About alternatives to Matlab
Bill Maxwell
bill_maxwell_notMyRealAddress at notreal.net
Thu Nov 30 05:44:45 CET 2006
On 16 Nov 2006 13:09:03 -0800, "sturlamolden" <sturlamolden at yahoo.no>
wrote:
...SNIP...
>To compare Matlab with NumPy we can e.g. use the D4 discrete wavelet
>transform. I have here coded it in Matlab and Python/NumPy using Tim
>Swelden's lifting scheme.
>
>First the Matlab version (D4_Transform.m):
>
>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 - C2*even;
> s1(1) = even(1) + C2*d1(1) + C3*d1(end);
> s1(2:end) = even(2:end) + C2*d1(2:end) + C3*d1(1:end-1);
> d2(1) = d1(1) + s1(end);
> d2(2:end) = d1(2:end) + s1(1:end-1);
> x(1:2:end-1) = C4*s1;
> x(2:2:end) = C5*d2;
> if (length(x) >2)
> x(1:2:end-1) = D4_Transform(x(1:2:end-1));
> end
>
>
>Then the Python version (D4.py):
>
>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[0] = even[0] + C2*d1[0] + C3*d1[-1]
> s1[1:] = even[1:] + C2*d1[1:] + C3*d1[:-1]
> d2[0] = d1[0] + s1[-1]
> d2[1:] = d1[1:] + s1[:-1]
> even[:] = C4 * s1[:]
> odd[:] = C5 * d2[:]
> if x.size > 2:
>
>D4_Transform(even,s1[0:even.size/2],d1[0:even.size/2],d2[0:even.size/2])
>
>if __name__ == "__main__":
> x = numpy.random.rand(2**23)
> t0 = time.clock()
> D4_Transform(x)
> t = time.clock()
> print "Elapsed time is %.6f seconds" % (t-t0)
>
...SNIP...
I couldn't help but notice that the following two lines from the above
code are doing different things, but I think they are supposed to do the
same things (the first is the Matlab version, the 2nd is the Python
version):
> d1(:) = odd - C2*even;
> d1[:] = odd[:] - C1*even[:]
I don't understand what this code is doing, so I don't know which is
wrong. I don't even know if this is the actual code you are using. Just
thought I'd mention it.
Bill
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