Vectorized "and" for pandas columns

Question

With a data like this one

import pandas as pd
tcd = pd.DataFrame({
 'a': {'p_1': 1, 'p_2': 1, 'p_3': 0, 'p_4': 0}, 
 'b': {'p_1': 0, 'p_2': 1, 'p_3': 1, 'p_4': 1}, 
 'c': {'p_1': 0, 'p_2': 0, 'p_3': 1, 'p_4': 0}})
tcd
#      a  b  c
# p_1  1  0  0
# p_2  1  1  0
# p_3  0  1  1
# p_4  0  1  0

(but with 40e3 columns)

I look for a vectorized way to put the boolean and in a result Series:

a & b = ab -> 1 or True    a & c = ac -> 0 or False
1   0   0                  1   0   0
1   1   0                  1   0   0
0   1   1                  0   1   0
0   1   0                  0   0   0

For now I only get an ugly solution with a for loop::

res = pd.Series(index=['a&a', 'a&b', 'a&c'])
for i in range(3):
  res[i] = (tcd.iloc[:, 0] & tcd.iloc[:, i]).any()

res 
aa    1
ab    1
ac    0

with the B.M. answer I get this

def get_shared_p(tcd, i):
    res = (tcd.iloc[:, i][:, None] & tcd).any()
    res.index += '&_{}'.format(i)
    return res

res = pd.DataFrame(columns=range(cols), index=range(cols))
for col_i in range(cols):
    res.iloc[:, col_i] = list(get_shared_p(tcd, col_i))

print res
#        0     1      2
# 0   True  True  False
# 1   True  True   True
# 2  False  True   True

We can probably avoid this new for loop.

Answer 1

You can use np.logical_and and numpy's broadcasting.

Say you define x and y as the first column, and entire matrix, respectively:

import numpy as np

x = tcd.as_matrix()
y = tcd.a.values.reshape((len(tcd), 1))

now, using broadcasting, find the logical and of x and y, and place it in and_:

and_ = np.logical_and(x, y)

Finally, find if any of the rows in any of the columns is true:

>>> np.sum(and_) > 0
array([ True,  True, False], dtype=bool)

Answer 2

Use [:,None] to align data and force broadcasting :

In[1] : res=(tcd.a[:,None] & tcd).any(); res.index+='&a'; res

Out[1]:
a&a     True
b&a     True
c&a    False
dtype: bool