<!DOCTYPE html> <html> <head> <meta charset="utf-8"> <title>scipy.integrate.cumtrapz — SciPy v1.1.0.dev0+4e64658 Reference Guide</title> <link rel="stylesheet" type="text/css" href="../_static/css/spc-bootstrap.css"> <link rel="stylesheet" type="text/css" href="../_static/css/spc-extend.css"> <link rel="stylesheet" href="../_static/scipy.css" type="text/css" > <link rel="stylesheet" href="../_static/pygments.css" type="text/css" > <script type="text/javascript"> var DOCUMENTATION_OPTIONS = { URL_ROOT: '../', VERSION: '1.1.0.dev0+4e64658', COLLAPSE_INDEX: false, FILE_SUFFIX: '.html', HAS_SOURCE: false }; </script> <script type="text/javascript" src="../_static/jquery.js"></script> <script type="text/javascript" src="../_static/underscore.js"></script> <script type="text/javascript" src="../_static/doctools.js"></script> <script type="text/javascript" src="../_static/scipy-mathjax/MathJax.js?config=scipy-mathjax"></script> <script type="text/javascript" src="../_static/js/copybutton.js"></script> <link rel="index" title="Index" href="../genindex.html" > <link rel="search" title="Search" href="../search.html" > <link rel="top" title="SciPy v1.1.0.dev0+4e64658 Reference Guide" href="../index.html" > <link rel="up" title="Integration and ODEs (scipy.integrate)" href="../integrate.html" > <link rel="next" title="scipy.integrate.simps" href="scipy.integrate.simps.html" > <link rel="prev" title="scipy.integrate.trapz" href="scipy.integrate.trapz.html" > </head> <body> <div class="container"> <div class="header"> </div> </div> <div class="container"> <div class="main"> <div class="row-fluid"> <div class="span12"> <div class="spc-navbar"> <ul class="nav nav-pills pull-left"> <li class="active"><a href="../index.html">SciPy v1.1.0.dev0+4e64658 Reference Guide</a></li> <li class="active"><a href="../integrate.html" accesskey="U">Integration and ODEs (<code class="docutils literal"><span class="pre">scipy.integrate</span></code>)</a></li> </ul> <ul class="nav nav-pills pull-right"> <li class="active"> <a href="../genindex.html" title="General Index" accesskey="I">index</a> </li> <li class="active"> <a href="../py-modindex.html" title="Python Module Index" >modules</a> </li> <li class="active"> <a href="scipy.integrate.simps.html" title="scipy.integrate.simps" accesskey="N">next</a> </li> <li class="active"> <a href="scipy.integrate.trapz.html" title="scipy.integrate.trapz" accesskey="P">previous</a> </li> </ul> </div> </div> </div> <div class="row-fluid"> <div class="spc-rightsidebar span3"> <div class="sphinxsidebarwrapper"> <p class="logo"><a href="../index.html"> <img class="logo" src="../_static/scipyshiny_small.png" alt="Logo"> </a></p> <h4>Previous topic</h4> <p class="topless"><a href="scipy.integrate.trapz.html" title="previous chapter">scipy.integrate.trapz</a></p> <h4>Next topic</h4> <p class="topless"><a href="scipy.integrate.simps.html" title="next chapter">scipy.integrate.simps</a></p> </div> </div> <div class="span9"> <div class="bodywrapper"> <div class="body" id="spc-section-body"> <div class="section" id="scipy-integrate-cumtrapz"> <h1>scipy.integrate.cumtrapz<a class="headerlink" href="#scipy-integrate-cumtrapz" title="Permalink to this headline">¶</a></h1> <dl class="function"> <dt id="scipy.integrate.cumtrapz"> <code class="descclassname">scipy.integrate.</code><code class="descname">cumtrapz</code><span class="sig-paren">(</span><em>y</em>, <em>x=None</em>, <em>dx=1.0</em>, <em>axis=-1</em>, <em>initial=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scipy/scipy/blob/4e64658/scipy/integrate/quadrature.py#L209-L298"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#scipy.integrate.cumtrapz" title="Permalink to this definition">¶</a></dt> <dd><p>Cumulatively integrate y(x) using the composite trapezoidal rule.</p> <table class="docutils field-list" frame="void" rules="none"> <col class="field-name" /> <col class="field-body" /> <tbody valign="top"> <tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>y</strong> : array_like</p> <blockquote> <div><p>Values to integrate.</p> </div></blockquote> <p><strong>x</strong> : array_like, optional</p> <blockquote> <div><p>The coordinate to integrate along. If None (default), use spacing <em class="xref py py-obj">dx</em> between consecutive elements in <em class="xref py py-obj">y</em>.</p> </div></blockquote> <p><strong>dx</strong> : float, optional</p> <blockquote> <div><p>Spacing between elements of <em class="xref py py-obj">y</em>. Only used if <em class="xref py py-obj">x</em> is None.</p> </div></blockquote> <p><strong>axis</strong> : int, optional</p> <blockquote> <div><p>Specifies the axis to cumulate. Default is -1 (last axis).</p> </div></blockquote> <p><strong>initial</strong> : scalar, optional</p> <blockquote> <div><p>If given, uses this value as the first value in the returned result. Typically this value should be 0. Default is None, which means no value at <code class="docutils literal"><span class="pre">x[0]</span></code> is returned and <em class="xref py py-obj">res</em> has one element less than <em class="xref py py-obj">y</em> along the axis of integration.</p> </div></blockquote> </td> </tr> <tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>res</strong> : ndarray</p> <blockquote class="last"> <div><p>The result of cumulative integration of <em class="xref py py-obj">y</em> along <em class="xref py py-obj">axis</em>. If <em class="xref py py-obj">initial</em> is None, the shape is such that the axis of integration has one less value than <em class="xref py py-obj">y</em>. If <em class="xref py py-obj">initial</em> is given, the shape is equal to that of <em class="xref py py-obj">y</em>.</p> </div></blockquote> </td> </tr> </tbody> </table> <div class="admonition seealso"> <p class="first admonition-title">See also</p> <p><a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.cumsum.html#numpy.cumsum" title="(in NumPy v1.13)"><code class="xref py py-obj docutils literal"><span class="pre">numpy.cumsum</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.cumprod.html#numpy.cumprod" title="(in NumPy v1.13)"><code class="xref py py-obj docutils literal"><span class="pre">numpy.cumprod</span></code></a></p> <dl class="last docutils"> <dt><a class="reference internal" href="scipy.integrate.quad.html#scipy.integrate.quad" title="scipy.integrate.quad"><code class="xref py py-obj docutils literal"><span class="pre">quad</span></code></a></dt> <dd>adaptive quadrature using QUADPACK</dd> <dt><a class="reference internal" href="scipy.integrate.romberg.html#scipy.integrate.romberg" title="scipy.integrate.romberg"><code class="xref py py-obj docutils literal"><span class="pre">romberg</span></code></a></dt> <dd>adaptive Romberg quadrature</dd> <dt><a class="reference internal" href="scipy.integrate.quadrature.html#scipy.integrate.quadrature" title="scipy.integrate.quadrature"><code class="xref py py-obj docutils literal"><span class="pre">quadrature</span></code></a></dt> <dd>adaptive Gaussian quadrature</dd> <dt><a class="reference internal" href="scipy.integrate.fixed_quad.html#scipy.integrate.fixed_quad" title="scipy.integrate.fixed_quad"><code class="xref py py-obj docutils literal"><span class="pre">fixed_quad</span></code></a></dt> <dd>fixed-order Gaussian quadrature</dd> <dt><a class="reference internal" href="scipy.integrate.dblquad.html#scipy.integrate.dblquad" title="scipy.integrate.dblquad"><code class="xref py py-obj docutils literal"><span class="pre">dblquad</span></code></a></dt> <dd>double integrals</dd> <dt><a class="reference internal" href="scipy.integrate.tplquad.html#scipy.integrate.tplquad" title="scipy.integrate.tplquad"><code class="xref py py-obj docutils literal"><span class="pre">tplquad</span></code></a></dt> <dd>triple integrals</dd> <dt><a class="reference internal" href="scipy.integrate.romb.html#scipy.integrate.romb" title="scipy.integrate.romb"><code class="xref py py-obj docutils literal"><span class="pre">romb</span></code></a></dt> <dd>integrators for sampled data</dd> <dt><a class="reference internal" href="scipy.integrate.ode.html#scipy.integrate.ode" title="scipy.integrate.ode"><code class="xref py py-obj docutils literal"><span class="pre">ode</span></code></a></dt> <dd>ODE integrators</dd> <dt><a class="reference internal" href="scipy.integrate.odeint.html#scipy.integrate.odeint" title="scipy.integrate.odeint"><code class="xref py py-obj docutils literal"><span class="pre">odeint</span></code></a></dt> <dd>ODE integrators</dd> </dl> </div> <p class="rubric">Examples</p> <div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">scipy</span> <span class="k">import</span> <span class="n">integrate</span> <span class="gp">>>> </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span> </pre></div> </div> <div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </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="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span> <span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="n">x</span> <span class="gp">>>> </span><span class="n">y_int</span> <span class="o">=</span> <span class="n">integrate</span><span class="o">.</span><span class="n">cumtrapz</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">initial</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y_int</span><span class="p">,</span> <span class="s1">'ro'</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="s1">'b-'</span><span class="p">)</span> <span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> </pre></div> </div> <div class="figure"> <img alt="../_images/scipy-integrate-cumtrapz-1.png" src="../_images/scipy-integrate-cumtrapz-1.png" /> </div> </dd></dl> </div> </div> </div> </div> </div> </div> </div> <div class="container container-navbar-bottom"> <div class="spc-navbar"> </div> </div> <div class="container"> <div class="footer"> <div class="row-fluid"> <ul class="inline pull-left"> <li> © Copyright 2008-2016, The Scipy community. </li> <li> Last updated on Sep 21, 2017. </li> <li> Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.6.3. </li> </ul> </div> </div> </div> </body> </html>