/// <summary>
/// Deviations squared sum. Сумма ошибок отклонений аппроксимирующей функции от известных значений
/// </summary>
/// <param name="dvDataValues">The data values. Значения аппроксимируемой функции</param>
/// <param name="dvSpace">The space. Значения независимой переменной</param>
/// <param name="approxFunc">The approximation function. Аппроксимирующая функция с фиксированными параметрами, заданными вектором параметров.
/// Значения вычисляются над пространством независимой переменной</param>
/// <param name="currentParametersSpacePoint">The current parameters space point.
/// Тот самый фиксированный вектор параметров, используемый для вычисления значений аппроксимирующей функции над пространсовм независимой переменной</param>
/// <returns>System.Double. Значение абсолютного </returns>
private static double DeviationsSquaredSumRelative(
DenseVector dvDataValues,
DenseVector dvSpace,
Func <DenseVector, double, double> approxFunc,
DenseVector currentParametersSpacePoint,
DenseVector dvWeights)
{
double distanceRelative = 0.0d;
if (dvWeights == null)
{
DenseVector dvApproxFuncValues = DenseVector.Create(dvSpace.Count, ix =>
{
return(approxFunc(currentParametersSpacePoint, dvSpace[ix]));
});
DenseVector dvDistanceAbs = dvApproxFuncValues - dvDataValues;
distanceRelative = dvDistanceAbs.Abs() / dvDataValues.Abs();
}
else
{
DenseVector dvApproxFuncValues = DenseVector.Create(dvSpace.Count, ix =>
{
return(approxFunc(currentParametersSpacePoint, dvSpace[ix]));
});
DenseVector dvDistanceAbs = dvApproxFuncValues - dvDataValues;
dvDistanceAbs.MapInplace(d => Math.Abs(d));
DenseVector dvDistanceRelative = (DenseVector)(dvDistanceAbs / dvDataValues.Map(Math.Abs));
dvDistanceRelative = (DenseVector)dvDistanceRelative.PointwiseMultiply(dvWeights);
distanceRelative = dvDistanceRelative.Abs();
}
return(distanceRelative);
}
private DenseVector GradOfEvaluatingValueRidder(Func <DenseVector, double> inputFunction,
DenseVector dvCurrentParametersPoint,
DenseVector dvPreviousParametersIncrement, out DenseVector dvNewParametersIncrement, double maxRelativeError = 0.005d)
{
DenseVector dvCurrentParametersIncrement = dvPreviousParametersIncrement.Copy() * 2.0d;
Func <DenseVector, double> theFunction = inputFunction;
double maxRelPartialDerivAboveMin = 1000.0d;
for (int i = 0; i < dvCurrentParametersIncrement.Count; i++)
{
if (Math.Abs(dvCurrentParametersIncrement[i]) / dvParametersScale[i] < 1.0e-2)
{
dvCurrentParametersIncrement[i] = dvParametersScale[i] * 1.0e-2;
}
else if (Math.Abs(dvCurrentParametersIncrement[i]) / dvParametersScale[i] > 1.0e+2)
{
dvCurrentParametersIncrement[i] = dvParametersScale[i];
}
}
DenseVector grad = DenseVector.Create(dvCurrentParametersPoint.Count, (index) =>
{
DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
(i => (i == index) ? (dvCurrentParametersIncrement[i]) : (0.0d)));
return((theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
theFunction(dvCurrentParametersPoint - dvPartialParametersIncrement)) / (2.0d * dvPartialParametersIncrement.Sum()));
});
DenseVector gradHalfed = DenseVector.Create(dvCurrentParametersPoint.Count, (index) =>
{
DenseVector dvPartialParametersIncrementHalfed = DenseVector.Create(dvCurrentParametersIncrement.Count,
(i => (i == index) ? (dvCurrentParametersIncrement[i] / 2.0d) : (0.0d)));
return((theFunction(dvCurrentParametersPoint + dvPartialParametersIncrementHalfed) -
theFunction(dvCurrentParametersPoint - dvPartialParametersIncrementHalfed)) / (2.0d * dvPartialParametersIncrementHalfed.Sum()));
});
double relativeError = (grad - gradHalfed).Abs() / grad.Abs();
for (int varIndex = 0; varIndex < dvCurrentParametersIncrement.Count; varIndex++)
{
double partialRelativeError = relativeError;
double currentVarIncrement = dvCurrentParametersIncrement[varIndex];
List <Tuple <double, double, int> > lTplRelErrAndPartDeriv = new List <Tuple <double, double, int> >();
DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
(i => (i == varIndex) ? (dvCurrentParametersIncrement[i]) : (0.0d)));
List <DenseVector> dvParametersPointsToDetermineDerivative = new List <DenseVector>();
dvParametersPointsToDetermineDerivative.Add(dvCurrentParametersPoint - dvPartialParametersIncrement);
dvParametersPointsToDetermineDerivative.Add(dvCurrentParametersPoint + dvPartialParametersIncrement);
NevillePolynomialInterpolation interpolator = new NevillePolynomialInterpolation(
dvParametersPointsToDetermineDerivative.ConvertAll <double>(dv => dv[varIndex]).ToArray(),
dvParametersPointsToDetermineDerivative.ConvertAll <double>(dv => theFunction(dv)).ToArray());
double prevPartialDeriv = interpolator.Differentiate(dvCurrentParametersPoint[varIndex]);
int iNumberOfPointsBetween = 0;
while (partialRelativeError > maxRelativeError)
{
iNumberOfPointsBetween += 2;
List <DenseVector> dvCurrParametersPoints = new List <DenseVector>();
dvCurrParametersPoints.InsertRange(0, dvParametersPointsToDetermineDerivative);
for (int i = 1; i <= iNumberOfPointsBetween; i++)
{
dvCurrParametersPoints.Add(dvParametersPointsToDetermineDerivative[0] +
(dvParametersPointsToDetermineDerivative[1] -
dvParametersPointsToDetermineDerivative[0]) / (i + 1));
}
dvCurrParametersPoints.Sort(
(dv1, dv2) => (dv1[varIndex] < dv2[varIndex]) ? (-1) : (1));
NevillePolynomialInterpolation currInterpolator = new NevillePolynomialInterpolation(
dvCurrParametersPoints.ConvertAll <double>(dv => dv[varIndex]).ToArray(),
dvCurrParametersPoints.ConvertAll <double>(dv => theFunction(dv)).ToArray());
double currPartialDeriv = currInterpolator.Differentiate(dvCurrentParametersPoint[varIndex]);
#region // OBSOLETE
//currentVarIncrement = currentVarIncrement / 2.0d;
//if (Math.Abs(currentVarIncrement) / dvParametersScale[varIndex] < 1.0e-20)
//{
// currentVarIncrement = currentVarIncrement * 2.0d;
// break;
//}
//else if (Math.Abs(currentVarIncrement) / dvParametersScale[varIndex] > 1.0e+20)
//{
// currentVarIncrement = currentVarIncrement / 2.0d;
// break;
//}
//DenseVector gradPartial = DenseVector.Create(dvCurrentParametersPoint.Count, new Func<int, double>((index) =>
//{
// if (index != varIndex) return 0.0d;
// DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
// (i => (i == index) ? (currentVarIncrement) : (0.0d)));
// return (theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
// theFunction(dvCurrentParametersPoint)) / currentVarIncrement;
//}));
//
//DenseVector gradPartialHalfed = DenseVector.Create(dvCurrentParametersPoint.Count, new Func<int, double>((index) =>
//{
// if (index != varIndex) return 0.0d;
// DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
// (i => (i == index) ? (currentVarIncrement / 2.0d) : (0.0d)));
// return (theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
// theFunction(dvCurrentParametersPoint)) / (currentVarIncrement / 2.0d);
//}));
//double gradPartialModule = gradPartial.Abs();
//double gradPartialHalfedModule = gradPartialHalfed.Abs();
//if ((gradPartialModule == 0.0d) || (gradPartialHalfedModule == 0.0d))
//{
// currentVarIncrement = currentVarIncrement * 2.0d;
// break;
//}
// (gradPartial - gradPartialHalfed).Abs() / gradPartial.Abs();
#endregion // OBSOLETE
partialRelativeError = Math.Abs((currPartialDeriv - prevPartialDeriv) / prevPartialDeriv);
prevPartialDeriv = currPartialDeriv;
dvCurrentParametersIncrement[varIndex] = currentVarIncrement / (iNumberOfPointsBetween + 2);
lTplRelErrAndPartDeriv.Add(new Tuple <double, double, int>(partialRelativeError, currPartialDeriv, iNumberOfPointsBetween));
if (partialRelativeError / lTplRelErrAndPartDeriv.Min(tpl => tpl.Item1) > maxRelPartialDerivAboveMin)
{
prevPartialDeriv = lTplRelErrAndPartDeriv.Min(tpl => tpl.Item2);
dvCurrentParametersIncrement[varIndex] = currentVarIncrement / (lTplRelErrAndPartDeriv.Min(tpl => tpl.Item3) + 2);
break;
}
if (SelfWorker != null)
{
if (SelfWorker.CancellationPending)
{
break;
}
}
}
grad[varIndex] = prevPartialDeriv;
}
#region // OBSOLETE
//grad = DenseVector.Create(dvCurrentParametersPoint.Count, new Func<int, double>((index) =>
//{
// DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
// (i => (i == index) ? (dvCurrentParametersIncrement[i]) : (0.0d)));
// return (theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
// theFunction(dvCurrentParametersPoint - dvPartialParametersIncrement)) / (2.0d*dvPartialParametersIncrement.Sum());
//}));
#endregion // OBSOLETE
dvNewParametersIncrement = DenseVector.OfEnumerable(dvCurrentParametersIncrement);
dvNewParametersIncrement = (grad / grad.Abs()) * dvNewParametersIncrement.Abs();
return(grad);
}
/// <summary>
/// Grads the of evaluating value.
/// </summary>
/// <param name="theFunction">Функция, от которой берется градиент в пространстве параметров.
/// В качестве аргументов типа DenseVector должна принимать текущую точку в пространстве парметров
/// Возвращать функция должна собственно свое значение в зависимости от вектора параметров</param>
/// <param name="dvCurrentParametersPoint">The current parameters point vector. Текущая точка в пространстве параметров, в которой вычисляется градиент.</param>
/// <param name="dvPreviousParametersIncrement">The previous parameters increment.
/// Вектор используемых дифференциалов компонент вектора параметров, давший удовлетворительную точность определения градиента на предыдущем шаге приближения</param>
/// <param name="maxRelativeError">The maximum relative error. Максимальная относительная ошибка определения градиента</param>
/// <param name="dvNewParametersIncrement">The new parameters increment. Новый вектор дифференциалов компонент вектора параметров,
/// давший удовлетворительную точность определения градиента на этом шаге</param>
/// <returns>DenseVector - значение градиента в пространстве параметров.</returns>
private DenseVector GradOfEvaluatingValue(Func <DenseVector, double> inputFunction,
DenseVector dvCurrentParametersPoint,
DenseVector dvPreviousParametersIncrement, out DenseVector dvNewParametersIncrement, double maxRelativeError = 0.005d)
{
DenseVector dvCurrentParametersIncrement = dvPreviousParametersIncrement.Copy() * 2.0d;
Func <DenseVector, double> theFunction = inputFunction;
for (int i = 0; i < dvCurrentParametersIncrement.Count; i++)
{
if (Math.Abs(dvCurrentParametersIncrement[i]) / dvParametersScale[i] < 1.0e-2)
{
dvCurrentParametersIncrement[i] = dvParametersScale[i] * 1.0e-2;
}
else if (Math.Abs(dvCurrentParametersIncrement[i]) / dvParametersScale[i] > 1.0e+2)
{
dvCurrentParametersIncrement[i] = dvParametersScale[i];
}
}
DenseVector grad = DenseVector.Create(dvCurrentParametersPoint.Count, (index) =>
{
DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
(i => (i == index) ? (dvCurrentParametersIncrement[i]) : (0.0d)));
return((theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
theFunction(dvCurrentParametersPoint - dvPartialParametersIncrement)) /
2.0d * dvPartialParametersIncrement[index]);
});
DenseVector gradHalfed = DenseVector.Create(dvCurrentParametersPoint.Count, (index) =>
{
DenseVector dvPartialParametersIncrementHalfed = DenseVector.Create(dvCurrentParametersIncrement.Count,
(i => (i == index) ? (dvCurrentParametersIncrement[i] / 2.0d) : (0.0d)));
return((theFunction(dvCurrentParametersPoint + dvPartialParametersIncrementHalfed) -
theFunction(dvCurrentParametersPoint - dvPartialParametersIncrementHalfed)) /
2.0d * dvPartialParametersIncrementHalfed[index]);
});
double relativeError = (grad - gradHalfed).Abs() / grad.Abs();
for (int varIndex = 0; varIndex < dvCurrentParametersIncrement.Count; varIndex++)
{
double partialRelativeError = relativeError;
double currentVarIncrement = dvCurrentParametersIncrement[varIndex];
while (partialRelativeError > maxRelativeError)
{
currentVarIncrement = currentVarIncrement / 2.0d;
if (Math.Abs(currentVarIncrement) / dvParametersScale[varIndex] < 1.0e-20)
{
currentVarIncrement = currentVarIncrement * 2.0d;
break;
}
else if (Math.Abs(currentVarIncrement) / dvParametersScale[varIndex] > 1.0e+20)
{
currentVarIncrement = currentVarIncrement / 2.0d;
break;
}
DenseVector gradPartial = DenseVector.Create(dvCurrentParametersPoint.Count,
(index) =>
{
if (index != varIndex)
{
return(0.0d);
}
DenseVector dvPartialParametersIncrement =
DenseVector.Create(
dvCurrentParametersIncrement.Count,
(i => (i == index) ? (currentVarIncrement) : (0.0d)));
return((theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
theFunction(dvCurrentParametersPoint - dvPartialParametersIncrement)) /
2.0d * currentVarIncrement);
});
DenseVector gradPartialHalfed = DenseVector.Create(dvCurrentParametersPoint.Count,
(index) =>
{
if (index != varIndex)
{
return(0.0d);
}
DenseVector dvPartialParametersIncrement =
DenseVector.Create(
dvCurrentParametersIncrement.Count,
(i => (i == index) ? (currentVarIncrement / 2.0d) : (0.0d)));
return((theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
theFunction(dvCurrentParametersPoint - dvPartialParametersIncrement)) /
currentVarIncrement);
});
if ((gradPartial.Abs() == 0.0d) || (gradPartialHalfed.Abs() == 0.0d))
{
currentVarIncrement = currentVarIncrement * 2.0d;
break;
}
partialRelativeError = (gradPartial - gradPartialHalfed).Abs() / gradPartial.Abs();
if (SelfWorker != null)
{
if (SelfWorker.CancellationPending)
{
break;
}
}
}
dvCurrentParametersIncrement[varIndex] = currentVarIncrement;
}
grad = DenseVector.Create(dvCurrentParametersPoint.Count, (index) =>
{
DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
(i => (i == index) ? (dvCurrentParametersIncrement[index]) : (0.0d)));
return((theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
theFunction(dvCurrentParametersPoint - dvPartialParametersIncrement)) /
2.0d * dvPartialParametersIncrement[index]);
});
dvNewParametersIncrement = dvCurrentParametersIncrement.Copy();
return(grad);
}
//public DenseVector Approximation_ILOptimizer(DenseVector dvInitialParametersValues,
// double maxRelativeError = 1.0e-8d)
//{
// // найдем некое максимальное значение функции - для формирования высокого градиента
// // на границе запрещенных областей по параметрам
// // DenseVector dvInitFuncValues = (DenseVector) dvSpace.Map(x => approxFunc(dvInitialParametersValues, x));
// // approxFuncMaxValue_FAKE = dvInitFuncValues.Max();
//
// Optimization.ObjectiveFunction<double> devFunc = (parametersPoint) =>
// {
// using (ILScope.Enter(parametersPoint))
// {
// DenseVector dvParametersPoint = DenseVector.OfEnumerable(parametersPoint);
// DenseVector dvDevValues =
// DeviationsArray_ILOptimizer(dvDataValues, dvSpace, approxFunc, dvParametersPoint,
// dvWeights);
// return (ILRetArray<double>)(dvDevValues.ToArray());
// }
// };
//
//
// ILArray<double> initParameters = dvInitialParametersValues.ToArray();
// double[] resDoub;
// using (ILScope.Enter(initParameters))
// {
// ILRetArray<double> result = Optimization.leastsq_pdl(
// devFunc,
// initParameters,
// tol: maxRelativeError);
// resDoub = result.ToArray();
// }
//
// return DenseVector.OfEnumerable(resDoub);
//}
//public DenseVector Approximation_ILOptimizerConstrained(DenseVector dvInitialParametersValues,
// double maxRelativeError = 1.0e-8d)
//{
// Optimization.ObjectiveFunction<double> devFunc = (parametersPoint) =>
// {
// using (ILScope.Enter(parametersPoint))
// {
// DenseVector dvParametersPoint = DenseVector.OfEnumerable(parametersPoint);
// DenseVector dvDevValues =
// DeviationsArray_ILOptimizer(dvDataValues, dvSpace, approxFunc, dvParametersPoint,
// dvWeights);
// return (ILRetArray<double>)(dvDevValues.ToArray());
// }
// };
//
// //Optimization.ObjectiveFunction<double> eqFunc =
// // (parametersPoint) => (ILRetArray<double>) (DenseVector.Create(dvSpace.Count, 0.0d).ToArray());
// Optimization.ObjectiveFunction<double> eqFunc = (parametersPoint) => 0.0d;
// if (parametersConditionsEquals0.Count > 0)
// {
// eqFunc = (parametersPoint) =>
// {
// using (ILScope.Enter(parametersPoint))
// {
// // посольку ограничений на равенство нулю может быть несколько
// // одновременно они все обратятся в ноль только если сумма квадратов будет равна нулю
// // значит, итоговая функция должна возвращать сумму квадратов функций
//
// DenseVector dvParametersPoint = DenseVector.OfEnumerable(parametersPoint);
// DenseVector dvResSumSq = DenseVector.Create(dvSpace.Count, 0.0d);
// foreach (Func<DenseVector, double, double> func in parametersConditionsEquals0)
// {
// DenseVector eqConstraintFuncValues = DenseVector.Create(dvSpace.Count,
// i => func(dvParametersPoint, dvSpace[i]));
// eqConstraintFuncValues.MapInplace(dVal => dVal*dVal);
// dvResSumSq += eqConstraintFuncValues;
// }
//
// return (ILRetArray<double>) (dvResSumSq.ToArray());
// }
// };
// }
//
// Optimization.ObjectiveFunction<double> ineqFunc =
// (parametersPoint) => (ILRetArray<double>)(DenseVector.Create(dvSpace.Count, -1.0d).ToArray());
// if (parametersConditionsLessThan0.Count > 0)
// {
// ineqFunc = (parametersPoint) =>
// {
// using (ILScope.Enter(parametersPoint))
// {
// // посольку ограничений на отрицательное значение может быть несколько
// // поэтому сделаем так: преобразуем условия в булевы по принципу "верно ли неравенство"
// // потом - логическим И получим результат по всем условиям
// // выдадим результат: true = -1, false = +1
//
// DenseVector dvParametersPoint = DenseVector.OfEnumerable(parametersPoint);
// List<bool> resValues = new List<bool>();
// foreach (double d in dvSpace)
// {
// resValues.Add(false);
// }
// foreach (Func<DenseVector, double, double> func in parametersConditionsLessThan0)
// {
// DenseVector ineqConstraintFuncValues = DenseVector.Create(dvSpace.Count,
// i => func(dvParametersPoint, dvSpace[i]));
// List<double> currResult = new List<double>(ineqConstraintFuncValues);
// List<bool> currResultBool = currResult.ConvertAll<bool>(dVal => (dVal < 0) ? (true) : (false));
// resValues = new List<bool>(resValues.Zip(currResultBool, (b1, b2) => b1 && b2));
// }
//
// return (resValues.Aggregate((bv1, bv2) => bv1 && bv2)) ? (-1) : (1);
//
// //return
// // (ILRetArray<double>)
// // (resValues.ConvertAll<double>(bVal => (bVal) ? (-1.0d) : (1.0d)).ToArray());
//
// }
// };
// }
//
//
// ILArray<double> initParameters = dvInitialParametersValues.ToArray();
// double[] resDoub;
// using (ILScope.Enter(initParameters))
// {
// ILRetArray<double> result = Optimization.fmin(
// devFunc,
// initParameters,
// EqualityConstraint: eqFunc,
// InequalityConstraint: ineqFunc,
// tol: maxRelativeError);
// resDoub = result.ToArray();
// }
//
// return DenseVector.OfEnumerable(resDoub);
//}
/// <summary>
/// Approximations using gradient descent method. The ordinary function case.
/// </summary>
/// <param name="dvInitialParametersValues">The dv initioal parameters values.</param>
/// <param name="dvInitialParametersIncrement">The dv initial parameters increment.</param>
/// <param name="maxRelativeError">The maximum relative error.</param>
/// <returns>DenseVector.</returns>
public DenseVector ApproximationGradientDescentMultidim(
DenseVector dvInitialParametersValues,
ref DenseVector dvInitialParametersIncrement,
double maxRelativeError = 0.0001d)
{
DenseVector currentParametersValues = dvInitialParametersValues.Copy();
updateParametersScale(currentParametersValues);
DenseVector dvCurrentParametersIncrement = dvInitialParametersIncrement.Copy();
double stepFollowingGradKoeff = 1.0d;
double relativeMinimizingValueDiffIncrement = maxRelativeError * 2.0d;
double previousRelativeMinimizingValueIncrement = 1.0d;
DenseVector nextParametersValues = currentParametersValues.Copy();
while (Math.Abs(relativeMinimizingValueDiffIncrement) > maxRelativeError)
{
stepFollowingGradKoeff = stepFollowingGradKoeff * 2.0d;
DenseVector dvNewParametersIncrements;
//DenseVector dvCurrentGrad = GradOfEvaluatingValueRidder(
DenseVector dvCurrentGrad = GradOfEvaluatingValue(
dvParametersPoint => DeviationsSquaredSumRelative(dvDataValues, dvSpace, approxFunc, dvParametersPoint, dvWeights),
currentParametersValues,
dvCurrentParametersIncrement,
out dvNewParametersIncrements);
dvCurrentParametersIncrement = dvNewParametersIncrements.Copy();
nextParametersValues = currentParametersValues - stepFollowingGradKoeff * dvCurrentGrad;
//DenseVector dvNextGrad = GradOfEvaluatingValueRidder(
DenseVector dvNextGrad = GradOfEvaluatingValue(
dvParametersPoint => DeviationsSquaredSumRelative(dvDataValues, dvSpace, approxFunc, dvParametersPoint, dvWeights),
nextParametersValues,
dvCurrentParametersIncrement,
out dvNewParametersIncrements);
dvCurrentParametersIncrement = dvNewParametersIncrements.Copy();
DenseVector gradIncrement = dvNextGrad - dvCurrentGrad;
double gradRelativeIncrement = gradIncrement.Abs() / dvCurrentGrad.Abs();
while (gradRelativeIncrement > 0.2d)
{
//stepFollowingGradKoeff adjusting
double stepFollowingGradKoeffPrev = stepFollowingGradKoeff;
if (gradRelativeIncrement > 0.2d)
{
stepFollowingGradKoeff = stepFollowingGradKoeff * RandomWithLimits(0.3d, 0.7d);
if (stepFollowingGradKoeff == 0.0d)
{
stepFollowingGradKoeff = stepFollowingGradKoeffPrev * 2.0d;
break;
}
}
nextParametersValues = currentParametersValues - stepFollowingGradKoeff * dvCurrentGrad;
//dvNextGrad = GradOfEvaluatingValueRidder(
dvNextGrad = GradOfEvaluatingValue(
dvParametersPoint => DeviationsSquaredSumRelative(dvDataValues, dvSpace, approxFunc, dvParametersPoint, dvWeights),
nextParametersValues,
dvCurrentParametersIncrement,
out dvNewParametersIncrements);
dvCurrentParametersIncrement = dvNewParametersIncrements.Copy();
gradIncrement = dvNextGrad - dvCurrentGrad;
gradRelativeIncrement = gradIncrement.Abs() / dvCurrentGrad.Abs();
}
#region // Проверка условий
//if (parametersConditions.Count > 0)
//{
// DenseVector modifiedParametersIncrement = stepFollowingGradKoeff * dvCurrentGrad;
// bool conditionsTrue = false;
// int testimgParamenerIndex = 0;
// while (!conditionsTrue)
// {
// if (testimgParamenerIndex > 0)
// modifiedParametersIncrement[testimgParamenerIndex - 1] =
// -modifiedParametersIncrement[testimgParamenerIndex - 1];
// modifiedParametersIncrement[testimgParamenerIndex] =
// -modifiedParametersIncrement[testimgParamenerIndex];
// nextParametersValues = currentParametersValues - modifiedParametersIncrement;
// conditionsTrue = true;
// foreach (Func<DenseVector, bool> condition in parametersConditions)
// {
// conditionsTrue = conditionsTrue && condition(nextParametersValues);
// }
// }
//}
#endregion // Проверка условий
double currentMinimizingValue = DeviationsSquaredSumRelative(dvDataValues, dvSpace, approxFunc, currentParametersValues, dvWeights);
double nextMinimizingValue = DeviationsSquaredSumRelative(dvDataValues, dvSpace, approxFunc, currentParametersValues - stepFollowingGradKoeff * dvCurrentGrad, dvWeights);
double currentRelativeIncrement = (nextMinimizingValue - currentMinimizingValue) / currentMinimizingValue;
//relativeMinimizingValueDiffIncrement = (currentRelativeIncrement - previousRelativeMinimizingValueIncrement) / currentRelativeIncrement;
relativeMinimizingValueDiffIncrement = currentRelativeIncrement;
if (currentRelativeIncrement == 0.0d)
{
currentRelativeIncrement = currentRelativeIncrement +
RandomWithLimits(0.2d, 0.6d);
relativeMinimizingValueDiffIncrement = (currentRelativeIncrement -
previousRelativeMinimizingValueIncrement) /
currentRelativeIncrement;
nextParametersValues = nextParametersValues +
DenseVector.Create(dvNextGrad.Count, (i => rnd.NextDouble() * dvNextGrad[i]));
}
previousRelativeMinimizingValueIncrement = currentRelativeIncrement;
currentParametersValues = nextParametersValues;
//updateParametersScale(currentParametersValues);
if (SelfWorker != null)
{
MinimizingFunctionValues.Add(currentMinimizingValue);
List <double> subSample = MinimizingFunctionValues;
if (MinimizingFunctionValues.Count > 100)
{
subSample = MinimizingFunctionValues.GetRange(MinimizingFunctionValues.Count - 101, 100);
}
DescriptiveStatistics stats = new DescriptiveStatistics(subSample);
//Thread.Sleep(10);
Tuple <DenseVector, double> theObject = new Tuple <DenseVector, double>(currentParametersValues,
stats.StandardDeviation / stats.Mean);
SelfWorker.ReportProgress(50, theObject);
if (SelfWorker.CancellationPending)
{
break;
}
}
else
{
//theSelfLogWindow = ServiceTools.LogAText(theSelfLogWindow, densevectorToString(nextParametersValues), false);
}
}
if (SelfWorker == null)
{
//theSelfLogWindow = ServiceTools.LogAText(theSelfLogWindow, "DONE" + Environment.NewLine + densevectorToString(nextParametersValues), false);
}
dvInitialParametersIncrement = DenseVector.OfVector(dvCurrentParametersIncrement);
return(nextParametersValues);
}
/// <summary>
/// Approximations using gradient descent method. The points list case.
/// </summary>
/// <param name="dvInitioalParametersValues">The dv initioal parameters values.</param>
/// <param name="dvInitialParametersIncrement">The dv initial parameters increment.</param>
/// <param name="maxRelativeError">The maximum relative error.</param>
/// <returns>DenseVector.</returns>
public DenseVector ApproximationGradientDescent2DPt(DenseVector dvInitioalParametersValues, DenseVector dvInitialParametersIncrement, double maxRelativeError = 0.0001d)
{
DenseVector currentParametersValues = dvInitioalParametersValues.Copy();
updateParametersScale(currentParametersValues);
DenseVector dvCurrentParametersIncrement = dvInitialParametersIncrement.Copy();
DenseVector dvNewParametersIncrements;
double stepFollowingGradKoeff = 1.0d;
double relativeMinimizingValueDiffIncrement = 1.0d;
double previousRelativeMinimizingValueIncrement = 1.0d;
DenseVector nextParametersValues = currentParametersValues.Copy();
while (Math.Abs(relativeMinimizingValueDiffIncrement) > maxRelativeError)
{
stepFollowingGradKoeff = stepFollowingGradKoeff * 2.0d;
DenseVector dvCurrentGrad = GradOfEvaluatingValue(
DeviationsSquaredSumPt,
currentParametersValues,
dvCurrentParametersIncrement,
out dvNewParametersIncrements);
dvCurrentParametersIncrement = dvNewParametersIncrements.Copy();
nextParametersValues = currentParametersValues - stepFollowingGradKoeff * dvCurrentGrad;
DenseVector dvNextGrad = GradOfEvaluatingValue(
DeviationsSquaredSumPt,
nextParametersValues,
dvCurrentParametersIncrement,
out dvNewParametersIncrements);
dvCurrentParametersIncrement = dvNewParametersIncrements.Copy();
DenseVector gradIncrement = dvNextGrad - dvCurrentGrad;
double gradRelativeIncrement = gradIncrement.Abs() / dvCurrentGrad.Abs();
while (gradRelativeIncrement > 0.1d)
{
//stepFollowingGradKoeff adjusting
double stepFollowingGradKoeffPrev = stepFollowingGradKoeff;
stepFollowingGradKoeff = stepFollowingGradKoeff / 2.0d;
if (stepFollowingGradKoeff == 0.0d)
{
stepFollowingGradKoeff = stepFollowingGradKoeffPrev * 2;
break;
}
nextParametersValues = currentParametersValues - stepFollowingGradKoeff * dvCurrentGrad;
dvNextGrad = GradOfEvaluatingValue(
dvParametersVector =>
{
//здесь должна быть функция, от которой берем градиент
return(DeviationsSquaredSumPt(dvParametersVector));
},
nextParametersValues,
dvCurrentParametersIncrement,
out dvNewParametersIncrements);
dvCurrentParametersIncrement = dvNewParametersIncrements.Copy();
gradIncrement = dvNextGrad - dvCurrentGrad;
gradRelativeIncrement = gradIncrement.Abs() / dvCurrentGrad.Abs();
}
#region Проверка условий
//if (parametersConditions.Count > 0)
//{
// DenseVector modifiedParametersIncrement = stepFollowingGradKoeff * dvCurrentGrad;
// bool conditionsTrue = false;
// int testimgParamenerIndex = 0;
// while (!conditionsTrue)
// {
// if (testimgParamenerIndex > 0)
// modifiedParametersIncrement[testimgParamenerIndex - 1] =
// -modifiedParametersIncrement[testimgParamenerIndex - 1];
// modifiedParametersIncrement[testimgParamenerIndex] =
// -modifiedParametersIncrement[testimgParamenerIndex];
// nextParametersValues = currentParametersValues - modifiedParametersIncrement;
// conditionsTrue = true;
// foreach (Func<DenseVector, bool> condition in parametersConditions)
// {
// conditionsTrue = conditionsTrue && condition(nextParametersValues);
// }
// }
//}
#endregion Проверка условий
double currentMinimizingValue = DeviationsSquaredSumPt(currentParametersValues);
//DeviationsSquaredSumRelative(currentParametersValues);
double nextMinimizingValue = DeviationsSquaredSumPt(currentParametersValues - stepFollowingGradKoeff * dvCurrentGrad);
//DeviationsSquaredSumRelative(approxFunc, (currentParametersValues - stepFollowingGradKoeff * dvCurrentGrad));
double currentRelativeIncrement = (nextMinimizingValue - currentMinimizingValue) / currentMinimizingValue;
//relativeMinimizingValueDiffIncrement = (currentRelativeIncrement - previousRelativeMinimizingValueIncrement) / currentRelativeIncrement;
relativeMinimizingValueDiffIncrement = currentRelativeIncrement;
//previousRelativeMinimizingValueIncrement = currentRelativeIncrement;
currentParametersValues = nextParametersValues;
//updateParametersScale(currentParametersValues);
if (SelfWorker != null)
{
MinimizingFunctionValues.Add(currentMinimizingValue);
List <double> subSample = MinimizingFunctionValues;
if (MinimizingFunctionValues.Count > 100)
{
subSample = MinimizingFunctionValues.GetRange(MinimizingFunctionValues.Count - 101, 100);
}
DescriptiveStatistics stats = new DescriptiveStatistics(subSample);
//Thread.Sleep(10);
Tuple <DenseVector, double> theObject = new Tuple <DenseVector, double>(currentParametersValues, stats.StandardDeviation / stats.Mean);
SelfWorker.ReportProgress(50, theObject);
if (SelfWorker.CancellationPending)
{
break;
}
}
else
{
//theSelfLogWindow = ServiceTools.LogAText(theSelfLogWindow, densevectorToString(nextParametersValues), false);
}
}
if (SelfWorker == null)
{
//theSelfLogWindow = ServiceTools.LogAText(theSelfLogWindow, "DONE" + Environment.NewLine + densevectorToString(nextParametersValues), false);
}
return(nextParametersValues);
}
