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<dd class="field-even"><p>April 22, 2025</p>
</dd>
</dl>
<p>This reference manual details functions, modules, and objects
included in NumPy, describing what they are and what they do.
For learning how to use NumPy, see the <a class="reference internal" href="../index.html#numpy-docs-mainpage"><span class="std std-ref">complete documentation</span></a>.</p>
<section id="python-api">
<h2>Python API<a class="headerlink" href="#python-api" title="Link to this heading">#</a></h2>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="module_structure.html">NumPy’s module structure</a></li>
</ul>
</div>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="arrays.html">Array objects</a><ul>
<li class="toctree-l2"><a class="reference internal" href="arrays.ndarray.html">The N-dimensional array (<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>)</a></li>
<li class="toctree-l2"><a class="reference internal" href="arrays.scalars.html">Scalars</a></li>
<li class="toctree-l2"><a class="reference internal" href="arrays.dtypes.html">Data type objects (<code class="xref py py-class docutils literal notranslate"><span class="pre">dtype</span></code>)</a></li>
<li class="toctree-l2"><a class="reference internal" href="arrays.promotion.html">Data type promotion in NumPy</a></li>
<li class="toctree-l2"><a class="reference internal" href="arrays.nditer.html">Iterating over arrays</a></li>
<li class="toctree-l2"><a class="reference internal" href="arrays.classes.html">Standard array subclasses</a></li>
<li class="toctree-l2"><a class="reference internal" href="maskedarray.html">Masked arrays</a></li>
<li class="toctree-l2"><a class="reference internal" href="arrays.interface.html">The array interface protocol</a></li>
<li class="toctree-l2"><a class="reference internal" href="arrays.datetime.html">Datetimes and timedeltas</a></li>
</ul>
</li>
</ul>
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<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="ufuncs.html">Universal functions (<code class="xref py py-class docutils literal notranslate"><span class="pre">ufunc</span></code>)</a></li>
</ul>
</div>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="routines.html">Routines and objects by topic</a><ul>
<li class="toctree-l2"><a class="reference internal" href="constants.html">Constants</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.array-creation.html">Array creation routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.array-manipulation.html">Array manipulation routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.bitwise.html">Bit-wise operations</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.strings.html">String functionality</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.datetime.html">Datetime support functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.dtype.html">Data type routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.emath.html">Mathematical functions with automatic domain</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.err.html">Floating point error handling</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.exceptions.html">Exceptions and Warnings</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.fft.html">Discrete Fourier Transform</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.functional.html">Functional programming</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.io.html">Input and output</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.indexing.html">Indexing routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.linalg.html">Linear algebra</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.logic.html">Logic functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.ma.html">Masked array operations</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.math.html">Mathematical functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.other.html">Miscellaneous routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.polynomials.html">Polynomials</a></li>
<li class="toctree-l2"><a class="reference internal" href="random/index.html">Random sampling</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.set.html">Set routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.sort.html">Sorting, searching, and counting</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.statistics.html">Statistics</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.testing.html">Test support</a></li>
<li class="toctree-l2"><a class="reference internal" href="routines.window.html">Window functions</a></li>
</ul>
</li>
</ul>
</div>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="typing.html">Typing (<code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.typing</span></code>)</a></li>
<li class="toctree-l1"><a class="reference internal" href="distutils.html">Packaging</a></li>
</ul>
</div>
</section>
<section id="c-api">
<h2>C API<a class="headerlink" href="#c-api" title="Link to this heading">#</a></h2>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="c-api/index.html">NumPy C-API</a><ul>
<li class="toctree-l2"><a class="reference internal" href="c-api/types-and-structures.html">Python types and C-structures</a></li>
<li class="toctree-l2"><a class="reference internal" href="c-api/config.html">System configuration</a></li>
<li class="toctree-l2"><a class="reference internal" href="c-api/dtype.html">Data type API</a></li>
<li class="toctree-l2"><a class="reference internal" href="c-api/array.html">Array API</a></li>
<li class="toctree-l2"><a class="reference internal" href="c-api/iterator.html">Array iterator API</a></li>
<li class="toctree-l2"><a class="reference internal" href="c-api/ufunc.html">ufunc API</a></li>
<li class="toctree-l2"><a class="reference internal" href="c-api/generalized-ufuncs.html">Generalized universal function API</a></li>
<li class="toctree-l2"><a class="reference internal" href="c-api/strings.html">NpyString API</a></li>
<li class="toctree-l2"><a class="reference internal" href="c-api/coremath.html">NumPy core math library</a></li>
<li class="toctree-l2"><a class="reference internal" href="c-api/datetimes.html">Datetime API</a></li>
<li class="toctree-l2"><a class="reference internal" href="c-api/deprecations.html">C API deprecations</a></li>
<li class="toctree-l2"><a class="reference internal" href="c-api/data_memory.html">Memory management in NumPy</a></li>
</ul>
</li>
</ul>
</div>
</section>
<section id="other-topics">
<h2>Other topics<a class="headerlink" href="#other-topics" title="Link to this heading">#</a></h2>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="array_api.html">Array API standard compatibility</a></li>
<li class="toctree-l1"><a class="reference internal" href="simd/index.html">CPU/SIMD optimizations</a></li>
<li class="toctree-l1"><a class="reference internal" href="thread_safety.html">Thread Safety</a></li>
<li class="toctree-l1"><a class="reference internal" href="global_state.html">Global Configuration Options</a></li>
<li class="toctree-l1"><a class="reference internal" href="security.html">NumPy security</a></li>
<li class="toctree-l1"><a class="reference internal" href="distutils_status_migration.html">Status of <code class="docutils literal notranslate"><span class="pre">numpy.distutils</span></code> and migration advice</a></li>
<li class="toctree-l1"><a class="reference internal" href="distutils_guide.html"><code class="docutils literal notranslate"><span class="pre">numpy.distutils</span></code> user guide</a></li>
<li class="toctree-l1"><a class="reference internal" href="swig.html">NumPy and SWIG</a></li>
</ul>
</div>
</section>
<section id="acknowledgements">
<h2>Acknowledgements<a class="headerlink" href="#acknowledgements" title="Link to this heading">#</a></h2>
<p>Large parts of this manual originate from Travis E. Oliphant’s book
<a class="reference external" href="https://archive.org/details/NumPyBook">Guide to NumPy</a> (which generously
entered Public Domain in August 2008). The reference documentation for many of
the functions are written by numerous contributors and developers of
NumPy.</p>
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