def __init__(self, y, w, permutations=0, significance_level=0.05):
y = y.transpose()
pml = pysal.Moran_Local
#################################################################
# have to optimize conditional spatial permutations over a
# time series - this is a place holder for the foreclosure paper
ml = [pml(yi, w, permutations=permutations) for yi in y]
#################################################################
q = np.array([mli.q for mli in ml]).transpose()
classes = np.arange(1, 5) # no guarantee all 4 quadrants are visited
Markov.__init__(self, q, classes)
self.q = q
self.w = w
n, k = q.shape
k -= 1
self.significance_level = significance_level
move_types = np.zeros((n, k), int)
sm = np.zeros((n, k), int)
self.significance_level = significance_level
if permutations > 0:
p = np.array([mli.p_z_sim for mli in ml]).transpose()
self.p_values = p
pb = p <= significance_level
else:
pb = np.zeros_like(y.T)
for t in range(k):
origin = q[:, t]
dest = q[:, t + 1]
p_origin = pb[:, t]
p_dest = pb[:, t]
for r in range(n):
move_types[r, t] = TT[origin[r], dest[r]]
key = (origin[r], dest[r], p_origin[r], p_dest[r])
sm[r, t] = MOVE_TYPES[key]
if permutations > 0:
self.significant_moves = sm
self.move_types = move_types
# null of own and lag moves being independent
ybar = y.mean(axis=0)
r = y / ybar
ylag = np.array([pysal.lag_spatial(w, yt) for yt in y])
rlag = ylag / ybar
rc = r < 1.
rlagc = rlag < 1.
markov_y = pysal.Markov(rc)
markov_ylag = pysal.Markov(rlagc)
A = np.matrix([[1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0]])
kp = A * np.kron(markov_y.p, markov_ylag.p) * A.T
trans = self.transitions.sum(axis=1)
t1 = np.diag(trans) * kp
t2 = self.transitions
t1 = t1.getA()
self.chi_2 = pysal.spatial_dynamics.markov.chi2(t1, t2)
self.expected_t = t1
self.permutations = permutations
def test___init__(self):
import numpy as np
f = pysal.open(pysal.examples.get_path('usjoin.csv'))
pci = np.array([f.by_col[str(y)] for y in range(1929, 2010)])
q5 = np.array([pysal.Quantiles(y).yb for y in pci]).transpose()
m = pysal.Markov(q5)
np.testing.assert_array_almost_equal(markov.shorrock(m.p),
0.19758992000997844)
def test___init__(self):
import numpy as np
f = pysal.open(pysal.examples.get_path('usjoin.csv'))
pci = np.array([f.by_col[str(y)] for y in range(1929, 2010)])
q5 = np.array([pysal.Quantiles(y).yb for y in pci]).transpose()
m = pysal.Markov(q5)
res = np.matrix(
[[0.08988764, 0.21468144, 0.21125, 0.20194986, 0.07259074]])
np.testing.assert_array_almost_equal(markov.prais(m.p), res)
def test___init__(self):
# markov = Markov(class_ids, classes)
import pysal
f = pysal.open(pysal.examples.get_path('usjoin.csv'))
pci = np.array([f.by_col[str(y)] for y in range(1929, 2010)])
q5 = np.array([pysal.Quantiles(y).yb for y in pci]).transpose()
m = pysal.Markov(q5)
expected = np.array([[729., 71., 1., 0., 0.], [72., 567., 80., 3., 0.],
[0., 81., 631., 86.,
2.], [0., 3., 86., 573., 56.],
[0., 0., 1., 57., 741.]])
np.testing.assert_array_equal(m.transitions, expected)
expected = np.matrix(
[[0.91011236, 0.0886392, 0.00124844, 0., 0.],
[0.09972299, 0.78531856, 0.11080332, 0.00415512, 0.],
[0., 0.10125, 0.78875, 0.1075, 0.0025],
[0., 0.00417827, 0.11977716, 0.79805014, 0.07799443],
[0., 0., 0.00125156, 0.07133917, 0.92740926]])
np.testing.assert_array_almost_equal(m.p.getA(), expected.getA())
expected = np.matrix([[0.20774716], [0.18725774], [0.20740537],
[0.18821787], [0.20937187]]).getA()
np.testing.assert_array_almost_equal(m.steady_state.getA(), expected)
def markov(observations, w=None, numQuints=5, method="regular"):
result = None
s = None
if method == "regular": # non spatial analysis
quintiles = np.array([pysal.Quantiles(y, k=numQuints).yb for y in observations]).transpose()
result = pysal.Markov(quintiles)
#s = result.steady_state
else:
observations = observations.transpose()
if method == "spatial":
# standardize observations for smoother calculations:
observations = observations / (observations.mean(axis=0))
result = pysal.Spatial_Markov(observations, w, fixed=True, k=numQuints)
#s = result.S
else: # method == lisa
result = pysal.LISA_Markov(observations, w)
#s = result.steady_state
return result.transitions, result.p, s, pysal.ergodic.fmpt(result.p)
import numpy as np
import pysal
c = np.array([['b', 'a', 'c'], ['c', 'c', 'a'], ['c', 'b', 'c'],
['a', 'a', 'b'], ['a', 'b', 'c']])
print(c)
m = pysal.Markov(c)
print(m.classes)
print(m.transitions)
#################################################################Classic Markov
f = pysal.open(
r'C:\Anaconda\Lib\site-packages\pysal\examples\us_income\usjoin.csv')
pci = np.array([f.by_col[str(y)] for y in range(1929, 2010)])
print(pci.shape)
print(pci)
q5 = np.array([pysal.Quantiles(y).yb for y in pci]).transpose()
print(q5.shape)
print(q5[:, 0])
print(q5[4, :])
m5 = pysal.Markov(q5)
print(m5.transitions)
print(m5.p)
print(m5.steady_state)
print(pysal.ergodic.fmpt(m5.p))
plt.scatter(range(1, 32), q5[:, 0])
plt.title('GDP Class in 1993')
plt.ylabel('Class')
plt.xlabel('Province')
plt.show()
# 1993年各省GDP类别分布
print(f'GDP in 1993:\n{q5[:,0]}')
# Beijing’s quintile time series
print(f'Beijing’s quintile time series:\n{q5[0,:]}')
plt.scatter(range(1993, 2014), q5[0, :])
plt.show()
# instantiate a Markov object
m5 = pysal.Markov(q5)
print(f'instantiate a Markov object:\n{m5.transitions}')
print(f'the transition probabilities:\n{m5.p}')
print(f'the long run steady state distribution:\n{m5.steady_state}')
print(f'the first mean passage time:\n{pysal.ergodic.fmpt(m5.p)}')
# Spatial Markov######################################################
pci = pci.transpose()
rpci = pci / (pci.mean(axis=0))
w = pysal.open(r"D:\pysal_task\data\GDP_China.swm").read()
