How to use arithmetic operators on trajectories?

Visualization with the | (or) operator
Concatenation with the + (plus) operator
Differences on trajectories with the - (minus) operator
Differences on collections with the - (minus) operator
Indexation with the [] (bracket) operator
Overlapping of trajectories with the & (and) operator
Intersection of collections with the & (and) operator

Visualization with the | (or) operator

The | (prononce “or”) operator is very useful in interactive environments (IPython, Jupyter, etc.) in order to put data structures next to each other. The result of this operation is not designed to be stored in any variable.

For example, we can preview two trajectories on the same line:

from traffic.data.samples import belevingsvlucht

belevingsvlucht | belevingsvlucht.next("aligned_on_ils('EHAM')")

Flight

callsign: TRA051
aircraft: 484506 · 🇳🇱 PH-HZO (B738)
start: 2018-05-30 15:21:38+00:00
stop: 2018-05-30 20:22:56+00:00
duration: 0 days 05:01:18
sampling rate: 1 second(s)

Flight

callsign: TRA051
aircraft: 484506 · 🇳🇱 PH-HZO (B738)
start: 2018-05-30 20:14:29+00:00
stop: 2018-05-30 20:17:58+00:00
duration: 0 days 00:03:29
sampling rate: 1 second(s)

Concatenation with the + (plus) operator

The + operator is a simple concatenation operator. In other words, all the pandas DataFrames of the given structures are concatenated and wrapped in a Traffic object.

Flight.__add__(other)

Concatenation operator.

Parameters:: other (Union[Literal[0], Flight, Traffic]) – is the other Flight or Traffic.
Return type:: Traffic
Returns:: The sum of two Flights returns a Traffic collection. Summing a Flight with 0 returns a Traffic collection with only one trajectory, for compatibility reasons with the sum() builtin.

Traffic.__add__(other)

Concatenation operator.

Parameters:: other (Union[Literal[0], Flight, Traffic]) – is the other Flight or Traffic.
Return type:: Traffic
Returns:: The sum of two Traffic returns a Traffic collection. Summing a Traffic with 0 returns the same Traffic, for compatibility reasons with the sum() builtin.

With the same trajectories as above, we can construct a Traffic object:

from traffic.data.samples import belevingsvlucht, pixair_toulouse

belevingsvlucht + pixair_toulouse

Traffic

with 2 identifiers

		count
icao24	callsign
484506	TRA051	16005
39b861	PXR31F	1819

The sum built-in function can be used to concatenate many flights into a Traffic collection.

Differences on trajectories with the - (minus) operator

The - operator serves a way to remove segments in a trajectory. The resulting structure will consist in 0, 1 or many trajectory segments wrapped in a FlightIterator object.

Flight.__sub__(other)

Difference operator.

Parameters:: other (Flight | FlightIterator | Interval | IntervalCollection) – refers to anything having one or several start and end (a.k.a. stop) dates.
Return type:: FlightIterator
Returns:: After intervals are pruned from a trajectory, unconnected segments may remain. You should iterate on the result of the - operator.

For example, on the following sample trajectory, the aircraft performs many landing attempts at Lelystad airport (EHLE) in the Netherlands, which are easily labelled as go-arounds. The difference operator will result in the trajectory section before and after all the landing attempts.

belevingsvlucht - belevingsvlucht.go_around("EHLE")

FlightIterator

Flight

callsign: TRA051
aircraft: 484506 · 🇳🇱 PH-HZO (B738)
start: 2018-05-30 15:21:38+00:00
stop: 2018-05-30 16:00:56+00:00
duration: 0 days 00:39:18
sampling rate: 1 second(s)

Flight

callsign: TRA051
aircraft: 484506 · 🇳🇱 PH-HZO (B738)
start: 2018-05-30 19:47:46+00:00
stop: 2018-05-30 20:22:56+00:00
duration: 0 days 00:35:10
sampling rate: 1 second(s)

Differences on collections with the - (minus) operator

The - operators also serves as a way to remove flights from a Traffic collection. The operator behaves slightly differently if both collections are equipped with a flight_id attribute or not.

Traffic.__sub__(other)

Remove trajectories from a Traffic object.

Parameters:

other (str | list[str] | set[str] | Flight | Traffic) –

When the other attribute is a string, or a list/set of strings, all flights matching the flight_id, callsign or icao24 attribute are removed from the collection;
When the other attribute is a Flight, the collection will be pruned of the trajectory with the same flight_id; or the segment of trajectory for that icao24 address between the start and stop timestamps;
When the other attribute is a Traffic object, the difference is computed based on the flight_id if both structures have one; otherwise, we iterate through flights and consider removing part of the trajectory.

Return type:

None | Traffic

Returns:

a new collection of trajectories as a Traffic object

For example, in the following sample dataset, we build a sub dataset of all trajectories going through a navaid point called “ODINA” at the border between Switzerland and Italy. The - operator produces a new dataset of trajectories not going through ODINA.

from traffic.data.samples import switzerland

through_odina = switzerland.has('aligned_on_navpoint("ODINA")').eval()
difference = switzerland - through_odina

through_odina | difference

Traffic

with 113 identifiers

		count
icao24	callsign
440005	EZY12VJ	169
39e46f	CCM531D	155
40123f	BAW544K	147
3946e2	AFR85EZ	145
400e4a	EXS88C	145
3950c0	AFR36RB	143
44c24d	OOPRM	142
4bb852	PGT89P	142
396672	FPO09P	141
4ca2c0	RYR248Z	141

Traffic

with 1130 identifiers

		count
icao24	callsign
500142	T7STK	282
4baa61	THY7WR	186
344417	IBE3279	185
40755f	EZY24DP	184
4068cb	EXS33W	180
3c5ee9	EWG5938	178
3420ca	IBE31CW	176
4009f9	BAW585E	175
4006d6	CLJ6325	174
42428d	AFL2603	174

Indexation with the [] (bracket) operator

Flight.__getitem__(key)

Indexation of flights.

Parameters:

key (str | Interval | IntervalCollection) – the key parameter passed in the brackets

Return type:

Any

Returns:

if key is a string, the bracket operator is equivalent to the dot notation(e.g. flight["duration"] is equivalent to flight.duration)
if key is an Interval, the bracket operator is equivalent to the between() method
if key is an IntervalCollection, the operator iterates on all the intervals provided

The indexation of a Traffic collection is intended to be used in the most versatile way. Any object that could identify a particular trajectory can be used as a key.

Traffic.__getitem__(key)

Indexation of collections.

Parameters:

key (Union[int, slice, str, List[str], Set[str], Series, DataFrame, Traffic]) –

if the key is an integer, will return a Flight object (in order of iteration);
if the key is a slice, will return a Traffic object (in order of iteration);
if the key is a string, will return a Flight object, based on the flight_id, icao24 or callsign;
if the key is a list of string, will return a Traffic object, based on the same criteria as above;
if the key is a pd.Series, will return a Flight object. The key must contain an icao24 feature. It may contain a callsign, a start (or firstSeen) timestamp, a stop (or lastSeen) timestamp. If it contains a flight_id column, this will be assigned to the Flight.
if the key is a pd.DataFrame, will return a Traffic object. The key must contain an icao24 feature. It may contain a callsign, a start (or firstSeen) timestamp, a stop (or lastSeen) timestamp. If it contains a flight_id column, this will be assigned to the Flight.
if the key is a Traffic object, will return a new Traffic collection, based on the flight_id elements present in key. If no flight_id is available, it will return the subset of trajectories in self that overlap with any trajectory in key (with the same icao24 indicator)

Return type:

Flight | Traffic

Returns:

According to the type of the key, the result could be a Flight or a Traffic object.

The following lets us get one or many trajectories:

# The first trajectory in the dataset
switzerland[0]
# The ten first trajectories in the dataset
switzerland[:10]
# The trajectory assigned with callsign ``EZY12VJ``
switzerland['EZY12VJ']

The DataFrame indexation can be useful for example with the following use case. We want to get full trajectories of aircraft entering the Swiss airspace at a particular hour. We first compute the statistics for each trajectory, then build a trajectory subcollection.

from traffic.data import eurofirs

stats = (
    switzerland.clip(eurofirs["LSAS"])
    .summary(["icao24", "callsign", "start", "stop"])
    .eval(max_workers=2)
)
stats

	icao24	callsign	start	stop
0	34150f	VLG86TM	2018-08-01 06:04:30+00:00	2018-08-01 06:19:30+00:00
1	341682	IBS3674	2018-08-01 19:24:10+00:00	2018-08-01 19:34:30+00:00
2	345101	VLG56RH	2018-08-01 18:37:30+00:00	2018-08-01 18:47:10+00:00
3	342441	IBE3122	2018-08-01 15:57:40+00:00	2018-08-01 16:15:20+00:00
4	04c117	KQA117	2018-08-01 20:43:30+00:00	2018-08-01 20:56:30+00:00
...	...	...	...	...
1218	a954ca	CKS9557	2018-08-01 21:45:20+00:00	2018-08-01 21:56:20+00:00
1219	adf775	N9997X	2018-08-01 06:00:30+00:00	2018-08-01 06:14:00+00:00
1220	ab1deb	N815WH	2018-08-01 10:08:00+00:00	2018-08-01 10:16:10+00:00
1221	e80444	LAN705	2018-08-01 18:31:10+00:00	2018-08-01 18:41:50+00:00
1222	c078b1	TSC300	2018-08-01 08:32:50+00:00	2018-08-01 08:41:30+00:00

1223 rows × 4 columns

# All trajectories quitting the airspace between 15:30 and 15:40
subset = stats.query('stop.dt.floor("10 min") == "2018-08-01 15:30Z"')
subset_1530 = switzerland[subset]  # subset is a pd.DataFrame
subset_1530

Traffic

with 13 identifiers

		count
icao24	callsign
4006c8	BAW66GA	95
478771	NAX3YO	94
406ae0	TCX702	88
440005	EZY12VJ	88
3c6628	DLH52X	82
8005ec	AIC143	81
4ca4ed	RYR87WH	75
501d1d	CTN476	66
484aa1	TRA93U	58
44064a	EZY97QR	57

The start and stop timestamps are based on the clipping of the trajectories within the LSAS FIR boundaries. If we want to select the subset of the original trajectories matching those (shorter) selected in subset_1530, we can use the bracket operator again:

# We might prefer the full trajectories that have been matched in subset_1530
switzerland[subset_1530]  # subset is a Traffic object

Traffic

with 13 identifiers

		count
icao24	callsign
440005	EZY12VJ	169
501d1d	CTN476	159
8005ec	AIC143	144
4006c8	BAW66GA	124
3c6628	DLH52X	114
4ca4ed	RYR87WH	108
406ae0	TCX702	107
478771	NAX3YO	107
484aa1	TRA93U	98
4ca175	RYR31CR	98

Overlapping of trajectories with the & (and) operator

When applied on Flight structures, the & operator expresses the concurrency of two trajectories, i.e. the piece of trajectory that is flown while another aircraft is flying.

Flight.__and__(other)

Overlapping of trajectories.

Parameters:: other (Flight)
Return type:: None | Flight
Returns:: the segment of trajectory that overlaps other, if any.

from traffic.data.samples import dreamliner_airfrance

# expansion of the collection into two flights
video, dreamliner = dreamliner_airfrance
# the operator is not commutative
video & dreamliner | dreamliner & video

Flight

callsign: FWKDL
aircraft: 3900fb · 🇫🇷 F-WKDL (TBM7)
start: 2017-12-01 14:40:34+00:00
stop: 2017-12-01 15:59:58+00:00
duration: 0 days 01:19:24
sampling rate: 1 second(s)

Flight

callsign: AFR787V
aircraft: 39c424 · 🇫🇷 F-HRBE (B789)
start: 2017-12-01 14:40:34+00:00
stop: 2017-12-01 15:59:58+00:00
duration: 0 days 01:19:24
sampling rate: 1 second(s)

Intersection of collections with the & (and) operator

When applied on collections, the & operator returns the subset of trajectories that are present in both collections.

Traffic.__and__(other)

Intersection of collections.

Parameters:: other (Traffic)
Return type:: Optional[Traffic]
Returns:: the subset of trajectories present in both collections. The result is based on the flight_id if present, and on intervals otherwise.

# All trajectories entering or quitting the airspace between 15:30 and 15:40 through ODINA
result = through_odina & switzerland[subset_1530]
result

Traffic

with 2 identifiers

		count
icao24	callsign
440005	EZY12VJ	169
4ca4ed	RYR87WH	108

from traffic.data import navaids

ODINA = navaids['ODINA']
m = result.map_leaflet(
    center=ODINA.latlon,
    highlight=dict(red="aligned_on_navpoint('ODINA')")
)
m.add(ODINA)
m