Re: [eigen] How to raise double to array powers in Eigen

[Mark Borgerding <mark@xxxxxxxxxxxxxx>]

You are right off course.  I should know by now to avoid being cocky and 
posting code I haven't run.


On 08/19/2014 09:07 AM, Christoph Hertzberg wrote:
> On 19.08.2014 15:05, Mark Borgerding wrote:
> > Correction below: "+=" changed to "*="
>
> And you should return accum;
>
> > On 08/19/2014 09:03 AM, Mark Borgerding wrote:
> > >     pow(x,k) can be accomplished on O(log2(k)) time by
> > >
> > >     y = x;
> > >     accum = 1;
> > >     while (k) {
> > >         if (k&1)
> > >             accum *= y;
> > >         k>>=1;
> > >         y = y*y;
> > >     }
> > >     return y
> > >
> > > e.g.  pow(x,11) = x^8 * x^2 * x^1
> > >
> > >
> > > On 08/18/2014 01:30 PM, Ian Bell wrote:
> > > > Chen-Pang,
> > > >
> > > > Can you provide a bit more detail on the exponentiation by squaring?
> > > > How would I re-write my simple c++ loop above using your method?
> > > >
> > > > Thanks,
> > > > Ian
> > > >
> > > >
> > > > On Mon, Aug 18, 2014 at 2:30 PM, Chen-Pang He <jdh8@xxxxxxxxxxxxxx
> > > > <mailto:jdh8@xxxxxxxxxxxxxx>> wrote:
> > > >
> > > >     If you need no optimization and want functional programming,
> > > >     ArrayBase::unaryExpr with a homemade functor is enough.
> > > >
> > > >     If you need optimization, because all exponents are integers,
> > > >     binary powering (aka exponentiation by squaring) is *the*
> > > >     algorithm.   We can reuse `pow(delta, (1 << k))`.
> > > >
> > > >     Cheers,
> > > >     Chen-Pang
> > > >
> > > >     在 2014 八月 18 週一 13:42:46，Ian Bell 寫道:
> > > >     > On Mon, Aug 18, 2014 at 1:28 PM, Christoph Hertzberg <
> > > >     > chtz@xxxxxxxxxxxxxxxxxxxxxxxx
> > > >     <mailto:chtz@xxxxxxxxxxxxxxxxxxxxxxxx>> wrote:
> > > >     >
> > > >     > > On 18.08.2014 00:23, Ian Bell wrote:
> > > >     > >
> > > >     > >> cross-posted to stack overflow...
> > > >     > >>
> > > >     > >
> > > >     > > If you cross-post, could you post a link as well?
> > > >     >
> > > >     > Here's the link:
> > > >     >
> > > >
> > > > http://stackoverflow.com/questions/25354205/how-to-raise-double-to-array-powers-in-eigen 
> > > >
> > > >
> > > >     >
> > > >     > >
> > > >     > >
> > > >     > >  I need to raise a double value to an array of integer
> > > >     powers, in c++ this
> > > >     > >> would look something like
> > > >     > >>
> > > >     > >
> > > >     > > Could you be a bit more specific about the "array of integer
> > > >     powers" (I
> > > >     > > guess 'exponents')?
> > > >     > > If they are a sequence 0,1,2,3,... your proposed solution is
> > > >     definitely
> > > >     > > very inefficient. If they are of great range, with no
> > > >     apparent pattern, I
> > > >     > > would say the exp(log(delta)*exponent) approach is basically
> > > >     the most
> > > >     > > efficient solution (maybe using log2 and exp2 would be more
> > > >     efficient, if
> > > >     > > they were available).
> > > >     > >
> > > >     >
> > > >     > The exponents are typically in the range [0, 10), and can be
> > > >     sorted if that
> > > >     > is of use.  They are not necessarily linearly increasing, we
> > > >     might have
> > > >     > exponents 0,0,0,1,1,1,1,2,2 for instance. Obviously it would be
> > > >     better to
> > > >     > short-circuit the 0 powers as well since they yield 1 again
> > > >     (x^0=1).  This
> > > >     > method with the exp(log(delta)*exponent) also doesn't allow you
> > > >     to skip
> > > >     > those powers.  I think that the >0 comparison should be cheaper
> > > >     than doing
> > > >     > pow(x, 0) when 0 is integer.  Especially this will be true when
> > > >     using exp().
> > > >     --
> > > >     何震邦 | jdh8@xxxxxxxxxxxxxx <mailto:jdh8@xxxxxxxxxxxxxx> |
> > > >     http://jdh8.org