Re: [eigen] cache-friendly matrix inverse |

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*To*: eigen <eigen@xxxxxxxxxxxxxxxxxxx>*Subject*: Re: [eigen] cache-friendly matrix inverse*From*: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>*Date*: Thu, 14 May 2009 01:28:19 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:in-reply-to:references :date:message-id:subject:from:to:content-type :content-transfer-encoding; bh=QtAkgUXyNc/KpqxnzlLs7L1Ib7eUXolT0PTGg1yEn9k=; b=b9LqZHBGHi9g+5p44HvlET04XY8IKPfA3XYBBdfkTqjsnIaJgdWmL7ji5P8xxnpE9l YNs3c+Z4N/a8ppOJkmorLfr21nRRDEEefGnGw/ZElKD7Wx1JpPb4PC+hdFUxNBeVhPyO NcRj9RhUlGP6tfubxznXU3+fCFRhHXpU1z+n0=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type:content-transfer-encoding; b=nFhvrADxwooUrRlbmWSHaxkMULUyk58ZKctc3c50Z4TJMgKHfV5NKCQqzwtv4kcuKk xRPcEi5moOCaF0X0ej33YIhaqC/0qIlYWvbIW9AK+Hz7/y9Jm96tid7PzbL0GSXFRUoJ NaB1ZitwqLCVUkYtpEytuHiyFWg53SPJcUQ2g=

[Oops, my turn to reply to Jitse instead of the list...] 2009/5/14, Benoit Jacob <jacob.benoit.1@xxxxxxxxx>: > 2009/5/14, Jitse Niesen <jitse@xxxxxxxxxxxxxxxxx>: >>> Good point. I think you're right for very large sizes, asymptotically >>> they're the same. >>> [...] >>> But for a size like 10x10, the matrix-vector product will be much >>> faster. >> >> Can you give some proof for that? >> >> Perhaps you're right (though I think the cross-over point is closer to 3 >> that 10), but it flies against what people in numerical analysis have >> been >> teaching for the last thirty years. I don't know myself, I only do >> matrices of larger size, and for e.g. 100 x 100 I can only repeat what >> Christian said: >> * LU decomp instead of inverse takes the same time, AND >> * LU decomp instead of inverse is more precise > > So, we agree that multiplying by the inverse will be faster for small > enough sizes, and that LU solving will be faster for large enough > sizes, and the only question is what the crossover point is. > > I don't have any idea about that to be honest, and since we're talking > about small sizes here it'll even depend on e.g. whether the size of a > column (assuming column-major storage) is a multiple of the SIMD > vector size, etc... so one can't give a very general answer. About > testing with Eigen, well since we're talking about small sizes > unrolling will be very important, currently the matrix-vector product > is unrolled but not the triangular solver so i don't think this will > produce useful numbers. > > Cheers, > Benoit >

**Follow-Ups**:**Re: [eigen] cache-friendly matrix inverse***From:*Jitse Niesen

**References**:**[eigen] cache-friendly matrix inverse***From:*Benoit Jacob

**Re: [eigen] cache-friendly matrix inverse***From:*Robert Lupton the Good

**Re: [eigen] cache-friendly matrix inverse***From:*Christian Mayer

**Re: [eigen] cache-friendly matrix inverse***From:*Robert Lupton the Good

**Re: [eigen] cache-friendly matrix inverse***From:*Christian Mayer

**Re: [eigen] cache-friendly matrix inverse***From:*Benoit Jacob

**Re: [eigen] cache-friendly matrix inverse***From:*Christian Mayer

**Re: [eigen] cache-friendly matrix inverse***From:*Benoit Jacob

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