diff --git a/Classes/PHPExcel/Shared/JAMA/docs/docs.php b/Classes/PHPExcel/Shared/JAMA/docs/docs.php deleted file mode 100644 index d27a42f..0000000 --- a/Classes/PHPExcel/Shared/JAMA/docs/docs.php +++ /dev/null @@ -1,6 +0,0 @@ - diff --git a/Classes/PHPExcel/Shared/JAMA/docs/download.php b/Classes/PHPExcel/Shared/JAMA/docs/download.php deleted file mode 100644 index 2df6e0c..0000000 --- a/Classes/PHPExcel/Shared/JAMA/docs/download.php +++ /dev/null @@ -1,65 +0,0 @@ -create($files); - - // create the download url - $webDir = substr($_SERVER['PHP_SELF'], 0, -18); - $urlPath = "http://".$_SERVER['HTTP_HOST'].$webDir."/downloads"; - - // redirect to download url - header("Location: $urlPath/$tarName"); - -} - -include_once "includes/header.php"; -include_once "includes/navbar.php"; -?> -
-Download current version: -
--The Jama distribution comes with a magic square example that is used to -test and benchmark the LU, QR, SVD and symmetric Eig decompositions. -The example outputs a multi-column table with these column headings: -
- -n | -Order of magic square. | -
trace | -Diagonal sum, should be the magic sum, (n^3 + n)/2. | -
max_eig | -Maximum eigenvalue of (A + A')/2, should equal trace. | -
rank | -Linear algebraic rank, should equal n if n is odd, be less than n if n is even. | -
cond | -L_2 condition number, ratio of singular values. | -
lu_res | -test of LU factorization, norm1(L*U-A(p,:))/(n*eps). | -
qr_res | -test of QR factorization, norm1(Q*R-A)/(n*eps). | -
-Running the Java-based version of the matix square example produces these results: -
- -n | -trace | -max_eig | -rank | -cond | -lu_res | -qr_res | -
---|---|---|---|---|---|---|
3 | 15 | 15.000 | 3 | 4.330 | 0.000 | 11.333 | -
4 | 34 | 34.000 | 3 | Inf | 0.000 | 13.500 | -
5 | 65 | 65.000 | 5 | 5.462 | 0.000 | 14.400 | -
6 | 111 | 111.000 | 5 | Inf | 5.333 | 16.000 | -
7 | 175 | 175.000 | 7 | 7.111 | 2.286 | 37.714 | -
8 | 260 | 260.000 | 3 | Inf | 0.000 | 59.000 | -
9 | 369 | 369.000 | 9 | 9.102 | 7.111 | 53.333 | -
10 | 505 | 505.000 | 7 | Inf | 3.200 | 159.200 | -
11 | 671 | 671.000 | 11 | 11.102 | 2.909 | 215.273 | -
12 | 870 | 870.000 | 3 | Inf | 0.000 | 185.333 | -
13 | 1105 | 1105.000 | 13 | 13.060 | 4.923 | 313.846 | -
14 | 1379 | 1379.000 | 9 | Inf | 4.571 | 540.571 | -
15 | 1695 | 1695.000 | 15 | 15.062 | 4.267 | 242.133 | -
16 | 2056 | 2056.000 | 3 | Inf | 0.000 | 488.500 | -
17 | 2465 | 2465.000 | 17 | 17.042 | 7.529 | 267.294 | -
18 | 2925 | 2925.000 | 11 | Inf | 7.111 | 520.889 | -
19 | 3439 | 3439.000 | 19 | 19.048 | 16.842 | 387.368 | -
20 | 4010 | 4010.000 | 3 | Inf | 14.400 | 584.800 | -
21 | 4641 | 4641.000 | 21 | 21.035 | 6.095 | 1158.095 | -
22 | 5335 | 5335.000 | 13 | Inf | 6.545 | 1132.364 | -
23 | 6095 | 6095.000 | 23 | 23.037 | 11.130 | 1268.870 | -
24 | 6924 | 6924.000 | 3 | Inf | 10.667 | 827.500 | -
25 | 7825 | 7825.000 | 25 | 25.029 | 35.840 | 1190.400 | -
26 | 8801 | 8801.000 | 15 | Inf | 4.923 | 1859.077 | -
27 | 9855 | 9855.000 | 27 | 27.032 | 37.926 | 1365.333 | -
28 | 10990 | 10990.000 | 3 | Inf | 34.286 | 1365.714 | -
29 | 12209 | 12209.000 | 29 | 29.025 | 30.897 | 1647.448 | -
30 | 13515 | 13515.000 | 17 | Inf | 8.533 | 2571.733 | -
31 | 14911 | 14911.000 | 31 | 31.027 | 33.032 | 1426.581 | -
32 | 16400 | 16400.000 | 3 | Inf | 0.000 | 1600.125 | -
-The magic square example does not fare well when run as a PHP script. For a 32x32 matrix array -it takes around a second to complete just the last row of computations in the above table. -Hopefully this result will spur PHP developers to find optimizations and better attuned algorithms -to speed things up. Matrix algebra is a great testing ground for ideas about time and memory -performance optimation. Keep in perspective that PHP JAMA scripts are still plenty fast for use as -a tool for learning about matrix algebra and quickly extending your knowledge with new scripts -to apply knowledge. -
- -
-To learn more about the subject of magic squares you can visit the Drexel Math Forum on Magic Squares.
-You can also learn more by carefully examining the MagicSquareExample.php
source code below.
-
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