giddy.markov.GeoRank_Markov¶
-
class
giddy.markov.GeoRank_Markov(y)[source]¶ Geographic Rank Markov. Geographic units are considered as Markov states.
- Parameters
- yarray
(n, t) with t>>n, one row per observation (n total), one column recording the value of each observation, with as many columns as time periods.
Notes
Refer to [Rey14b] Equation (13)-(16) for details. Ties are resolved by assigning distinct ranks, corresponding to the order that the values occur in each cross section.
Examples
US nominal per capita income 48 states 81 years 1929-2009
>>> from giddy.markov import GeoRank_Markov >>> import libpysal as ps >>> import numpy as np >>> f = ps.io.open(ps.examples.get_path("usjoin.csv")) >>> pci = np.array([f.by_col[str(y)] for y in range(1929,2010)]).transpose() >>> m = GeoRank_Markov(pci) >>> m.transitions array([[38., 0., 8., ..., 0., 0., 0.], [ 0., 15., 0., ..., 0., 1., 0.], [ 6., 0., 44., ..., 5., 0., 0.], ..., [ 2., 0., 5., ..., 34., 0., 0.], [ 0., 0., 0., ..., 0., 18., 2.], [ 0., 0., 0., ..., 0., 3., 14.]]) >>> m.p array([[0.475 , 0. , 0.1 , ..., 0. , 0. , 0. ], [0. , 0.1875, 0. , ..., 0. , 0.0125, 0. ], [0.075 , 0. , 0.55 , ..., 0.0625, 0. , 0. ], ..., [0.025 , 0. , 0.0625, ..., 0.425 , 0. , 0. ], [0. , 0. , 0. , ..., 0. , 0.225 , 0.025 ], [0. , 0. , 0. , ..., 0. , 0.0375, 0.175 ]]) >>> m.fmpt array([[ 48. , 63.35532038, 92.75274652, ..., 82.47515731, 71.01114491, 68.65737127], [108.25928005, 48. , 127.99032986, ..., 92.03098299, 63.36652935, 61.82733039], [ 76.96801786, 64.7713783 , 48. , ..., 73.84595169, 72.24682723, 69.77497173], ..., [ 93.3107474 , 62.47670463, 105.80634118, ..., 48. , 69.30121319, 67.08838421], [113.65278078, 61.1987031 , 133.57991745, ..., 96.0103924 , 48. , 56.74165107], [114.71894813, 63.4019776 , 134.73381719, ..., 97.287895 , 61.45565054, 48. ]]) >>> m.sojourn_time array([ 1.9047619 , 1.23076923, 2.22222222, 1.73913043, 1.15942029, 3.80952381, 1.70212766, 1.25 , 1.31147541, 1.11111111, 1.73913043, 1.37931034, 1.17647059, 1.21212121, 1.33333333, 1.37931034, 1.09589041, 2.10526316, 2. , 1.45454545, 1.26984127, 26.66666667, 1.19402985, 1.23076923, 1.09589041, 1.56862745, 1.26984127, 2.42424242, 1.50943396, 2. , 1.29032258, 1.09589041, 1.6 , 1.42857143, 1.25 , 1.45454545, 1.29032258, 1.6 , 1.17647059, 1.56862745, 1.25 , 1.37931034, 1.45454545, 1.42857143, 1.29032258, 1.73913043, 1.29032258, 1.21212121])
- Attributes
- parray
(n, n), transition probability matrix for geographic rank Markov.
- steady_statearray
(n, ), ergodic distribution.
- transitionsarray
(n, n), count of rank transitions between each geographic unit i and j.
- fmptarray
(n, n), first mean passage times.
- sojourn_timearray
(n, ), sojourn times.