Python: how to interpret Pysal results for a checkerboard in the case of the Queen contiguity?

Question

I am trying to get a grip on pysal. Say I have a checkerboard created like this:

import numpy as np
import pysal

def build_checkerboard(w, h) :
    re = np.r_[ w*[0,1] ]        # even-numbered rows
    ro = np.r_[ w*[1,0] ]        # odd-numbered rows
    return np.row_stack(h*(re, ro))

cb = build_checkerboard(5, 5)

Now I delete the last row and column to match the dimensions available in the weight matrix of pysal:

cb = np.delete(cb, (9), axis=0)
cb = np.delete(cb, (9), axis=1)

In[1]: cb
Out[1]:
array
  ([[0, 1, 0, 1, 0, 1, 0, 1, 0],
   [1, 0, 1, 0, 1, 0, 1, 0, 1],
   [0, 1, 0, 1, 0, 1, 0, 1, 0],
   [1, 0, 1, 0, 1, 0, 1, 0, 1],
   [0, 1, 0, 1, 0, 1, 0, 1, 0],
   [1, 0, 1, 0, 1, 0, 1, 0, 1],
   [0, 1, 0, 1, 0, 1, 0, 1, 0],
   [1, 0, 1, 0, 1, 0, 1, 0, 1],
   [0, 1, 0, 1, 0, 1, 0, 1, 0]])

Now let's use the Join Count Statistics (the values in my cb are either 0 or 1) using the Queen contiguity rule (aka the Moore neighborhood):

w=pysal.lat2W(3,3, rook=False) #This yields a 9x9 matrix
jc=pysal.Join_Counts(cb,w) #The Join Counts

Now, the results:

In[2]: jc.bb #The 1-to-1 joins
Out[2]: array([ 4.,  4.,  4.,  4.,  4.,  4.,  4.,  4.,  4.])

In[3]: jc.bw #The 1-to-0 joins
Out[3]: array([ 12.,  12.,  12.,  12.,  12.,  12.,  12.,  12.,  12.])

In[4]: jc.ww #The 0-to-0 joins
Out[5]: array([ 4.,  4.,  4.,  4.,  4.,  4.,  4.,  4.,  4.])

In[5]: jc.J #The total number of joins
Out[5]: 20.0

My questions:

1. Why am I not getting a single value for the different joins, but an array instead? Also, each value of the array seems to refer to one single matrix cell, but I don't get the total sum.
2. That 20.0 in terms of total number of joins is 4+4+12. Given the size and structure of the matrix I expected a higher number of joins (changes). Why is the number I get a far cry from what is expected?

Answer 1

The first argument to pysal.JoinCounts is an array of dimension (n,) For your checkerboard case I think you want something like:

>>> import numpy as np
>>> import pysal as ps
>>> w = ps.lat2W(3, 3, rook=False) # n=9, so W is 9x9
>>> y = np.array([0, 1, 0, 1, 0, 1, 0, 1, 0]) # attribute array n elements
>>> jc = ps.Join_Counts(y, w)
>>> jc.bb  # number of bb joins
4.0
>>> jc.ww  # number of ww joins
4.0
>>> jc.bw  # number of bw (wb) joins
12.0
>>> w.s0   # 2x total number of joins
40.0
>>> w.s0 == (jc.bb + jc.ww + jc.bw) * 2
True

For more details see the guide.