<div dir="ltr"><div><div><div><div>Sorry, I have to correct myself, as per: <a href="http://docs.continuum.io/mkl-optimizations/index">http://docs.continuum.io/mkl-optimizations/index</a> it seems that Anaconda is not linking with MKL by default (I thought that was the case before?). After installing MKL (conda install mkl), I am getting:<br></div><br>
<div>
<span style="font-family:monospace"><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">In [</span><span style="font-weight:bold;color:rgb(84,255,84);background-color:rgb(255,255,255)">1</span><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">]: </span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">import numpy as np
</span><br>Vendor: Continuum Analytics, Inc.
<br>Package: mkl
<br>Message: trial mode expires in 30 days
<br>
<br><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">In [</span><span style="font-weight:bold;color:rgb(84,255,84);background-color:rgb(255,255,255)">2</span><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">]: </span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">testA = np.random.randn(15000, 15000) </span><br>
<br><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">In [</span><span style="font-weight:bold;color:rgb(84,255,84);background-color:rgb(255,255,255)">3</span><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">]: </span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">testb = np.random.randn(15000) </span><br>
<br><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">In [</span><span style="font-weight:bold;color:rgb(84,255,84);background-color:rgb(255,255,255)">4</span><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">]: </span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">%time testx = np.linalg.solve(testA, testb)
</span><br>CPU times: user 1min, sys: 468 ms, total: 1min 1s
<br>Wall time: 15.3 s<br>
<br></span></div>
<br></div>so, it looks like you will need to buy a MKL license separately (which makes sense for a commercial product).<br><br></div>Sorry for the confusion.<br></div>Francesc<br><div><div><div><br></div></div></div></div><div class="gmail_extra"><br><div class="gmail_quote">2015-12-16 18:59 GMT+01:00 Francesc Alted <span dir="ltr"><<a href="mailto:faltet@gmail.com" target="_blank">faltet@gmail.com</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><div><div>Hi,<br><br></div>Probably MATLAB is shipping with Intel MKL enabled, which probably is the fastest LAPACK implementation out there. NumPy supports linking with MKL, and actually Anaconda does that by default, so switching to Anaconda would be a good option for you.<br><br></div>Here you have what I am getting with Anaconda's NumPy and a machine with 8 cores:<br><br>
<div>
<span style="font-family:monospace"><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">In [</span><span style="font-weight:bold;color:rgb(84,255,84);background-color:rgb(255,255,255)">1</span><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">]: </span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">import numpy as np
</span><br>
<br><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">In [</span><span style="font-weight:bold;color:rgb(84,255,84);background-color:rgb(255,255,255)">2</span><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">]: </span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">testA = np.random.randn(15000, 15000)
</span><br>
<br><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">In [</span><span style="font-weight:bold;color:rgb(84,255,84);background-color:rgb(255,255,255)">3</span><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">]: </span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">testb = np.random.randn(15000)
</span><br>
<br><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">In [</span><span style="font-weight:bold;color:rgb(84,255,84);background-color:rgb(255,255,255)">4</span><span style="color:rgb(24,178,24);background-color:rgb(255,255,255)">]: </span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">%time testx = np.linalg.solve(testA, testb)
</span><br>CPU times: user 5min 36s, sys: 4.94 s, total: 5min 41s
<br>Wall time: 46.1 s
<br><br>
</span></div>This is not 20 sec, but it is not 3 min either (but of course that depends on your machine).<br><br></div>Francesc<br></div><div class="gmail_extra"><br><div class="gmail_quote"><div><div class="h5">2015-12-16 18:34 GMT+01:00 Edward Richards <span dir="ltr"><<a href="mailto:edwardlrichards@gmail.com" target="_blank">edwardlrichards@gmail.com</a>></span>:<br></div></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div class="h5">
<div text="#000000" bgcolor="#FFFFFF">
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">I
recently did a conceptual experiment to estimate the
computational time required to solve an exact expression in
contrast to an approximate solution (Helmholtz vs.
Helmholtz-Kirchhoff integrals). The exact solution requires a
matrix inversion, and in my case the matrix would contain ~15000
rows.</span></p>
<br>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">On
my machine MATLAB seems to perform this matrix inversion with
random matrices about 9x faster (20 sec vs 3 mins). I thought
the performance would be roughly the same because </span><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">I
presume</span> both rely on the same LAPACK solvers.</span></p>
<br>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">I
will not actually need to solve this problem (even at 20 sec it
is prohibitive for broadband simulation), but if I needed to I
would reluctantly choose MATLAB . I am simply wondering why
there is this performance gap, and if there is a better way to
solve this problem in numpy?</span></p>
<br>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">Thank
you,</span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">Ned</span></p>
<br>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">#Python
version<br>
</span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">import
numpy as np</span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">testA
= np.random.randn(15000, 15000)</span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">testb
= np.random.randn(15000)</span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">%time
testx = np.linalg.solve(testA, testb)</span></p>
<br>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">%MATLAB
version<br>
</span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">testA
= randn(15000);</span></p>
<p dir="ltr" style="line-height:1.38;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">testb
= randn(15000, 1);</span></p>
<span style="font-size:14.666666666666666px;font-family:Arial;color:#000000;background-color:transparent;font-weight:400;font-style:normal;font-variant:normal;text-decoration:none;vertical-align:baseline">tic();
testx = testA \ testb; toc();</span>
</div>
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<br></blockquote></div><span class="HOEnZb"><font color="#888888"><br><br clear="all"><br>-- <br><div>Francesc Alted</div>
</font></span></div>
</blockquote></div><br><br clear="all"><br>-- <br><div class="gmail_signature">Francesc Alted</div>
</div>