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NumPy_demo.html
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<!DOCTYPE html>
<html>
<head><meta charset="utf-8" />
<title>NumPy_demo2</title><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
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<h1 id="numpy-文档">numpy 文档<a class="anchor-link" href="#numpy-文档">¶</a></h1>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># https://numpy.org/devdocs/user/quickstart.html</span>
<span class="c1">#推荐 https://www.yiibai.com/numpy/</span>
<span class="c1">#https://www.jianshu.com/p/83c8ef18a1e8</span>
<span class="c1"># NumPy 通常与 SciPy（Scientific Python）和 Matplotlib（绘图库）一起使用。</span>
<span class="c1">#NumPy是Python语言的一个扩充程序库。支持高级大量的维度数组与矩阵运算，</span>
<span class="c1">#此外也针对数组运算提供大量的数学函数库。Numpy内部解除了Python的PIL(全局解释器锁),</span>
<span class="c1">#运算效率极好,是大量机器学习框架的基础库!</span>
<span class="c1"># pip install numpy</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="n">a</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]</span>
<span class="n">b</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"1>"</span><span class="p">,</span><span class="n">b</span><span class="o">.</span><span class="n">size</span><span class="p">)</span> <span class="c1">#数组元素个数</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"2>"</span><span class="p">,</span><span class="n">b</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="c1">#数组形状</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"3>"</span><span class="p">,</span><span class="n">b</span><span class="o">.</span><span class="n">ndim</span><span class="p">)</span> <span class="c1">#数组维度</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"4>"</span><span class="p">,</span><span class="n">b</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span> <span class="c1">#数组元素类型</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"5>"</span><span class="p">,</span><span class="n">b</span><span class="o">.</span><span class="n">itemsize</span><span class="p">)</span> <span class="c1">#对象中每个元素的大小，以字节为单位</span>
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<pre>[1, 2, 3, 4]
[1 2 3 4]
1> 4
2> (4,)
3> 1
4> int32
5> 4
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<h1 id="创建与获取">创建与获取<a class="anchor-link" href="#创建与获取">¶</a></h1>
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<h2 id="一维数组">一维数组<a class="anchor-link" href="#一维数组">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 一维数组</span>
<span class="n">a</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">23</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span>
<span class="n">b</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span><span class="mi">23</span><span class="p">,</span><span class="mi">4</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'a='</span><span class="p">,</span><span class="n">a</span><span class="p">,</span> <span class="s1">'; b='</span><span class="p">,</span><span class="n">b</span><span class="p">)</span>
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<pre>a= [ 1 23 4] ; b= [ 1 23 4]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1">## 指定数据类型</span>
<span class="n">a</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">23</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span><span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="c1">#np.array([1,23,4])</span>
<span class="n">a</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">23</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span><span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="c1">#float64</span>
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<pre>int32 [ 1 23 4]
float64 [ 1 23 4]
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<h2 id="二维数组">二维数组<a class="anchor-link" href="#二维数组">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 二维数组</span>
<span class="n">array</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">],</span>
<span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">]</span>
<span class="p">])</span>
<span class="n">array</span>
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<pre>array([[1, 2, 3],
[4, 5, 6]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 获取元素(从0开始计数)</span>
<span class="nb">print</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">array</span><span class="p">),</span> <span class="n">array</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="c1">#2个元素(每个元素也是数组)，第0个元素是数组[1 2 3]</span>
<span class="nb">print</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">array</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">array</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">1</span><span class="p">],</span> <span class="n">array</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span> <span class="c1">#第0个元素长度是3，里面的第一个元素是2；</span>
<span class="c1"># 二维数组的元素，可以[i][j]获取，也可以[i,j]获取</span>
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<pre>2 [1 2 3]
3 2 2
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 获取数组的元素总数，形状，维度个数</span>
<span class="nb">print</span><span class="p">(</span><span class="n">array</span><span class="o">.</span><span class="n">size</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">array</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">array</span><span class="o">.</span><span class="n">ndim</span><span class="p">)</span>
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<pre>6
(2, 3)
2
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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">array</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">array</span><span class="o">.</span><span class="n">dtype</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">array</span><span class="o">.</span><span class="n">itemsize</span><span class="p">)</span>
<span class="nb">type</span><span class="p">(</span><span class="n">array</span><span class="p">)</span>
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<pre>int32
int32
4
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<pre>numpy.ndarray</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 行列转置</span>
<span class="n">array</span><span class="o">.</span><span class="n">T</span>
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<pre>array([[1, 4],
[2, 5],
[3, 6]])</pre>
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<h2 id="reshape变形、多维数组">reshape变形、多维数组<a class="anchor-link" href="#reshape变形、多维数组">¶</a></h2>
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<p>reshape()能把arange()产生的数据序列再排序，按照第一维从左到右，其余从上到下;</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1">#一维数组</span>
<span class="n">a</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">12</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"a="</span><span class="p">,</span><span class="n">a</span><span class="p">)</span>
<span class="c1">#变成4行3列</span>
<span class="n">a2</span><span class="o">=</span><span class="n">a</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'a2='</span><span class="p">,</span><span class="n">a2</span><span class="p">)</span>
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<pre>a= [ 0 1 2 3 4 5 6 7 8 9 10 11]
a2= [[ 0 1 2]
[ 3 4 5]
[ 6 7 8]
[ 9 10 11]]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1">#变成竖排的4行3列，思路：先变成3行4列，再行列转置</span>
<span class="n">a3</span><span class="o">=</span><span class="n">a</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'a3='</span><span class="p">,</span><span class="n">a3</span><span class="p">)</span>
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<pre>a3= [[ 0 4 8]
[ 1 5 9]
[ 2 6 10]
[ 3 7 11]]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 更高维度的数组</span>
<span class="n">a</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">24</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span> <span class="c1">#2个，每个3行4列。C语言风格的下标，越往后的维度，下标变动越快。</span>
<span class="n">a</span>
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<pre>array([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="s2">"</span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="c1">#最外围的维度，包含元素越多。</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">],</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">][</span><span class="mi">1</span><span class="p">],</span> <span class="s2">"</span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span> <span class="c1">#最外围的第一个维度中，下一维度是行，最后是列(一个数字)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
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<pre>[[ 0 1 2 3]
[ 4 5 6 7]
[ 8 9 10 11]]
[0 1 2 3] 1
[[12 13 14 15]
[16 17 18 19]
[20 21 22 23]]
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<h2 id="创建0矩阵、单位矩阵">创建0矩阵、单位矩阵<a class="anchor-link" href="#创建0矩阵、单位矩阵">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">a</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">));</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="c1">#3行4列的0矩阵。</span>
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<pre>[[0. 0. 0. 0.]
[0. 0. 0. 0.]
[0. 0. 0. 0.]]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">))</span> <span class="c1">#2行4列的1矩阵</span>
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<pre>array([[1., 1., 1., 1.],
[1., 1., 1., 1.]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span> <span class="c1">#单位矩阵</span>
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<pre>array([[1., 0., 0., 0.],
[0., 1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.]])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span> <span class="p">)</span> <span class="c1"># uninitialized #空矩阵，受到上一个初始化矩阵的影响</span>
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<pre>array([[4.45619116e-313, 1.38338381e-322, 9.47957064e-312,
4.94065646e-324, 0.00000000e+000, 5.51718906e-313],
[7.90505033e-323, 9.47972338e-312, 9.47972338e-312,
9.47972338e-312, 3.60739285e-313, 2.96439388e-323],
[9.47972338e-312, 9.47972338e-312, 0.00000000e+000,
0.00000000e+000, 0.00000000e+000, 1.69759663e-313],
[4.94065646e-324, 9.88131292e-324, 4.94065646e-324,
9.47972338e-312, 8.39911598e-323, 9.72228417e-315],
[0.00000000e+000, 0.00000000e+000, 5.51718906e-313,
1.38338381e-322, 9.47955314e-312, 4.94065646e-324],
[0.00000000e+000, 2.33419537e-313, 4.94065646e-324,
9.47972338e-312, 0.00000000e+000, 0.00000000e+000]])</pre>
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<h2 id="创建等差数列">创建等差数列<a class="anchor-link" href="#创建等差数列">¶</a></h2>
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<p>有2种实现：</p>
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<li>np.arange() 指定首尾，间隔。</li>
<li>np.linspace() 指定首尾，输出几个。</li>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># arange区间是[左闭，右开)的，参数顺序 start, end, space</span>
<span class="n">a1</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">20</span><span class="p">)</span> <span class="c1">#array([10, 11, 12, 13, 14, 15, 16, 17, 18, 19])</span>
<span class="n">a2</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">20</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="c1">#等差是2 array([10, 12, 14, 16, 18])</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a1</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a2</span><span class="p">)</span>
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<pre>[10 11 12 13 14 15 16 17 18 19]
[10 12 14 16 18]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1">#在-5,5之间，每隔0.5产生一个数</span>
<span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mf">0.5</span><span class="p">)</span>
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<pre>array([-5. , -4.5, -4. , -3.5, -3. , -2.5, -2. , -1.5, -1. , -0.5, 0. ,
0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1">#太多则显示时会跳过</span>
<span class="nb">print</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10000</span><span class="p">))</span>
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<pre>[ 0 1 2 ... 9997 9998 9999]
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1">#更严谨的，对小数位数控制更精确的是np.linspace()</span>
<span class="c1">#在-5,5之间，相同间隔，产生n=10个数字</span>
<span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">10</span><span class="p">)</span>
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<pre>array([-5. , -3.88888889, -2.77777778, -1.66666667, -0.55555556,
0.55555556, 1.66666667, 2.77777778, 3.88888889, 5. ])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 常用于画图时的坐标</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">50</span> <span class="p">)</span> <span class="c1"># useful to evaluate function at lots of points</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">f</span><span class="p">),</span> <span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">10</span><span class="p">])</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">f</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<pre>50 [0. 0.12787716 0.25365458 0.375267 0.49071755 0.59811053
0.69568255 0.78183148 0.85514276 0.91441262]
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<pre><Figure size 640x480 with 1 Axes></pre>
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<h2 id="切片后还是数组">切片后还是数组<a class="anchor-link" href="#切片后还是数组">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 切片也是[左闭右开)区间</span>
<span class="n">t</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span><span class="o">**</span><span class="mi">3</span>
<span class="nb">print</span><span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="c1">#取出一位</span>
<span class="nb">print</span><span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">1</span><span class="p">])</span> <span class="c1">#数组切片后还是数组</span>
<span class="n">t</span>
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<pre>0
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