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

[Bill Baxter]

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.

--bb