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numpy.linalg.norm(x, ord=None, axis=None, keepdims=False)[source]
顾名思义,,则表示范数,首先需要注意的是范数是对向量(或者矩阵)的度量,是一个标量(scalar):
首先help(np.linalg.norm)
查看其文档:
<code class="hljs mathematica 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;">norm(x, ord=<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">None</span>, axis=<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">None</span>, keepdims=<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">False</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-width: 1px; border-right-style: solid; border-right-color: 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></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-width: 1px; border-right-style: solid; border-right-color: 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></ul>
这里我们只对常用设置进行说明,表示要度量的向量,表示范数的种类,
参数 | 说明 | 计算方法 |
---|---|---|
默认 | 二范数: | |
ord=2 | 二范数: | 同上 |
ord=1 | 一范数: | |
ord=np.inf | 无穷范数: |
<code class="hljs avrasm 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-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">x</span> = np<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">.array</span>([<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>]) >>> np<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">.linalg</span><span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">.norm</span>(<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">x</span>) <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5.</span> >>> np<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">.linalg</span><span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">.norm</span>(<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">x</span>, ord=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>) <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5.</span> >>> np<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">.linalg</span><span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">.norm</span>(<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">x</span>, ord=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>) <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">7.</span> >>> np<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">.linalg</span><span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">.norm</span>(<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">x</span>, ord=np<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">.inf</span>) <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</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-width: 1px; border-right-style: solid; border-right-color: 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></ul><div class="save_code tracking-ad" data-mod="popu_249" style="box-sizing: border-box; position: absolute; height: 60px; right: 30px; top: 5px; color: rgb(255, 255, 255); cursor: pointer; z-index: 2;"><a target=_blank target="_blank" style="color: rgb(202, 0, 0); box-sizing: border-box;"><img src="http://static.blog.csdn.net/images/save_snippets.png" style="border: none; box-sizing: border-box; max-width: 100%;" alt="" /></a></div><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-width: 1px; border-right-style: solid; border-right-color: 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></ul>
范数理论的一个小推论告诉我们:
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