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Re: Setting Negatives to Zero

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82783] Re: Setting Negatives to Zero
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 31 Oct 2007 06:04:57 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fg6qha$dj0$1@smc.vnet.net>

Kevin J. McCann wrote:

> I have a very large data set (64000 x 583) in which negative values 
> indicate "no data", unfortunately these negatives are not all the same. 
> I would like to efficiently set all these negatives to zero. I know that 
> I will likely be embarrassed when I see how to do it, but I can't seem 
> to remember or figure it out. I should emphasize that because of the 
> size of the data set, this needs to be done efficiently. Another 
> programming language does it as follows:
> 
> 		x(x < 0) = 0;

Here is a couple of solutions. They works fine but speaking about 
efficiency they are about 70 times *slower* than the vectorization you 
used with the other product.

First, we create a small set of data to show the principle.

data = RandomReal[{-10, 100}, {6, 4}]

{{90.6031, 16.644, 15.2568, 88.4432}, {95.3404, -0.391179, 22.6264,
   41.0332}, {18.7866, 90.8717, 48.073, 59.3251}, {24.2224, 21.1771,
   91.7082, 50.719}, {96.9408, 27.4581, 56.9265, 2.22925}, {31.6366,
   0.266302, 68.7124, 7.80917}}

Then we use a replacement rule,

data /. x_ /; x < 0 -> 0.

{{90.6031, 16.644, 15.2568, 88.4432}, {95.3404, 0., 22.6264,
   41.0332}, {18.7866, 90.8717, 48.073, 59.3251}, {24.2224, 21.1771,
   91.7082, 50.719}, {96.9408, 27.4581, 56.9265, 2.22925}, {31.6366,
   0.266302, 68.7124, 7.80917}}

We can also do it we *Cases*,

Cases[data, x_ /; x < 0 -> 0., {-1}]

{0.}

Now we test both method on a matrix of doubles of the size you 
specified, and check the time spent in seconds.

data = RandomReal[{-10, 100}, {64000, 583}];
Timing[data /. x_ /; x < 0 -> 0.;][[1]]
Timing[Cases[data, x_ /; x < 0 -> 0., {-1}];][[1]]

62.046

49.797

In comparison, a similar replacement on a similar matrix done with the 
other product takes less than a second.

  >> x = -10 + (100 - (-10)).*rand(64000,583);
  >> tic; x(x < 0) = 0; toc
  Elapsed time is 0.867847 seconds.
  >> whos x
    Name          Size                 Bytes  Class     Attributes

    x         64000x583            298496000  double

I am confident that we can improve the performances for Mathematica; but 
I draw a blank right now (though I suspect something is going on with 
the packed array technology used by Mathematica).

Regards,
-- 
Jean-Marc


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