public static double OptimizeConstants(ISymbolicDataAnalysisExpressionTreeInterpreter interpreter,
                                               ISymbolicExpressionTree tree, IRegressionProblemData problemData, IEnumerable <int> rows, bool applyLinearScaling,
                                               int maxIterations, bool updateVariableWeights = true,
                                               double lowerEstimationLimit = double.MinValue, double upperEstimationLimit              = double.MaxValue,
                                               bool updateConstantsInTree  = true, Action <double[], double, object> iterationCallback = null, EvaluationsCounter counter = null)
        {
            // numeric constants in the tree become variables for constant opt
            // variables in the tree become parameters (fixed values) for constant opt
            // for each parameter (variable in the original tree) we store the
            // variable name, variable value (for factor vars) and lag as a DataForVariable object.
            // A dictionary is used to find parameters
            double[] initialConstants;
            var      parameters = new List <TreeToAutoDiffTermConverter.DataForVariable>();

            TreeToAutoDiffTermConverter.ParametricFunction         func;
            TreeToAutoDiffTermConverter.ParametricFunctionGradient func_grad;
            if (!TreeToAutoDiffTermConverter.TryConvertToAutoDiff(tree, updateVariableWeights, applyLinearScaling, out parameters, out initialConstants, out func, out func_grad))
            {
                throw new NotSupportedException("Could not optimize constants of symbolic expression tree due to not supported symbols used in the tree.");
            }
            if (parameters.Count == 0)
            {
                return(0.0);                             // gkronber: constant expressions always have a R² of 0.0
            }
            var parameterEntries = parameters.ToArray(); // order of entries must be the same for x

            //extract inital constants
            double[] c;
            if (applyLinearScaling)
            {
                c    = new double[initialConstants.Length + 2];
                c[0] = 0.0;
                c[1] = 1.0;
                Array.Copy(initialConstants, 0, c, 2, initialConstants.Length);
            }
            else
            {
                c = (double[])initialConstants.Clone();
            }

            double originalQuality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(interpreter, tree, lowerEstimationLimit, upperEstimationLimit, problemData, rows, applyLinearScaling);

            if (counter == null)
            {
                counter = new EvaluationsCounter();
            }
            var rowEvaluationsCounter = new EvaluationsCounter();

            alglib.lsfitstate  state;
            alglib.lsfitreport rep;
            int retVal;

            IDataset ds = problemData.Dataset;

            double[,] x = new double[rows.Count(), parameters.Count];
            int row = 0;

            foreach (var r in rows)
            {
                int col = 0;
                foreach (var info in parameterEntries)
                {
                    if (ds.VariableHasType <double>(info.variableName))
                    {
                        x[row, col] = ds.GetDoubleValue(info.variableName, r + info.lag);
                    }
                    else if (ds.VariableHasType <string>(info.variableName))
                    {
                        x[row, col] = ds.GetStringValue(info.variableName, r) == info.variableValue ? 1 : 0;
                    }
                    else
                    {
                        throw new InvalidProgramException("found a variable of unknown type");
                    }
                    col++;
                }
                row++;
            }
            double[] y = ds.GetDoubleValues(problemData.TargetVariable, rows).ToArray();
            int      n = x.GetLength(0);
            int      m = x.GetLength(1);
            int      k = c.Length;

            alglib.ndimensional_pfunc function_cx_1_func = CreatePFunc(func);
            alglib.ndimensional_pgrad function_cx_1_grad = CreatePGrad(func_grad);
            alglib.ndimensional_rep   xrep = (p, f, obj) => iterationCallback(p, f, obj);

            try {
                alglib.lsfitcreatefg(x, y, c, n, m, k, false, out state);
                alglib.lsfitsetcond(state, 0.0, 0.0, maxIterations);
                alglib.lsfitsetxrep(state, iterationCallback != null);
                //alglib.lsfitsetgradientcheck(state, 0.001);
                alglib.lsfitfit(state, function_cx_1_func, function_cx_1_grad, xrep, rowEvaluationsCounter);
                alglib.lsfitresults(state, out retVal, out c, out rep);
            } catch (ArithmeticException) {
                return(originalQuality);
            } catch (alglib.alglibexception) {
                return(originalQuality);
            }

            counter.FunctionEvaluations += rowEvaluationsCounter.FunctionEvaluations / n;
            counter.GradientEvaluations += rowEvaluationsCounter.GradientEvaluations / n;

            //retVal == -7  => constant optimization failed due to wrong gradient
            if (retVal != -7)
            {
                if (applyLinearScaling)
                {
                    var tmp = new double[c.Length - 2];
                    Array.Copy(c, 2, tmp, 0, tmp.Length);
                    UpdateConstants(tree, tmp, updateVariableWeights);
                }
                else
                {
                    UpdateConstants(tree, c, updateVariableWeights);
                }
            }
            var quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(interpreter, tree, lowerEstimationLimit, upperEstimationLimit, problemData, rows, applyLinearScaling);

            if (!updateConstantsInTree)
            {
                UpdateConstants(tree, initialConstants, updateVariableWeights);
            }

            if (originalQuality - quality > 0.001 || double.IsNaN(quality))
            {
                UpdateConstants(tree, initialConstants, updateVariableWeights);
                return(originalQuality);
            }
            return(quality);
        }