[SciPy-user] complex vector scalar product: wrong implementation

[Vladimir Roudnev]

Robert Kern wrote:

>>              innerproduct(z1,z2)==conjugate(innerproduct(z2,z1))
>> Scipy implementation, however, does not satisfy this property, what 
>> can lead to serious complications when adapting real vector 
>> algorithms to complex arithmetics. In particular, the existing 
>> implementation breaks the complex vector space metric [...]
>
> [...]If you are doing serious linear algebra with complex matrices 
> (and not everyone who uses innerproduct on complex arrays does), I 
> suggest you write a function that does the appropriate conjugation.
>
> def cdot(a, b):
>     return dot(conjugate(a), b)

Indeed, one can write the function, but my message was that the 
misimplemented scalar product is a major Scipy library DESIGN ISSUE. I 
am not even talking about the perfomance. The structure of a good 
program must reflect the structure of the problem it solves, this is the 
basic structure programming principle. It is the structure of the Scipy 
linear algebra library that does not reflect the structure of linear 
algebraic problems in general, and cheating with writing functions at 
the user level does not fix it. A real vector space code should work 
flawlessly with complex vector spaces  when the algorithm is applicable, 
isn't it in the Python programming spirit? Otherwise we end up with 
programming good old Fortran 77. (Or Fortran 777, if you wish ;) )

BW,
  VR