[Numpy-discussion] why a[0][0].__mul__(a[0][0]) where a is np.array, gives 'missing 1 required positional argument'?

[Larry Evans]

The following code:

--{--cut here--
#Purpose:
#  Demonstrate class with __add__ and __mult__ methods
#  to demonstrate shortestPath calculations.
#OriginalSource:
#  ./shortestPath.py
#References:
#  [1] 
http://www.marinamele.com/2014/04/modifying-add-method-of-python-class.html
#  [2] 
https://docs.scipy.org/doc/numpy/reference/c-api.types-and-structures.html#c.PyArray_Descr
#  [3] 
https://www.abebooks.com/book-search/title/graphs-networks/author/carre-bernard/
#      Table 3.1, path algebra P2.
#  [4] https://docs.python.org/3/library/abc.html
###########################################
import numpy as np
from abc import ABCMeta, abstractmethod
class PathAbstract(metaclass=ABCMeta):
     @abstractmethod
     def __repr__(self):
         pass
     @abstractmethod
     def __add__(self, other):
         pass
     @abstractmethod
     def __radd__(self, other):
         pass
     @abstractmethod
     def __mul__(self, other):
         pass
     @abstractmethod
     def __rmul__(self, other):
         pass

class ShortestNull(PathAbstract):
     '''Null object in ShortestPath algebra[3]'''
     def __str__(self):
         return "<0>"
     def __repr__(self):
         return self.__str__()
     def __addreal__(self, other):
         return other
     def __add__(self, other):
         return other
     def __radd__(self, other):
         return other
     def __mulreal__(self, other):
         return self
     def __mul__(self, other):
         return self
     def __rmul__(self, other):
         return self

class ShortestUnit(PathAbstract):
     '''Unit object in ShortestPath algebra[3]'''
     def __str__(self):
         return "<1>"
     def __repr__(self):
         return self.__str__()
     def __addreal__(self, other):
         return self
     def __add__(self, other):
         return self
     def __radd__(self, other):
         return self
     def __mulreal__(self, other):
         return other
     def __mul__(self, other):
         return other
     def __rmul__(self, other):
         return other

class ShortestPath(PathAbstract):
     def __init__(self, distance):
         self.distance = distance
     def __str__(self):
         return "{0:4.1f}".format(self.distance)
     def __repr__(self):
         return self.__str__()
     def __addreal__(self, other):
         #paths composed of following shortest of self path or other path.
         min_dist=min(self.distance,other.distance)
         return ShortestPath(min_dist)
     def __add__(self, other):
         #paths composed of following shortest of self path or other path.
         if(other == 0):
             n=ShortestNull()
             return n.__addreal__(self)
         else:
             return other.__addreal__(self)
     def __radd__(self, other):
         return self.__add__(other)
     def __mulreal__(self, other):
         #path composed of self path followed by other path.
         min_dist=self.distance+other.distance
         return ShortestPath(min_dist)
     def __mul__(self, other):
         return other.__mulreal__(self)
     def __rmul__(self, other):
         return other.__mulreal__(self)


d0=ShortestNull()
d1=ShortestUnit()
d2=ShortestPath(3)
d3=ShortestPath(6)
print(' d0=',d0,' d1=',d1,' d2=',d2,' d3=',d3)
print(' type(d0)=',type(d0).__name__)
d4=d0+d2+d3
print('d4=',d4)
d5=d2*d3
print('d5=',d5)
d6=d0*d2
print('d6=',d6)
d7=d1*d2
print('d7=',d7)
d8=d2*d0
print('d8=',d8)
d9=d2*d1
print('d9=',d9)
a=np.array([[ShortestNull,ShortestPath(12)],[ShortestPath(12),ShortestNull()]],dtype=object)
print('a=',a,sep='\n')
print('a[0]=',a[0],sep='\n')
print('a[0][0]=',a[0][0],sep='\n')
#a00mul=a[0][0]*a[0][0]
a00mul=a[0][0].__mul__(a[0][0])
print('a00mul=',a00mul,sep='\n')
#at=a.transpose()
#print('at=',at,sep='\n')
#aat=a.dot(at)
print('aat=',aat,sep='\n')
#mp=np.matmul(a,at)#this gives error about Object arrays not supported.
#print('mp=',mp)
--}--cut here--


When run by make, gives this result:


--{--cut here--
make -k
python3 shortestPathABC.py
  d0= <0>  d1= <1>  d2=  3.0  d3=  6.0
  type(d0)= ShortestNull
d4=  3.0
d5=  9.0
d6= <0>
d7=  3.0
d8= <0>
d9=  3.0
a=
[[<class '__main__.ShortestNull'> 12.0]
  [12.0 <0>]]
a[0]=
[<class '__main__.ShortestNull'> 12.0]
a[0][0]=
<class '__main__.ShortestNull'>
Traceback (most recent call last):
   File "shortestPathABC.py", line 123, in <module>
     a00mul=a[0][0].__mul__(a[0][0])
TypeError: __mul__() missing 1 required positional argument: 'other'
Makefile:7: recipe for target 'all' failed
make: *** [all] Error 1
--}--cut here--

I don't understand why.  Apparently, a[0][0] is not a ShortestNull 
because otherwise, the .__mul__ would have the positional argument,
'other' equal to a[0][0].

What am I missing?

TIA.

-regards,
Larry