[Numpy-discussion] Simple multi-arg wrapper for dot()

[Colin J. Williams]

Bill Baxter wrote:
> On 3/24/07, Anne Archibald <peridot.faceted at gmail.com> wrote:
>> On 24/03/07, Bill Baxter <wbaxter at gmail.com> wrote:
>>> I mentioned in another thread Travis started on the scipy list that I
>>> would find it useful if there were a function like dot() that could
>>> multiply more than just two things.
>>>
>>> Here's a sample implementation called 'mdot'.
>>>
>>> mdot(a,b,c,d) ==> dot(dot(dot(a,b),c),d)
>>> mdot(a,(b,c),d) ==> dot(dot(a,dot(b,c),d)
>>> mdot(a,(b,(c,d))) ==> dot(a,dot(b,dot(c,d))
>>>
>>> ---
>>> def mdot(*args):
>>>     """Multiply all the arguments using matrix product rules.
>>>     The output is equivalent to multiplying the arguments one by one
>>>     from left to right using dot().
>>>     Precedence can be controlled by creating tuples of arguments,
>>>     for instance mdot(a,((b,c),d)) multiplies a (a*((b*c)*d)).
>>>     Note that this means the output of dot(a,b) and mdot(a,b) will differ if
>>>     a or b is a pure tuple of numbers.
>>>     """
>>>     if len(args)==1:
>>>         return args[0]
>>>     elif len(args)==2:
>>>         return _mdot_r(args[0],args[1])
>>>     else:
>>>         return _mdot_r(args[:-1],args[-1])
>>>
>>> def _mdot_r(a,b):
>>>     """Recursive helper for mdot"""
>>>     if type(a)==types.TupleType:
>>>         if len(a)>1:
>>>             a = mdot(*a)
>>>         else:
>>>             a = a[0]
>>>     if type(b)==types.TupleType:
>>>         if len(b)>1:
>>>             b = mdot(*b)
>>>         else:
>>>             b = b[0]
>>>     return numpy.dot(a,b)
>> You can do better:
>> In [1]: from numpy import *
>>
>> In [2]: a = array([[0,-1],[1,0]])
>>
>> In [3]: reduce(dot,(a,a,a,a))
>> Out[3]:
>> array([[1, 0],
>>        [0, 1]])
>>
>> In [4]: def mdot(*args):
>>    ...:     return reduce(dot,args)
>>    ...:
>>
>> In [5]: mdot(a,a,a,a)
>> Out[5]:
>> array([[1, 0],
>>        [0, 1]])
>>
> 
> Nice, but how does that fare on things like mdot(a,(b,c),d) ?  I'm
> pretty sure it doesn't handle it.
> I think an mdot that can only multiply things left to right comes up
> short compared to an infix operator that can easily use parentheses to
> control order.
+1 for infix

Colin W.
> 
> --bb