Thanks David for the explanation . That makes things clearer . <br><br><br><div class="gmail_quote">On Thu, May 3, 2012 at 1:37 PM, David Thompson <span dir="ltr"><<a href="mailto:dcthomp@sandia.gov" target="_blank">dcthomp@sandia.gov</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Hi Darshan,<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
I was just goings through the Testing Cxx for vtkMultiCorrelativeteStatistic<u></u>s class . ... tables below ...<div class="im"><br>
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.<br>
</div></blockquote>
<br>
<br>
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<br>
<br>
5.9829 6.1452<br>
<a href="tel:6.1452%20%20%207.5484" value="+16145275484" target="_blank">6.1452 7.5484</a><br>
<br>
The Cholesky factorization of this matrix is<br>
<br>
2.44599 2.51234<br>
0.00000 1.11199<br>
<br>
whose transpose is presented below the covariance matrix as<br>
<br>
2.44599 --<br>
2.51234 1.11199<br>
<br>
(where I've put "--" in place of the covariance entry reported by VTK).<br>
<br>
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.<div class="im">
<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Also in the Primary Statistics , what are those values after row 4 ...<br>
</blockquote>
<br></div>
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.<span class="HOEnZb"><font color="#888888"><br>
<br>
David</font></span><div class="HOEnZb"><div class="h5"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Primary Statistics<br>
+-----------------+-----------<u></u>------+------------------+<br>
| Column1 | Column2 | Entries |<br>
+-----------------+-----------<u></u>------+------------------+<br>
| Cardinality | | 32 |<br>
| M0 | | 49.2188 |<br>
| M1 | | 49.5 |<br>
| M2 | | -1.00003 |<br>
| M0 | M0 | 185.469 |<br>
| M0 | M1 | 190.5 |<br>
| M0 | M2 | -0.00278125 |<br>
| M1 | M1 | 234 |<br>
| M1 | M2 | -0.0045 |<br>
| M2 | M2 | 9.6875e-007 |<br>
+-----------------+-----------<u></u>------+------------------+<br>
Derived Statistics 0<br>
+-----------------+-----------<u></u>------+-----------------+-----<u></u>-------------+<br>
| Column | Mean | M0 | M1 |<br>
+-----------------+-----------<u></u>------+-----------------+-----<u></u>-------------+<br>
| M0 | 49.2188 | 5.98286 | 6.14516 |<br>
| M1 | 49.5 | 2.44599 | 7.54839 |<br>
| Cholesky | 32 | 2.51234 | 1.11199 |<br>
+-----------------+-----------<u></u>------+-----------------+-----<u></u>-------------+<br>
Derived Statistics 1<br>
+-----------------+-----------<u></u>------+-----------------+-----<u></u>------------+-------<br>
-----------+<br>
| Column | Mean | M0 | M1 | M2<br>
|<br>
+-----------------+-----------<u></u>------+-----------------+-----<u></u>------------+-------<br>
-----------+<br>
| M0 | 49.2188 | 5.98286 | 6.14516 | -8.971<br>
77e-005 |<br>
| M1 | 49.5 | 2.44599 | 7.54839 | -0.000<br>
145161 |<br>
| M2 | -1.00003 | 2.51234 | 1.11199 | 3.125e<br>
-008 |<br>
| Cholesky | 32 | -3.66795e-005 | -4.7671e-005 | 0.0001<br>
66229 |<br>
+-----------------+-----------<u></u>------+-----------------+-----<u></u>------------+-------<br>
<br>
</blockquote>
<br>
<br>
</div></div></blockquote></div><br>