[Numpy-discussion] Need a good idea: calculate the mean of many vectors
Robert Kern
robert.kern@gmail....
Tue Feb 8 10:32:46 CST 2011
On Tue, Feb 8, 2011 at 09:24, EMMEL Thomas <Thomas.EMMEL@3ds.com> wrote:
> Hi,
>
> here is something I am thinking about for some time and I am wondering
> whether there is a better solution
> within numpy.
>
> The task is:
> I have an array (300000+ entries) with arrays each with length == 3, that is
> initially empty like this:
>
> n = 100 # for test otherwise ~300000
> a1 = reshape(zeros(3*n).astype(float), (n,3))
>
> (Speaking literally this is a field of displacements in a
> Finite-Element-Mesh)
> Now I have a lot of triangles where the corners are the nodes, each with an
> index between 0 and n-1
> and I like to add a unique displacement for all three nodes to a1 like this
>
> a2 = zeros(n).astype(int)
>
> for indices, data in [...]:
> #data = array((1.,2.,3.))
> #indices = (1,5,60)
> for index in indices:
> a1[index] += data
> a2[index] += 1
>
> Now after filling a1 and a2 over and over (for a lot of triangles) I can
> finally calculate the
> averaged displacement on all points by this
>
> meand = a1/reshape(a2,(n,1))
Use np.bincount() on each coordinate.
[~]
|10> xyz = np.random.random_sample([10, 3])
[~]
|11> ind = np.array([1,3,4,3,4,5,0,0,1,2])
[~]
|12> sum_xyz = np.column_stack([np.bincount(ind, xyz[:,i]) for i in
range(xyz.shape[1])])
[~]
|13> sum_xyz
array([[ 1.56632447, 0.88193741, 0.20253585],
[ 1.36661663, 0.98698521, 0.79892009],
[ 0.26787528, 0.12850502, 0.76042557],
[ 1.08489219, 0.70099349, 1.56665748],
[ 0.56662843, 1.3502819 , 0.15531993],
[ 0.34900915, 0.34282216, 0.48250042]])
[~]
|14> counts = np.bincount(ind)
[~]
|15> counts
array([2, 2, 1, 2, 2, 1])
[~]
|17> mean_xyz = sum_xyz / counts[:,np.newaxis]
[~]
|18> mean_xyz
array([[ 0.78316224, 0.4409687 , 0.10126793],
[ 0.68330832, 0.4934926 , 0.39946005],
[ 0.26787528, 0.12850502, 0.76042557],
[ 0.54244609, 0.35049674, 0.78332874],
[ 0.28331422, 0.67514095, 0.07765996],
[ 0.34900915, 0.34282216, 0.48250042]])
Watch out for divisions by 0 when you calculate the mean.
--
Robert Kern
"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
-- Umberto Eco
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