Hi, Thanks for doing this as it helps determine which approach to take when coding problems. Could you add the Numeric and numarray to these benchmarks? If for no other reason to show the advantage of the new numpy.
I am curious in your code because you get very different results for matrix class depending on whether x or y is transposed. Do you first transpose the x or y first before the multiplication or is the multiplication done in place by just switching the indices?
Also, for x'*y, is the results for Dimension 50 and Dimension 500 switched?
On 1/18/06, Paulo Jose da Silva e Silva firstname.lastname@example.org wrote:
Travis asked me to benchmark numpy versus matlab in some basic linear algebra operations. Here are the resuts for matrices/vectors of dimensions 5, 50 and 500:
Operation x'*y x*y' A*x A*B A'*x Half 2in2
Dimension 5 Array 0.94 0.7 0.22 0.28 1.12 0.98 1.1 Matrix 7.06 1.57 0.66 0.79 1.6 3.11 4.56 Matlab 1.88 0.44 0.41 0.35 0.37 1.2 0.98
Dimension 50 Array 9.74 3.09 0.56 18.12 13.93 4.2 4.33 Matrix 81.99 3.81 1.04 19.13 14.58 6.3 7.88 Matlab 16.98 1.94 1.07 17.86 0.73 1.57 1.77
Dimension 500 Array 1.2 8.97 2.03 166.59 20.34 3.99 4.31 Matrix 17.95 9.09 2.07 166.62 20.67 4.11 4.45 Matlab 2.09 6.07 2.17 169.45 2.1 2.56 3.06
Obs: The operation Half is actually A*x using only the lower half of the matrix and vector. The operation 2in2 is A*x using only the even indexes.
Of course there are many repetitions of the same operation: 100000 for dim 5 and 50 and 1000 for dim 500. The inner product is number of repetitions is multiplied by dimension (it is very fast).
The software is
numpy svn version 1926 Matlab 126.96.36.199913a Release 13 (Jun 18 2002)
Both softwares are using the *same* BLAS and LAPACK (ATLAS for sse).
As you can see, numpy array looks very competitive. The matrix class in numpy has too much overhead for small dimension though. This overhead is very small for medium size arrays. Looking at the results above (specially the small dimensions ones, for higher dimensions the main computations are being performed by the same BLAS) I believe we can say:
- Numpy array is faster on usual operations but outerproduct (I believe
the reason is that the dot function uses the regular matrix multiplication to compute outer-products, instead of using a special function. This can "easily" changes). In particular numpy was faster in matrix times vector operations, which is the most usual in numerical linear algebra.
- Any operation that involves transpose suffers a very big penalty in
numpy. Compare A'*x and A*x, it is 10 times slower. In contrast Matlab deals with transpose quite well. Travis is already aware of this and it can be probably solved.
- When using subarrays, numpy is a slower. The difference seems
acceptable. Travis, can this be improved?
Obs: Latter on (in a couple of days) I may present less synthetic benchmarks (a QR factorization and a Modified Cholesky).
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