Need opinions on P vs NP

Paddy paddy3118 at gmail.com
Sat Apr 18 07:11:48 CEST 2015


On Saturday, 18 April 2015 03:34:57 UTC+1, Ian  wrote:
> On Fri, Apr 17, 2015 at 7:19 PM, Paddy <paddy3118 at ..l.com> wrote:
> > Having just seen Raymond's talk on Beyond PEP-8 here: https://www.youtube.com/watch?v=wf-BqAjZb8M, it reminded me of my own recent post where I am soliciting opinions from non-newbies on the relative Pythonicity of different versions of a routine that has non-simple array manipulations.
> >
> > The blog post: http://paddy3118.blogspot.co.uk/2015/04/pythonic-matrix-manipulation.html
> >
> > The first, (and original), code sample:
> >
> > def cholesky(A):
> >     L = [[0.0] * len(A) for _ in range(len(A))]
> >     for i in range(len(A)):
> >         for j in range(i+1):
> >             s = sum(L[i][k] * L[j][k] for k in range(j))
> >             L[i][j] = sqrt(A[i][i] - s) if (i == j) else \
> >                       (1.0 / L[j][j] * (A[i][j] - s))
> >     return L
> >
> >
> > The second equivalent code sample:
> >
> > def cholesky2(A):
> >     L = [[0.0] * len(A) for _ in range(len(A))]
> >     for i, (Ai, Li) in enumerate(zip(A, L)):
> >         for j, Lj in enumerate(L[:i+1]):
> >             s = sum(Li[k] * Lj[k] for k in range(j))
> >             Li[j] = sqrt(Ai[i] - s) if (i == j) else \
> >                       (1.0 / Lj[j] * (Ai[j] - s))
> >     return L
> >
> >
> > The third:
> >
> > def cholesky3(A):
> >     L = [[0.0] * len(A) for _ in range(len(A))]
> >     for i, (Ai, Li) in enumerate(zip(A, L)):
> >         for j, Lj in enumerate(L[:i]):
> >             #s = fsum(Li[k] * Lj[k] for k in range(j))
> >             s = fsum(Lik * Ljk for Lik, Ljk in zip(Li, Lj[:j]))
> >             Li[j] = (1.0 / Lj[j] * (Ai[j] - s))
> >         s = fsum(Lik * Lik for Lik in Li[:i])
> >         Li[i] = sqrt(Ai[i] - s)
> >     return L
> >
> > My blog post gives a little more explanation, but I have yet to receive any comments on relative Pythonicity.
> 
> I prefer the first version. You're dealing with mathematical formulas
> involving matrices here, so subscripting seems appropriate, and
> enumerating out rows and columns just feels weird to me.
> 
> That said, I also prefer how the third version pulls the last column
> of each row out of the inner loop instead of using a verbose
> conditional expression that you already know will be false for every
> column except the last one. Do that in the first version, and I think
> you've got it.

But shouldn't the maths transcend the slight change in representation? A programmer in the J language might have a conceptually neater representation of the same thing due to its grounding in arrays (maybe) and for a J representation it would become J-thonic. In Python, it is usual to iterate over collections and also to use enumerate where we must have indices. 

Could it be that there is a also a strong pull in the direction of using indices because that is what is predominantly given in the way matrix maths is likely to be expressed mathematically? A case of "TeX likes indices so we should too"?



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