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1   package org.opentrafficsim.draw.egtf;
2   
3   import java.util.LinkedHashMap;
4   import java.util.LinkedHashSet;
5   import java.util.Map;
6   import java.util.NavigableMap;
7   import java.util.Objects;
8   import java.util.Optional;
9   import java.util.Set;
10  import java.util.SortedMap;
11  import java.util.TreeMap;
12  import java.util.stream.IntStream;
13  
14  /**
15   * Extended Generalized Treiber-Helbing Filter (van Lint and Hoogendoorn, 2009). This is an extension of the Adaptive Smoothing
16   * Method (Treiber and Helbing, 2002). A fast filter for equidistant grids (Schreiter et al., 2010) is available. This fast
17   * implementation also supports multiple data sources.
18   * <p>
19   * To allow flexible usage the EGTF works with {@code DataSource}, {@code DataStream} and {@code Quantity}.
20   * <p>
21   * A {@code DataSource}, such as "loop detectors", "floating-car data" or "camera" is mostly an identifier, but can be requested
22   * to provide several data streams.
23   * <p>
24   * A {@code DataStream} is one {@code DataSource} supplying one {@code Quantity}. For instance "loop detectors" supplying
25   * "flow". In a {@code DataStream}, supplied by the {@code DataSource}, standard deviation of measurements in congestion and
26   * free flow are defined. These determine the reliability of the {@code Quantity} data from the given {@code DataSource}, and
27   * thus ultimately the weight of the data in the estimation of the quantity.
28   * <p>
29   * A {@code Quantity}, such as "flow" or "density" defines what is measured and what is requested as output. The output can be
30   * in typed format using a {@code Converter}. Default quantities are available under {@code SPEED_SI}, {@code FLOW_SI} and
31   * {@code DENSITY_SI}, all under {@code Quantity}.
32   * <p>
33   * Data can be added using several methods for point data, vector data (multiple independent location-time combinations) and
34   * grid data (data in a grid pattern). Data is added for a particular {@code DataStream}.
35   * <p>
36   * For simple use-cases where a single data source is used, data can be added directly with a {@code Quantity}, in which case a
37   * default {@code DataSource}, and default {@code DataStream} for each {@code Quantity} is internally used. All data should
38   * either be added using {@code Quantity}'s, or it should all be added using {@code DataSource}'s. Otherwise relative data
39   * reliability is undefined.
40   * <p>
41   * Output can be requested from the EGTF using a {@code Kernel}, a spatiotemporal pattern determining measurement weights. The
42   * {@code Kernel} defines an optional maximum spatial and temporal range for measurements to consider, and uses a {@code Shape}
43   * to determine the weight for a given distance and time from the estimated point. By default this is an exponential function. A
44   * Gaussian kernel is also available, while any other shape could be also be implemented.
45   * <p>
46   * Parameters from the EGTF are found in the following places:
47   * <ul>
48   * <li>{@code EGTF}: <i>cCong</i>, <i>cFree</i>, <i>deltaV</i> and <i>vc</i>, defining the overall traffic flow properties.</li>
49   * <li>{@code Kernel}: <i>tMax</i> and <i>xMax</i>, defining the maximum range to consider.</li>
50   * <li>{@code KernelShape}: <i>sigma</i> and <i>tau</i>, determining the decay of weights for further measurements in space and
51   * time. (Specifically {@code GaussKernelShape})</li>
52   * <li>{@code DataStream}: <i>thetaCong</i> and <i>thetaFree</i>, defining the reliability by the standard deviation of measured
53   * data in free flow and congestion from a particular data stream.</li>
54   * </ul>
55   * References:
56   * <ul>
57   * <li>van Lint, J. W. C. and Hoogendoorn, S. P. (2009). A robust and efficient method for fusing heterogeneous data from
58   * traffic sensors on freeways. Computer Aided Civil and Infrastructure Engineering, accepted for publication.</li>
59   * <li>Schreiter, T., van Lint, J. W. C., Treiber, M. and Hoogendoorn, S. P. (2010). Two fast implementations of the Adaptive
60   * Smoothing Method used in highway traffic state estimation. 13th International IEEE Conference on Intelligent Transportation
61   * Systems, 19-22 Sept. 2010, Funchal, Portugal.</li>
62   * <li>Treiber, M. and Helbing, D. (2002). Reconstructing the spatio-temporal traffic dynamics from stationary detector data.
63   * Cooper@tive Tr@nsport@tion Dyn@mics, 1:3.1–3.24.</li>
64   * </ul>
65   * <p>
66   * Copyright (c) 2013-2024 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved. <br>
67   * BSD-style license. See <a href="https://opentrafficsim.org/docs/license.html">OpenTrafficSim License</a>.
68   * </p>
69   * @author <a href="https://github.com/wjschakel">Wouter Schakel</a>
70   */
71  public class Egtf
72  {
73  
74      /** Default sigma value. */
75      private static final double DEFAULT_SIGMA = 300.0;
76  
77      /** Default tau value. */
78      private static final double DEFAULT_TAU = 30.0;
79  
80      /** Filter kernel. */
81      private Kernel kernel;
82  
83      /** Shock wave speed in congestion. */
84      private final double cCong;
85  
86      /** Shock wave speed in free flow. */
87      private final double cFree;
88  
89      /** Speed range between congestion and free flow. */
90      private final double deltaV;
91  
92      /** Flip-over speed below which we have congestion. */
93      private final double vc;
94  
95      /** Data sources by label so we can return the same instances upon repeated request. */
96      private final Map<String, DataSource> dataSources = new LinkedHashMap<>();
97  
98      /** Default data source for cases where a single data source is used. */
99      private DataSource defaultDataSource = null;
100 
101     /** Default data streams for cases where a single data source is used. */
102     private Map<Quantity<?, ?>, DataStream<?>> defaultDataStreams = null;
103 
104     /** True if data is currently being added using a quantity, in which case a check should not occur. */
105     private boolean addingByQuantity;
106 
107     /** All point data sorted by space and time, and per data stream. */
108     private NavigableMap<Double, NavigableMap<Double, Map<DataStream<?>, Double>>> data = new TreeMap<>();
109 
110     /** Whether the calculation was interrupted. */
111     private boolean interrupted = false;
112 
113     /** Listeners. */
114     private Set<EgtfListener> listeners = new LinkedHashSet<>();
115 
116     /**
117      * Constructor using cCong = -18km/h, cFree = 80km/h, deltaV = 10km/h and vc = 80km/h. A default kernel is set.
118      */
119     public Egtf()
120     {
121         this(-18.0, 80.0, 10.0, 80.0);
122     }
123 
124     /**
125      * Constructor defining global settings. A default kernel is set.
126      * @param cCong shock wave speed in congestion [km/h]
127      * @param cFree shock wave speed in free flow [km/h]
128      * @param deltaV speed range between congestion and free flow [km/h]
129      * @param vc flip-over speed below which we have congestion [km/h]
130      */
131     public Egtf(final double cCong, final double cFree, final double deltaV, final double vc)
132     {
133         this.cCong = cCong / 3.6;
134         this.cFree = cFree / 3.6;
135         this.deltaV = deltaV / 3.6;
136         this.vc = vc / 3.6;
137         setKernel();
138     }
139 
140     /**
141      * Convenience constructor that also sets a specified kernel.
142      * @param cCong shock wave speed in congestion [km/h]
143      * @param cFree shock wave speed in free flow [km/h]
144      * @param deltaV speed range between congestion and free flow [km/h]
145      * @param vc flip-over speed below which we have congestion [km/h]
146      * @param sigma spatial kernel size in [m]
147      * @param tau temporal kernel size in [s]
148      * @param xMax maximum spatial range in [m]
149      * @param tMax maximum temporal range in [s]
150      */
151     @SuppressWarnings("parameternumber")
152     public Egtf(final double cCong, final double cFree, final double deltaV, final double vc, final double sigma,
153             final double tau, final double xMax, final double tMax)
154     {
155         this(cCong, cFree, deltaV, vc);
156         setKernelSI(sigma, tau, xMax, tMax);
157     }
158 
159     // ********************
160     // *** DATA METHODS ***
161     // ********************
162 
163     /**
164      * Return a data source, which is created if necessary.
165      * @param name unique name for the data source
166      * @return data source
167      * @throws IllegalStateException when data has been added without a data source
168      */
169     public DataSource getDataSource(final String name)
170     {
171         if (this.defaultDataSource != null)
172         {
173             throw new IllegalStateException(
174                     "Obtaining a (new) data source after data has been added without a data source is not allowed.");
175         }
176         return this.dataSources.computeIfAbsent(name, (key) -> new DataSource(key));
177     }
178 
179     /**
180      * Removes all data from before the given time. This is useful in live usages of this class, where older data is no longer
181      * required.
182      * @param time time before which all data can be removed
183      */
184     public synchronized void clearDataBefore(final double time)
185     {
186         for (SortedMap<Double, Map<DataStream<?>, Double>> map : this.data.values())
187         {
188             map.subMap(Double.NEGATIVE_INFINITY, time).clear();
189         }
190     }
191 
192     /**
193      * Adds point data.
194      * @param quantity quantity of the data
195      * @param location location in [m]
196      * @param time time in [s]
197      * @param value data value
198      * @throws IllegalStateException if data was added with a data stream previously
199      */
200     public synchronized void addPointDataSI(final Quantity<?, ?> quantity, final double location, final double time,
201             final double value)
202     {
203         this.addingByQuantity = true;
204         addPointDataSI(getDefaultDataStream(quantity), location, time, value);
205         this.addingByQuantity = false;
206     }
207 
208     /**
209      * Adds point data.
210      * @param dataStream data stream of the data
211      * @param location location in [m]
212      * @param time time in [s]
213      * @param value data value
214      * @throws IllegalStateException if data was added with a quantity previously
215      */
216     public synchronized void addPointDataSI(final DataStream<?> dataStream, final double location, final double time,
217             final double value)
218     {
219         checkNoQuantityData();
220         Objects.requireNonNull(dataStream, "Datastream may not be null.");
221         if (!Double.isNaN(value))
222         {
223             getSpacioTemporalData(getSpatialData(location), time).put(dataStream, value);
224         }
225     }
226 
227     /**
228      * Adds vector data.
229      * @param quantity quantity of the data
230      * @param location locations in [m]
231      * @param time times in [s]
232      * @param values data values in SI unit
233      * @throws IllegalStateException if data was added with a data stream previously
234      */
235     public synchronized void addVectorDataSI(final Quantity<?, ?> quantity, final double[] location, final double[] time,
236             final double[] values)
237     {
238         this.addingByQuantity = true;
239         addVectorDataSI(getDefaultDataStream(quantity), location, time, values);
240         this.addingByQuantity = false;
241     }
242 
243     /**
244      * Adds vector data.
245      * @param dataStream data stream of the data
246      * @param location locations in [m]
247      * @param time times in [s]
248      * @param values data values in SI unit
249      * @throws IllegalStateException if data was added with a quantity previously
250      */
251     public synchronized void addVectorDataSI(final DataStream<?> dataStream, final double[] location, final double[] time,
252             final double[] values)
253     {
254         checkNoQuantityData();
255         Objects.requireNonNull(dataStream, "Datastream may not be null.");
256         Objects.requireNonNull(location, "Location may not be null.");
257         Objects.requireNonNull(time, "Time may not be null.");
258         Objects.requireNonNull(values, "Values may not be null.");
259         if (location.length != time.length || time.length != values.length)
260         {
261             throw new IllegalArgumentException(String.format("Unequal lengths: location %d, time %d, data %d.", location.length,
262                     time.length, values.length));
263         }
264         for (int i = 0; i < values.length; i++)
265         {
266             if (!Double.isNaN(values[i]))
267             {
268                 getSpacioTemporalData(getSpatialData(location[i]), time[i]).put(dataStream, values[i]);
269             }
270         }
271     }
272 
273     /**
274      * Adds grid data.
275      * @param quantity quantity of the data
276      * @param location locations in [m]
277      * @param time times in [s]
278      * @param values data values in SI unit
279      * @throws IllegalStateException if data was added with a data stream previously
280      */
281     public synchronized void addGridDataSI(final Quantity<?, ?> quantity, final double[] location, final double[] time,
282             final double[][] values)
283     {
284         this.addingByQuantity = true;
285         addGridDataSI(getDefaultDataStream(quantity), location, time, values);
286         this.addingByQuantity = false;
287     }
288 
289     /**
290      * Adds grid data.
291      * @param dataStream data stream of the data
292      * @param location locations in [m]
293      * @param time times in [s]
294      * @param values data values in SI unit
295      * @throws IllegalStateException if data was added with a quantity previously
296      */
297     public synchronized void addGridDataSI(final DataStream<?> dataStream, final double[] location, final double[] time,
298             final double[][] values)
299     {
300         checkNoQuantityData();
301         Objects.requireNonNull(dataStream, "Datastream may not be null.");
302         Objects.requireNonNull(location, "Location may not be null.");
303         Objects.requireNonNull(time, "Time may not be null.");
304         Objects.requireNonNull(values, "Values may not be null.");
305         if (values.length != location.length)
306         {
307             throw new IllegalArgumentException(
308                     String.format("%d locations while length of data is %d", location.length, values.length));
309         }
310         for (int i = 0; i < location.length; i++)
311         {
312             if (values[i].length != time.length)
313             {
314                 throw new IllegalArgumentException(
315                         String.format("%d times while length of data is %d", time.length, values[i].length));
316             }
317             Map<Double, Map<DataStream<?>, Double>> spatialData = getSpatialData(location[i]);
318             for (int j = 0; j < time.length; j++)
319             {
320                 if (!Double.isNaN(values[i][j]))
321                 {
322                     getSpacioTemporalData(spatialData, time[j]).put(dataStream, values[i][j]);
323                 }
324             }
325         }
326     }
327 
328     /**
329      * Check that no data was added using a quantity.
330      * @throws IllegalStateException if data was added with a quantity previously
331      */
332     private void checkNoQuantityData()
333     {
334         if (!this.addingByQuantity && this.defaultDataSource != null)
335         {
336             throw new IllegalStateException(
337                     "Adding data with a data stream is not allowed after data has been added with a quantity.");
338         }
339     }
340 
341     /**
342      * Returns a default data stream and checks that no data with a data stream was added.
343      * @param quantity quantity
344      * @return default data stream
345      * @throws IllegalStateException if data was added with a data stream previously
346      */
347     private DataStream<?> getDefaultDataStream(final Quantity<?, ?> quantity)
348     {
349         Objects.requireNonNull(quantity, "Quantity may not be null.");
350         if (!this.dataSources.isEmpty())
351         {
352             throw new IllegalStateException(
353                     "Adding data with a quantity is not allowed after data has been added with a data stream.");
354         }
355         if (this.defaultDataSource == null)
356         {
357             this.defaultDataSource = new DataSource("default");
358             this.defaultDataStreams = new LinkedHashMap<>();
359         }
360         return this.defaultDataStreams.computeIfAbsent(quantity,
361                 (key) -> this.defaultDataSource.addStreamSI(quantity, 1.0, 1.0));
362     }
363 
364     /**
365      * Returns data from a specific location as a subset from all data. An empty map is returned if no such data exists.
366      * @param location location in [m]
367      * @return data from a specific location
368      */
369     private SortedMap<Double, Map<DataStream<?>, Double>> getSpatialData(final double location)
370     {
371         return this.data.computeIfAbsent(location, (key) -> new TreeMap<>());
372     }
373 
374     /**
375      * Returns data from a specific time as a subset of data from a specific location. An empty map is returned if no such data
376      * exists.
377      * @param spatialData spatially selected data
378      * @param time time in [s]
379      * @return data from a specific time, from data from a specific location
380      */
381     private Map<DataStream<?>, Double> getSpacioTemporalData(final Map<Double, Map<DataStream<?>, Double>> spatialData,
382             final double time)
383     {
384         return spatialData.computeIfAbsent(time, (key) -> new LinkedHashMap<>());
385     }
386 
387     // **********************
388     // *** KERNEL METHODS ***
389     // **********************
390 
391     /**
392      * Sets a default exponential kernel with infinite range, sigma = 300m, and tau = 30s.
393      */
394     public void setKernel()
395     {
396         setKernelSI(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, new ExpKernelShape(DEFAULT_SIGMA, DEFAULT_TAU));
397     }
398 
399     /**
400      * Sets an exponential kernel with infinite range.
401      * @param sigma spatial kernel size
402      * @param tau temporal kernel size
403      */
404     public void setKernelSI(final double sigma, final double tau)
405     {
406         setKernelSI(sigma, tau, Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
407     }
408 
409     /**
410      * Sets an exponential kernel with limited range.
411      * @param sigma spatial kernel size in [m]
412      * @param tau temporal kernel size in [s]
413      * @param xMax maximum spatial range in [m]
414      * @param tMax maximum temporal range in [s]
415      */
416     public void setKernelSI(final double sigma, final double tau, final double xMax, final double tMax)
417     {
418         setKernelSI(xMax, tMax, new ExpKernelShape(sigma, tau));
419     }
420 
421     /**
422      * Sets a Gaussian kernel with infinite range.
423      * @param sigma spatial kernel size
424      * @param tau temporal kernel size
425      */
426     public void setGaussKernelSI(final double sigma, final double tau)
427     {
428         setGaussKernelSI(sigma, tau, Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
429     }
430 
431     /**
432      * Sets a Gaussian kernel with limited range.
433      * @param sigma spatial kernel size in [m]
434      * @param tau temporal kernel size in [s]
435      * @param xMax maximum spatial range in [m]
436      * @param tMax maximum temporal range in [s]
437      */
438     public void setGaussKernelSI(final double sigma, final double tau, final double xMax, final double tMax)
439     {
440         setKernelSI(xMax, tMax, new GaussKernelShape(sigma, tau));
441     }
442 
443     /**
444      * Sets a kernel with limited range and provided shape. The shape allows using non-exponential kernels.
445      * @param xMax maximum spatial range
446      * @param tMax maximum temporal range
447      * @param shape shape of the kernel
448      */
449     public synchronized void setKernelSI(final double xMax, final double tMax, final KernelShape shape)
450     {
451         this.kernel = new Kernel(xMax, tMax, shape);
452     }
453 
454     /**
455      * Returns the wave speed in congestion.
456      * @return wave speed in congestion
457      */
458     final double getWaveSpeedCongestion()
459     {
460         return this.cCong;
461     }
462 
463     /**
464      * Returns the wave speed in free flow.
465      * @return wave speed in free flow
466      */
467     final double getWaveSpeedFreeFlow()
468     {
469         return this.cFree;
470     }
471 
472     // **********************
473     // *** FILTER METHODS ***
474     // **********************
475 
476     /**
477      * Executes filtering in parallel. The returned listener can be used to report progress and wait until the filtering is
478      * done. Finally, the filtering results can then be obtained from the listener.
479      * @param location location of output grid in [m]
480      * @param time time of output grid in [s]
481      * @param quantities quantities to calculate filtered data of
482      * @return listener to notify keep track of the progress
483      */
484     public EgtfParallelListener filterParallelSI(final double[] location, final double[] time,
485             final Quantity<?, ?>... quantities)
486     {
487         Objects.requireNonNull(location, "Location may not be null.");
488         Objects.requireNonNull(time, "Time may not be null.");
489         EgtfParallelListener listener = new EgtfParallelListener();
490         addListener(listener);
491         new Thread(new Runnable()
492         {
493             @Override
494             public void run()
495             {
496                 Optional<Filter> filter = filterSI(location, time, quantities);
497                 if (filter.isPresent())
498                 {
499                     listener.setFilter(filter.get());
500                 }
501                 removeListener(listener);
502             }
503         }, "Egtf calculation thread").start();
504         return listener;
505     }
506 
507     /**
508      * Executes fast filtering in parallel. The returned listener can be used to report progress and wait until the filtering is
509      * done. Finally, the filtering results can then be obtained from the listener.
510      * @param xMin minimum location value of output grid [m]
511      * @param xStep location step of output grid [m]
512      * @param xMax maximum location value of output grid [m]
513      * @param tMin minimum time value of output grid [s]
514      * @param tStep time step of output grid [s]
515      * @param tMax maximum time value of output grid [s]
516      * @param quantities quantities to calculate filtered data of
517      * @return listener to notify keep track of the progress
518      */
519     public EgtfParallelListener filterParallelFastSI(final double xMin, final double xStep, final double xMax,
520             final double tMin, final double tStep, final double tMax, final Quantity<?, ?>... quantities)
521     {
522         EgtfParallelListener listener = new EgtfParallelListener();
523         addListener(listener);
524         new Thread(new Runnable()
525         {
526             @Override
527             public void run()
528             {
529                 Optional<Filter> filter = filterFastSI(xMin, xStep, xMax, tMin, tStep, tMax, quantities);
530                 if (filter.isPresent())
531                 {
532                     listener.setFilter(filter.get());
533                 }
534                 removeListener(listener);
535             }
536         }, "Egtf calculation thread").start();
537         return listener;
538     }
539 
540     /**
541      * Returns filtered data. This is the standard EGTF implementation.
542      * @param location location of output grid in [m]
543      * @param time time of output grid in [s]
544      * @param quantities quantities to calculate filtered data of
545      * @return filtered data, empty when interrupted
546      */
547     @SuppressWarnings("methodlength")
548     public Optional<Filter> filterSI(final double[] location, final double[] time, final Quantity<?, ?>... quantities)
549     {
550         Objects.requireNonNull(location, "Location may not be null.");
551         Objects.requireNonNull(time, "Time may not be null.");
552 
553         // initialize data
554         Map<Quantity<?, ?>, double[][]> map = new LinkedHashMap<>();
555         for (Quantity<?, ?> quantity : quantities)
556         {
557             map.put(quantity, new double[location.length][time.length]);
558         }
559 
560         // loop grid locations
561         for (int i = 0; i < location.length; i++)
562         {
563             double xGrid = location[i];
564 
565             // filter applicable data for location
566             Map<Double, NavigableMap<Double, Map<DataStream<?>, Double>>> spatialData =
567                     this.data.subMap(this.kernel.fromLocation(xGrid), true, this.kernel.toLocation(xGrid), true);
568 
569             // loop grid times
570             for (int j = 0; j < time.length; j++)
571             {
572                 double tGrid = time[j];
573 
574                 // notify
575                 if (notifyListeners((i + (double) j / time.length) / location.length))
576                 {
577                     return Optional.empty();
578                 }
579 
580                 // initialize data per stream
581                 // quantity z assuming congestion and free flow
582                 Map<DataStream<?>, DualWeightedMean> zCongFree = new LinkedHashMap<>();
583 
584                 // filter and loop applicable data for time
585                 for (Map.Entry<Double, NavigableMap<Double, Map<DataStream<?>, Double>>> xEntry : spatialData.entrySet())
586                 {
587                     double dx = xEntry.getKey() - xGrid;
588                     Map<Double, Map<DataStream<?>, Double>> temporalData =
589                             xEntry.getValue().subMap(this.kernel.fromTime(tGrid), true, this.kernel.toTime(tGrid), true);
590 
591                     for (Map.Entry<Double, Map<DataStream<?>, Double>> tEntry : temporalData.entrySet())
592                     {
593                         double dt = tEntry.getKey() - tGrid;
594                         Map<DataStream<?>, Double> pData = tEntry.getValue();
595 
596                         double phiCong = this.kernel.weight(this.cCong, dx, dt);
597                         double phiFree = this.kernel.weight(this.cFree, dx, dt);
598 
599                         // loop streams data at point
600                         for (Map.Entry<DataStream<?>, Double> vEntry : pData.entrySet())
601                         {
602                             DataStream<?> stream = vEntry.getKey();
603                             if (map.containsKey(stream.getQuantity()) || stream.getQuantity().isSpeed())
604                             {
605                                 double v = vEntry.getValue();
606                                 DualWeightedMean zCongFreeOfStream =
607                                         zCongFree.computeIfAbsent(stream, (key) -> new DualWeightedMean());
608                                 zCongFreeOfStream.addCong(v, phiCong);
609                                 zCongFreeOfStream.addFree(v, phiFree);
610                             }
611                         }
612                     }
613                 }
614 
615                 // figure out the congestion level estimated for each data source
616                 Map<DataSource, Double> w = new LinkedHashMap<>();
617                 for (Map.Entry<DataStream<?>, DualWeightedMean> streamEntry : zCongFree.entrySet())
618                 {
619                     DataStream<?> dataStream = streamEntry.getKey();
620                     if (dataStream.getQuantity().isSpeed()) // only one speed quantity allowed per data source
621                     {
622                         DualWeightedMean zCongFreeOfStream = streamEntry.getValue();
623                         double u = Math.min(zCongFreeOfStream.getCong(), zCongFreeOfStream.getFree());
624                         w.put(dataStream.getDataSource(), // 1 speed quantity per source allowed
625                                 .5 * (1.0 + Math.tanh((Egtf.this.vc - u) / Egtf.this.deltaV)));
626                         continue;
627                     }
628                 }
629 
630                 // sum available data sources per quantity
631                 Double wMean = null;
632                 for (Map.Entry<Quantity<?, ?>, double[][]> qEntry : map.entrySet())
633                 {
634                     Quantity<?, ?> quantity = qEntry.getKey();
635                     WeightedMean z = new WeightedMean();
636                     for (Map.Entry<DataStream<?>, DualWeightedMean> zEntry : zCongFree.entrySet())
637                     {
638                         DataStream<?> dataStream = zEntry.getKey();
639                         if (dataStream.getQuantity().equals(quantity))
640                         {
641                             // obtain congestion level
642                             double wCong;
643                             if (!w.containsKey(dataStream.getDataSource()))
644                             {
645                                 // this data source has no speed data, but congestion level can be estimated from other sources
646                                 if (wMean == null)
647                                 {
648                                     // let's see if speed was estimated already
649                                     for (Quantity<?, ?> prevQuant : quantities)
650                                     {
651                                         if (prevQuant.equals(quantity))
652                                         {
653                                             // it was not, get mean of other data source
654                                             wMean = 0.0;
655                                             for (double ww : w.values())
656                                             {
657                                                 wMean += ww / w.size();
658                                             }
659                                             break;
660                                         }
661                                         else if (prevQuant.isSpeed())
662                                         {
663                                             wMean = .5 * (1.0
664                                                     + Math.tanh((Egtf.this.vc - map.get(prevQuant)[i][j]) / Egtf.this.deltaV));
665                                             break;
666                                         }
667                                     }
668                                 }
669                                 wCong = wMean;
670                             }
671                             else
672                             {
673                                 wCong = w.get(dataStream.getDataSource());
674                             }
675                             // calculate estimated value z of this data source (no duplicate quantities per source allowed)
676                             double wfree = 1.0 - wCong;
677                             DualWeightedMean zCongFreej = zEntry.getValue();
678                             double zStream = wCong * zCongFreej.getCong() + wfree * zCongFreej.getFree();
679                             double weight;
680                             if (w.size() > 1)
681                             {
682                                 // data source more important if more and nearer measurements
683                                 double beta = wCong * zCongFreej.getDenominatorCong() + wfree * zCongFreej.getDenominatorFree();
684                                 // more important if more reliable (smaller standard deviation) at congestion level
685                                 double alpha = wCong / dataStream.getThetaCong() + wfree / dataStream.getThetaFree();
686                                 weight = alpha * beta;
687                             }
688                             else
689                             {
690                                 weight = 1.0;
691                             }
692                             z.add(zStream, weight);
693                         }
694                     }
695                     qEntry.getValue()[i][j] = z.get();
696                 }
697             }
698         }
699         notifyListeners(1.0);
700 
701         return Optional.of(new FilterDouble(location, time, map));
702     }
703 
704     /**
705      * Returns filtered data that is processed using fast fourier transformation. This is much faster than the standard filter,
706      * at the cost that all input data is discretized to the output grid. The gain in computation speed is however such that
707      * finer output grids can be used to alleviate this. For discretization the output grid needs to be equidistant. It is
708      * recommended to set a Kernel with maximum bounds before using this method.
709      * <p>
710      * More than being a fast implementation of the Adaptive Smoothing Method, this implementation includes all data source like
711      * the Extended Generalized Treiber-Helbing Filter.
712      * @param xMin minimum location value of output grid [m]
713      * @param xStep location step of output grid [m]
714      * @param xMax maximum location value of output grid [m]
715      * @param tMin minimum time value of output grid [s]
716      * @param tStep time step of output grid [s]
717      * @param tMax maximum time value of output grid [s]
718      * @param quantities quantities to calculate filtered data of
719      * @return filtered data, empty when interrupted
720      */
721     @SuppressWarnings("methodlength")
722     public Optional<Filter> filterFastSI(final double xMin, final double xStep, final double xMax, final double tMin,
723             final double tStep, final double tMax, final Quantity<?, ?>... quantities)
724     {
725         if (xMin > xMax || xStep <= 0.0 || tMin > tMax || tStep <= 0.0)
726         {
727             throw new IllegalArgumentException(
728                     "Ill-defined grid. Make sure that xMax >= xMin, dx > 0, tMax >= tMin and dt > 0");
729         }
730         if (notifyListeners(0.0))
731         {
732             return Optional.empty();
733         }
734 
735         // initialize data
736         int n = 1 + (int) ((xMax - xMin) / xStep);
737         double[] location = new double[n];
738         IntStream.range(0, n).forEach(i -> location[i] = xMin + i * xStep);
739         n = 1 + (int) ((tMax - tMin) / tStep);
740         double[] time = new double[n];
741         IntStream.range(0, n).forEach(j -> time[j] = tMin + j * tStep);
742         Map<Quantity<?, ?>, double[][]> map = new LinkedHashMap<>();
743         Map<Quantity<?, ?>, double[][]> weights = new LinkedHashMap<>();
744         for (Quantity<?, ?> quantity : quantities)
745         {
746             map.put(quantity, new double[location.length][time.length]);
747             weights.put(quantity, new double[location.length][time.length]);
748         }
749 
750         // discretize Kernel
751         double xFrom = this.kernel.fromLocation(0.0);
752         xFrom = Double.isInfinite(xFrom) ? 2.0 * (xMin - xMax) : xFrom;
753         double xTo = this.kernel.toLocation(0.0);
754         xTo = Double.isInfinite(xTo) ? 2.0 * (xMax - xMin) : xTo;
755         double[] dx = equidistant(xFrom, xStep, xTo);
756         double tFrom = this.kernel.fromTime(0.0);
757         tFrom = Double.isInfinite(tFrom) ? 2.0 * (tMin - tMax) : tFrom;
758         double tTo = this.kernel.toTime(0.0);
759         tTo = Double.isInfinite(tTo) ? 2.0 * (tMax - tMin) : tTo;
760         double[] dt = equidistant(tFrom, tStep, tTo);
761         double[][] phiCong = new double[dx.length][dt.length];
762         double[][] phiFree = new double[dx.length][dt.length];
763         for (int i = 0; i < dx.length; i++)
764         {
765             for (int j = 0; j < dt.length; j++)
766             {
767                 phiCong[i][j] = this.kernel.weight(this.cCong, dx[i], dt[j]);
768                 phiFree[i][j] = this.kernel.weight(this.cFree, dx[i], dt[j]);
769             }
770         }
771 
772         // discretize data
773         Map<DataStream<?>, double[][]> dataSum = new LinkedHashMap<>();
774         Map<DataStream<?>, double[][]> dataCount = new LinkedHashMap<>(); // integer counts, must be double[][] for convolution
775         // loop grid locations
776         for (int i = 0; i < location.length; i++)
777         {
778             // filter applicable data for location
779             Map<Double, NavigableMap<Double, Map<DataStream<?>, Double>>> spatialData =
780                     this.data.subMap(location[i] - 0.5 * xStep, true, location[i] + 0.5 * xStep, true);
781             // loop grid times
782             for (int j = 0; j < time.length; j++)
783             {
784                 // filter and loop applicable data for time
785                 for (NavigableMap<Double, Map<DataStream<?>, Double>> locationData : spatialData.values())
786                 {
787                     NavigableMap<Double, Map<DataStream<?>, Double>> temporalData =
788                             locationData.subMap(time[j] - 0.5 * tStep, true, time[j] + 0.5 * tStep, true);
789                     for (Map<DataStream<?>, Double> timeData : temporalData.values())
790                     {
791                         for (Map.Entry<DataStream<?>, Double> timeEntry : timeData.entrySet())
792                         {
793                             if (map.containsKey(timeEntry.getKey().getQuantity()) || timeEntry.getKey().getQuantity().isSpeed())
794                             {
795                                 dataSum.computeIfAbsent(timeEntry.getKey(),
796                                         (key) -> new double[location.length][time.length])[i][j] += timeEntry.getValue();
797                                 dataCount.computeIfAbsent(timeEntry.getKey(),
798                                         (key) -> new double[location.length][time.length])[i][j]++;
799                             }
800                         }
801                     }
802                 }
803             }
804         }
805 
806         // figure out the congestion level estimated for each data source
807         double steps = quantities.length + 1; // speed (for congestion level) and then all in quantities
808         double step = 0;
809         // store maps to prevent us from calculating the convolution for speed again later
810         Map<DataSource, double[][]> w = new LinkedHashMap<>();
811         Map<DataSource, double[][]> zCongSpeed = new LinkedHashMap<>();
812         Map<DataSource, double[][]> zFreeSpeed = new LinkedHashMap<>();
813         Map<DataSource, double[][]> nCongSpeed = new LinkedHashMap<>();
814         Map<DataSource, double[][]> nFreeSpeed = new LinkedHashMap<>();
815         for (Map.Entry<DataStream<?>, double[][]> zEntry : dataSum.entrySet())
816         {
817             DataStream<?> dataStream = zEntry.getKey();
818             if (dataStream.getQuantity().isSpeed()) // only one speed quantity allowed per data source
819             {
820                 // notify
821                 double[][] vCong = Convolution.convolution(phiCong, zEntry.getValue());
822                 if (notifyListeners((step + 0.25) / steps))
823                 {
824                     return null;
825                 }
826                 double[][] vFree = Convolution.convolution(phiFree, zEntry.getValue());
827                 if (notifyListeners((step + 0.5) / steps))
828                 {
829                     return null;
830                 }
831                 double[][] count = dataCount.get(dataStream);
832                 double[][] nCong = Convolution.convolution(phiCong, count);
833                 if (notifyListeners((step + 0.75) / steps))
834                 {
835                     return null;
836                 }
837                 double[][] nFree = Convolution.convolution(phiFree, count);
838                 double[][] wSource = new double[vCong.length][vCong[0].length];
839                 for (int i = 0; i < vCong.length; i++)
840                 {
841                     for (int j = 0; j < vCong[0].length; j++)
842                     {
843                         double u = Math.min(vCong[i][j] / nCong[i][j], vFree[i][j] / nFree[i][j]);
844                         wSource[i][j] = .5 * (1.0 + Math.tanh((Egtf.this.vc - u) / Egtf.this.deltaV));
845                     }
846                 }
847                 w.put(dataStream.getDataSource(), wSource);
848                 zCongSpeed.put(dataStream.getDataSource(), vCong);
849                 zFreeSpeed.put(dataStream.getDataSource(), vFree);
850                 nCongSpeed.put(dataStream.getDataSource(), nCong);
851                 nFreeSpeed.put(dataStream.getDataSource(), nFree);
852             }
853         }
854         step++;
855         if (notifyListeners(step / steps))
856         {
857             return null;
858         }
859 
860         // sum available data sources per quantity
861         double[][] wMean = null;
862         for (Quantity<?, ?> quantity : quantities)
863         {
864             // gather place for this quantity
865             double[][] qData = map.get(quantity);
866             double[][] qWeights = weights.get(quantity);
867             // loop streams that provide this quantity
868             Set<Map.Entry<DataStream<?>, double[][]>> zEntries = new LinkedHashSet<>();
869             for (Map.Entry<DataStream<?>, double[][]> zEntry : dataSum.entrySet())
870             {
871                 if (zEntry.getKey().getQuantity().equals(quantity))
872                 {
873                     zEntries.add(zEntry);
874                 }
875             }
876             double streamCounter = 0;
877             for (Map.Entry<DataStream<?>, double[][]> zEntry : zEntries)
878             {
879                 DataStream<?> dataStream = zEntry.getKey();
880 
881                 // obtain congestion level
882                 double[][] wj;
883                 if (!w.containsKey(dataStream.getDataSource()))
884                 {
885                     // this data source has no speed data, but congestion level can be estimated from other sources
886                     if (wMean == null)
887                     {
888                         // let's see if speed was estimated already
889                         for (Quantity<?, ?> prevQuant : quantities)
890                         {
891                             if (prevQuant.equals(quantity))
892                             {
893                                 // it was not, get mean of other data source
894                                 wMean = new double[location.length][time.length];
895                                 for (double[][] ww : w.values())
896                                 {
897                                     for (int i = 0; i < location.length; i++)
898                                     {
899                                         for (int j = 0; j < time.length; j++)
900                                         {
901                                             wMean[i][j] += ww[i][j] / w.size();
902                                         }
903                                     }
904                                 }
905                                 break;
906                             }
907                             else if (prevQuant.isSpeed())
908                             {
909                                 wMean = new double[location.length][time.length];
910                                 double[][] v = map.get(prevQuant);
911                                 for (int i = 0; i < location.length; i++)
912                                 {
913                                     for (int j = 0; j < time.length; j++)
914                                     {
915                                         wMean[i][j] = .5 * (1.0 + Math.tanh((Egtf.this.vc - v[i][j]) / Egtf.this.deltaV));
916                                     }
917                                 }
918                                 break;
919                             }
920                         }
921                     }
922                     wj = wMean;
923                 }
924                 else
925                 {
926                     wj = w.get(dataStream.getDataSource());
927                 }
928 
929                 // convolutions of filters with discretized data and data counts
930                 double[][] zCong;
931                 double[][] zFree;
932                 double[][] nCong;
933                 double[][] nFree;
934                 if (dataStream.getQuantity().isSpeed())
935                 {
936                     zCong = zCongSpeed.get(dataStream.getDataSource());
937                     zFree = zFreeSpeed.get(dataStream.getDataSource());
938                     nCong = nCongSpeed.get(dataStream.getDataSource());
939                     nFree = nFreeSpeed.get(dataStream.getDataSource());
940                 }
941                 else
942                 {
943                     zCong = Convolution.convolution(phiCong, zEntry.getValue());
944                     if (notifyListeners((step + (streamCounter + 0.25) / zEntries.size()) / steps))
945                     {
946                         return null;
947                     }
948                     zFree = Convolution.convolution(phiFree, zEntry.getValue());
949                     if (notifyListeners((step + (streamCounter + 0.5) / zEntries.size()) / steps))
950                     {
951                         return null;
952                     }
953                     double[][] count = dataCount.get(dataStream);
954                     nCong = Convolution.convolution(phiCong, count);
955                     if (notifyListeners((step + (streamCounter + 0.75) / zEntries.size()) / steps))
956                     {
957                         return null;
958                     }
959                     nFree = Convolution.convolution(phiFree, count);
960                 }
961 
962                 // loop grid to add to each weighted sum (weighted per data source)
963                 for (int i = 0; i < location.length; i++)
964                 {
965                     for (int j = 0; j < time.length; j++)
966                     {
967                         double wCong = wj[i][j];
968                         double wFree = 1.0 - wCong;
969                         double value = wCong * zCong[i][j] / nCong[i][j] + wFree * zFree[i][j] / nFree[i][j];
970                         // the fast filter supplies convoluted data counts, i.e. amount of data and filter proximity; this
971                         // is exactly what the EGTF method needs to weigh data sources
972                         double beta = wCong * nCong[i][j] + wFree * nFree[i][j];
973                         double alpha = wCong / dataStream.getThetaCong() + wFree / dataStream.getThetaFree();
974                         double weight = beta * alpha;
975                         qData[i][j] += (value * weight);
976                         qWeights[i][j] += weight;
977                     }
978                 }
979                 streamCounter++;
980                 if (notifyListeners((step + streamCounter / zEntries.size()) / steps))
981                 {
982                     return null;
983                 }
984             }
985             for (int i = 0; i < location.length; i++)
986             {
987                 for (int j = 0; j < time.length; j++)
988                 {
989                     qData[i][j] /= qWeights[i][j];
990                 }
991             }
992             step++;
993         }
994 
995         return Optional.of(new FilterDouble(location, time, map));
996     }
997 
998     /**
999      * Returns an equidistant vector that includes 0.
1000      * @param from lowest value to include
1001      * @param step step
1002      * @param to highest value to include
1003      * @return equidistant vector that includes 0
1004      */
1005     private double[] equidistant(final double from, final double step, final double to)
1006     {
1007         int n1 = (int) (-from / step);
1008         int n2 = (int) (to / step);
1009         int n = n1 + n2 + 1;
1010         double[] array = new double[n];
1011         for (int i = 0; i < n; i++)
1012         {
1013             array[i] = i < n1 ? step * (-n1 + i) : step * (i - n1);
1014         }
1015         return array;
1016     }
1017 
1018     // *********************
1019     // *** EVENT METHODS ***
1020     // *********************
1021 
1022     /**
1023      * Interrupt the calculation.
1024      */
1025     public final void interrupt()
1026     {
1027         this.interrupted = true;
1028     }
1029 
1030     /**
1031      * Add listener.
1032      * @param listener listener
1033      */
1034     public final void addListener(final EgtfListener listener)
1035     {
1036         this.listeners.add(listener);
1037     }
1038 
1039     /**
1040      * Remove listener.
1041      * @param listener listener
1042      */
1043     public final void removeListener(final EgtfListener listener)
1044     {
1045         this.listeners.remove(listener);
1046     }
1047 
1048     /**
1049      * Notify all listeners.
1050      * @param progress progress, a value in the range [0 ... 1]
1051      * @return whether the filter is interrupted
1052      */
1053     private boolean notifyListeners(final double progress)
1054     {
1055         if (!this.listeners.isEmpty())
1056         {
1057             EgtfEvent event = new EgtfEvent(this, progress);
1058             for (EgtfListener listener : this.listeners)
1059             {
1060                 listener.notifyProgress(event);
1061             }
1062         }
1063         return this.interrupted;
1064     }
1065 
1066     // **********************
1067     // *** HELPER CLASSES ***
1068     // **********************
1069 
1070     /**
1071      * Small class to build up a weighted mean under the congestion and free flow assumption.
1072      */
1073     private final class DualWeightedMean
1074     {
1075         /** Cumulative congestion numerator of weighted mean fraction, i.e. weighted sum. */
1076         private double numeratorCong;
1077 
1078         /** Cumulative free flow numerator of weighted mean fraction, i.e. weighted sum. */
1079         private double numeratorFree;
1080 
1081         /** Cumulative congestion denominator of weighted mean fraction, i.e. sum of weights. */
1082         private double denominatorCong;
1083 
1084         /** Cumulative free flow denominator of weighted mean fraction, i.e. sum of weights. */
1085         private double denominatorFree;
1086 
1087         /**
1088          * Adds a congestion value with weight.
1089          * @param value value
1090          * @param weight weight
1091          */
1092         public void addCong(final double value, final double weight)
1093         {
1094             this.numeratorCong += value * weight;
1095             this.denominatorCong += weight;
1096         }
1097 
1098         /**
1099          * Adds a free flow value with weight.
1100          * @param value value
1101          * @param weight weight
1102          */
1103         public void addFree(final double value, final double weight)
1104         {
1105             this.numeratorFree += value * weight;
1106             this.denominatorFree += weight;
1107         }
1108 
1109         /**
1110          * Returns the weighted congestion mean of available data.
1111          * @return weighted mean of available data
1112          */
1113         public double getCong()
1114         {
1115             return this.numeratorCong / this.denominatorCong;
1116         }
1117 
1118         /**
1119          * Returns the weighted free flow mean of available data.
1120          * @return weighted free flow mean of available data
1121          */
1122         public double getFree()
1123         {
1124             return this.numeratorFree / this.denominatorFree;
1125         }
1126 
1127         /**
1128          * Returns the sum of congestion weights.
1129          * @return the sum of congestion weights
1130          */
1131         public double getDenominatorCong()
1132         {
1133             return this.denominatorCong;
1134         }
1135 
1136         /**
1137          * Returns the sum of free flow weights.
1138          * @return the sum of free flow weights
1139          */
1140         public double getDenominatorFree()
1141         {
1142             return this.denominatorFree;
1143         }
1144 
1145         @Override
1146         public String toString()
1147         {
1148             return "DualWeightedMean [numeratorCong=" + this.numeratorCong + ", numeratorFree=" + this.numeratorFree
1149                     + ", denominatorCong=" + this.denominatorCong + ", denominatorFree=" + this.denominatorFree + "]";
1150         }
1151 
1152     }
1153 
1154     /**
1155      * Small class to build up a weighted mean.
1156      */
1157     private final class WeightedMean
1158     {
1159         /** Cumulative numerator of weighted mean fraction, i.e. weighted sum. */
1160         private double numerator;
1161 
1162         /** Cumulative denominator of weighted mean fraction, i.e. sum of weights. */
1163         private double denominator;
1164 
1165         /**
1166          * Adds a value with weight.
1167          * @param value value
1168          * @param weight weight
1169          */
1170         public void add(final double value, final double weight)
1171         {
1172             this.numerator += value * weight;
1173             this.denominator += weight;
1174         }
1175 
1176         /**
1177          * Returns the weighted mean of available data.
1178          * @return weighted mean of available data
1179          */
1180         public double get()
1181         {
1182             return this.numerator / this.denominator;
1183         }
1184 
1185         @Override
1186         public String toString()
1187         {
1188             return "WeightedMean [numerator=" + this.numerator + ", denominator=" + this.denominator + "]";
1189         }
1190 
1191     }
1192 
1193     @Override
1194     public String toString()
1195     {
1196         return "EGTF [kernel=" + this.kernel + ", cCong=" + this.cCong + ", cFree=" + this.cFree + ", deltaV=" + this.deltaV
1197                 + ", vc=" + this.vc + ", dataSources=" + this.dataSources + ", data=" + this.data + ", interrupted="
1198                 + this.interrupted + ", listeners=" + this.listeners + "]";
1199     }
1200 
1201 }