Bug 461472

Description of problem:

NumPy uses BLAS for the dot() function only if built against ATLAS (math-atlas.sf.net), a generic BLAS library isn't sufficient. See http://scipy.org/scipy/numpy/ticket/667

In case ATLAS isn't available, dot() performance will be very poor.

Here are matrix multiplication benchmark results using the numpy currently in EPEL:

Double precision matrix multiplication test using NumPy.
Multiplying two NxN matrices.

   N   Gflops/s
===============
   2      0.007
   4      0.058
   8      0.301
  16      0.785
  32      1.166
  64      1.217
 128      0.839
 256      0.872
 512      0.469
1024      0.215
2048      0.125

With an optimized BLAS, the equivalent Fortran code using dgemm performance:

  Double precision matrix multiplication test
  Matrix side size    Matmul (Gflops/s)    dgemm (Gflops/s)
  =========================================================
     2                0.150                0.001
     4                0.303                0.005
     8                0.530                0.042
    16                0.829                0.245
    32                1.405                1.366
    64                1.669                3.533
   128                2.030                5.611
   256                2.369                6.792
   512                2.596                7.058
  1024                0.601                7.428
  2048                0.565                7.766

(The matmul column is performance using the F90 MATMUL intrinsic, which is in this case the same one would get using the generic netlib BLAS library). So one can see that for large matrices, NumPy without ATLAS is just incredibly slow.

Python benchmark code below:

#!/usr/bin/python

# Matmul benchmark in python/numpy

import numpy as npy
import time

def mm_timing(nn):
    """Matrix multiplication benchmark for nxn matrices until nnxnn."""
    n = 2
    print "Double precision matrix multiplication test using NumPy."
    print "Multiplying two NxN matrices."
    print ""
    print "   N   Gflops/s"
    print "==============="
    while n < nn:
        a = npy.random.rand(n, n)
        b = npy.random.rand(n, n)
        flops = (2 * float(n) - 1) * float(n)**2
        # Assuming an on average 1 gflop/s cpu, 1e9 flops takes about 1 second and
        # should be enough. We also do a maximum of 1e5 loops, since
        # for small arrays the overhead is large.
        loop = int(max(min(1.e9 / flops, 1e5), 1))
        t1 = time.time()
        for i in xrange(loop):
            c = npy.dot(a, b)
        t2 = time.time()
        perf = flops * loop / (t2 - t1) / 1.e9
        print "%4i" % n + "     " + "%6.3f" % perf
        n *= 2
        if n > nn:
            break

mm_timing(3000)