public virtual double Laguerre(double lo, double hi, double fLo, double fHi)
{
Complex[] c = ComplexUtils.convertToComplex(Coefficients);
Complex initial = new Complex(0.5 * (lo + hi), 0);
Complex z = ComplexSolver.Solve(c, initial);
if (ComplexSolver.IsRoot(lo, hi, z))
{
return z.Real;
}
else
{
double r = double.NaN;
// Solve all roots and select the one we are seeking.
Complex[] root = ComplexSolver.SolveAll(c, initial);
for (int i = 0; i < root.Length; i++)
{
if (ComplexSolver.IsRoot(lo, hi, root[i]))
{
r = root[i].Real;
break;
}
}
return r;
}
}
public virtual double Laguerre(double lo, double hi, double fLo, double fHi)
{
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final org.apache.commons.math3.complex.Complex c[] = org.apache.commons.math3.complex.ComplexUtils.convertToComplex(getCoefficients());
Complex[] c = ComplexUtils.ConvertToComplex(GetCoefficients());
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final org.apache.commons.math3.complex.Complex initial = new org.apache.commons.math3.complex.Complex(0.5 * (lo + hi), 0);
Complex initial = new Complex(0.5 * (lo + hi), 0);
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final org.apache.commons.math3.complex.Complex z = complexSolver.solve(c, initial);
Complex z = complexSolver.Solve(c, initial);
if (complexSolver.IsRoot(lo, hi, z))
{
return(z.GetReal());
}
else
{
double r = Double.NaN;
// Solve all roots and select the one we are seeking.
Complex[] root = complexSolver.SolveAll(c, initial);
for (int i = 0; i < root.Length; i++)
{
if (complexSolver.IsRoot(lo, hi, root[i]))
{
r = root[i].GetReal();
break;
}
}
return(r);
}
}
void paraDT(PolynomialTrie trie, out DataTable substitutaions, out DataTable definiteIntegral)
{
substitutaions = new DataTable("subtitutions in polynomial");
definiteIntegral = new DataTable("Definite integral on polynomial");
foreach (var title in Constants.SubstitutionColumnsName)
{
substitutaions.Columns.Add(title, typeof(string));
}
foreach (var title in Constants.DefiniteIntColumnsName)
{
definiteIntegral.Columns.Add(title, typeof(string));
}
Polynomial SoFar = new Polynomial();
Stack <Tuple <Node, Term, bool> > dfsStack = new Stack <Tuple <Node, Term, bool> >();
dfsStack.Push(new Tuple <Node, Term, bool>(trie.main.root, new Term(0, 0), false));
while (dfsStack.Count != 0)
{
if (dfsStack.Peek().Item3)
{
dfsStack.Pop();
if (SoFar.Count != 0)
{
SoFar.Remove(SoFar.Back.Degree);
}
continue;
}
Node current = dfsStack.Peek().Item1;
Term edge = dfsStack.Peek().Item2;
if (edge.Coefficient != 0)
{
SoFar.Add(edge);
}
dfsStack.Pop();
dfsStack.Push(new Tuple <Node, Term, bool>(current, edge, true));
foreach (var child in current._children)
{
dfsStack.Push(new Tuple <Node, Term, bool>(child.Value, new Term(child.Key), false));
}
if (current.isEnd)
{
substitutaions.Rows.Add(substitutaions.NewRow());
definiteIntegral.Rows.Add(definiteIntegral.NewRow());
int indexSub = substitutaions.Rows.Count - 1;
int indexDefint = definiteIntegral.Rows.Count - 1;
substitutaions.Rows[indexSub]["Polynomial"] = SoFar.ToString();
definiteIntegral.Rows[indexDefint]["Polynomial"] = SoFar.ToString();
bool foundSubstitution = false;
bool foundDefint = false;
foreach (var special in current._special)
{
if (special.Key == 's')
{
foundSubstitution = true;
foreach (var substitutaion in special.Value as paraStore)
{
substitutaions.Rows[indexSub]["X"] = ComplexUtils.ComplexToString(substitutaion.Key[0]);
substitutaions.Rows[indexSub]["Result"] = ComplexUtils.ComplexToString(substitutaion.Value);
}
}
else if (special.Key == 'd')
{
foundDefint = true;
foreach (var defint in special.Value as paraStore)
{
definiteIntegral.Rows[indexSub]["A"] = ComplexUtils.ComplexToString(defint.Key[0]);
definiteIntegral.Rows[indexSub]["B"] = ComplexUtils.ComplexToString(defint.Key[1]);
definiteIntegral.Rows[indexSub]["Result"] = ComplexUtils.ComplexToString(defint.Value);
}
}
}
if (!foundSubstitution)
{
substitutaions.Rows.RemoveAt(substitutaions.Rows.Count - 1);
}
if (!foundDefint)
{
definiteIntegral.Rows.RemoveAt(definiteIntegral.Rows.Count - 1);
}
}
}
}
DataTable OneOperationDT(PolynomialTrie trie)
{
DataTable result = new DataTable("Operations on one polynomial");
foreach (var title in Constants.OnePolynomialColumnsName)
{
result.Columns.Add(title.Value, typeof(string));
}
Polynomial SoFar = new Polynomial();
Stack <Tuple <Node, Term, bool> > dfsStack = new Stack <Tuple <Node, Term, bool> >();
dfsStack.Push(new Tuple <Node, Term, bool>(trie.main.root, new Term(0, 0), false));
while (dfsStack.Count != 0)
{
if (dfsStack.Peek().Item3)
{
dfsStack.Pop();
if (SoFar.Count != 0)
{
SoFar.Remove(SoFar.Back.Degree);
}
continue;
}
Node current = dfsStack.Peek().Item1;
Term edge = dfsStack.Peek().Item2;
if (edge.Coefficient != 0)
{
SoFar.Add(edge);
}
dfsStack.Pop();
dfsStack.Push(new Tuple <Node, Term, bool>(current, edge, true));
foreach (var child in current._children)
{
dfsStack.Push(new Tuple <Node, Term, bool>(child.Value, new Term(child.Key), false));
}
if (current.isEnd)
{
result.Rows.Add(result.NewRow());
int index = result.Rows.Count - 1;
result.Rows[index]["Polynomial"] = SoFar.ToString();
bool foundOperation = false;
foreach (var special in current._special)
{
if (Constants.operationsName[special.Key] == "Result")
{
foundOperation = true;
result.Rows[index][Constants.OnePolynomialColumnsName[special.Key]] = (special.Value as Polynomial).ToString();
}
else if (Constants.operationsName[special.Key] == "listComplex")
{
foundOperation = true;
result.Rows[index][Constants.OnePolynomialColumnsName[special.Key]] = ComplexUtils.ComplexListToString(special.Value as List <Complex>);
}
}
if (!foundOperation)
{
result.Rows.RemoveAt(result.Rows.Count - 1);
}
}
}
return(result);
}
XElement dfs(Node root)
{
XElement Xroot = new XElement("Node");
Stack <List <Object> > dfsStack = new Stack <List <Object> >();
dfsStack.Push(new List <Object>());
dfsStack.Peek().Add(Xroot);
dfsStack.Peek().Add(null);
dfsStack.Peek().Add(root);
while (dfsStack.Count != 0)
{
var temporaryList = dfsStack.Pop();
XElement Xcurrent = temporaryList[0] as XElement;
XElement Xparent = temporaryList[1] as XElement;
Node currentNode = temporaryList[2] as Node;
Xcurrent.Add(new XElement("isEnd", currentNode.isEnd.ToString()));
if (Xparent != null)
{
Xparent.Add(Xcurrent);
}
foreach (var edge in currentNode._children)
{
var newChild = new XElement("Node");
newChild.Add(new XElement("Edge",
new XElement("Degree", edge.Key.Key.ToString()),
new XElement("Coefficient",
new XElement("Real", edge.Key.Value.Real),
new XElement("Imaginary", edge.Key.Value.Imaginary))));
dfsStack.Push(new List <Object>());
dfsStack.Peek().Add(newChild);
dfsStack.Peek().Add(Xcurrent);
dfsStack.Peek().Add(edge.Value);
}
if (currentNode.isEnd)
{
foreach (var special in currentNode._special)
{
string Name = Constants.operationsName[special.Key];
XElement newChild = new XElement(Name);
if (Name == "listComplex")
{
foreach (var solution in (special.Value as List <Complex>))
{
newChild.Add(new XElement("root", ComplexUtils.ComplexToString(solution)));
}
}
else if (Name == "Result")
{
newChild.Add(new XElement("poly", special.Value.ToString()));
}
else if (Name == "params")
{
foreach (var operation in (special.Value as paraStore))
{
XElement op = new XElement("operation");
foreach (var para in operation.Key)
{
op.Add(new XElement("para", para.ToString()));
}
op.Add(new XElement("Result", operation.Value.ToString()));
newChild.Add(op);
}
}
else if (Name == "Tree")
{
newChild = dfs((special.Value as Trie).root);
}
newChild.Name = Name;
newChild.Add(new XElement("Edge", special.Key.ToString()));
Xcurrent.Add(newChild);
}
}
}
return(Xroot);
}
Node dfs(XElement Xroot)
{
Node root = new Node();
Stack <List <Object> > dfsStack = new Stack <List <Object> >();
dfsStack.Push(new List <Object>());
dfsStack.Peek().Add(root);
dfsStack.Peek().Add(null);
dfsStack.Peek().Add(null);
dfsStack.Peek().Add(Xroot);
while (dfsStack.Count != 0)
{
var temporaryList = dfsStack.Pop();
Node currentNode = temporaryList[0] as Node;
Node parentNode = temporaryList[1] as Node;
XElement currentXNode = temporaryList[3] as XElement;
currentNode.isEnd = currentXNode.Element("isEnd").Value == "True";
if (parentNode != null)
{
KeyValuePair <int, Complex> Edge = (KeyValuePair <int, Complex>)temporaryList[2];
parentNode._children.Add(Edge, currentNode);
}
foreach (var edge in currentXNode.Elements("Node"))
{
int degree = int.Parse(edge.Element("Edge").Element("Degree").Value);
double real = double.Parse(edge.Element("Edge").Element("Coefficient").Element("Real").Value);
double imaginary = double.Parse(edge.Element("Edge").Element("Coefficient").Element("Imaginary").Value);
Node newNode = new Node();
dfsStack.Push(new List <Object>());
dfsStack.Peek().Add(newNode);
dfsStack.Peek().Add(currentNode);
dfsStack.Peek().Add(new KeyValuePair <int, Complex>(degree, new Complex(real, imaginary)));
dfsStack.Peek().Add(edge);
}
if (currentNode.isEnd)
{
foreach (var edge in currentXNode.Elements("Tree"))
{
char edgeChar = edge.Element("Edge").Value[0];
currentNode._special.Add(edgeChar, new Trie(dfs(edge)));
}
foreach (var edge in currentXNode.Elements("listComplex"))
{
char edgeChar = edge.Element("Edge").Value[0];
currentNode._special.Add(edgeChar, ComplexUtils.complexListParse(edge.Elements("root")));
}
foreach (var edge in currentXNode.Elements("params"))
{
char edgeChar = edge.Element("Edge").Value[0];
var operations = new paraStore(new ListComparer <Complex>());
foreach (var op in edge.Elements("operation"))
{
operations.Add(ComplexUtils.complexListParse(op.Elements("para")), ComplexUtils.ParseComplex(op.Element("Result").Value));
}
currentNode._special.Add(edgeChar, operations);
}
foreach (var edge in currentXNode.Elements("Result"))
{
char edgeChar = edge.Element("Edge").Value[0];
var resultPoly = new Polynomial(edge.Element("poly").Value);
currentNode._special.Add(edgeChar, resultPoly);
}
}
}
return(root);
}
/// <summary>
/// Find a complex root for the polynomial with the given coefficients,
/// starting from the given initial value.
/// <br/>
/// Note: This method is not part of the API of <seealso cref="BaseUnivariateSolver"/>.
/// </summary>
/// <param name="coefficients"> Polynomial coefficients. </param>
/// <param name="initial"> Start value. </param>
/// <returns> the point at which the function value is zero. </returns>
/// <exception cref="org.apache.commons.math3.exception.TooManyEvaluationsException">
/// if the maximum number of evaluations is exceeded. </exception>
/// <exception cref="NullArgumentException"> if the {@code coefficients} is
/// {@code null}. </exception>
/// <exception cref="NoDataException"> if the {@code coefficients} array is empty.
/// @since 3.1 </exception>
public virtual Complex SolveComplex(double[] coefficients, double initial)
{
Setup(int.MaxValue, new PolynomialFunction(coefficients), double.NegativeInfinity, double.PositiveInfinity, initial);
return ComplexSolver.Solve(ComplexUtils.convertToComplex(coefficients), new Complex(initial, 0d));
}
/// <summary>
/// Find all complex roots for the polynomial with the given
/// coefficients, starting from the given initial value.
/// <para>
/// Note: This method is not part of the API of <seealso cref="BaseUnivariateSolver"/>.</para>
/// </summary>
/// <param name="coefficients"> polynomial coefficients </param>
/// <param name="initial"> start value </param>
/// <param name="maxEval"> maximum number of evaluations </param>
/// <returns> the full set of complex roots of the polynomial </returns>
/// <exception cref="org.apache.commons.math3.exception.TooManyEvaluationsException">
/// if the maximum number of evaluations is exceeded when solving for one of the roots </exception>
/// <exception cref="NullArgumentException"> if the {@code coefficients} is
/// {@code null} </exception>
/// <exception cref="NoDataException"> if the {@code coefficients} array is empty
/// @since 3.5 </exception>
public virtual Complex[] SolveAllComplex(double[] coefficients, double initial, int maxEval)
{
Setup(maxEval, new PolynomialFunction(coefficients), double.NegativeInfinity, double.PositiveInfinity, initial);
return(complexSolver.SolveAll(ComplexUtils.ConvertToComplex(coefficients), new Complex(initial, 0d)));
}
public override string ToString()
{
return(ComplexUtils.ComplexToString(Coefficient) + "X" + Degree.ToString());
}
public Term(string _input)
{
string[] seperate = _input.Split('X');
Coefficient = ComplexUtils.ParseComplex(seperate[0]);
Degree = int.Parse(seperate[1]);
}
