[vtkusers] [EXTERNAL] vtkMultiCorrelativeStatistics

[Darshan Pai]

Thanks David for the explanation . That makes things clearer .


On Thu, May 3, 2012 at 1:37 PM, David Thompson <dcthomp at sandia.gov> wrote:

> Hi Darshan,
>
>  I was just goings through the Testing Cxx for
>> vtkMultiCorrelativeteStatistic**s class . ... tables below ...
>>
>> I am trying to understand the result in the Derived Statistics part . In
>> the Derived Statistics 0 the Cholesky value for M1,M1 , which is the result
>> in the last column , last row , the output is 1.11199 , If I understand
>> correctly , the answer should be sqrt(7.54) = 2.74 , isn't it ? Just
>> wondering about the result.
>>
>
>
> I believe the values in the table are correct, if perhaps a little
> difficult to parse. The covariance matrix -- of which only the upper
> triangle of the symmetric matrix is presented in the table below -- is
>
>   5.9829   6.1452
>   6.1452 7.5484
>
> The Cholesky factorization of this matrix is
>
>   2.44599   2.51234
>   0.00000   1.11199
>
> whose transpose is presented below the covariance matrix as
>
>   2.44599     --
>   2.51234   1.11199
>
> (where I've put "--" in place of the covariance entry reported by VTK).
>
> When I multiply the above by its transpose, I get the original, symmetric
> covariance matrix. The actual relationship between the covariance entry and
> its Cholesky decomposition is 7.54839 = 2.51234**2 + 1.11199**2 because the
> transpose leaves both terms in the Cholesky matrix row-column product
> non-zero.
>
>
>  Also in the Primary Statistics , what are those values after row 4 ...
>>
>
> Those are the sums of centered moments used to derive the covariance
> matrices. Dividing by (Cardinality - 1) will get you the covariance matrix
> entry. For example, take the M0,M0 entry of row 5: 185.469 / (32-1) ==
> 5.98286.
>
>        David
>
>
>  Primary Statistics
>> +-----------------+-----------**------+------------------+
>> | Column1         | Column2         | Entries          |
>> +-----------------+-----------**------+------------------+
>> | Cardinality     |                 | 32               |
>> | M0              |                 | 49.2188          |
>> | M1              |                 | 49.5             |
>> | M2              |                 | -1.00003         |
>> | M0              | M0              | 185.469          |
>> | M0              | M1              | 190.5            |
>> | M0              | M2              | -0.00278125      |
>> | M1              | M1              | 234              |
>> | M1              | M2              | -0.0045          |
>> | M2              | M2              | 9.6875e-007      |
>> +-----------------+-----------**------+------------------+
>> Derived Statistics 0
>> +-----------------+-----------**------+-----------------+-----**
>> -------------+
>> | Column          | Mean            | M0              | M1               |
>> +-----------------+-----------**------+-----------------+-----**
>> -------------+
>> | M0              | 49.2188         | 5.98286         | 6.14516          |
>> | M1              | 49.5            | 2.44599         | 7.54839          |
>> | Cholesky        | 32              | 2.51234         | 1.11199          |
>> +-----------------+-----------**------+-----------------+-----**
>> -------------+
>> Derived Statistics 1
>> +-----------------+-----------**------+-----------------+-----**
>> ------------+-------
>> -----------+
>> | Column          | Mean            | M0              | M1              |
>> M2
>>           |
>> +-----------------+-----------**------+-----------------+-----**
>> ------------+-------
>> -----------+
>> | M0              | 49.2188         | 5.98286         | 6.14516         |
>> -8.971
>> 77e-005    |
>> | M1              | 49.5            | 2.44599         | 7.54839         |
>> -0.000
>> 145161     |
>> | M2              | -1.00003        | 2.51234         | 1.11199         |
>> 3.125e
>> -008       |
>> | Cholesky        | 32              | -3.66795e-005   | -4.7671e-005    |
>> 0.0001
>> 66229      |
>> +-----------------+-----------**------+-----------------+-----**
>> ------------+-------
>>
>>
>
>
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