Databases
StackOverflow2013
Postsdbo
PO
 

Note that there are some explanatory texts on larger screens.

plurals
  1. PO
    primarykey
    data
    text
    <p>@Evan and @Martinis Group are on the right track - to expand on Evan's answer, here's a function that uses broadcasting to quickly calculate the n-dimensional weighted euclidean distance without Python loops:</p> <pre><code>import numpy as np def fast_wdist(A, B, W): """ Compute the weighted euclidean distance between two arrays of points: D{i,j} = sqrt( ((A{0,i}-B{0,j})/W{0,i})^2 + ... + ((A{k,i}-B{k,j})/W{k,i})^2 ) inputs: A is an (k, m) array of coordinates B is an (k, n) array of coordinates W is an (k, m) array of weights returns: D is an (m, n) array of weighted euclidean distances """ # compute the differences and apply the weights in one go using # broadcasting jujitsu. the result is (n, k, m) wdiff = (A[np.newaxis,...] - B[np.newaxis,...].T) / W[np.newaxis,...] # square and sum over the second axis, take the sqrt and transpose. the # result is an (m, n) array of weighted euclidean distances D = np.sqrt((wdiff*wdiff).sum(1)).T return D </code></pre> <p>To check that this works OK, we'll compare it to a slower version that uses nested Python loops:</p> <pre><code>def slow_wdist(A, B, W): k,m = A.shape _,n = B.shape D = np.zeros((m, n)) for ii in xrange(m): for jj in xrange(n): wdiff = (A[:,ii] - B[:,jj]) / W[:,ii] D[ii,jj] = np.sqrt((wdiff**2).sum()) return D </code></pre> <p>First, let's make sure that the two functions give the same answer:</p> <pre><code># make some random points and weights def setup(k=2, m=100, n=300): return np.random.randn(k,m), np.random.randn(k,n),np.random.randn(k,m) a, b, w = setup() d0 = slow_wdist(a, b, w) d1 = fast_wdist(a, b, w) print np.allclose(d0, d1) # True </code></pre> <p>Needless to say, the version that uses broadcasting rather than Python loops is several orders of magnitude faster:</p> <pre><code>%%timeit a, b, w = setup() slow_wdist(a, b, w) # 1 loops, best of 3: 647 ms per loop %%timeit a, b, w = setup() fast_wdist(a, b, w) # 1000 loops, best of 3: 620 us per loop </code></pre>
    singulars
    1. This table or related slice is empty.
    1. POFast weighted euclidean distance between points in arrays
      singulars
      1. PTQuestion
    1. PTAnswer
    1. USali_m
    1. USali_m
    plurals
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. POFast weighted euclidean distance between points in arrays
      singulars
      1. PTQuestion
    1. This table or related slice is empty.
    1. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    3. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTAcceptedByOriginator
    1. COI have no idea what 90% of this code does but it sure does is fast :) Give me a couple of hours to check it and I'll come back to either mark it as accepted or comment on it. Oh and I've proposed an edit to your answer, please check it and see if it is right. Thank you!
      singulars
      1. PO
      1. USGabriel
    2. COAre you happy that you understand what this function does? The weights are applied to the differences in _x,y,..._ coordinates for A and B before squaring, the same as in your code. The _i,j_ th point in the output array is the weighted euclidean distance between the _i_ th point in A and the _j_ th point in B.
      singulars
      1. PO
      1. USali_m
    3. COI don't understand why you added a `.sum()` function to sum all the distances. My code doesn't do that, was it a slip or am I getting it all wrong?
      singulars
      1. PO
      1. USGabriel
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload