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Formatting (MATH-677). 

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1208949 13f79535-47bb-0310-9956-ffa450edef68
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Sebastien Brisard 2011-12-01 04:27:49 +00:00
parent c39cd6eefd
commit 56c8f7ba91
1 changed files with 71 additions and 23 deletions
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94
src/main/java/org/apache/commons/math/transform/FastHadamardTransformer.java
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@ -86,29 +86,62 @@ public class FastHadamardTransformer implements RealTransformer {
* <li><b>y</b> is the output vector which is our desired result</li>
* <li>a and b are just helper rows</li>
* </ol>
* <pre>
* <code>
* +----+----------+---------+----------+
* | <b>x</b> | <b>a</b> | <b>b</b> | <b>y</b> |
* +----+----------+---------+----------+
* | x<sub>0</sub> | a<sub>0</sub>=x<sub>0</sub>+x<sub>1</sub> | b<sub>0</sub>=a<sub>0</sub>+a<sub>1</sub> | y<sub>0</sub>=b<sub>0</sub>+b<sub>1</sub> |
* +----+----------+---------+----------+
* | x<sub>1</sub> | a<sub>1</sub>=x<sub>2</sub>+x<sub>3</sub> | b<sub>0</sub>=a<sub>2</sub>+a<sub>3</sub> | y<sub>0</sub>=b<sub>2</sub>+b<sub>3</sub> |
* +----+----------+---------+----------+
* | x<sub>2</sub> | a<sub>2</sub>=x<sub>4</sub>+x<sub>5</sub> | b<sub>0</sub>=a<sub>4</sub>+a<sub>5</sub> | y<sub>0</sub>=b<sub>4</sub>+b<sub>5</sub> |
* +----+----------+---------+----------+
* | x<sub>3</sub> | a<sub>3</sub>=x<sub>6</sub>+x<sub>7</sub> | b<sub>0</sub>=a<sub>6</sub>+a<sub>7</sub> | y<sub>0</sub>=b<sub>6</sub>+b<sub>7</sub> |
* +----+----------+---------+----------+
* | x<sub>4</sub> | a<sub>0</sub>=x<sub>0</sub>-x<sub>1</sub> | b<sub>0</sub>=a<sub>0</sub>-a<sub>1</sub> | y<sub>0</sub>=b<sub>0</sub>-b<sub>1</sub> |
* +----+----------+---------+----------+
* | x<sub>5</sub> | a<sub>1</sub>=x<sub>2</sub>-x<sub>3</sub> | b<sub>0</sub>=a<sub>2</sub>-a<sub>3</sub> | y<sub>0</sub>=b<sub>2</sub>-b<sub>3</sub> |
* +----+----------+---------+----------+
* | x<sub>6</sub> | a<sub>2</sub>=x<sub>4</sub>-x<sub>5</sub> | b<sub>0</sub>=a<sub>4</sub>-a<sub>5</sub> | y<sub>0</sub>=b<sub>4</sub>-b<sub>5</sub> |
* +----+----------+---------+----------+
* | x<sub>7</sub> | a<sub>3</sub>=x<sub>6</sub>-x<sub>7</sub> | b<sub>0</sub>=a<sub>6</sub>-a<sub>7</sub> | y<sub>0</sub>=b<sub>6</sub>-b<sub>7</sub> |
* +----+----------+---------+----------+
* </code>
* </pre>
* <table border="1" align="center">
* <tr>
* <th>x</th>
* <th>a</th>
* <th>b</th>
* <th>y</th>
* </tr>
* <tr>
* <td>x<sub>0</sub></td>
* <td>a<sub>0</sub> = x<sub>0</sub> + x<sub>1</sub></td>
* <td>b<sub>0</sub> = a<sub>0</sub> + a<sub>1</sub></td>
* <td>y<sub>0</sub> = b<sub>0</sub >+ b<sub>1</sub></td>
* </tr>
* <tr>
* <td>x<sub>1</sub></td>
* <td>a<sub>1</sub> = x<sub>2</sub> + x<sub>3</sub></td>
* <td>b<sub>0</sub> = a<sub>2</sub> + a<sub>3</sub></td>
* <td>y<sub>0</sub> = b<sub>2</sub> + b<sub>3</sub></td>
* </tr>
* <tr>
* <td>x<sub>2</sub></td>
* <td>a<sub>2</sub> = x<sub>4</sub> + x<sub>5</sub></td>
* <td>b<sub>0</sub> = a<sub>4</sub> + a<sub>5</sub></td>
* <td>y<sub>0</sub> = b<sub>4</sub> + b<sub>5</sub></td>
* </tr>
* <tr>
* <td>x<sub>3</sub></td>
* <td>a<sub>3</sub> = x<sub>6</sub> + x<sub>7</sub></td>
* <td>b<sub>0</sub> = a<sub>6</sub> + a<sub>7</sub></td>
* <td>y<sub>0</sub> = b<sub>6</sub> + b<sub>7</sub></td>
* </tr>
* <tr>
* <td>x<sub>4</sub></td>
* <td>a<sub>0</sub> = x<sub>0</sub> - x<sub>1</sub></td>
* <td>b<sub>0</sub> = a<sub>0</sub> - a<sub>1</sub></td>
* <td>y<sub>0</sub> = b<sub>0</sub> - b<sub>1</sub></td>
* </tr>
* <tr>
* <td>x<sub>5</sub></td>
* <td>a<sub>1</sub> = x<sub>2</sub> - x<sub>3</sub></td>
* <td>b<sub>0</sub> = a<sub>2</sub> - a<sub>3</sub></td>
* <td>y<sub>0</sub> = b<sub>2</sub> - b<sub>3</sub></td>
* </tr>
* <tr>
* <td>x<sub>6</sub></td>
* <td>a<sub>2</sub> = x<sub>4</sub> - x<sub>5</sub></td>
* <td>b<sub>0</sub> = a<sub>4</sub> - a<sub>5</sub></td>
* <td>y<sub>0</sub> = b<sub>4</sub> - b<sub>5</sub></td>
* </tr>
* <tr>
* <td>x<sub>7</sub></td>
* <td>a<sub>3</sub> = x<sub>6</sub> - x<sub>7</sub></td>
* <td>b<sub>0</sub> = a<sub>6</sub> - a<sub>7</sub></td>
* <td>y<sub>0</sub> = b<sub>6</sub> - b<sub>7</sub></td>
* </tr>
* </table>
*
* <b><u>How it works</u></b>
* <ol>
@ -129,6 +162,21 @@ public class FastHadamardTransformer implements RealTransformer {
* </ol>
* <br>
* <b><u>Visually</u></b>
* <table border="1" align="center">
* <tr>
* <td>0</td>
* <td>1</td>
* <td>2</td>
* <td>3</td>
* <td>...</td>
* <td>n + 1</td>
* </tr>
* <tr>
* <td>0</td>
* <td>x<sub>0</sub></td>
* <td colspan="5">&uarr;</td>
* </tr>
* </table>
* <pre>
* +--------+---+---+---+-----+---+
* | 0 | 1 | 2 | 3 | ... |n+1|