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<link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/hint.css/2.4.1/hint.min.css"><p>对以前所学的numpy进行整理，详细使用说明参见<a href="https://numpy.org/" target="_blank" rel="noopener">官网</a>，或者翻阅《Python for Data Analysis, 2nd Edition》一书，有其他博主进行翻译过。<br><a id="more"></a></p>
<h2 id="数组和矩阵"><a href="#数组和矩阵" class="headerlink" title="数组和矩阵"></a>数组和矩阵</h2><p>numpy主要有两大类，数组<code><class 'numpy.ndarray'></code>和矩阵<code><class 'numpy.matrix'></code>。两大类方法有些类似，但在有些操作上是不同的，也可以相互转换。<br><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> numpy <span class="keyword">as</span> np</span><br><span class="line"></span><br><span class="line"><span class="comment"># 数组</span></span><br><span class="line">a = np.array([[<span class="number">1</span>, <span class="number">2</span>],</span><br><span class="line"> [<span class="number">3</span>, <span class="number">4</span>]])</span><br><span class="line"><span class="comment"># 矩阵b</span></span><br><span class="line">b = np.mat([[<span class="number">1</span>, <span class="number">2</span>],</span><br><span class="line"> [<span class="number">3</span>, <span class="number">4</span>]])</span><br><span class="line"><span class="comment"># 数组转矩阵</span></span><br><span class="line">b = np.mat(a)</span><br><span class="line"><span class="comment"># 矩阵转数组</span></span><br><span class="line">b.A</span><br></pre></td></tr></table></figure></p>
<p>矩阵和数组在乘法上有所区别，矩阵可以直接相乘，而数组需要<code>dot</code>方法，如果数组直接相乘，结果是相应位置相乘，矩阵要实现相应位置相乘，要调用<code>np.multiply</code>方法。</p>
<ul>
<li><p>$X = A_{m \times n} * B_{n \times m}$</p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"># a.shape = (m, n)</span></span><br><span class="line"><span class="comment"># b.shape = (n, m)</span></span><br><span class="line"><span class="comment"># 矩阵相乘</span></span><br><span class="line">x = a * b</span><br><span class="line"><span class="comment"># 数组相乘</span></span><br><span class="line">x = a.dot(b)</span><br><span class="line">x = np.dot(a, b)</span><br></pre></td></tr></table></figure>
</li>
<li><p>$X_{ij} = A_{ij}*B_{ij}$</p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"># a.shape = b.shape</span></span><br><span class="line"><span class="comment"># 矩阵相乘</span></span><br><span class="line">x = np.multiply(a, b)</span><br><span class="line"><span class="comment"># 数组相乘</span></span><br><span class="line">x = a * b</span><br></pre></td></tr></table></figure>
</li>
</ul>
<h2 id="常用方法"><a href="#常用方法" class="headerlink" title="常用方法"></a>常用方法</h2><p>摘自《Python for Data Analysis, 2nd Edition》。</p>
<h3 id="数组创建"><a href="#数组创建" class="headerlink" title="数组创建"></a>数组创建</h3><table>
<thead>
<tr>
<th>Function</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td>array</td>
<td>Convert input data (list, tuple, array, or other sequence type) to an ndarray either by inferring a dtype or explicitly specifying a dtype; copies the input data by default</td>
</tr>
<tr>
<td>asarray</td>
<td>Convert input to ndarray, but do not copy if the input is already an ndarray </td>
</tr>
<tr>
<td>arange</td>
<td>Like the built-in range but returns an ndarray instead of a list</td>
</tr>
<tr>
<td>ones, ones_like</td>
<td>Produce an array of all 1s with the given shape and dtype; ones_like takes another array and produces a ones array of the same shape and dtype</td>
</tr>
<tr>
<td>zeros, zeros_like</td>
<td>Like ones and ones_like but producing arrays of 0s instead</td>
</tr>
<tr>
<td>empty, empty_like</td>
<td>Create new arrays by allocating new memory, but do not populate with any values like ones and zeros</td>
</tr>
<tr>
<td>full, full_like</td>
<td>Produce an array of the given shape and dtype with all values set to the indicated “fill value”; full_like takes another array and produces a filled array of the same shape and dtype</td>
</tr>
<tr>
<td>eye, identity</td>
<td>Create a square N × N identity matrix (1s on the diagonal and 0s elsewhere)</td>
</tr>
</tbody>
</table>
<h3 id="线性代数"><a href="#线性代数" class="headerlink" title="线性代数"></a>线性代数</h3><p>使用<code>numpy.linalg</code>函数</p>
<table>
<thead>
<tr>
<th>Function</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td>diag</td>
<td>Return the diagonal (or off-diagonal) elements of a square matrix as a 1D array, or convert a 1D array into a square matrix with zeros on the off-diagonal</td>
</tr>
<tr>
<td>dot</td>
<td>Matrix multiplication</td>
</tr>
<tr>
<td>trace</td>
<td>Compute the sum of the diagonal elements</td>
</tr>
<tr>
<td>det</td>
<td>Compute the matrix determinant</td>
</tr>
<tr>
<td>eig</td>
<td>Compute the eigenvalues and eigenvectors of a square matrix</td>
</tr>
<tr>
<td>inv</td>
<td>Compute the inverse of a square matrix</td>
</tr>
<tr>
<td>pinv</td>
<td>Compute the Moore-Penrose pseudo-inverse of a matrix</td>
</tr>
<tr>
<td>qr</td>
<td>Compute the QR decomposition</td>
</tr>
<tr>
<td>svd</td>
<td>Compute the singular value decomposition (SVD)</td>
</tr>
<tr>
<td>solve</td>
<td>Solve the linear system Ax = b for x, where A is a square matrix</td>
</tr>
<tr>
<td>lstsq</td>
<td>Compute the least-squares solution to Ax = b</td>
</tr>
</tbody>
</table>
<h2 id="one-hot编码"><a href="#one-hot编码" class="headerlink" title="one-hot编码"></a>one-hot编码</h2><p>使用numpy进行one-hot编码。<br><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"># label.shape = (1, )</span></span><br><span class="line"><span class="comment"># 将label转换成int，因为index是int</span></span><br><span class="line">label_int = label.astype(int) </span><br><span class="line"><span class="comment"># 计算标签种类</span></span><br><span class="line">k = len(set(label_int))</span><br><span class="line"><span class="comment"># one-hot编码</span></span><br><span class="line">label = np.eye(k)[label_int]</span><br></pre></td></tr></table></figure></p>
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