/// <summary>
/// Checks whether a tree has a fiction
/// </summary>
/// <param name="tree">The tree</param>
/// <returns>True if operation has fictoin</returns>
static public bool HasFiction(this ObjectFormulaTree tree)
{
if (tree == null)
{
return(true);
}
IObjectOperation op = tree.Operation;
if (op == null)
{
return(true);
}
if (StaticExtensionBaseTypes.HasAttributeBT <Attributes.FictionAttribute>(op))
{
return(true);
}
for (int i = 0; i < tree.Count; i++)
{
if (tree[i].HasFiction())
{
return(true);
}
}
return(false);
}
MathFormula IFormulaCreatorOperation.CreateFormula(ObjectFormulaTree tree, byte level, int[] sizes)
{
MathFormula form = new MathFormula(level, sizes);
for (int i = 0; i < 2; i++)
{
IFormulaCreatorOperation op = tree[i].Operation as IFormulaCreatorOperation;
MathFormula f = op.CreateFormula(tree[i], level, sizes);
MathFormula fp = null;
if (op.OperationPriority < (int)ElementaryOperationPriorities.Divide)
{
fp = new MathFormula(level, sizes);
MathSymbol s = new BracketsSymbol();
s.Append(fp);
fp.First[0] = f;
}
else
{
fp = f;
}
form.Add(fp);
if (i == 0)
{
MathSymbol s = new BinarySymbol(symbol);
s.Append(form);
}
}
return(form);
}
/// <summary>
/// Gets unary indexes of tree
/// </summary>
/// <param name="tree">The tree</param>
/// <returns>List of indexes</returns>
public static List <int> GetUnaryIndexes(ObjectFormulaTree tree)
{
List <int> l = new List <int>();
GetUnaryIndexes(tree, l);
l.Sort();
return(l);
}
/// <summary>
/// Gets conditional value of tree
/// </summary>
/// <param name="tree">The tree</param>
/// <returns>Conditional value</returns>
public static object GetValue(ObjectFormulaTree tree)
{
if (!IsConst(tree))
{
return(null);
}
return(tree.Result);
}
/// <summary>
/// Creates distribution from formula tree
/// </summary>
/// <param name="tree">The tree</param>
/// <returns>The distribution</returns>
static public IDistribution GetDistribution(ObjectFormulaTree tree)
{
if (!CheckDelta(tree))
{
return(null);
}
return(new FormulaDistribution(tree));
}
/// <summary>
/// Calculates derivation
/// </summary>
/// <param name="tree">The function for derivation calculation</param>
/// <param name="variableName">Derivation string</param>
/// <returns>The derivation</returns>
public ObjectFormulaTree Derivation(ObjectFormulaTree tree, string variableName)
{
Double a = 0;
bool[] b = new bool[] { false, false };
ObjectFormulaTree[] fc = new ObjectFormulaTree[2];
ObjectFormulaTree[] fd = new ObjectFormulaTree[2];
for (int i = 0; i < 2; i++)
{
fc[i] = tree[1 - i];
fd[i] = fc[i].Derivation(variableName);
b[i] = ZeroPerformer.IsZero(fd[i]);
}
if (b[0] & b[1])
{
return(ElementaryRealConstant.RealZero);
}
IObjectOperation nom = new ElementaryBinaryOperation('-', new object[] { a, a });
List <ObjectFormulaTree> nomList = new List <ObjectFormulaTree>();
for (int i = 0; i < 2; i++)
{
List <ObjectFormulaTree> l = new List <ObjectFormulaTree>();
l.Add(fd[1 - i]); //.Clone() as ObjectFormulaTree);
l.Add(fc[i]); //.Clone() as ObjectFormulaTree);
IObjectOperation o = new ElementaryBinaryOperation('*', new object[] { a, a });
nomList.Add(new ObjectFormulaTree(o, l));
}
List <ObjectFormulaTree> list = new List <ObjectFormulaTree>();
if (b[0] | b[1])
{
for (int i = 0; i < 2; i++)
{
if (b[i])
{
List <ObjectFormulaTree> lt = new List <ObjectFormulaTree>();
lt.Add(nomList[i]);
list.Add(new ObjectFormulaTree(new ElementaryFunctionOperation('-'), lt));
}
}
}
else
{
list.Add(new ObjectFormulaTree(nom, nomList));
}
IObjectOperation square = ElementaryFunctionsCreator.Object.GetPowerOperation(a, a);
List <ObjectFormulaTree> squareList = new List <ObjectFormulaTree>();
squareList.Add(fc[0]);
squareList.Add(new ObjectFormulaTree(new ElementaryRealConstant(2), new List <ObjectFormulaTree>()));
list.Add(new ObjectFormulaTree(square, squareList));
if (list.Count != 2)
{
// list = list;
}
return(new ObjectFormulaTree(new ElementaryFraction(), list));
}
/// <summary>
/// Initialization of derivation calculation functions
/// </summary>
public static void InitDeri()
{
functionDerivations = new ObjectFormulaTree[formStrings.Length];
for (int i = 0; i < formStrings.Length; i++)
{
MathFormula f = MathFormula.FromString(MAX_SIZES, formStrings[i]);
functionDerivations[i] = ObjectFormulaTree.CreateTree(f.FullTransform(null));
}
}
/// <summary>
/// Simplfies tree
/// </summary>
/// <param name="tree">Simplfied tree</param>
/// <returns>Simplfication result</returns>
public override ObjectFormulaTree Simplify(ObjectFormulaTree tree)
{
ObjectFormulaTree t = tree;//.Clone() as ObjectFormulaTree;
t = simplify(t);
t = PolyMult.MultMult(t);
t = simplify(t);
return(PolyMult.MultMultReverse(t));
}
private static ObjectFormulaTree sumSum(ObjectFormulaTree tree)
{
List <ObjectFormulaTree> l = new List <ObjectFormulaTree>();
for (int i = 0; i < tree.Count; i++)
{
ObjectFormulaTree t = tree[i];
// t = ElementaryFormulaSimplification.Object.Simplify(t);
l.Add(sumSum(t));
}
IObjectOperation op = tree.Operation;
if (op is ElementaryBinaryOperation)
{
ElementaryBinaryOperation bo = op as ElementaryBinaryOperation;
char c = bo.Symbol;
PolySum ps = new PolySum(true);
if (c == '+' | c == '-')
{
bool b = c == '+';
PolySum p = new PolySum(true);
Dictionary <ObjectFormulaTree, bool> dic = p.summands;
for (int i = 0; i < l.Count; i++)
{
ObjectFormulaTree t = l[i];
if (PolyMult.IsZero(t))
{
continue;
}
bool kb = true;
if (i > 0)
{
kb = b;
}
IObjectOperation oo = t.Operation;
if (oo is PolySum)
{
PolySum pss = oo as PolySum;
Dictionary <ObjectFormulaTree, bool> d = pss.summands;
foreach (ObjectFormulaTree tr in d.Keys)
{
bool rb = d[tr];
if (!kb)
{
rb = !rb;
}
dic[tr] = rb;
}
continue;
}
dic[t] = kb;
}
return(new ObjectFormulaTree(p, new List <ObjectFormulaTree>()));
}
}
return(new ObjectFormulaTree(op, l));
}
/// <summary>
/// Checks whether tree is zero
/// </summary>
/// <param name="tree">The tree</param>
/// <returns>True in case of zero and false otherwise</returns>
static public bool IsZero(ObjectFormulaTree tree)
{
IObjectOperation op = tree.Operation;
if (op is ISupportsZero)
{
ISupportsZero sz = op as ISupportsZero;
return(sz.IsZero(tree));
}
return(false);
}
internal Variable(IObjectOperation variable, ObjectFormulaTree[] children)
{
this.variable = variable;
this.children = children;
type = children[0].ReturnType;
types = new object[] { type };
ArrayReturnType art = children[0].ReturnType as ArrayReturnType;
retType = art.ElementType;
tree = Convert(children[1]);
}
internal static ObjectFormulaTree signed(ObjectFormulaTree tree, bool sign)
{
if (sign)
{
return(tree);
}
ElementaryFunctionOperation eo = new ElementaryFunctionOperation('-');
List <ObjectFormulaTree> l = new List <ObjectFormulaTree>();
l.Add(tree);
return(new ObjectFormulaTree(eo, l));
}
/// <summary>
/// Creates formula
/// </summary>
/// <param name="tree">Operation tree</param>
/// <param name="level">Formula level</param>
/// <param name="sizes">Sizes of symbols</param>
/// <returns>The formula</returns>
public MathFormula CreateFormula(ObjectFormulaTree tree, byte level, int[] sizes)
{
MathFormula form = new MathFormula(level, sizes);
MathSymbol sym = new SeriesSymbol(index);
sym.Append(form);
sym = new BracketsSymbol();
sym.Append(form);
form.Last[0] = FormulaCreator.CreateFormula(tree[0], level, sizes);
form.Last[1] = new MathFormula((byte)(level + 1), sizes);
return(form);
}
/// <summary>
/// Creates formula
/// </summary>
/// <param name="tree">Operation tree</param>
/// <param name="level">Formula level</param>
/// <param name="sizes">Sizes of symbols</param>
/// <returns>The formula</returns>
public MathFormula CreateFormula(ObjectFormulaTree tree, byte level, int[] sizes)
{
MathFormula form = new MathFormula(level, sizes);
BinaryFunctionSymbol atan = new BinaryFunctionSymbol('A', "atan2");
atan.Append(form);
for (int i = 0; i < 2; i++)
{
form.First[i] = FormulaCreator.CreateFormula(tree[i], level, sizes);
}
return(form);
}
/// <summary>
/// Calculates derivation
/// </summary>
/// <param name="tree">The function for derivation calculation</param>
/// <param name="variableName">Name of variable</param>
/// <returns>The derivation</returns>
public ObjectFormulaTree Derivation(ObjectFormulaTree tree, string variableName)
{
if (arity == 1)
{
return(tree[0].Derivation(variableName));
}
IDerivationOperation pow =
ElementaryFunctionsCreator.Object.GetPowerOperation(tree[0].ReturnType, tree[1].ReturnType)
as IDerivationOperation;
return(pow.Derivation(tree, variableName));
}
/// <summary>
/// Creates formula
/// </summary>
/// <param name="tree">Operation tree</param>
/// <param name="level">Formula level</param>
/// <param name="sizes">Sizes of symbols</param>
/// <returns>The formula</returns>
public MathFormula CreateFormula(ObjectFormulaTree tree, byte level, int[] sizes)
{
MathFormula form = new MathFormula(level, sizes);
MathSymbol sym = new FractionSymbol();
sym.Append(form);
for (int i = 0; i < 2; i++)
{
form.First[i] = FormulaCreator.CreateFormula(tree[i], level, sizes);
}
return(form);
}
private void Normalize()
{
if (operation is ElementaryBrackets)
{
ObjectFormulaTree tr = children[0];
children = tr.children;
operation = tr.Operation;
y = tr.y;
result = tr.result;
tag = tr.tag;
}
}
/// <summary>
/// Creates formula
/// </summary>
/// <param name="tree">Operation tree</param>
/// <param name="level">Formula level</param>
/// <param name="sizes">Sizes of symbols</param>
/// <returns>The formula</returns>
public MathFormula CreateFormula(ObjectFormulaTree tree, byte level, int[] sizes)
{
MathFormula form = new MathFormula(level, sizes);
MathFormula f = new MathFormula(level, sizes);
MathSymbol sym = new SimpleSymbol('¬', (byte)FormulaConstants.Unary, false, "¬");
sym.Append(form);
sym = new BracketsSymbol();
sym.Append(form);
form.Last[0] = FormulaCreator.CreateFormula(tree[0], level, sizes);
return(form);
}
/// <summary>
/// Calculates derivation
/// </summary>
/// <param name="tree">The function for derivation calculation</param>
/// <param name="s">Derivation string</param>
/// <returns>The derivation</returns>
public ObjectFormulaTree Derivation(ObjectFormulaTree tree, string s)
{
int i = 0;
if (symbol == '-')
{
i = functionDerivations.Length - 1;
}
else
{
i = MathSymbol.FUNCTIONS.IndexOf(symbol);
}
return(Derivation(tree, i, s));
}
static internal ObjectFormulaTree reduceTree(ObjectFormulaTree tree, bool simple)
{
bool b;
simple = true;
ObjectFormulaTree t = reduce(tree);
ObjectFormulaTree st = simplify(t, out b);
if (!b)
{
simple = false;
}
return(st);
}
private static void AddUnique(ObjectFormulaTree tree, List <ObjectFormulaTree> l)
{
foreach (ObjectFormulaTree t in tree.children)
{
if (l.Contains(t))
{
continue;
}
AddUnique(t, l);
}
if (!l.Contains(tree))
{
l.Add(tree);
}
}
/// <summary>
/// Resets distributons of tree
/// </summary>
/// <param name="tree">The tree</param>
static public void Reset(ObjectFormulaTree tree)
{
IObjectOperation op = tree.Operation;
if (op is IDistribution)
{
IDistribution d = op as IDistribution;
d.Reset();
return;
}
for (int i = 0; i < tree.Count; i++)
{
Reset(tree[i]);
}
}
/// <summary>
/// Gets integral of multiplication
/// </summary>
/// <param name="tree">The tree</param>
/// <returns>The integral</returns>
private static double getMult(ObjectFormulaTree tree)
{
double a = Integral(tree[0]);
double b = Integral(tree[1]);
if (a != 0)
{
return(a * (double)tree[1].Result);
}
if (b != 0)
{
return(b * (double)tree[0].Result);
}
return(0);
}
private ObjectFormulaTree simplify(ObjectFormulaTree tree)
{
ObjectFormulaTree t = tree;
while (true)
{
bool b;
t = PolyMult.simplify(t, out b);
t = PolySum.Simplify(t, ref b);
if (b)
{
break;
}
}
return(t);
}
static private ObjectFormulaTree simplifyRecursive(ObjectFormulaTree tree)
{
ObjectFormulaTree t = tree;
while (true)
{
bool b;
t = simplify(t, out b);
// t = PolyMult.Simplify(t, ref b);
if (b)
{
break;
}
}
return(t);
}
/// <summary>
/// Creates formula
/// </summary>
/// <param name="tree">Operation tree</param>
/// <param name="level">Formula level</param>
/// <param name="sizes">Sizes of symbols</param>
/// <returns>The formula</returns>
public MathFormula CreateFormula(ObjectFormulaTree tree, byte level, int[] sizes)
{
MathFormula form = new MathFormula(level, sizes);
MathSymbol sym = null;
if (symbol is Char)
{
sym = new SimpleSymbol((char)symbol);
}
else if (symbol is StringPair)
{
StringPair sp = symbol as StringPair;
sym = new SubscriptedSymbol(sp.First, sp.Second);
}
sym.Append(form);
return(form);
}
/// <summary>
/// Creates formula
/// </summary>
/// <param name="tree">Operation tree</param>
/// <param name="level">Formula level</param>
/// <param name="sizes">Sizes of symbols</param>
/// <returns>The formula</returns>
public MathFormula CreateFormula(ObjectFormulaTree tree, byte level, int[] sizes)
{
MathFormula f = FormulaCreator.CreateFormula(tree[0], level, sizes);
MathFormula form = new MathFormula(level, sizes);
AbsSymbol root = new AbsSymbol();
root.Append(form);
form.First[0] = f;
if (arity == 1)
{
return(form);
}
MathFormula p = FormulaCreator.CreateFormula(tree[1], (byte)((int)level + 1), sizes);
form.First[1] = p;
return(form);
}
/// <summary>
/// Inserts formula instead variable
/// </summary>
/// <param name="tree">Prototype</param>
/// <param name="insert">Inerted formula</param>
/// <returns>Result of the operation</returns>
private static ObjectFormulaTree insertVariable(ObjectFormulaTree tree, ObjectFormulaTree insert)
{
Double a = 0;
if (tree.Operation is ElementaryObjectVariable & tree.ReturnType.Equals(a))
{
return(insert);//.Clone() as ObjectFormulaTree;
}
List <ObjectFormulaTree> children = new List <ObjectFormulaTree>();
for (int i = 0; i < tree.Count; i++)
{
ObjectFormulaTree t = tree[i];//.Clone() as ObjectFormulaTree;
children.Add(insertVariable(t, insert));
}
return(new ObjectFormulaTree(tree.Operation, children));
}
/// <summary>
/// Creates formula
/// </summary>
/// <param name="tree">Operation tree</param>
/// <param name="level">Formula level</param>
/// <param name="sizes">Sizes of symbols</param>
/// <returns>The formula</returns>
public MathFormula CreateFormula(ObjectFormulaTree tree, byte level, int[] sizes)
{
MathFormula form = new MathFormula(level, sizes);
IFormulaCreatorOperation op = tree[0].Operation as IFormulaCreatorOperation;
MathFormula f = op.CreateFormula(tree[0], level, sizes);
MathSymbol s = new BracketsSymbol();
s.Append(form);
form.First[0] = f;
if (arity > 1)
{
IFormulaCreatorOperation opPower = tree[1].Operation as IFormulaCreatorOperation;
MathFormula p = opPower.CreateFormula(tree[0], level, sizes);
form.First[1] = p;
}
return(form);
}
/// <summary>
/// Checks whether tree is const
/// </summary>
/// <param name="tree">The tree</param>
/// <returns>True in case of const and false otherwise</returns>
public static bool IsConst(ObjectFormulaTree tree)
{
for (int i = 0; i < tree.Count; i++)
{
if (!IsConst(tree[i]))
{
return(false);
}
}
IObjectOperation op = tree.Operation;
if (op is ElementaryRealConstant)
{
return(true);
}
return(false);
}