RE: [ojAlgo-user] Questions

[Inger, M. <In...@Sy...>]

In my test, yes, they are the same, but in practice, they
will not be.  What's an A-Matrix?

-----Original Message-----
From: Anders Peterson [mailto:and...@op...]
Sent: Tuesday, April 20, 2004 4:53 AM
To: Inger, Matthew
Cc: 'oja...@li...'
Subject: Re: [ojAlgo-user] Questions


Do you re-use the A-matrix? Are the x values the same for the 10k 
regressions?

On 2004-04-19, at 21.03, Inger, Matthew wrote:

> There are a small number of variables.  In most cases, we
> have a single variable equation, and up to 24 points with
> which to fit the linear regression.
>
> Then, we do that 10,000 times.
>
> Basically, each row in the database contains time elapsed
> data (typically one value per month).  We use the # of the
> month as the x values, and the data as the y value, and try
> to fit a line to it to determine short term trends.
>
> So for each row, we calculate 1 set of coefficients (b0 and b1,
> aka intercept & slope), and make 1 more predictions.
>
> However, there are potentially millions of rows in the database.
>
>
> -----Original Message-----
> From: Anders Peterson [mailto:and...@op...]
> Sent: Monday, April 19, 2004 2:32 PM
> To: Inger, Matthew
> Subject: Re: [ojAlgo-user] Questions
>
>
> This is just a naive first attempt...
>
> On 2004-04-19, at 20.06, Inger, Matthew wrote:
>
>> PS:  As far as solving the equations, i basically have two
>> matrices.  X and Y.  Any kind of code snippet would help here.
>> Keep in mind, equations are of the form
>>
>> 	y = b0 + b1*X
>
> 1*b0 + x*b1 = y
>
> A*X = B
>
> where
>
> A:
> 1	x1
> 1	x2
> 1	x3
> ...	...
>
> B:
> y1
> y2
> y3
> ...
>
> X:
> b0
> b1
>
> X = A.solve(B);
>
> Are you doing this 10 000 times with a relatively small number of x-
> and y-values or do you have 10 000 x- and y-values for each
> calculation?
>
> /Anders
>
>> -----Original Message-----
>> From: Anders Peterson [mailto:and...@op...]
>> Sent: Monday, April 19, 2004 2:02 PM
>> To: Inger, Matthew
>> Cc: 'oja...@li...'
>> Subject: Re: [ojAlgo-user] Questions
>>
>>
>> On 2004-04-19, at 18.33, Inger, Matthew wrote:
>>
>>> 1.  Have any performance tests been run with BigMatrix?
>>
>> Not really...
>>
>>>    I'm using
>>> BigMatrix to do a
>>>      LinearRegression algorithm.  I had previously been using Jama
>>> directly,
>>> but our FD
>>>      department noticed a difference between the results given by 
>>> java
>>> and
>>> the LINEST
>>>      function in Excel.  I have determined that the difference is
>>> DEFINATELY
>>> due to rounding
>>>      limitations in the java double primitive type.
>>>
>>>      These issues go away when i use ojAlgo library,
>>
>> That's great news to me - that is the reason I created ojAlgo!
>>
>>> however, the time
>>> required to do the
>>>      calculations increases to about 12-13x what it was using regular
>>> double
>>> calculations.
>>>
>>>      Doing 10,000 linear regressions with Jama took about .781s
>>> (according
>>> to junit), and
>>>      with BigMatrix, took 10.345s
>>
>> I wasn't aware the difference was that big. ;-)
>>
>>>      Any idea why such a hug disparity?
>>
>> Try altering the scale. A larger scale means better results, but it
>> takes longer. You can change a matrix' scale whenever you want - the
>> new scale will be used from then on. Elements are not rounded unless
>> you call enforceScale().
>>
>> Internally BigMatrix uses various decompositions for some of the more
>> complex calculations. These decompositions inherit a scale from the
>> parent matrix. It is however not the same - it's bigger. I believe the
>> formula is 2 * (3 + max(9, matrixScale)) and this formula is evaluated
>> when the decomposition is created. After the decomposition is created
>> its scale wont change even if you change the matrix' scale. The scale
>> of a decomposition is never smaller than 24 (according to the above
>> formula).
>>
>> I'm not happy with this, and have been meaning to change it.
>> Decompositions should have the same scale as its parent matrix, and
>> when it is changed, updated "everywhere".
>>
>> Would you prefer that?
>>
>>> 2.  Is there a way to use the solvers in OjAlg to do the linear
>>> regression?
>>> Or is that not
>>>      something that is provided?
>>
>> How are you currently doing it?
>>
>> I imagine the best way would be to simply build an over-determined set
>> of linear equations - Ax=B - and call A.solve(B). Internally BigMatrix
>> would then use the QR decomposition to give a least squares estimation
>> of x. That would be my first attempt.
>>
>> You could use the QP solver do the same thing, but I don't see how 
>> that
>> would simplify or improve anything.
>>
>> What version of ojAlgo are you using - v1, v2 or CVS?
>>
>> I recommend working from CVS. Unfortunately I have moved things around
>> a bit in between version...
>>
>> I don't have access to a profiling tool, but I know they can be very
>> useful in finding bottlenecks. If you can identify a problem, and/or
>> suggest a specific improvement, I'll be happy to help you implement 
>> it.
>>
>> /Anders
>>
>>> ----------------------
>>> Matthew Inger
>>> Design Architect
>>> Synygy, Inc
>>> 610-664-7433 x7770
>>>
>>>
>>>
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