Breeze库 常用函数
来源：互联网 发布：js判断变量是否为对象 编辑：程序博客网 时间：2024/06/06 18:10
运算
加，减，乘，除
向量与向量
- 加：+
- 减：-
- 乘：:*
- 除：:/
规则1:乘除前面，加冒号；单独的乘号和除号分别表示点积和线性求解 规则2:累加效果，加等号
<code class="hljs go has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.linalg.DenseVectorobject Test { def main(args: Array[String]) { val v1 = DenseVector<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">(1.0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;"> 2.0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;"> 3.0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;"> 4.0</span>) val v2 = DenseVector<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">(0.5</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;"> 0.5</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;"> 0.5</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;"> 0.5</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(1.5, 2.5, 3.5, 4.5)</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 + v2 : "</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(v1 + v2) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(0.5, 1.5, 2.5, 3.5)</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 - v2 : "</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(v1 - v2) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(0.5, 1.0, 1.5, 2.0)</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 :* v2 : "</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 规则1：乘号前面多了冒号</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(v1 :* v2) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(2.0, 4.0, 6.0, 8.0)</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 :/ v2 : "</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 规则1：除号前面多了冒号</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(v1 :/ v2) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 但是v1 和 v2并没有改变</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(1.0, 2.0, 3.0, 4.0)</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 : "</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(v1) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(0.5, 0.5, 0.5, 0.5)</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv2 : "</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(v2) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 规则2</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 如果想把最后的结果保存到v1上，需要加等号</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(1.5, 2.5, 3.5, 4.5)</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 += v2 : "</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(v1 += v2) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(1.0, 2.0, 3.0, 4.0)</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 -= v2 : "</span>) <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(v1 -= v2) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(0.5, 1.0, 1.5, 2.0)</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 :*= v2 : "</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 注意：乘号前面多了冒号</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(v1 :*= v2) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(1.0, 2.0, 3.0, 4.0)</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 :/= v2 : "</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 注意：除号前面多了冒号</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">println</span>(v1 :/= v2) }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li></ul>矩阵与矩阵
跟向量与向量完全一样
- 加：+
- 减：-
- 乘：:*
- 除：:/
规则1:乘除前面，加冒号；单独的乘号和除号分别表示点积和线性求解 规则2:累加效果，加等号
<code class="hljs scala has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.linalg.DenseMatrix<span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">object</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Test1</span> {</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> main(args: Array[String]) { <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> m1 = DenseMatrix((<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>), (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.0</span>)) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> m2 = DenseMatrix((<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>), (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>)) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.5 2.5 * 3.5 4.5 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 + m2 : "</span>) println(m1 + m2) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.5 1.5 * 2.5 3.5 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 - m2 : "</span>) println(m1 - m2) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.5 1.0 * 1.5 2.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 :* m2 : "</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 注意：乘号前面多了冒号</span> println(m1 :* m2) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 2.0 4.0 * 6.0 8.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 :/ m2 : "</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 注意：除号前面多了冒号</span> println(m1 :/ m2) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 但是m1 和 m2并没有改变</span> <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 2.0 * 3.0 4.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 : "</span>) println(m1) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.5 0.5 * 0.5 0.5 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm2 : "</span>) println(m2) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 如果想把最后的结果保存到m1上，需要加等号</span> <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.5 2.5 * 3.5 4.5 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 += m2 : "</span>) println(m1 += m2) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 2.0 * 3.0 4.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 -= m2 : "</span>) println(m1 -= m2) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.5 1.0 * 1.5 2.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 :*= m2 : "</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 注意：乘号前面多了冒号</span> println(m1 :*= m2) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 2.0 * 3.0 4.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 :/= m2 : "</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 注意：除号前面多了冒号</span> println(m1 :/= m2) }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li></ul>矩阵或向量与数值
- 加：+
- 减：-
- 乘：*
- 除：/
规则1:累加效果，加等号
注意：乘除号前不需要冒号，因为没有矩阵与数值的点积等计算
<code class="hljs scala has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.linalg.{DenseMatrix, DenseVector}<span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">object</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Test1</span> {</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> main(args: Array[String]) { <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> v1 = DenseVector(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.0</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(1.5, 2.5, 3.5, 4.5)</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"v1 + 0.5 : "</span>) println(v1 + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(0.5, 1.5, 2.5, 3.5)</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 - 0.5 : "</span>) println(v1 - <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(0.5, 1.0, 1.5, 2.0)</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 * 0.5 : "</span>) println(v1 * <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(2.0, 4.0, 6.0, 8.0)</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 / 0.5 : "</span>) println(v1 / <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// v1依然不变</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(1.0, 2.0, 3.0, 4.0)</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 : "</span>) println(v1) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(1.5, 2.5, 3.5, 4.5)</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 += 0.5 : "</span>) println(v1 += <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(1.0, 2.0, 3.0, 4.0)</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 -= 0.5 : "</span>) println(v1 -= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(0.5, 1.0, 1.5, 2.0)</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 *= 0.5 : "</span>) println(v1 *= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(5.0, 10.0, 15.0, 20.0)</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 /= 0.1 : "</span>) println(v1 /= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.1</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(5.0, 10.0, 15.0, 20.0)</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nv1 : "</span>) println(v1) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> m1 = DenseMatrix((<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>), (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.0</span>)) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.5 2.5 * 3.5 4.5 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"m1 + 0.5 : "</span>) println(m1 + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.5 1.5 * 2.5 3.5 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 - 0.5 : "</span>) println(m1 - <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.5 1.0 * 1.5 2.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 * 0.5 : "</span>) println(m1 * <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 2.0 4.0 * 6.0 8.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 / 0.5 : "</span>) println(m1 / <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// m1依然不变</span> <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 2.0 * 3.0 4.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 : "</span>) println(m1) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.5 2.5 * 3.5 4.5 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 += 0.5 : "</span>) println(m1 += <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 2.0 * 3.0 4.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 -= 0.5 : "</span>) println(m1 -= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.5 1.0 * 1.5 2.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 *= 0.5 : "</span>) println(m1 *= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 5.0 10.0 * 15.0 20.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 /= 0.1 : "</span>) println(m1 /= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.1</span>) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 5.0 10.0 * 15.0 20.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 : "</span>) println(m1) }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li><li style="box-sizing: border-box; padding: 0px 5px;">97</li><li style="box-sizing: border-box; padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li><li style="box-sizing: border-box; padding: 0px 5px;">119</li><li style="box-sizing: border-box; padding: 0px 5px;">120</li><li style="box-sizing: border-box; padding: 0px 5px;">121</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li><li style="box-sizing: border-box; padding: 0px 5px;">97</li><li style="box-sizing: border-box; padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li><li style="box-sizing: border-box; padding: 0px 5px;">119</li><li style="box-sizing: border-box; padding: 0px 5px;">120</li><li style="box-sizing: border-box; padding: 0px 5px;">121</li></ul>矩阵与向量
- 加：+
- 减：-
- 乘：:*
- 除：:/
规则1:乘除前面，加冒号；单独的乘号和除号分别表示点积和线性求解 规则2:累加效果，加等号 规则3:必须有星号 规则4:星号在左，逐行；星号在右，逐列；与向量是列向量还是行向量无关 规则5:向量必须是列向量
<code class="hljs scala has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.linalg.{*, DenseMatrix, DenseVector}<span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">object</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Test1</span> {</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> main(args: Array[String]) { <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> m1 = DenseMatrix( (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>), (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.0</span>) ) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> v1 = DenseVector(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// val v1 = DenseVector(1.0, 2.0).t // 运行时异常，规则5，向量必须是列向量</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// val v1 = DenseVector(1.0, 2.0).t.t // 正确，如果是一个列向量，需要转换成行向量</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 规则4: 星号在左，逐行；星号在右，逐列</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"-------------星号在左边，就逐行操作-----------------"</span>) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 2.0 4.0 * 4.0 6.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1(*, ::) + v1 : "</span>) println(m1(*, ::) + v1) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.0 0.0 * 2.0 2.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1(*, ::) - v1 : "</span>) println(m1(*, ::) - v1) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 规则1: 乘除前面，加冒号</span> <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 4.0 * 3.0 8.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1(*, ::) :* v1 : "</span>) println(m1(*, ::) :* v1) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 1.0 * 3.0 2.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1(*, ::) :/ v1 : "</span>) println(m1(*, ::) :/ v1) println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"-------------星号在右边，就逐列操作-----------------"</span>) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 2.0 3.0 * 5.0 6.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1(::, *) + v1 : "</span>) println(m1(::, *) + v1) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.0 1.0 * 1.0 2.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1(::, *) - v1 : "</span>) println(m1(::, *) - v1) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 2.0 * 6.0 8.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1(::, *) :* v1 : "</span>) println(m1(::, *) :* v1) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 2.0 * 1.5 2.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1(::, *) :/ v1 : "</span>) println(m1(::, *) :/ v1) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 无论星号在哪，m1都不会改变</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"-------------规则2: 累加效果，加等号-----------------"</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 下面以整除为例，注意星号的位置，一个在左，一个在右</span> <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 2.0 * 3.0 4.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 : "</span>) println(m1) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * BroadcastedRows(1.0 4.0 * 3.0 8.0 ) */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1(*, ::) :*= v1 : "</span>) println(m1(*, ::) :*= v1) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 4.0 * 3.0 8.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 : "</span>) println(m1) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * BroadcastedColumns(1.0 4.0 * 1.5 4.0 ) */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1(::, *) :/= v1 : "</span>) println(m1(::, *) :/= v1) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 4.0 * 1.5 4.0 */</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nm1 : "</span>) println(m1) }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li><li style="box-sizing: border-box; padding: 0px 5px;">97</li><li style="box-sizing: border-box; padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li><li style="box-sizing: border-box; padding: 0px 5px;">97</li><li style="box-sizing: border-box; padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li></ul>函数
统计
求和
<code class="hljs scala has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.linalg.{Axis, DenseMatrix, sum}<span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">object</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Test1</span> {</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> main(args: Array[String]) { <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> m1 = DenseMatrix( (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>), (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.0</span>) ) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// Axis._0 纵向</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 4.0 6.0</span> println(sum(m1, Axis._0)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// Axis._1 横向</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 3.0 7.0</span> println(sum(m1, Axis._1)) }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li></ul>均值
<code class="hljs scala has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.linalg.{Axis, DenseMatrix}<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.stats.mean<span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">object</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Test1</span> {</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> main(args: Array[String]) { <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> m1 = DenseMatrix( (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>), (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.0</span>) ) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// Axis._0 纵向</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 4.0 6.0</span> println(mean(m1, Axis._0)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// Axis._1 横向</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 1.5 3.5</span> println(mean(m1, Axis._1)) }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li></ul>方差和标准差
<code class="hljs scala has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.linalg.{Axis, DenseMatrix}<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.stats.{stddev, variance}<span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">object</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Test1</span> {</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> main(args: Array[String]) { <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> m1 = DenseMatrix( (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>), (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.0</span>) ) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// Axis._0 纵向</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 2.0 2.0 </span> println(variance(m1, Axis._0)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// Axis._1 横向</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 0.5, 0.5</span> println(variance(m1, Axis._1)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// Axis._0 纵向</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 2.0 2.0 </span> println(stddev(m1, Axis._0)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// Axis._1 横向</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 0.5, 0.5</span> println(stddev(m1, Axis._1)) }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li></ul>N次方和开方
<code class="hljs scala has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.linalg.DenseMatrix<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.numerics.{pow, sqrt}<span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">object</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Test1</span> {</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> main(args: Array[String]) { <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> m1 = DenseMatrix( (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>), (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.0</span>) ) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 4.0 * 9.0 16.0 */</span> println(pow(m1, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>)) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 8.0 * 27.0 64.0 */</span> println(pow(m1, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>)) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 1.4142135623730951 * 1.7320508075688772 2.0 */</span> println(sqrt(m1)) }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li></ul>E和log
<code class="hljs scala has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.linalg.DenseMatrix<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.numerics.{exp, log, log10, log1p}<span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">object</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Test1</span> {</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> main(args: Array[String]) { <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> m1 = DenseMatrix( (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>), (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.0</span>) ) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 2.718281828459045 7.38905609893065 * 20.085536923187668 54.598150033144236 */</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// e = 2.718281828459045</span> println(exp(m1)) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.0 0.6931471805599453 * 1.0986122886681098 1.3862943611198906 */</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 以e为底</span> println(log(m1)) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.0 0.3010299956639812 * 0.47712125471966244 0.6020599913279624 */</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 以10为底</span> println(log10(m1)) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.6931471805599453 1.0986122886681096 * 1.3862943611198906 1.6094379124341003 */</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 以e为底</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// log1p() 以返回 log(1 + x)，甚至当 x 的值接近零也能计算出准确结果。</span> println(log1p(m1)) }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li></ul>三角
- sin, sinh, asin, asinh
- cos, cosh, acos, acosh
- tan, tanh, atan, atanh
- atan2
- sinc(x) == sin(x)/x
- sincpi(x) == sinc(x * Pi)
取整
<code class="hljs livecodeserver has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;">import breeze.linalg.DenseVectorimport breeze.numerics._object Test1 { def main(args: Array[String]) { val <span class="hljs-operator" style="box-sizing: border-box;">a</span> = DenseVector(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.4</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.5</span>, -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.3</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"> // 四舍五入</span> println(<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">round</span>(<span class="hljs-operator" style="box-sizing: border-box;">a</span>)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"> // 向上取整</span> println(ceil(<span class="hljs-operator" style="box-sizing: border-box;">a</span>)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"> // 向下取整</span> println(floor(<span class="hljs-operator" style="box-sizing: border-box;">a</span>)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"> // 大于0，为1；小于0，为-1</span> println(signum(<span class="hljs-operator" style="box-sizing: border-box;">a</span>)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"> // 绝对值</span> println(<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">abs</span>(<span class="hljs-operator" style="box-sizing: border-box;">a</span>)) }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li></ul>示例
模拟逻辑回归
利用Breze进行，归一化，添加截距项，预测
<code class="hljs scala has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.linalg._<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.numerics._<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> breeze.stats._<span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">object</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Work2</span> {</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> main(args: Array[String]) { <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 随机产生数据</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// val featuresMatrix = DenseMatrix.rand[Double](3, 3)</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// val labelMatrix = DenseMatrix.rand[Double](3, 1)</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 测试数据</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> featuresMatrix = DenseMatrix( (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3.0</span>), (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6.0</span>), (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">8.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9.0</span>) ) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> labelMatrix = DenseMatrix( <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.0</span> ) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 均值</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(4.0, 5.0, 6.0)</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> featuresMean = mean(featuresMatrix(::, *)).toDenseVector println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"均值："</span>) println(featuresMean) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 标准差</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// DenseVector(3.0, 3.0, 3.0)</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> featuresStddev = stddev(featuresMatrix(::, *)).toDenseVector println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\n标准差："</span>) println(featuresStddev) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 减去均值</span> <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * -3.0 -3.0 -3.0 * 0.0 0.0 0.0 * 3.0 3.0 3.0 */</span> featuresMatrix(*, ::) -= featuresMean println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\n减去均值："</span>) println(featuresMatrix) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 除以标准差</span> <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * -1.0 -1.0 -1.0 * 0.0 0.0 0.0 * 1.0 1.0 1.0 */</span> featuresMatrix(*, ::) /= featuresStddev println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\n除以标准差："</span>) println(featuresMatrix) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 生成截距</span> <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 * 1.0 * 1.0 */</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> intercept = DenseMatrix.ones[Double](featuresMatrix.rows, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>) println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\n截距："</span>) println(intercept) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 拼接成为最终的训练集</span> <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 -1.0 -1.0 -1.0 * 1.0 0.0 0.0 0.0 * 1.0 1.0 1.0 1.0 */</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> train = DenseMatrix.horzcat(intercept, featuresMatrix) println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\n训练集："</span>) println(train) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 参数</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 为方便检查结果，这里全部设置为1</span> <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 1.0 * 1.0 * 1.0 * 1.0 */</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> w = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> DenseMatrix(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>, Array(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>)) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// val w = DenseMatrix.rand[Double](4, 1) // 随机生成, 一定要指定类型</span> println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\n参数："</span>) println(w) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * -2.0 * 1.0 * 4.0 */</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 随机生成w时，如果没有指定类型，A的计算结果虽然不会有错，但是后面将无法计算，除非通过asInstanceOf进行类型转换</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 如果w指定了类型，那么在idea中，转换语句会是灰色的，意思是这句话没有作用，可以不写</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> A = (train * w).asInstanceOf[DenseMatrix[Double]] println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nA："</span>) println(A) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * 0.11920292202211755 * 0.7310585786300049 * 0.9820137900379085 */</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// Sigmoid函数</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> probability = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span> / (exp(A * -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>) + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1.0</span>) println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nprobability："</span>) println(probability) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * MSE : 0.6041613548425021 */</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> MSE = mean(pow(probability - labelMatrix, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>)) println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nMSE："</span>) println(MSE) <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/** * RMSE : 0.777278170825929 */</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">val</span> RMSE = sqrt(MSE) println(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\nRMSE："</span>) println(RMSE) }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li><li style="box-sizing: border-box; padding: 0px 5px;">97</li><li style="box-sizing: border-box; padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li><li style="box-sizing: border-box; padding: 0px 5px;">119</li><li style="box-sizing: border-box; padding: 0px 5px;">120</li><li style="box-sizing: border-box; padding: 0px 5px;">121</li><li style="box-sizing: border-box; padding: 0px 5px;">122</li><li style="box-sizing: border-box; padding: 0px 5px;">123</li><li style="box-sizing: border-box; padding: 0px 5px;">124</li><li style="box-sizing: border-box; padding: 0px 5px;">125</li><li style="box-sizing: border-box; padding: 0px 5px;">126</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li><li style="box-sizing: border-box; padding: 0px 5px;">97</li><li style="box-sizing: border-box; padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li><li style="box-sizing: border-box; padding: 0px 5px;">119</li><li style="box-sizing: border-box; padding: 0px 5px;">120</li><li style="box-sizing: border-box; padding: 0px 5px;">121</li><li style="box-sizing: border-box; padding: 0px 5px;">122</li><li style="box-sizing: border-box; padding: 0px 5px;">123</li><li style="box-sizing: border-box; padding: 0px 5px;">124</li><li style="box-sizing: border-box; padding: 0px 5px;">125</li><li style="box-sizing: border-box; padding: 0px 5px;">126</li></ul>参考
Quickstart
Linear Algebra Cheat Sheet
0 0
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