/// <summary>
/// The method looks for a stability region.
/// threshold value = limitValue + sigmaCoefficient * sigma;
/// </summary>
/// <param name="data">can't be null</param>
/// <param name="limitValue"></param>
/// <param name="sigmaCoefficient">defines filter amplitude and direction; see threshold value calculation</param>
/// <returns>
/// true cells defines stability region
/// false cells defines instability region
/// </returns>
public static bool[,] FindStabilityRegion(double[,] data, double sigmaFactor, BinaryFunction predicate, double limitValue = 1)
{
int rows = data.GetLength(0);
int columns = data.GetLength(1);
List <double> deviations = new List <double>();
for (int row = 0; row < rows; ++row)
{
for (int column = 0; column < columns; ++column)
{
double value = data[row, column];
if (row - 1 >= 0)
{
double delta = data[row - 1, column] - value;
deviations.Add(delta);
}
if (row < rows - 1)
{
double delta = data[row + 1, column] - value;
deviations.Add(delta);
}
if (column - 1 >= 0)
{
double delta = data[row, column - 1] - value;
deviations.Add(delta);
}
if (column < columns - 1)
{
double delta = data[row, column + 1] - value;
deviations.Add(delta);
}
}
}
double sigma = Statistics.CalculateSampleVariance(deviations.ToArray());
sigma = NumericalMethods.Sqrt(sigma);
sigma *= sigmaFactor;
double threshold = predicate(1, 0) ? (limitValue - sigma) : (limitValue + sigma);
bool[,] result = new bool[rows, columns];
for (int row = 0; row < rows; ++row)
{
for (int column = 0; column < columns; ++column)
{
result[row, column] = predicate(data[row, column], threshold);
}
}
double ry = NumericalMethods.Sqrt(rows);
double rx = NumericalMethods.Sqrt(columns);
int r = (int)Math.Min(rx, ry) - 1;
for (int index = 0; index < r; ++index)
{
result = Morphology.Erosion(result);
}
return(result);
}
public static Portfolio CalculateLinear(double[,] equity, double reliability, double maximumLoss, double minimumCoefficientValue)
{
CalculateLinearValidation(reliability, maximumLoss);
double[,] deltaEquity = NumericalMethods.CalculateAbsoluteVariation(equity);
double[,] sigma = Statistics.CalculateCovarianceMatrix(deltaEquity);
double factor = NumericalMethods.Sqrt(sigma.Maximum());
if (factor <= 0)
{
string st = string.Format("Runtime error: invalid factor = {0}", factor);
throw new InvalidOperationException(st);
}
NumericalMethods.Multiply(deltaEquity, 1 / factor);
double[] profit = Statistics.CalculateAverage(deltaEquity);
sigma = Statistics.CalculateCovarianceMatrix(deltaEquity);
MathArgs args = new MathArgs();
args.Add("$profit", profit);
args.Add("$reliability", reliability);
args.Add("$covariance", sigma);
args.Add("$loss", maximumLoss / factor);
args.Add("$coefficient", minimumCoefficientValue);
Dictionary <string, object> output = MathematicaKernel.Execute(s_portfolioDiscrete, args);
Portfolio result = new Portfolio();
result.Profit = (double)output["profit"] * factor;
result.When = (double)output["when"];
result.Coefficients = (double[])output["result"];
return(result);
}
public static Portfolio CalculateLinearFast(double[,] equity, double reliability, double maximumLoss, double minimumCoefficientValue)
{
CalculateLinearValidation(reliability, maximumLoss);
double[,] deltaEquity = NumericalMethods.CalculateAbsoluteVariation(equity);
double[,] sigma = Statistics.CalculateCovarianceMatrix(deltaEquity);
Log.Technical("sigma = ", MathFormatProvider.InputStringFromTable(sigma));
double[] profit = Statistics.CalculateAverage(deltaEquity);
Log.Technical("sigma = ", MathFormatProvider.InputStringFromData(profit));
int n = profit.Length;
Portfolio result = new Portfolio();
result.Coefficients = new double[n];
result.When = double.NaN;
bool[] zeros = new bool[n];
bool status = false;
do
{
status = CalculateLinearFastInternal(result, zeros, sigma, profit, reliability, maximumLoss, minimumCoefficientValue, FastAbsoluteMinimalThreshold);
} while (!status);
return(result);
}
public static Portfolio CalculateLinearMarginBalance(PortfolioInput input, Vector[] balance)
{
CalculateLinearValidation(input.Reliability, input.MaximumLoss);
if (input.InitialDeposit <= input.MaximumLoss)
{
string st = string.Format("Initial deposit = {0} should be more than maximum loss = {1}", input.InitialDeposit, input.MaximumLoss);
throw new ArgumentException();
}
if (input.MarginLevelThreshold <= 0)
{
string st = string.Format("Margin level = {0}, but must be positive", input.MarginLevelThreshold);
throw new ArgumentException();
}
double marginThreshold = (input.InitialDeposit - input.MaximumLoss) / input.MarginLevelThreshold;
double[,] deltaEquity = NumericalMethods.CalculateAbsoluteVariation(input.Equity);
double[,] sigma = Statistics.CalculateCovarianceMatrix(deltaEquity);
int count = sigma.GetLength(0);
for (int i = 0; i < count; ++i)
{
for (int j = 1 + i; j < count; ++j)
{
sigma[i, j] = 0;
sigma[j, i] = 0;
}
}
double[] profit = Statistics.CalculateAverage(deltaEquity);
Log.Technical("sigma = {0}", MathFormatProvider.InputStringFromTable(sigma));
Log.Technical("profit = {0}", MathFormatProvider.InputStringFromData(profit));
int n = profit.Length;
double[] m = input.Margin.MaximumByRow();
Portfolio result = new Portfolio();
result.Coefficients = new double[n];
result.When = double.NaN;
bool[] zeros = new bool[n];
Vector[] _balance = new Vector[balance.Length - 1];
for (int index = 1; index < balance.Length; ++index)
{
_balance[index - 1] = balance[index] - balance[0];
}
double[] margin = input.Margin.MaximumByRow();
bool status = false;
do
{
status = CalculateLinearMarginBalanceInternal(result, zeros, sigma, profit, margin, input, _balance);
} while (!status);
return(result);
}
public static bool[,] Erosion(bool[,] data, int row, int column)
{
int rows = data.GetLength(0);
int columns = data.GetLength(1);
double ry = NumericalMethods.Sqrt(rows);
double rx = NumericalMethods.Sqrt(columns);
int radius = (int)Math.Min(rx, ry);
bool[,] result = Erosion(data, row, column, radius);
return(result);
}
public static Portfolio CalculateLinearFast(double[,] equity, double[,] margin, double initialDeposit, double reliability, double maximumLoss,
double marginLevel, double minimumCoefficientValue)
{
CalculateLinearValidation(reliability, maximumLoss);
if (maximumLoss <= 0)
{
string st = string.Format("maximumLoss = {0}, but must be positive", maximumLoss);
throw new ArgumentException();
}
if (initialDeposit <= maximumLoss)
{
string st = string.Format("Initial deposit = {0} should be more than maximum loss = {1}", initialDeposit, maximumLoss);
throw new ArgumentException();
}
if (marginLevel <= 0)
{
string st = string.Format("Margin level = {0}, but must be positive", marginLevel);
throw new ArgumentException();
}
double marginThreshold = (initialDeposit - maximumLoss) / marginLevel;
double[,] deltaEquity = NumericalMethods.CalculateAbsoluteVariation(equity);
double[,] sigma = Statistics.CalculateCovarianceMatrix(deltaEquity);
double[] profit = Statistics.CalculateAverage(deltaEquity);
Log.Technical("sigma = {0}", MathFormatProvider.InputStringFromTable(sigma));
Log.Technical("profit = {0}", MathFormatProvider.InputStringFromData(profit));
int n = profit.Length;
double[] m = margin.MaximumByRow();
Portfolio result = new Portfolio();
result.Coefficients = new double[n];
result.When = double.NaN;
bool[] zeros = new bool[n];
bool status = false;
do
{
status = CalculateLinearFastInternal(result, zeros, sigma, profit, m, reliability, maximumLoss, minimumCoefficientValue, marginThreshold);
} while (!status);
return(result);
}
public static List <Pixel2> FindStabilityExtremums(double[,] data, double sigmaFactor, BinaryFunction predicate)
{
List <Pixel2> result = new List <Pixel2>();
bool[,] region = FindStabilityRegion(data, sigmaFactor, predicate);
for (; ;)
{
int row = -1;
int column = -1;
bool status = NumericalMethods.FindConditionalExtremum(data, region, predicate, out row, out column);
if (!status)
{
break;
}
result.Add(new Pixel2(column, row));
region = Morphology.Erosion(region, row, column);
}
return(result);
}
private static bool CalculateLinearFastInternal(Portfolio portfolio, bool[] zeros, double[,] sigma, double[] profit, double[] margin, double reliability, double maximumLoss,
double minimumCoefficientValue, double marginThreshold)
{
int count = 0;
Dictionary <int, int> map = new Dictionary <int, int>();
for (int index = 0; index < zeros.Length; ++index)
{
bool status = zeros[index];
if (!status)
{
map[map.Count] = index;
++count;
}
}
if (0 == count)
{
return(true); // nothing to do
}
// create sub-matrix
double[,] _sigma = new double[count, count];
double[] _profit = new double[count];
double[] _margin = new double[count];
for (int row = 0; row < _profit.Length; ++row)
{
int r = map[row];
_profit[row] = profit[r];
_margin[row] = margin[r];
for (int column = 0; column < _profit.Length; ++column)
{
int c = map[column];
_sigma[row, column] = sigma[r, c];
}
}
// calculate factor and check it
double factor = NumericalMethods.Sqrt(_sigma.Maximum());
if (factor <= 0)
{
string st = string.Format("Runtime error: invalid factor = {0}", factor);
throw new InvalidOperationException(st);
}
// normalize data
NumericalMethods.Multiply(_sigma, 1 / factor / factor);
NumericalMethods.Multiply(_profit, 1 / factor);
NumericalMethods.Multiply(_margin, 1 / factor);
MathArgs args = new MathArgs();
args.Add("$profit", _profit);
args.Add("$reliability", reliability);
args.Add("$covariance", _sigma);
args.Add("$loss", maximumLoss / factor);
args.Add("$threshold", marginThreshold / factor);
args.Add("$margin", _margin);
Dictionary <string, object> output = MathematicaKernel.Execute(s_portfolioMargin, args);
double[] coefficients = (double[])output["result"];
// check results
bool result = FastPositiveMinimalThreshold(zeros, minimumCoefficientValue, count, map, coefficients);
if (!result)
{
return(result);
}
// prepare results
for (int index = 0; index < count; ++index)
{
portfolio.Coefficients[map[index]] = coefficients[index];
}
portfolio.Profit = (double)output["profit"] * factor;
portfolio.When = (double)output["when"];
return(result);
}