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Instead of iterating on the coordinates using Python (GaryBishop's answer), you can have numpy do the looping, which constitutes a substantial speed-up (timings below): <pre><code>def sparse_mult(a, b, coords) : rows, cols = zip(*coords) rows, r_idx = np.unique(rows, return_inverse=True) cols, c_idx = np.unique(cols, return_inverse=True) C = np.dot(a[rows, :], b[:, cols]) return C[r_idx, c_idx] >>> A = np.arange(12).reshape(3, 4) >>> B = np.arange(15).reshape(3, 5) >>> np.dot(A.T, B) array([[100, 112, 124, 136, 148], [115, 130, 145, 160, 175], [130, 148, 166, 184, 202], [145, 166, 187, 208, 229]]) >>> sparse_mult(A.T, B, [(0, 0), (1, 2), (2, 4), (3, 3)]) array([100, 145, 202, 208]) </code></pre> <code>sparse_mult</code> returns a flattened array of the values at the coordinates you provide as a list of tuples. I am not very familiar with sparse matrix formats, so I don't know how to define CSC from the above data, but the following works: <pre><code>>>> coords = [(0, 0), (1, 2), (2, 4), (3, 3)] >>> sparse.coo_matrix((sparse_mult(A.T, B, coords), zip(*coords))).tocsc() <4x5 sparse matrix of type '<type 'numpy.int32'>' with 4 stored elements in Compressed Sparse Column format> </code></pre> This is a timing of various alternatives: <pre><code>>>> import timeit >>> a = np.random.rand(2000, 3000) >>> b = np.random.rand(3000, 5000) >>> timeit.timeit('np.dot(a,b)[[0, 0, 1999, 1999], [0, 4999, 0, 4999]]', 'from __main__ import np, a, b', number=1) 5.848562187263569 >>> timeit.timeit('sparse_mult(a, b, [(0, 0), (0, 4999), (1999, 0), (1999, 4999)])', 'from __main__ import np, a, b, sparse_mult', number=1) 0.0018596387374678613 >>> np.dot(a,b)[[0, 0, 1999, 1999], [0, 4999, 0, 4999]] array([ 758.76351111, 750.32613815, 751.4614542 , 758.8989648 ]) >>> sparse_mult(a, b, [(0, 0), (0, 4999), (1999, 0), (1999, 4999)]) array([ 758.76351111, 750.32613815, 751.4614542 , 758.8989648 ]) </code></pre>
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1. POCalculate subset of matrix multiplication
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1. COI'm trying to figure out how this works but I can't get it to work. Why is np.dot(A.T, B) a 5 by 4 matrix? Shouldn't it be 4x2? Using your example I get a failure in the function on line "C = np.dot(a[rows, :], b[:, cols])", "index error: index (2) out of range (0<=index<1) in dimension 1"
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