[Numpy-discussion] efficient norm of a vector
lorenzo bolla
lbolla at gmail.com
Wed Mar 14 04:21:58 EDT 2007
thanks. I hadn't seen it.
anyway, from very rough benchmarks I did, the quickest and easiest way of
computing the euclidean norm of a 1D array is:
n = sqrt(dot(x,x.conj()))
much faster than:
n = sqrt(sum(abs(x)**2))
and much much faster than:
n = scipy.linalg.norm(x)
regards,
lorenzo.
On 3/14/07, Bill Baxter <wbaxter at gmail.com> wrote:
>
> There is numpy.linalg.norm.
>
> Here's what it does:
>
> def norm(x, ord=None):
> x = asarray(x)
> nd = len(x.shape)
> if ord is None: # check the default case first and handle it
> immediately
> return sqrt(add.reduce((x.conj() * x).ravel().real))
> if nd == 1:
> if ord == Inf:
> return abs(x).max()
> elif ord == -Inf:
> return abs(x).min()
> elif ord == 1:
> return abs(x).sum() # special case for speedup
> elif ord == 2:
> return sqrt(((x.conj()*x).real).sum()) # special case for
> speedup
> else:
> return ((abs(x)**ord).sum())**(1.0/ord)
> elif nd == 2:
> if ord == 2:
> return svd(x, compute_uv=0).max()
> elif ord == -2:
> return svd(x, compute_uv=0).min()
> elif ord == 1:
> return abs(x).sum(axis=0).max()
> elif ord == Inf:
> return abs(x).sum(axis=1).max()
> elif ord == -1:
> return abs(x).sum(axis=0).min()
> elif ord == -Inf:
> return abs(x).sum(axis=1).min()
> elif ord in ['fro','f']:
> return sqrt(add.reduce((x.conj() * x).real.ravel()))
> else:
> raise ValueError, "Invalid norm order for matrices."
> else:
> raise ValueError, "Improper number of dimensions to norm."
>
>
>
> --bb
>
>
>
> On 3/14/07, lorenzo bolla <lbolla at gmail.com> wrote:
> > Hi all,
> > just a quick (and easy?) question.
> > what is the best (fastest) way to implement the euclidean norm of a
> vector,
> > i.e. the function:
> >
> > import scipy as S
> > def norm(x):
> > """normalize a vector."""
> > return S.sqrt(S.sum(S.absolute(x)**2))
> >
> > ?
> >
> > thanks in advance,
> > Lorenzo.
> > _______________________________________________
> > Numpy-discussion mailing list
> > Numpy-discussion at scipy.org
> > http://projects.scipy.org/mailman/listinfo/numpy-discussion
> >
> >
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