sign % 2 == 1)
{
// Add the const multiplier to the expression
if (symbols.Length > 0 && symbols.first.type == SymbolType.OperatorDivide)
{
// Put to the begin of the expression we are building
symbols.symbols.Insert(0, new Symbol(constMultiplier));
}
else if (symbols.Length > 0 && symbols.last.type == SymbolType.SubExpression && symbols.last.IsMonome())
{
// Add inside the last subexpression
SymbolList leftSideExpression = symbols.last.subExpression;
if (leftSideExpression.last.type == SymbolType.RealValue && leftSideExpression.last.IsImmutableConstant())
{
leftSideExpression.SetSymbolAtIndex(leftSideExpression.Length - 1, new Symbol(leftSideExpression.last.value * constMultiplier));
}
else
{
leftSideExpression.Append(new Symbol(constMultiplier));
}
}
else
{
// Put to the end of the expression we are building
symbols.Append(new Symbol(constMultiplier));
}
}
// Check if the final monome is just a real number, in which case we don't have to return a subexpression type
if (symbols.Length == 1 && symbols.first.IsImmutableConstant() && symbols.first.IsRealValueType())
{
return(symbols.first.type == SymbolType.RealValue ? symbols.first : new Symbol(GetSymbolValue(symbols.first)));
}
Symbol s = new Symbol(SymbolType.SubExpression);
s.subExpression = symbols;
s.Simplify();
return(s);
}
Symbol SymbolicateValue(string formula, int begin, int end, Expression exp)
{
if (formula[begin] == '+')
{
begin++;
}
// Check for string value
if (formula[begin] == '\'' && formula[end - 1] == '\'')
{
var svalue = formula.Substring(begin + 1, end - begin - 2).Replace("\\'", "'");
return(new Symbol(svalue));
}
int depth = 0;
for (int k = begin; k < end; k++)
{
if (formula[k] == '(')
{
depth++;
}
else if (formula[k] == ')')
{
depth--;
}
else if (depth == 0 && formula[k] == '^')
{
// Check for small integer powers: they will be done using multiplication instead!
Symbol lhs = Symbolicate(formula, begin, k, exp);
Symbol rhs = Symbolicate(formula, k + 1, end, exp);
var newSubExpression = new SymbolList();
if (end - k - 1 == 1 && lhs.type == SymbolType.RealValue && formula.Substring(k + 1, end - k - 1) == "2")
{
// Second power found
newSubExpression.Append(lhs);
newSubExpression.Append(lhs);
}
else if (end - k - 1 == 1 && lhs.type == SymbolType.RealValue && formula.Substring(k + 1, end - k - 1) == "3")
{
// Second power found
newSubExpression.Append(lhs);
newSubExpression.Append(lhs);
newSubExpression.Append(lhs);
}
else
{
newSubExpression.Append(new Symbol(SymbolType.Pow));
newSubExpression.Append(lhs);
newSubExpression.Append(rhs);
}
Symbol newSymbol = new Symbol(SymbolType.SubExpression);
newSymbol.subExpression = newSubExpression;
return(newSymbol);
}
}
if (formula[begin] == '(' && formula[end - 1] == ')')
{
var s = Symbolicate(formula, begin + 1, end - 1, exp);
s.Simplify();
return(s);
}
double valueAsRealNumber;
if (double.TryParse(formula.Substring(begin, end - begin), out valueAsRealNumber))
{
return(new Symbol(valueAsRealNumber));
}
// Check if the value is transformed by a function
if (formula[end - 1] == ')')
{
int i = begin;
while (i < end - 1)
{
if (formula[i] == '(')
{
break;
}
i++;
}
string funcName = formula.Substring(begin, i - begin);
CustomFunction customFunc;
if (customFuncs.TryGetValue(funcName, out customFunc))
{
int requiredParameterCount = customFunc.paramCount;
int foundParameterCount = SolverTools.CountParameters(formula, begin, end);
if (requiredParameterCount == foundParameterCount)
{
if (requiredParameterCount == 1)
{
SymbolList newSubExpression = new SymbolList();
newSubExpression.Append(new Symbol(customFunc));
newSubExpression.Append(Symbolicate(formula, i + 1, end - 1, exp));
return(new Symbol(newSubExpression));
}
else
{
List <SolverTools.IntPair> parameters = SolverTools.ParseParameters(formula, i, end);
SymbolList newSubExpression = new SymbolList();
newSubExpression.Append(new Symbol(customFunc));
for (int k = 0; k < requiredParameterCount; k++)
{
Symbol p = Symbolicate(formula, parameters[k].first, parameters[k].second, exp);
newSubExpression.Append(p);
}
Symbol newSymbol = new Symbol(SymbolType.SubExpression);
newSymbol.subExpression = newSubExpression;
return(newSymbol);
}
}
else
{
throw new ESInvalidParametersException(customFunc.name + " expects " + requiredParameterCount + " parameters, " + foundParameterCount + " given.");
}
}
else
{
throw new ESInvalidFunctionNameException(funcName);
}
}
var valueName = formula.Substring(begin, end - begin);
// Then a local constant specific to our expression
Variable variable;
if (exp.constants.TryGetValue(valueName, out variable))
{
return(new Symbol(variable));
}
// Non immutable globals
if (globalConstants.TryGetValue(valueName, out variable))
{
return(new Symbol(variable));
}
// Immutable globals
double constDouble;
if (immutableGlobalConstants.TryGetValue(valueName, out constDouble))
{
return(new Symbol(constDouble));
}
// Found an unknown value name. Check policy to see what to do.
Variable v = null;
switch (undefinedVariablePolicy)
{
case UndefinedVariablePolicy.DefineExpressionLocalVariable:
v = new Variable(valueName, 0);
exp.constants.Add(valueName, v);
return(new Symbol(v));
case UndefinedVariablePolicy.DefineGlobalVariable:
v = new Variable(valueName, 0);
globalConstants.Add(valueName, v);
return(new Symbol(v));
default:
throw new ESUnknownExpressionException(valueName);
}
}
Symbol SymbolicateValue(string formula, int begin, int end, Expression exp)
{
if (formula[begin] == '+')
{
begin++;
}
// Check for string value
if (formula[begin] == '\'' && formula[end - 1] == '\'')
{
var svalue = formula.Substring(begin+1,end-begin-2).Replace("\\'","'");
return new Symbol(svalue);
}
int depth=0;
for (int k = begin; k < end; k++)
{
if (formula[k]=='(')
depth++;
else if (formula[k]==')')
depth--;
else if (depth == 0 && formula[k] == '^')
{
// Check for small integer powers: they will be done using multiplication instead!
Symbol lhs = Symbolicate(formula,begin,k,exp);
Symbol rhs = Symbolicate(formula,k+1,end,exp);
var newSubExpression = new SymbolList();
if (end-k-1 == 1 && lhs.type == SymbolType.RealValue && formula.Substring(k+1,end-k-1)=="2")
{
// Second power found
newSubExpression.Append(lhs);
newSubExpression.Append(lhs);
}
else if (end-k-1 == 1 && lhs.type == SymbolType.RealValue && formula.Substring(k+1,end-k-1)=="3")
{
// Second power found
newSubExpression.Append(lhs);
newSubExpression.Append(lhs);
newSubExpression.Append(lhs);
}
else
{
newSubExpression.Append(new Symbol(SymbolType.Pow));
newSubExpression.Append(lhs);
newSubExpression.Append(rhs);
}
Symbol newSymbol = new Symbol(SymbolType.SubExpression);
newSymbol.subExpression = newSubExpression;
return newSymbol;
}
}
if (formula[begin] == '(' && formula[end - 1] == ')')
{
var s = Symbolicate(formula, begin + 1, end - 1,exp);
s.Simplify();
return s;
}
double valueAsRealNumber;
if (double.TryParse(formula.Substring(begin,end-begin),out valueAsRealNumber))
{
return new Symbol(valueAsRealNumber);
}
// Check if the value is transformed by a function
if (formula[end-1]==')') {
int i = begin;
while (i < end-1) {
if (formula[i]=='(') {
break;
}
i++;
}
string funcName = formula.Substring(begin,i-begin);
CustomFunction customFunc;
if (customFuncs.TryGetValue(funcName,out customFunc))
{
int requiredParameterCount = customFunc.paramCount;
int foundParameterCount = SolverTools.CountParameters(formula,begin,end);
if (requiredParameterCount == foundParameterCount) {
if (requiredParameterCount == 1) {
SymbolList newSubExpression = new SymbolList();
newSubExpression.Append(new Symbol(customFunc));
newSubExpression.Append(Symbolicate(formula,i+1,end-1,exp));
return new Symbol(newSubExpression);
}
else {
List<SolverTools.IntPair> parameters = SolverTools.ParseParameters(formula,i,end);
SymbolList newSubExpression = new SymbolList();
newSubExpression.Append(new Symbol(customFunc));
for (int k=0;k<requiredParameterCount;k++) {
Symbol p = Symbolicate(formula,parameters[k].first,parameters[k].second,exp);
newSubExpression.Append(p);
}
Symbol newSymbol = new Symbol(SymbolType.SubExpression);
newSymbol.subExpression = newSubExpression;
return newSymbol;
}
}
else
{
throw new ESInvalidParametersException(customFunc.name + " expects " + requiredParameterCount + " parameters, " + foundParameterCount + " given.");
}
}
else
{
throw new ESInvalidFunctionNameException(funcName);
}
}
var valueName = formula.Substring(begin,end-begin);
// Then a local constant specific to our expression
Variable variable;
if (exp.constants.TryGetValue(valueName,out variable)) {
return new Symbol(variable);
}
// Non immutable globals
if (globalConstants.TryGetValue(valueName,out variable)) {
return new Symbol(variable);
}
// Immutable globals
double constDouble;
if (immutableGlobalConstants.TryGetValue(valueName, out constDouble))
{
return new Symbol(constDouble);
}
// Found an unknown value name. Check policy to see what to do.
Variable v = null;
switch (undefinedVariablePolicy)
{
case UndefinedVariablePolicy.DefineExpressionLocalVariable:
v = new Variable(valueName,0);
exp.constants.Add(valueName,v);
return new Symbol(v);
case UndefinedVariablePolicy.DefineGlobalVariable:
v = new Variable(valueName,0);
globalConstants.Add(valueName,v);
return new Symbol(v);
default:
throw new ESUnknownExpressionException(valueName);
}
}
Symbol SymbolicateMonome(string formula, int begin, int end, Expression exp)
{
var symbols = new SymbolList();
int sign = 0;
int i = begin - 1;
int currentTermBegin = begin;
int numValues = 0;
int currentDepth = 0;
double constMultiplier = 1.0;
bool divideNext = false;
bool constMultiplierUsed = false;
for (;;)
{
i++;
if (i == end || (currentDepth == 0 && i > begin && (formula[i] == '*' || formula[i] == '/')))
{
numValues++;
// Unless we are dealing with a monome, symbolicate the term
Symbol newSymbol = SymbolicateValue(formula, formula[currentTermBegin] == '-' ? currentTermBegin + 1 : currentTermBegin, i,exp);
// Check if we can simplify the generated symbol
if (newSymbol.IsImmutableConstant() && newSymbol.IsRealValueType())
{
// Constants are multiplied/divided together
if (divideNext)
constMultiplier /= GetSymbolValue(newSymbol);
else
constMultiplier *= GetSymbolValue(newSymbol);
constMultiplierUsed = true;
}
else
{
if (divideNext)
symbols.Append(new Symbol(SymbolType.OperatorDivide));
newSymbol.Simplify();
symbols.Append(newSymbol);
}
if (i == end) {
break;
}
divideNext = formula[i] == '/';
currentTermBegin = i + 1;
}
else if (formula[i] == '(')
{
currentDepth++;
}
else if (formula[i] == ')')
{
currentDepth--;
}
else if (formula[i] == '-' && currentDepth == 0 && !(i>begin && formula[i-1] == '^') )
{
sign++;
}
}
// If the generated monome has negative number of minus signs, then we append *-1 to end of the list, or if the preceding symbol is constant real number that is part of a monome, we multiply it.
if (sign % 2 == 1)
{
constMultiplier =-constMultiplier;
}
if (constMultiplierUsed || sign % 2 == 1)
{
// Add the const multiplier to the expression
if (symbols.Length>0 && symbols.first.type==SymbolType.OperatorDivide)
{
// Put to the begin of the expression we are building
symbols.symbols.Insert(0,new Symbol(constMultiplier));
}
else if (symbols.Length > 0 && symbols.last.type == SymbolType.SubExpression && symbols.last.IsMonome())
{
// Add inside the last subexpression
SymbolList leftSideExpression = symbols.last.subExpression;
if (leftSideExpression.last.type==SymbolType.RealValue && leftSideExpression.last.IsImmutableConstant())
{
leftSideExpression.SetSymbolAtIndex(leftSideExpression.Length-1,new Symbol(leftSideExpression.last.value*constMultiplier));
}
else
{
leftSideExpression.Append(new Symbol(constMultiplier));
}
}
else
{
// Put to the end of the expression we are building
symbols.Append(new Symbol(constMultiplier));
}
}
// Check if the final monome is just a real number, in which case we don't have to return a subexpression type
if (symbols.Length == 1 && symbols.first.IsImmutableConstant() && symbols.first.IsRealValueType())
{
return symbols.first.type == SymbolType.RealValue ? symbols.first : new Symbol(GetSymbolValue(symbols.first));
}
Symbol s = new Symbol(SymbolType.SubExpression);
s.subExpression = symbols;
s.Simplify();
return s;
}
Symbol Symbolicate(string formula, int begin, int end, Expression exp)
{
var symbols = new SymbolList();
int i = begin - 1;
int currentTermBegin = formula[begin] == '+' ? begin + 1 : begin;
int currentDepth = 0;
for (;;)
{
i++;
if (i == end || (currentDepth == 0 && i > begin && (formula[i - 1] != '*' && formula[i - 1] != '/') && (formula[i] == '+' || formula[i] == '-')))
{
symbols.Append(SymbolicateMonome(formula, currentTermBegin, i,exp));
if (i == end)
{
break;
}
else {
// The sign of the term is included in the next monome only if its minus
currentTermBegin = (formula[i] == '-') ? i : i + 1;
symbols.Append(new Symbol(SymbolType.OperatorAdd));
}
}
else if (formula[i] == '(')
{
currentDepth++;
}
else if (formula[i] == ')')
{
currentDepth--;
}
else if (formula[i] == '^')
{
i = SolverTools.ParseUntilEndOfExponent(formula,i+1,end) - 1;
}
}
// If at this point we only have one real number left, just return it as a simple value.
if (symbols.Length == 1 && symbols.first.type == SymbolType.RealValue)
{
return symbols.first;
}
// We don't have that single expression, but:
// Now that we are here, we have symbol list which consists of only addition operators and value types. This is a great place to sum constant values together!
double constantSum = 0;
bool addedConstants = false;
for (int j = 0; j < symbols.Length; j++)
{
Symbol s = symbols.getSymbol(j);
if (s.IsImmutableConstant() && s.IsRealValueType()) {
constantSum += s.value;
addedConstants = true;
if (j == symbols.Length - 1)
{
// Destroy preceding +
symbols.symbols.RemoveAt (j);
break;
}
symbols.symbols.RemoveAt(j);
symbols.symbols.RemoveAt(j);
j--;
}
else
{
// Skip the following + symbol
j++;
}
}
if (addedConstants)
{
if (symbols.Length > 0 && symbols.getSymbol(symbols.Length - 1).IsRealValueType())
{
symbols.Append(new Symbol(SymbolType.OperatorAdd));
}
symbols.Append(new Symbol(constantSum));
}
// Finally, if the symbolicated sum is just a single real number, even varying, return just a simple symbol
if (symbols.Length == 1 && symbols.getSymbol(0).type == SymbolType.RealValue)
{
Symbol s = symbols.getSymbol(0);
return s;
}
// Optimization: get rid of unnecessary jumps to subexpressions
for (int j=0;j<symbols.Length;j++)
{
var s = symbols.getSymbol(j);
if (s.type==SymbolType.SubExpression)
{
var subExpression = s.subExpression;
int subExpressionLength = subExpression.Length;
s.CopyValuesFrom(subExpression.first);
for (int k=1;k<subExpressionLength;k++)
{
symbols.InsertBefore(j+k,subExpression.getSymbol(k));
}
j += subExpressionLength;
}
}
// We have turned the formula into a subexpression symbol
Symbol returnSymbol = new Symbol(symbols);
returnSymbol.Simplify();
return returnSymbol;
}