timeseries¶
This module defines tools for geometric analysis of one-dimensional (time-series) data sets. The main classes are
See timeseries-data for a more general outline.
Copyright¶
- This file is part of https://github.com/geomdata/gda-public/
- 2015, 2016, 2017 by Geometric Data Analytics, Inc. (http://geomdata.com)
- AGPL license. See LICENSE or https://github.com/geomdata/gda-public/blob/master/LICENSE
Examples¶
>>> el = Signal([2.0, 3.0, 0.0, 5.0, 2.5, 2.9])
>>> el.make_pers()
>>> el.pers.diagram
birth_index death_index birth death pers
0 0 1 2.0 3.0 1.0
1 4 3 2.5 5.0 2.5
2 2 3 0.0 5.0 5.0
>>> bin_counts, bins = el.pers.bin(1.0)
>>> print(bins)
[-inf 0. 1. 2. 3. 4. 5. inf]
>>> print(bin_counts)
[[ 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 1.]
[ 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 1. 1. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0. 0. 0.]]
>>> sorted(list(el.pers.domains.keys()))
[(0, 1), (2, 3), (3, 4)]
>>> for interval in el.iter_intervals():
... print("h_A( {} ) == {}".format(interval,el.interval_height(interval)))
h_A( (0, 1) ) == 1.0
h_A( (0, 2) ) == 0.0
h_A( (0, 3) ) == 0.0
h_A( (0, 4) ) == 0.0
h_A( (0, 5) ) == 0.0
h_A( (1, 2) ) == 0.0
h_A( (1, 3) ) == 0.0
h_A( (1, 4) ) == 0.0
h_A( (1, 5) ) == 0.0
h_A( (2, 3) ) == 5.0
h_A( (2, 4) ) == 0.0
h_A( (2, 5) ) == 0.0
h_A( (3, 4) ) == 2.5
h_A( (3, 5) ) == 0.0
h_A( (4, 5) ) == 0.0
>>> list(el.pers.forest.keys())
[None]
>>> sorted(list(el.pers.forest[None]))
[0, 1, 2]
>>> el.jagged(6.0)
0 0.0
1 0.0
2 0.0
3 0.0
4 0.0
5 0.0
dtype: float64
>>> el = Signal([6.5,0.0,2.0])
>>> el.make_pers()
>>> el.pers.diagram
birth_index death_index birth death pers
0 1 0 0.0 6.5 6.5
>>> list(el.pers.forest[None])
[0]
>>> el.vertices
time height
0 0.0 6.5
1 1.0 0.0
2 2.0 2.0
>>> el.jagged() #el.pers.diagram,el.vertices.index,el.vertices.dtype)
0 6.5
1 0.0
2 0.0
dtype: float64
>>> elN = el.sample_near(sigma=0.1)
>>> elN.make_pers()
>>> elN.pers.domains == el.pers.domains
True
>>> el = Signal([6.5,7.0,2.0,4.5,3.9,9.0,8.3,8.7,5.5,9.9])
>>> el.vertices
time height
0 0.0 6.5
1 1.0 7.0
2 2.0 2.0
3 3.0 4.5
4 4.0 3.9
5 5.0 9.0
6 6.0 8.3
7 7.0 8.7
8 8.0 5.5
9 9.0 9.9
>>> el.edges
src dst max height
2 2 3 3 4.5
3 3 4 3 4.5
0 0 1 1 7.0
1 1 2 1 7.0
6 6 7 7 8.7
7 7 8 7 8.7
4 4 5 5 9.0
5 5 6 5 9.0
8 8 9 9 9.9
>>> el.make_pers()
>>> el.pers.diagram
birth_index death_index birth death pers
2 6 7 8.3 8.7 0.4
1 0 1 6.5 7.0 0.5
0 4 3 3.9 4.5 0.6
3 8 5 5.5 9.0 3.5
4 2 9 2.0 9.9 7.9
>>> el.feature()
time height
2 2.0 2.0
3 3.0 4.5
4 4.0 3.9
5 5.0 9.0
6 6.0 8.3
7 7.0 8.7
8 8.0 5.5
9 9.0 9.9
>>> el.pers.syzygy((0,0))
2 0.4
1 0.5
0 0.6
3 3.5
4 7.9
dtype: float64
>>> el.pers.syzygy((1,2))
2 251.2908
1 159.2500
0 47.3850
3 1559.2500
4 1548.5580
dtype: float64
>>> el.pers.forest_parents == {0: 4, 1: None, 2: 3, 3: 4, 4: None}
True
>>> el.vertices['height'].sum()/len(el.vertices)
6.5299999999999994
>>> el.normalize()
>>> el2 = Signal(el.vertices)
>>> el2.make_pers()
>>> all(el2.pers.diagram == el.pers.diagram)
True
>>> el = Signal([0.0,3.0,1.5,2.2,0.001])
>>> el.make_pers()
>>> el.vertices
time height
0 0.0 0.000
1 1.0 3.000
2 2.0 1.500
3 3.0 2.200
4 4.0 0.001
>>> el.edges
src dst max height
2 2 3 3 2.2
3 3 4 3 2.2
0 0 1 1 3.0
1 1 2 1 3.0
>>> el.pers.diagram
birth_index death_index birth death pers
0 2 3 1.500 2.2 0.700
1 4 1 0.001 3.0 2.999
2 0 1 0.000 3.0 3.000
>>> el = Signal([0.0,0.7,0.45,0.55,0.3, 1.0],
... times=[0.1, 0.2, 0.3, 0.6, 0.8, 0.85])
>>> el.vertices
time height
0 0.10 0.00
1 0.20 0.70
2 0.30 0.45
3 0.60 0.55
4 0.80 0.30
5 0.85 1.00
>>> el.edges
src dst max height
2 2 3 3 0.55
3 3 4 3 0.55
0 0 1 1 0.70
1 1 2 1 0.70
4 4 5 5 1.00
>>> el.make_pers()
>>> el.pers.diagram
birth_index death_index birth death pers
0 2 3 0.45 0.55 0.1
1 4 1 0.30 0.70 0.4
2 0 5 0.00 1.00 1.0
>>> el = Signal([0.0,0.5,0.4,0.9,0.1,1.0])
>>> el.make_pers()
>>> el.pers.diagram
birth_index death_index birth death pers
0 2 1 0.4 0.5 0.1
1 4 3 0.1 0.9 0.8
2 0 5 0.0 1.0 1.0
>>> for F in el.iter_features(min_pers=0.5): print(F)
time height
0 0.0 0.0
1 1.0 0.5
2 2.0 0.4
3 3.0 0.9
4 4.0 0.1
5 5.0 1.0
time height
3 3.0 0.9
4 4.0 0.1
>>> el = Signal(np.sin(np.arange(0,8*np.pi,0.1)))
>>> el.make_pers()
>>> el.pers.domains == {(110, 204): 4, (204, 236): 3, (0, 16): 2, (47, 79): 0, (141, 173): 1}
True
>>> s = Signal([50.0, 120.0, 100, 180, 200, 150, 135])
>>> s.make_pers()
>>> s.pers.diagram
birth_index death_index birth death pers
0 2 1 100.0 120.0 20.0
1 6 4 135.0 200.0 65.0
2 0 4 50.0 200.0 150.0
>>> s.pers.mergetree
{1: (0, 2), 4: (1, 6)}
Functions
jagged(persdiag, index) |
Produce a piecewise-linear function that matches the given persistence diagram. |
wavy(pasrdiad, index) |
Produce a piecewise-sine function that matches the given persistence diagram. |
Classes
Signal(values[, times]) |
|
SpaceCurve(tn[, px, py, pz, quality, …]) |
SpaceCurve is a Python class for studying curves in \(\mathbb{R}^2\) or \(\mathbb{R}^3\). |