Roger,thank you for the paging time tip,the testing box has 512M
memory and vmstat indeed shows a lot of swap in/out.When I change the
length to 2^21,timings are:numpy -- 0.43,matlab -- 0.78, D4_Transform
-- 1.71,d4 -- 1.17,D4a -- 0.95.Since numpy doing more in-place
work,the speed difference is acceptable,so the original post is also
misleading.By the way,on a 2G mem server,for 2^23 data,the J timings
are:D4_Transform -- 5.39,d4 -- 4.09,D4a -- 2.92.
2006/12/26, Roger Hui <[EMAIL PROTECTED]>:
D4a runs faster than D4_Transform by a factor of
1.5 to 2. In doing benchmarks you have to be
careful with large arguments (length 2^23, say).
Depending on the amount of real memory on your
machine paging can take place and dominate the time.
C1=: 1.7320508075688772
C2=: 0.4330127018922193
C3=: -0.066987298107780702
C4=: 0.51763809020504137
C5=: 1.9318516525781364
D4a=: 3 : 0
e=. y#~(#y)$1 0
d=. (y#~(#y)$0 1) - C1*e
s=. e+(C2*d)+C3*1|.d
, (D4a^:(2<#y) C5*s) ,. C4*d+_1|.s
)
----- Original Message -----
From: Xu Zuoqian <[EMAIL PROTECTED]>
Date: Sunday, December 24, 2006 8:19 pm
Subject: Re: [Jprogramming] J vs Matlab vs NumPy for speed by wavelet
computing
> Boss,you are absolutely right and I 'm sorry for the typos.It seems
> the origin post also has some error according to the following
> responses.I try to update the three versions as:
> 1.Numpy version:
> import numpy
> import time
>
> def D4_Transform(x, s1=None, d1=None, d2=None):
> """
> D4 Wavelet transform in NumPy
> (C) Sturla Molden
> """
> C1 = 1.7320508075688772
> C2 = 0.4330127018922193
> C3 = -0.066987298107780702
> C4 = 0.51763809020504137
> C5 = 1.9318516525781364
> if d1 == None:
> d1 = numpy.zeros(x.size/2)
> s1 = numpy.zeros(x.size/2)
> d2 = numpy.zeros(x.size/2)
> odd = x[1::2]
> even = x[:-1:2]
> d1[:] = odd[:] - C1*even[:]
> s1[:-1] = even[:-1] + C2*d1[:-1] + C3*d1[1:]
> s1[-1] = even[-1] + C2*d1[-1] + C3*d1[0]
> d2[0] = d1[0] + s1[-1]
> d2[1:] = d1[1:] + s1[:-1]
> even[:] = C5 * s1[:]
> odd[:] = C4 * d2[:]
> if x.size > 2:
> D4_Transform(even,s1[0:even.size/2],d1[0:even.size/2],d2[0:even.size/2])
> 2.Matlab version:
> function x = D4_Transform(x)
> % D4 Wavelet transform in Matlab
> % (C) Sturla Molden
> C1 = 1.7320508075688772;
> C2 = 0.4330127018922193;
> C3 = -0.066987298107780702;
> C4 = 0.51763809020504137;
> C5 = 1.9318516525781364;
> s1 = zeros(ceil(size(x)/2));
> d1 = zeros(ceil(size(x)/2));
> d2 = zeros(ceil(size(x)/2));
> odd = x(2:2:end);
> even = x(1:2:end-1);
> d1(:) = odd - C1*even;
> s1(1:end-1) = even(1:end-1) + C2*d1(1:end-1) + C3*d1(2:end);
> s1(end) = even(end) + C2*d1(end) + C3*d1(1);
> d2(1) = d1(1) + s1(end);
> d2(2:end) = d1(2:end) + s1(1:end-1);
> x(1:2:end-1) = C5*s1;
> x(2:2:end) = C4*d2;
> if (length(x) >2)
> x(1:2:end-1) = D4_Transform(x(1:2:end-1));
> end
> 3. J Version
> D4_Transform=:3 :0
> NB. D4 Wavelet transform in Matlab
> NB. (C) Sturla Molden
> C1 =. 1.7320508075688772
> C2 =. 0.4330127018922193
> C3 =. -0.066987298107780702
> C4 =. 0.51763809020504137
> C5 =. 1.9318516525781364
> n=.>.-:#y
>
> r =. (#y)$0
> evenkey=.2*i.n
> oddkey=.<<<evenkey
> odd =.oddkey{y
> even =.evenkey{y
>
> d1 =. odd - C1*even
> s1 =.even+(C2*d1)+C3*1|.d1
> d2=.d1+_1|.s1
> r=.(C5*s1)evenkey}r
> r=.(C4*d2)oddkey}r
>
> if.2<#y do.
> r=.(D4_Transform evenkey{r) evenkey}r
> end.
> r
> )
> And using the code in
> http://groups.google.com/group/comp.lang.python/msg/a71a5bf00a88ad57
> to verify.
> For input 1,5,3,2,4,8,5,2,the outputs are all 10.606602 2.6736336
> _0.7589746 _0.29349422 1.272112 1.3541544 _4.8391016 _0.90586666.
> The new timings are: numpy -- 1.71 seconds,matlab -- 25 seconds,J -
> - 20s.
>
> 2006/12/23, Mike Powell <[EMAIL PROTECTED]>:
> > The use of the constant C1 looks odd. It is used in the numpy
> > version, but not in the Matlab or J versions.
> > Mike Powell
> >
> > On 22-Dec-06, at 6:01 AM, bill lam wrote:
> >
> > > Xu Zuoqian wrote:
> > >> And the timing is:
> > >> d=.?(2^23)$0
> > >> ts 'D4_Transform d'
> > >> 150.59277 7.718007e8
> > >
> > > Before talking about efficiency could you give the correct
> result of
> > > D4_Transform d
> > > for validation, and also use
> > > d=. ?.(2^23)$0
> > > so that experiment is repeatable.
> > >
> > > --
> > > regards,
> > > bill
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