# [SciPy-user] Python loops too slow

Ross Williamson Ross.Williamson@usap....
Wed Apr 8 18:15:59 CDT 2009

```Hi Guys

Thanks for all your help - My code is now super quick and I'll implement
meshgrid in other areas where I've got double loops.

Cheers

Ross
> Pauli Virtanen <pav <at> iki.fi> writes:
>
>> i = arange(ngrid/2 + 1)
>> j = arange(ngrid/2 + 1)
>> result = 2*pi*hypot(i[None,:], j[:,None])/reso/ngrid
>>
>>
>
> It seems Pauli's solution may need to be repeated in the final output as below.
> Is that what you really want though because the submatrix isn't reflected
> uniformly - i.e. the first row and column are missing.
>
> Anyway, timings are below - it seems using meshgrid is more efficient than
> hypot.
>
> -Dave
>
> Python 2.5.4 (r254:67916, Dec 23 2008, 15:10:54) [MSC v.1310 32 bit (Intel)]
>
> IPython 0.9.1 -- An enhanced Interactive Python.
>
>   Welcome to pylab, a matplotlib-based Python environment.
>
> In [2]: def f1(ngrid, reso):
>    ...:         result = zeros([ngrid, ngrid])
>    ...:     for i in arange((ngrid / 2)+1):
>    ...:            for j in arange((ngrid / 2)+1):
>    ...:               result[j,i] = 2. * pi * sqrt(i ** 2. + j ** 2) / reso /
> (ngrid*1.0)
>    ...:     for i in xrange(ngrid):
>    ...:            result[i,ngrid / 2+1:] = result[i,1:(ngrid / 2)][::-1]
>    ...:     for i in xrange(ngrid):
>    ...:            result[ngrid / 2+1:,i] = result[1:(ngrid / 2),i][::-1]
>    ...:     return result
>    ...: #
>    ...:
>
> In [3]: def f2(ngrid, reso):
>    ...:         nsub = ngrid/2+1
>    ...:     i = np.arange(nsub)
>    ...:     j = np.arange(nsub)
>    ...:     submatrix = 2*pi*np.hypot(i[None,:], j[:,None])/reso/np.float(ngrid)
>    ...:     result = zeros([ngrid, ngrid])
>    ...:     result[0:nsub,0:nsub] = submatrix
>    ...:     result[0:nsub,nsub:] = np.fliplr(submatrix[:,1:-1])
>    ...:     result[nsub:,:] = np.flipud(result[1:nsub-1,:])
>    ...:     return result
>    ...: #
>    ...:
>
> In [4]: def f3(ngrid, reso):
>    ...:         nsub = ngrid/2+1
>    ...:     i, j = meshgrid(np.arange(nsub),np.arange(nsub))
>    ...:     submatrix = 2*pi*np.sqrt(i**2 + j**2)/reso/np.float(ngrid)
>    ...:     result = zeros([ngrid, ngrid])
>    ...:     result[0:nsub,0:nsub] = submatrix
>    ...:     result[0:nsub,nsub:] = np.fliplr(submatrix[:,1:-1])
>    ...:     result[nsub:,:] = np.flipud(result[1:nsub-1,:])
>    ...:     return result
>    ...: #
>    ...:
>
> In [5]: np.allclose(f1(100,1),f2(100,1))
> Out[5]: True
>
> In [6]: np.allclose(f1(100,1),f3(100,1))
> Out[6]: True
>
> In [7]:
>
> In [8]: timeit f1(100,1)
> 10 loops, best of 3: 60.6 ms per loop
>
> In [9]:
>
> In [10]: timeit f2(100,1)
> 1000 loops, best of 3: 840 µs per loop
>
> In [11]:
>
> In [12]: timeit f3(100,1)
> 1000 loops, best of 3: 258 µs per loop
>
> In [13]:
>
>
>
>
>
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>
```