--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/artifacts/src/main/java/org/dive4elements/river/artifacts/model/fixings/fitting/LinearRegressionSqrtErrorFunction.java	Mon Dec 02 17:56:15 2019 +0100
@@ -0,0 +1,147 @@
+/** Copyright (C) 2017 by Bundesanstalt für Gewässerkunde
+ * Software engineering by
+ *  Björnsen Beratende Ingenieure GmbH
+ *  Dr. Schumacher Ingenieurbüro für Wasser und Umwelt
+ *
+ * This file is Free Software under the GNU AGPL (>=v3)
+ * and comes with ABSOLUTELY NO WARRANTY! Check out the
+ * documentation coming with Dive4Elements River for details.
+ */
+package org.dive4elements.river.artifacts.model.fixings.fitting;
+
+import org.apache.commons.math3.analysis.MultivariateFunction;
+import org.apache.commons.math3.analysis.UnivariateFunction;
+import org.apache.commons.math3.stat.descriptive.DescriptiveStatistics;
+import org.apache.commons.math3.stat.regression.SimpleRegression;
+
+/**
+ * @author Gernot Belger
+ *
+ */
+final class LinearRegressionSqrtErrorFunction implements MultivariateFunction, UnivariateFunction {
+
+    private final double[] obsDischarges;
+
+    private final double[] obsWaterlevels;
+
+    private final double waterlevelMean;
+
+    private final double waterlevelDeviation;
+
+    private final double[] standardizedWaterlevel;
+
+    private final SQRTFunction sqrtFunction;
+
+    private final TargetFunction targetFunction;
+
+    public LinearRegressionSqrtErrorFunction(final double[] obsDischarges, final double[] obsWaterlevels, final TargetFunction targetFunction) {
+
+        this.obsDischarges = obsDischarges;
+        this.obsWaterlevels = obsWaterlevels;
+
+        this.sqrtFunction = new SQRTFunction(obsWaterlevels);
+        this.targetFunction = targetFunction;
+
+        final DescriptiveStatistics stats = new DescriptiveStatistics(obsWaterlevels);
+
+        // Compute mean and standard deviation
+        this.waterlevelMean = stats.getMean();
+        this.waterlevelDeviation = stats.getStandardDeviation();
+        // -mittelwert durch standardabweichung /z-transformation)
+
+        // initialize the standardizedSample, which has the same length as the sample
+        this.standardizedWaterlevel = new double[obsWaterlevels.length];
+
+        for (int i = 0; i < obsWaterlevels.length; i++)
+            this.standardizedWaterlevel[i] = (obsWaterlevels[i] - this.waterlevelMean) / this.waterlevelDeviation;
+    }
+
+    @Override
+    public double value(final double[] point) {
+
+        final double a = point[0];
+
+        return value(a);
+    }
+
+    @Override
+    public double value(final double a) {
+
+        final double error = calc_sqrt_trans(a);
+        if (Double.isNaN(error))
+            return Double.POSITIVE_INFINITY;
+
+        return error;
+    }
+
+    private double calc_sqrt_trans(final double a) {
+
+        final double[] waterlevels = calc_stage_trans(a);
+
+        return this.sqrtFunction.calc_sqrt(waterlevels);
+    }
+
+    private double[] calc_stage_trans(final double a) {
+
+        final double[] params = calc_parameters_trans(a);
+
+        final double b = params[0];
+        final double m = params[1];
+
+        return this.targetFunction.calc_stages(a, b, m);
+    }
+
+    public double[] calc_parameters_trans(final double a) {
+
+        // stages_obs_trans = trans_stages(stages_obs, parameter_a);
+        final double[] transWaterlevels = trans_stages(this.obsWaterlevels, a);
+        final double[] discharges = this.obsDischarges;
+
+        // FIXME: z-nromalizing?
+
+        // printArray(discharges);
+        // printArray(transWaterlevels);
+
+        // final DescriptiveStatistics stats = new DescriptiveStatistics(transWaterlevels);
+        //
+        // // Compute mean and standard deviation
+        // final double mean = stats.getMean();
+        // final double deviation = stats.getStandardDeviation();
+        //
+        // final double[] normWaterlevel = new double[transWaterlevels.length];
+        // for (int i = 0; i < transWaterlevels.length; i++)
+        // normWaterlevel[i] = (transWaterlevels[i] - mean) / deviation;
+
+        final SimpleRegression regression = new SimpleRegression(true);
+        for (int i = 0; i < discharges.length; i++)
+            regression.addData(discharges[i], transWaterlevels[i]);
+
+        final double normSlope = regression.getSlope();
+        final double normIntercept = regression.getIntercept();
+
+        // unnormalize
+        // final double slope = normSlope * deviation;
+        // final double intercept = normIntercept + mean;
+        final double slope = normSlope;
+        final double intercept = normIntercept;
+
+        return new double[] { intercept, slope };
+    }
+
+    // private void printArray(final double[] discharges) {
+    // for (final double d : discharges) {
+    // System.out.print(d);
+    // System.out.print(", ");
+    // }
+    // System.out.println(" ");
+    // }
+
+    private double[] trans_stages(final double[] waterlevels, final double a) {
+
+        final double[] transWaterlevels = new double[waterlevels.length];
+        for (int i = 0; i < transWaterlevels.length; i++)
+            transWaterlevels[i] = Math.exp(waterlevels[i] / a);
+
+        return transWaterlevels;
+    }
+}
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