sascha@326: package de.intevation.flys.artifacts.model;
sascha@326: 
sascha@326: import java.io.Serializable;
sascha@326: 
sascha@326: 
sascha@427: import de.intevation.flys.artifacts.math.LinearRemap;
sascha@427: 
sascha@335: import java.util.Arrays;
sascha@326: import java.util.ArrayList;
sascha@326: import java.util.List;
sascha@326: import java.util.Collections;
sascha@326: 
sascha@339: import org.apache.log4j.Logger;
sascha@339: 
sascha@339: import org.apache.commons.math.analysis.interpolation.SplineInterpolator;
sascha@339: 
sascha@339: import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;
sascha@339: 
sascha@339: import org.apache.commons.math.ArgumentOutsideDomainException;
sascha@339: 
sascha@326: public class WstValueTable
sascha@326: implements   Serializable
sascha@326: {
sascha@339:     private static Logger log = Logger.getLogger(WstValueTable.class);
sascha@326: 
sascha@395:     public static final int DEFAULT_Q_STEPS = 500;
sascha@339: 
sascha@326:     public static class Column
sascha@326:     implements          Serializable
sascha@326:     {
sascha@326:         protected String name;
sascha@326: 
sascha@326:         public Column() {
sascha@326:         }
sascha@326: 
sascha@326:         public Column(String name) {
sascha@326:             this.name = name;
sascha@326:         }
sascha@326: 
sascha@326:         public String getName() {
sascha@326:             return name;
sascha@326:         }
sascha@326: 
sascha@326:         public void setName(String name) {
sascha@326:             this.name = name;
sascha@326:         }
sascha@326:     }
sascha@326:     // class Column
sascha@326: 
sascha@426:     public static class QPosition {
sascha@426: 
sascha@426:         protected double q;
sascha@426:         protected int    index;
sascha@426:         protected double weight;
sascha@426: 
sascha@426:         public QPosition() {
sascha@426:         }
sascha@426: 
sascha@426:         public QPosition(double q, int index, double weight) {
sascha@426:             this.index  = index;
sascha@426:             this.weight = weight;
sascha@426:         }
sascha@426: 
sascha@426:     } // class Position
sascha@426: 
sascha@326:     public static class Row
sascha@335:     implements          Serializable, Comparable<Row>
sascha@326:     {
sascha@326:         double    km;
sascha@335:         double [] ws;
sascha@335:         double [] qs;
sascha@335:         boolean   qSorted;
sascha@326: 
sascha@326:         public Row() {
sascha@326:         }
sascha@326: 
sascha@335:         public Row(double km) {
sascha@326:             this.km = km;
sascha@335:         }
sascha@335: 
sascha@335:         public Row(double km, double [] ws, double [] qs) {
sascha@335:             this(km);
sascha@335:             this.ws = ws;
sascha@335:             this.qs = qs;
sascha@335:         }
sascha@335: 
sascha@335:         public static final double linear(
sascha@335:             double x,
sascha@335:             double x1, double x2,
sascha@335:             double y1, double y2
sascha@335:         ) {
sascha@335:             // y1 = m*x1 + b
sascha@335:             // y2 = m*x2 + b
sascha@335:             // y2 - y1 = m*(x2 - x1)
sascha@335:             // m = (y2 - y1)/(x2 - x1) # x2 != x1
sascha@335:             // b = y1 - m*x1
sascha@335: 
sascha@335:             if (x1 == x2) {
sascha@335:                 return 0.5*(y1 + y2);
sascha@335:             }
sascha@335:             double m = (y2 - y1)/(x2 - x1);
sascha@335:             double b = y1 - m*x1;
sascha@335:             return x*m + b;
sascha@335:         }
sascha@335: 
sascha@335:         public static final double factor(double x, double p1, double p2) {
sascha@335:             // 0 = m*p1 + b <=> b = -m*p1
sascha@335:             // 1 = m*p2 + b
sascha@335:             // 1 = m*(p2 - p1)
sascha@335:             // m = 1/(p2 - p1) # p1 != p2
sascha@335:             // f(x) = x/(p2-p1) - p1/(p2-p1) <=> (x-p1)/(p2-p1)
sascha@335: 
sascha@335:             return p1 == p2 ? 0.0 : (x-p1)/(p2-p1);
sascha@335:         }
sascha@335: 
sascha@335:         public static final double weight(double factor, double a, double b) {
sascha@335:             return (1.0-factor)*a + factor*b;
sascha@335:         }
sascha@335: 
sascha@335:         public void interpolateW(
sascha@335:             Row       other,
sascha@335:             double    km,
sascha@335:             double [] input,
sascha@335:             double [] output
sascha@335:         ) {
sascha@335:             double factor = factor(km, this.km, other.km);
sascha@335: 
sascha@335:             for (int i = 0; i < input.length; ++i) {
sascha@335:                 double q = input[i];
sascha@335:                 int idx1 =       getQIndex(q);
sascha@335:                 int idx2 = other.getQIndex(q);
sascha@335: 
sascha@335:                 double w1 = idx1 >= 0
sascha@335:                     ? ws[idx1]
sascha@335:                     : interpolateW(-idx1-1, q);
sascha@335: 
sascha@335:                 double w2 = idx2 >= 0
sascha@335:                     ? other.ws[idx2]
sascha@335:                     : other.interpolateW(-idx2-1, q);
sascha@335: 
sascha@335:                 output[i] = weight(factor, w1, w2);
sascha@335:             }
sascha@335:         }
sascha@335: 
sascha@335:         public double interpolateW(int idx, double q) {
sascha@335:             return idx < 1 || idx >= qs.length
sascha@335:                 ? Double.NaN // do not extrapolate
sascha@335:                 : linear(q, qs[idx-1], qs[idx], ws[idx-1], ws[idx]);
sascha@335:         }
sascha@335: 
sascha@335:         public double interpolateW(double q) {
sascha@335:             if (Double.isNaN(q)) return Double.NaN;
sascha@335:             int index = getQIndex(q);
ingo@360:             return index >= 0 ? ws[index] : interpolateW(-index -1, q);
sascha@335:         }
sascha@335: 
sascha@335:         public int getQIndex(double q) {
sascha@335:             return qSorted ? binaryQIndex(q) : linearQIndex(q);
sascha@335:         }
sascha@335: 
sascha@335:         public int binaryQIndex(double q) {
sascha@335:             return Arrays.binarySearch(qs, q);
sascha@335:         }
sascha@335: 
sascha@335:         public int linearQIndex(double q) {
sascha@335:             switch (qs.length) {
sascha@335:                 case 0: break;
sascha@335:                 case 1:
sascha@335:                     if (qs[0] == q) return 0;
sascha@335:                     if (qs[0] <  q) return -(1+1);
sascha@335:                     return -(0+1);
sascha@335:                 default:
sascha@335:                     for (int i = 1; i < qs.length; ++i) {
sascha@335:                         double qa = qs[i-1];
sascha@335:                         double qb = qs[i];
sascha@335:                         if (qa == q) return i-1;
sascha@335:                         if (qb == q) return i;
sascha@335:                         if (qa > qb) { double t = qa; qa = qb; qb = t; }
sascha@335:                         if (q > qa && q < qb) return -(i+1);
sascha@335:                     }
sascha@335:                     return -qs.length;
sascha@335:             }
sascha@335: 
sascha@335:             return -1;
sascha@335:         }
sascha@335: 
sascha@335:         public int compareTo(Row other) {
sascha@335:             double d = km - other.km;
sascha@458:             if (d < -0.0001) return -1;
sascha@458:             if (d >  0.0001) return +1;
sascha@335:             return 0;
sascha@326:         }
sascha@339: 
sascha@395:         public double [][] interpolateWQ(Row other, double km, int steps) {
sascha@339: 
sascha@395:             int W = Math.min(ws.length, other.ws.length);
sascha@339: 
sascha@339:             if (W < 1) {
sascha@339:                 return new double[2][0];
sascha@339:             }
sascha@339: 
sascha@339:             double factor = factor(km, this.km, other.km);
sascha@339: 
sascha@395:             double [] splineQ = new double[W];
sascha@395:             double [] splineW = new double[W];
sascha@339: 
sascha@395:             double minQ =  Double.MAX_VALUE;
sascha@395:             double maxQ = -Double.MAX_VALUE;
sascha@339: 
sascha@339:             for (int i = 0; i < W; ++i) {
sascha@395:                 double wws = weight(factor, ws[i], other.ws[i]);
sascha@395:                 double wqs = weight(factor, qs[i], other.qs[i]);
sascha@395:                 splineW[i] = wws;
sascha@395:                 splineQ[i] = wqs;
sascha@395:                 if (wqs < minQ) minQ = wqs;
sascha@395:                 if (wqs > maxQ) maxQ = wqs;
sascha@339:             }
sascha@339: 
sascha@395:             double stepWidth = (maxQ - minQ)/steps;
sascha@395: 
sascha@339:             SplineInterpolator interpolator = new SplineInterpolator();
sascha@395:             PolynomialSplineFunction spline =
sascha@395:                 interpolator.interpolate(splineQ, splineW);
sascha@339: 
sascha@395:             double [] outWs = new double[steps];
sascha@395:             double [] outQs = new double[steps];
sascha@339: 
sascha@339:             try {
sascha@395:                 double q = minQ;
sascha@395:                 for (int i = 0; i < outWs.length; ++i, q += stepWidth) {
sascha@395:                     outWs[i] = spline.value(outQs[i] = q);
sascha@339:                 }
sascha@339:             }
sascha@339:             catch (ArgumentOutsideDomainException aode) {
sascha@339:                 log.error("Spline interpolation failed.", aode);
sascha@339:             }
sascha@339: 
sascha@339:             return new double [][] { outWs, outQs };
sascha@339:         }
sascha@339: 
sascha@395:         public double [][] interpolateWQ(int steps) {
sascha@395: 
sascha@395:             int W = ws.length;
sascha@339: 
sascha@339:             if (W < 1) {
sascha@339:                 return new double[2][0];
sascha@339:             }
sascha@339: 
sascha@395:             double [] splineW = new double[W];
sascha@395:             double [] splineQ = new double[W];
sascha@395: 
sascha@395:             double minQ =  Double.MAX_VALUE; 
sascha@395:             double maxQ = -Double.MAX_VALUE; 
sascha@339: 
sascha@339:             for (int i = 0; i < W; ++i) {
sascha@395:                 splineW[i] = ws[i];
sascha@395:                 splineQ[i] = qs[i];
sascha@395:                 if (qs[i] < minQ) minQ = qs[i];
sascha@395:                 if (qs[i] > maxQ) maxQ = qs[i];
sascha@339:             }
sascha@339: 
sascha@395:             double stepWidth = (maxQ - minQ)/steps;
sascha@395: 
sascha@339:             SplineInterpolator interpolator = new SplineInterpolator();
sascha@339: 
sascha@395:             PolynomialSplineFunction spline =
sascha@395:                 interpolator.interpolate(splineQ, splineW);
sascha@339: 
sascha@395:             double [] outWs = new double[steps];
sascha@395:             double [] outQs = new double[steps];
sascha@339: 
sascha@339:             try {
sascha@395:                 double q = minQ;
sascha@395:                 for (int i = 0; i < outWs.length; ++i, q += stepWidth) {
sascha@395:                     outWs[i] = spline.value(outQs[i] = q);
sascha@339:                 }
sascha@339:             }
sascha@339:             catch (ArgumentOutsideDomainException aode) {
sascha@339:                 log.error("Spline interpolation failed.", aode);
sascha@339:             }
sascha@339: 
sascha@339:             return new double [][] { outWs, outQs };
sascha@339:         }
sascha@339: 
sascha@426:         public QPosition getQPosition(double q) {
sascha@426:             int qIndex = getQIndex(q);
sascha@426: 
sascha@426:             if (qIndex >= 0) {
sascha@426:                 // direct column match
sascha@426:                 return new QPosition(q, qIndex, 1.0);
sascha@426:             }
sascha@426: 
sascha@426:             qIndex = -qIndex -1;
sascha@426: 
sascha@426:             if (qIndex < 0 || qIndex >= qs.length-1) {
sascha@426:                 // do not extrapolate
sascha@426:                 return null;
sascha@426:             }
sascha@426: 
sascha@426:             return new QPosition(
sascha@426:                 q, qIndex, factor(q, qs[qIndex-1], qs[qIndex]));
sascha@426:         }
sascha@426: 
sascha@426:         public QPosition getQPosition(Row other, double km, double q) {
sascha@426: 
sascha@426:             QPosition qpt = getQPosition(q);
sascha@426:             QPosition qpo = other.getQPosition(q);
sascha@426: 
sascha@426:             if (qpt == null || qpo == null) {
sascha@426:                 return null;
sascha@426:             }
sascha@426: 
sascha@426:             double kmWeight = factor(km, this.km, other.km);
sascha@426: 
sascha@426:             // XXX: Index interpolation is a bit sticky here!
sascha@426: 
sascha@426:             int index = (int)Math.round(
sascha@426:                 weight(kmWeight, qpt.index, qpo.index));
sascha@426: 
sascha@426:             double weight = weight(kmWeight, qpt.weight, qpo.weight);
sascha@426: 
sascha@426:             return new QPosition(q, index, weight);
sascha@426:         }
sascha@426: 
sascha@426:         public void storeWQ(
sascha@426:             QPosition qPosition,
sascha@426:             double [] ows,
sascha@426:             double [] oqs,
sascha@426:             int       index
sascha@426:         ) {
sascha@426:             int    qIdx    = qPosition.index;
sascha@426:             double qWeight = qPosition.weight;
sascha@426: 
sascha@426:             if (qWeight == 1.0) {
sascha@426:                 oqs[index] = qs[qIdx];
sascha@426:                 ows[index] = ws[qIdx];
sascha@426:             }
sascha@426:             else {
sascha@426:                 oqs[index] = weight(qWeight, qs[qIdx-1], qs[qIdx]); 
sascha@426:                 ows[index] = weight(qWeight, ws[qIdx-1], ws[qIdx]); 
sascha@426:             }
sascha@426:         }
sascha@426: 
sascha@426:         public void storeWQ(
sascha@426:             Row       other,
sascha@426:             double    km,
sascha@426:             QPosition qPosition,
sascha@426:             double [] ows,
sascha@426:             double [] oqs,
sascha@426:             int       index
sascha@426:         ) {
sascha@426:             double kmWeight = factor(km, this.km, other.km);
sascha@426: 
sascha@426:             double tq, tw;
sascha@426:             double oq, ow;
sascha@426: 
sascha@426:             int    qIdx    = qPosition.index;
sascha@426:             double qWeight = qPosition.weight;
sascha@426: 
sascha@426:             if (qWeight == 1.0) {
sascha@426:                 tq = qs[qIdx];
sascha@426:                 tw = ws[qIdx];
sascha@426:                 oq = other.qs[qIdx];
sascha@426:                 ow = other.ws[qIdx];
sascha@426:             }
sascha@426:             else {
sascha@426:                 tq = weight(qWeight, qs[qIdx-1], qs[qIdx]); 
sascha@426:                 tw = weight(qWeight, ws[qIdx-1], ws[qIdx]); 
sascha@426:                 oq = weight(qWeight, other.qs[qIdx-1], other.qs[qIdx]); 
sascha@426:                 ow = weight(qWeight, other.ws[qIdx-1], other.ws[qIdx]); 
sascha@426:             }
sascha@426: 
sascha@621:             oqs[index] = weight(kmWeight, tq, oq);
sascha@621:             ows[index] = weight(kmWeight, tw, ow);
sascha@426:         }
sascha@427: 
sascha@427:         public void storeWQ(
sascha@427:             QPosition   qPosition,
sascha@427:             LinearRemap remap,
sascha@427:             double []   ows,
sascha@427:             double []   oqs,
sascha@427:             int         index
sascha@427:         ) {
sascha@427:             int    qIdx    = qPosition.index;
sascha@427:             double qWeight = qPosition.weight;
sascha@427: 
sascha@427:             oqs[index] = remap.eval(km, qWeight == 1.0
sascha@427:                 ? qs[qIdx]
sascha@427:                 : weight(qWeight, qs[qIdx-1], qs[qIdx])); 
sascha@427: 
sascha@427:             ows[index] = interpolateW(oqs[index]);
sascha@427:         }
sascha@427: 
sascha@427:         public void storeWQ(
sascha@427:             Row         other,
sascha@427:             double      km,
sascha@427:             QPosition   qPosition,
sascha@427:             LinearRemap remap,
sascha@427:             double []   ows,
sascha@427:             double []   oqs,
sascha@427:             int         index
sascha@427:         ) {
sascha@427:             double kmWeight = factor(km, this.km, other.km);
sascha@427: 
sascha@427:             double tq, tw;
sascha@427:             double oq, ow;
sascha@427: 
sascha@427:             int    qIdx    = qPosition.index;
sascha@427:             double qWeight = qPosition.weight;
sascha@427: 
sascha@427:             if (qWeight == 1.0) {
sascha@427:                 tq = remap.eval(this.km,  qs[qIdx]);
sascha@427:                 oq = remap.eval(other.km, other.qs[qIdx]);
sascha@427:             }
sascha@427:             else {
sascha@427:                 tq = remap.eval(
sascha@427:                     this.km,
sascha@427:                     weight(qWeight, qs[qIdx-1], qs[qIdx]));
sascha@427:                 oq = remap.eval(
sascha@427:                     other.km,
sascha@427:                     weight(qWeight, other.qs[qIdx-1], other.qs[qIdx])); 
sascha@427:             }
sascha@427: 
sascha@427:             tw = interpolateW(tq);
sascha@427:             ow = other.interpolateW(oq);
sascha@427: 
sascha@621:             oqs[index] = weight(kmWeight, tq, oq);
sascha@621:             ows[index] = weight(kmWeight, tw, ow);
sascha@427:         }
sascha@326:     }
sascha@326:     // class Row
sascha@326: 
sascha@326:     protected List<Row> rows;
sascha@326: 
sascha@326:     protected Column [] columns;
sascha@326: 
sascha@326:     public WstValueTable() {
sascha@326:         rows = new ArrayList<Row>();
sascha@326:     }
sascha@326: 
sascha@326:     public WstValueTable(Column [] columns) {
sascha@326:         this();
sascha@326:         this.columns = columns;
sascha@326:     }
sascha@326: 
sascha@458:     public void sortRows() {
sascha@458:         Collections.sort(rows);
sascha@458:     }
sascha@458: 
sascha@458: 
sascha@335:     public double [] interpolateW(double km, double [] qs) {
sascha@380:         return interpolateW(km, qs, new double[qs.length]);
sascha@380:     }
sascha@335: 
sascha@380:     public double [] interpolateW(double km, double [] qs, double [] ws) {
sascha@335: 
sascha@335:         int rowIndex = Collections.binarySearch(rows, new Row(km));
sascha@335: 
sascha@335:         if (rowIndex >= 0) { // direct row match
sascha@335:             Row row = rows.get(rowIndex);
sascha@335:             for (int i = 0; i < qs.length; ++i) {
sascha@335:                 ws[i] = row.interpolateW(qs[i]);
sascha@335:             }
sascha@335:         }
sascha@335:         else { // needs bilinear interpolation
sascha@335:             rowIndex = -rowIndex -1;
sascha@335: 
sascha@335:             if (rowIndex < 1 || rowIndex >= rows.size()) {
sascha@335:                 // do not extrapolate
sascha@335:                 Arrays.fill(ws, Double.NaN);
sascha@335:             }
sascha@335:             else {
sascha@335:                 rows.get(rowIndex-1).interpolateW(
sascha@335:                     rows.get(rowIndex),
sascha@335:                     km, qs, ws);
sascha@335:             }
sascha@335:         }
sascha@335: 
sascha@335:         return ws;
sascha@335:     }
sascha@335: 
sascha@339: 
sascha@339:     public double [][] interpolateWQ(double km) {
sascha@395:         return interpolateWQ(km, DEFAULT_Q_STEPS);
sascha@339:     }
sascha@339: 
sascha@395:     public double [][] interpolateWQ(double km, int steps) {
sascha@395: 
sascha@339:         int rowIndex = Collections.binarySearch(rows, new Row(km));
sascha@339: 
sascha@339:         if (rowIndex >= 0) { // direct row match
sascha@339:             Row row = rows.get(rowIndex);
sascha@395:             return row.interpolateWQ(steps);
sascha@339:         }
sascha@339: 
sascha@339:         rowIndex = -rowIndex -1;
sascha@339: 
sascha@339:         if (rowIndex < 1 || rowIndex >= rows.size()) {
sascha@339:             // do not extrapolate
sascha@339:             return new double[2][0];
sascha@339:         }
sascha@339: 
sascha@339:         Row r1 = rows.get(rowIndex-1);
sascha@339:         Row r2 = rows.get(rowIndex);
sascha@339: 
sascha@395:         return r1.interpolateWQ(r2, km, steps);
sascha@339:     }
sascha@339: 
sascha@427:     public void interpolate(
sascha@427:         double []   kms,
sascha@427:         double []   ws,
sascha@427:         double []   qs,
sascha@427:         QPosition   qPosition,
sascha@427:         LinearRemap remap
sascha@427:     ) {
sascha@427:         int R1 = rows.size()-1;
sascha@427: 
sascha@427:         Row kmKey = new Row();
sascha@427:         for (int i = 0; i < kms.length; ++i) {
sascha@427:             kmKey.km = kms[i];
sascha@427:             int rowIndex = Collections.binarySearch(rows, kmKey);
sascha@427: 
sascha@427:             if (rowIndex >= 0) {
sascha@427:                 // direct row match
sascha@427:                 rows.get(rowIndex).storeWQ(qPosition, remap, ws, qs, i);
sascha@427:                 continue;
sascha@427:             }
sascha@427: 
sascha@427:             rowIndex = -rowIndex -1;
sascha@427: 
sascha@427:             if (rowIndex < 1 || rowIndex >= R1) {
sascha@427:                 // do not extrapolate
sascha@427:                 ws[i] = qs[i] = Double.NaN;
sascha@427:                 continue;
sascha@427:             }
sascha@427:             Row r1 = rows.get(rowIndex-1);
sascha@427:             Row r2 = rows.get(rowIndex);
sascha@427:             r1.storeWQ(r2, kms[i], qPosition, remap, ws, qs, i);
sascha@427:         }
sascha@427:     }
sascha@427: 
sascha@427:     public QPosition interpolate(
sascha@426:         double    q,
sascha@426:         int       referenceIndex,
sascha@426:         double [] kms,
sascha@426:         double [] ws,
sascha@426:         double [] qs
sascha@426:     ) {
sascha@426:         Row kmKey = new Row(kms[referenceIndex]);
sascha@426: 
sascha@426:         int rowIndex = Collections.binarySearch(rows, kmKey);
sascha@426: 
sascha@426:         int R1 = rows.size()-1;
sascha@426: 
sascha@426:         QPosition qPosition = null;
sascha@426: 
sascha@426:         if (rowIndex >= 0) { // direct row match
sascha@426:             qPosition = rows.get(rowIndex).getQPosition(q);
sascha@426:         }
sascha@426:         else {
sascha@426:             rowIndex = -rowIndex -1;
sascha@426: 
sascha@426:             if (rowIndex < 1 || rowIndex >= R1) {
sascha@426:                 // do not extrapolate
sascha@427:                 return null;
sascha@426:             }
sascha@426: 
sascha@426:             // interpolation case
sascha@426:             Row r1 = rows.get(rowIndex-1);
sascha@426:             Row r2 = rows.get(rowIndex);
sascha@426: 
sascha@426:             qPosition = r1.getQPosition(r2, kms[referenceIndex], q);
sascha@426:         }
sascha@426: 
sascha@426:         if (qPosition == null) {
sascha@426:             // we cannot locate q in reference row
sascha@427:             return null;
sascha@426:         }
sascha@426: 
sascha@426:         for (int i = 0; i < kms.length; ++i) {
sascha@426:             kmKey.km = kms[i];
sascha@458: 
sascha@426:             rowIndex = Collections.binarySearch(rows, kmKey);
sascha@426: 
sascha@426:             if (rowIndex >= 0) {
sascha@426:                 // direct row match
sascha@426:                 rows.get(rowIndex).storeWQ(qPosition, ws, qs, i);
sascha@426:                 continue;
sascha@426:             }
sascha@426: 
sascha@426:             rowIndex = -rowIndex -1;
sascha@426: 
sascha@426:             if (rowIndex < 1 || rowIndex >= R1) {
sascha@426:                 // do not extrapolate
sascha@426:                 ws[i] = qs[i] = Double.NaN;
sascha@426:                 continue;
sascha@426:             }
sascha@426:             Row r1 = rows.get(rowIndex-1);
sascha@426:             Row r2 = rows.get(rowIndex);
sascha@426:             r1.storeWQ(r2, kms[i], qPosition, ws, qs, i);
sascha@426:         }
sascha@426: 
sascha@427:         return qPosition;
sascha@426:     }
sascha@326: }
sascha@326: // vim:set ts=4 sw=4 si et sta sts=4 fenc=utf8 :