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<section id="the-n-dimensional-array-ndarray">
<span id="arrays-ndarray"></span><h1>The N-dimensional array (<a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a>)<a class="headerlink" href="#the-n-dimensional-array-ndarray" title="Link to this heading">#</a></h1>
<p>An <a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a> is a (usually fixed-size) multidimensional
container of items of the same type and size. The number of dimensions
and items in an array is defined by its <a class="reference internal" href="generated/numpy.ndarray.shape.html#numpy.ndarray.shape" title="numpy.ndarray.shape"><code class="xref py py-attr docutils literal notranslate"><span class="pre">shape</span></code></a>,
which is a <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.13)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a> of <em>N</em> non-negative integers that specify the
sizes of each dimension. The type of items in the array is specified by
a separate <a class="reference internal" href="arrays.dtypes.html#arrays-dtypes"><span class="std std-ref">data-type object (dtype)</span></a>, one of which
is associated with each ndarray.</p>
<p>As with other container objects in Python, the contents of an
<a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a> can be accessed and modified by <a class="reference internal" href="routines.indexing.html#arrays-indexing"><span class="std std-ref">indexing or
slicing</span></a> the array (using, for example, <em>N</em> integers),
and via the methods and attributes of the <a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a>.</p>
<p id="index-0">Different <a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarrays</span></code></a> can share the same data, so that
changes made in one <a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a> may be visible in another. That
is, an ndarray can be a <em>“view”</em> to another ndarray, and the data it
is referring to is taken care of by the <em>“base”</em> ndarray. ndarrays can
also be views to memory owned by Python <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.13)"><code class="xref py py-class docutils literal notranslate"><span class="pre">strings</span></code></a> or
objects implementing the <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#memoryview" title="(in Python v3.13)"><code class="xref py py-class docutils literal notranslate"><span class="pre">memoryview</span></code></a> or <a class="reference internal" href="arrays.interface.html#arrays-interface"><span class="std std-ref">array</span></a> interfaces.</p>
<div class="admonition-example admonition">
<p class="admonition-title">Example</p>
<div class="try_examples_outer_container docutils container" id="88a4b01a-22de-43bf-b23e-a88e2a684b94">
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<p>A 2-dimensional array of size 2 x 3, composed of 4-byte integer
elements:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><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">array</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="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">type</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="go"><class 'numpy.ndarray'></span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">shape</span>
<span class="go">(2, 3)</span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">dtype</span>
<span class="go">dtype('int32')</span>
</pre></div>
</div>
<p>The array can be indexed using Python container-like syntax:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="c1"># The element of x in the *second* row, *third* column, namely, 6.</span>
<span class="gp">>>> </span><span class="n">x</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="go"> 6</span>
</pre></div>
</div>
<p>For example <a class="reference internal" href="routines.indexing.html#arrays-indexing"><span class="std std-ref">slicing</span></a> can produce views of
the array:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">y</span>
<span class="go">array([2, 5], dtype=int32)</span>
<span class="gp">>>> </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="mi">9</span> <span class="c1"># this also changes the corresponding element in x</span>
<span class="gp">>>> </span><span class="n">y</span>
<span class="go">array([9, 5], dtype=int32)</span>
<span class="gp">>>> </span><span class="n">x</span>
<span class="go">array([[1, 9, 3],</span>
<span class="go"> [4, 5, 6]], dtype=int32)</span>
</pre></div>
</div>
</div>
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<section id="constructing-arrays">
<h2>Constructing arrays<a class="headerlink" href="#constructing-arrays" title="Link to this heading">#</a></h2>
<p>New arrays can be constructed using the routines detailed in
<a class="reference internal" href="routines.array-creation.html#routines-array-creation"><span class="std std-ref">Array creation routines</span></a>, and also by using the low-level
<a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a> constructor:</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray</span></code></a>(shape[, dtype, buffer, offset, ...])</p></td>
<td><p>An array object represents a multidimensional, homogeneous array of fixed-size items.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="indexing-arrays">
<span id="arrays-ndarray-indexing"></span><h2>Indexing arrays<a class="headerlink" href="#indexing-arrays" title="Link to this heading">#</a></h2>
<p>Arrays can be indexed using an extended Python slicing syntax,
<code class="docutils literal notranslate"><span class="pre">array[selection]</span></code>. Similar syntax is also used for accessing
fields in a <a class="reference internal" href="../glossary.html#term-structured-data-type"><span class="xref std std-term">structured data type</span></a>.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="routines.indexing.html#arrays-indexing"><span class="std std-ref">Array Indexing</span></a>.</p>
</div>
</section>
<section id="internal-memory-layout-of-an-ndarray">
<span id="memory-layout"></span><h2>Internal memory layout of an ndarray<a class="headerlink" href="#internal-memory-layout-of-an-ndarray" title="Link to this heading">#</a></h2>
<p>An instance of class <a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a> consists of a contiguous
one-dimensional segment of computer memory (owned by the array, or by
some other object), combined with an indexing scheme that maps <em>N</em>
integers into the location of an item in the block. The ranges in
which the indices can vary is specified by the <a class="reference internal" href="generated/numpy.ndarray.shape.html#numpy.ndarray.shape" title="numpy.ndarray.shape"><code class="xref py py-obj docutils literal notranslate"><span class="pre">shape</span></code></a> of the array. How many bytes each item takes and how
the bytes are interpreted is defined by the <a class="reference internal" href="arrays.dtypes.html#arrays-dtypes"><span class="std std-ref">data-type object</span></a> associated with the array.</p>
<p id="index-1">A segment of memory is inherently 1-dimensional, and there are many
different schemes for arranging the items of an <em>N</em>-dimensional array
in a 1-dimensional block. NumPy is flexible, and <a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a>
objects can accommodate any <em>strided indexing scheme</em>. In a strided
scheme, the N-dimensional index <span class="math notranslate nohighlight">\((n_0, n_1, ..., n_{N-1})\)</span>
corresponds to the offset (in bytes):</p>
<div class="math notranslate nohighlight">
\[n_{\mathrm{offset}} = \sum_{k=0}^{N-1} s_k n_k\]</div>
<p>from the beginning of the memory block associated with the
array. Here, <span class="math notranslate nohighlight">\(s_k\)</span> are integers which specify the <a class="reference internal" href="generated/numpy.ndarray.strides.html#numpy.ndarray.strides" title="numpy.ndarray.strides"><code class="xref py py-obj docutils literal notranslate"><span class="pre">strides</span></code></a> of the array. The <a class="reference internal" href="../glossary.html#term-column-major"><span class="xref std std-term">column-major</span></a> order (used,
for example, in the Fortran language and in <em>Matlab</em>) and
<a class="reference internal" href="../glossary.html#term-row-major"><span class="xref std std-term">row-major</span></a> order (used in C) schemes are just specific kinds of
strided scheme, and correspond to memory that can be <em>addressed</em> by the strides:</p>
<div class="math notranslate nohighlight">
\[s_k^{\mathrm{column}} = \mathrm{itemsize} \prod_{j=0}^{k-1} d_j ,
\quad s_k^{\mathrm{row}} = \mathrm{itemsize} \prod_{j=k+1}^{N-1} d_j .\]</div>
<p id="index-2">where <span class="math notranslate nohighlight">\(d_j\)</span> <em class="xref py py-obj">= self.shape[j]</em>.</p>
<p>Both the C and Fortran orders are <a class="reference internal" href="../glossary.html#term-contiguous"><span class="xref std std-term">contiguous</span></a>, <em>i.e.,</em>
single-segment, memory layouts, in which every part of the
memory block can be accessed by some combination of the indices.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p><em>Contiguous arrays</em> and <em>single-segment arrays</em> are synonymous
and are used interchangeably throughout the documentation.</p>
</div>
<p>While a C-style and Fortran-style contiguous array, which has the corresponding
flags set, can be addressed with the above strides, the actual strides may be
different. This can happen in two cases:</p>
<ol class="arabic simple">
<li><p>If <code class="docutils literal notranslate"><span class="pre">self.shape[k]</span> <span class="pre">==</span> <span class="pre">1</span></code> then for any legal index <code class="docutils literal notranslate"><span class="pre">index[k]</span> <span class="pre">==</span> <span class="pre">0</span></code>.
This means that in the formula for the offset <span class="math notranslate nohighlight">\(n_k = 0\)</span> and thus
<span class="math notranslate nohighlight">\(s_k n_k = 0\)</span> and the value of <span class="math notranslate nohighlight">\(s_k\)</span> <em class="xref py py-obj">= self.strides[k]</em> is
arbitrary.</p></li>
<li><p>If an array has no elements (<code class="docutils literal notranslate"><span class="pre">self.size</span> <span class="pre">==</span> <span class="pre">0</span></code>) there is no legal
index and the strides are never used. Any array with no elements may be
considered C-style and Fortran-style contiguous.</p></li>
</ol>
<p>Point 1. means that <code class="docutils literal notranslate"><span class="pre">self</span></code> and <code class="docutils literal notranslate"><span class="pre">self.squeeze()</span></code> always have the same
contiguity and <code class="docutils literal notranslate"><span class="pre">aligned</span></code> flags value. This also means
that even a high dimensional array could be C-style and Fortran-style
contiguous at the same time.</p>
<p id="index-3">An array is considered aligned if the memory offsets for all elements and the
base offset itself is a multiple of <a class="reference internal" href="generated/numpy.ndarray.itemsize.html#numpy.ndarray.itemsize" title="numpy.ndarray.itemsize"><code class="xref py py-obj docutils literal notranslate"><span class="pre">self.itemsize</span></code></a>. Understanding
<em>memory-alignment</em> leads to better performance on most hardware.</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>It does <em>not</em> generally hold that <code class="docutils literal notranslate"><span class="pre">self.strides[-1]</span> <span class="pre">==</span> <span class="pre">self.itemsize</span></code>
for C-style contiguous arrays or <code class="docutils literal notranslate"><span class="pre">self.strides[0]</span> <span class="pre">==</span> <span class="pre">self.itemsize</span></code> for
Fortran-style contiguous arrays is true.</p>
</div>
<p>Data in new <a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarrays</span></code></a> is in the <a class="reference internal" href="../glossary.html#term-row-major"><span class="xref std std-term">row-major</span></a> (C)
order, unless otherwise specified, but, for example, <a class="reference internal" href="routines.indexing.html#arrays-indexing"><span class="std std-ref">basic
array slicing</span></a> often produces <a class="reference internal" href="../glossary.html#term-view"><span class="xref std std-term">views</span></a>
in a different scheme.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Several algorithms in NumPy work on arbitrarily strided arrays.
However, some algorithms require single-segment arrays. When an
irregularly strided array is passed in to such algorithms, a copy
is automatically made.</p>
</div>
</section>
<section id="array-attributes">
<span id="arrays-ndarray-attributes"></span><h2>Array attributes<a class="headerlink" href="#array-attributes" title="Link to this heading">#</a></h2>
<p>Array attributes reflect information that is intrinsic to the array
itself. Generally, accessing an array through its attributes allows
you to get and sometimes set intrinsic properties of the array without
creating a new array. The exposed attributes are the core parts of an
array and only some of them can be reset meaningfully without creating
a new array. Information on each attribute is given below.</p>
<section id="id1">
<h3>Memory layout<a class="headerlink" href="#id1" title="Link to this heading">#</a></h3>
<p>The following attributes contain information about the memory layout
of the array:</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.flags.html#numpy.ndarray.flags" title="numpy.ndarray.flags"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.flags</span></code></a></p></td>
<td><p>Information about the memory layout of the array.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.shape.html#numpy.ndarray.shape" title="numpy.ndarray.shape"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.shape</span></code></a></p></td>
<td><p>Tuple of array dimensions.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.strides.html#numpy.ndarray.strides" title="numpy.ndarray.strides"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.strides</span></code></a></p></td>
<td><p>Tuple of bytes to step in each dimension when traversing an array.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.ndim.html#numpy.ndarray.ndim" title="numpy.ndarray.ndim"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.ndim</span></code></a></p></td>
<td><p>Number of array dimensions.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.data.html#numpy.ndarray.data" title="numpy.ndarray.data"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.data</span></code></a></p></td>
<td><p>Python buffer object pointing to the start of the array's data.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.size.html#numpy.ndarray.size" title="numpy.ndarray.size"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.size</span></code></a></p></td>
<td><p>Number of elements in the array.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.itemsize.html#numpy.ndarray.itemsize" title="numpy.ndarray.itemsize"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.itemsize</span></code></a></p></td>
<td><p>Length of one array element in bytes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.nbytes.html#numpy.ndarray.nbytes" title="numpy.ndarray.nbytes"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.nbytes</span></code></a></p></td>
<td><p>Total bytes consumed by the elements of the array.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.base.html#numpy.ndarray.base" title="numpy.ndarray.base"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.base</span></code></a></p></td>
<td><p>Base object if memory is from some other object.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="data-type">
<h3>Data type<a class="headerlink" href="#data-type" title="Link to this heading">#</a></h3>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="arrays.dtypes.html#arrays-dtypes"><span class="std std-ref">Data type objects</span></a></p>
</div>
<p>The data type object associated with the array can be found in the
<a class="reference internal" href="generated/numpy.ndarray.dtype.html#numpy.ndarray.dtype" title="numpy.ndarray.dtype"><code class="xref py py-attr docutils literal notranslate"><span class="pre">dtype</span></code></a> attribute:</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.dtype.html#numpy.ndarray.dtype" title="numpy.ndarray.dtype"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.dtype</span></code></a></p></td>
<td><p>Data-type of the array's elements.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="other-attributes">
<h3>Other attributes<a class="headerlink" href="#other-attributes" title="Link to this heading">#</a></h3>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.T.html#numpy.ndarray.T" title="numpy.ndarray.T"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.T</span></code></a></p></td>
<td><p>View of the transposed array.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.real.html#numpy.ndarray.real" title="numpy.ndarray.real"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.real</span></code></a></p></td>
<td><p>The real part of the array.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.imag.html#numpy.ndarray.imag" title="numpy.ndarray.imag"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.imag</span></code></a></p></td>
<td><p>The imaginary part of the array.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.flat.html#numpy.ndarray.flat" title="numpy.ndarray.flat"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.flat</span></code></a></p></td>
<td><p>A 1-D iterator over the array.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="array-interface">
<span id="arrays-ndarray-array-interface"></span><h3>Array interface<a class="headerlink" href="#array-interface" title="Link to this heading">#</a></h3>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="arrays.interface.html#arrays-interface"><span class="std std-ref">The array interface protocol</span></a>.</p>
</div>
<div class="pst-scrollable-table-container"><table class="table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="arrays.interface.html#object.__array_interface__" title="object.__array_interface__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">__array_interface__</span></code></a></p></td>
<td><p>Python-side of the array interface</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="arrays.interface.html#object.__array_struct__" title="object.__array_struct__"><code class="xref py py-obj docutils literal notranslate"><span class="pre">__array_struct__</span></code></a></p></td>
<td><p>C-side of the array interface</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="ctypes-foreign-function-interface">
<h3><a class="reference external" href="https://docs.python.org/3/library/ctypes.html#module-ctypes" title="(in Python v3.13)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">ctypes</span></code></a> foreign function interface<a class="headerlink" href="#ctypes-foreign-function-interface" title="Link to this heading">#</a></h3>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.ctypes.html#numpy.ndarray.ctypes" title="numpy.ndarray.ctypes"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.ctypes</span></code></a></p></td>
<td><p>An object to simplify the interaction of the array with the ctypes module.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
</section>
<section id="array-methods">
<span id="array-ndarray-methods"></span><h2>Array methods<a class="headerlink" href="#array-methods" title="Link to this heading">#</a></h2>
<p>An <a class="reference internal" href="generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray"><code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code></a> object has many methods which operate on or with
the array in some fashion, typically returning an array result. These
methods are briefly explained below. (Each method’s docstring has a
more complete description.)</p>
<p>For the following methods there are also corresponding functions in
<a class="reference internal" href="index.html#module-numpy" title="numpy"><code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy</span></code></a>: <a class="reference internal" href="generated/numpy.all.html#numpy.all" title="numpy.all"><code class="xref py py-func docutils literal notranslate"><span class="pre">all</span></code></a>, <a class="reference internal" href="generated/numpy.any.html#numpy.any" title="numpy.any"><code class="xref py py-func docutils literal notranslate"><span class="pre">any</span></code></a>, <a class="reference internal" href="generated/numpy.argmax.html#numpy.argmax" title="numpy.argmax"><code class="xref py py-func docutils literal notranslate"><span class="pre">argmax</span></code></a>,
<a class="reference internal" href="generated/numpy.argmin.html#numpy.argmin" title="numpy.argmin"><code class="xref py py-func docutils literal notranslate"><span class="pre">argmin</span></code></a>, <a class="reference internal" href="generated/numpy.argpartition.html#numpy.argpartition" title="numpy.argpartition"><code class="xref py py-func docutils literal notranslate"><span class="pre">argpartition</span></code></a>, <a class="reference internal" href="generated/numpy.argsort.html#numpy.argsort" title="numpy.argsort"><code class="xref py py-func docutils literal notranslate"><span class="pre">argsort</span></code></a>, <a class="reference internal" href="generated/numpy.choose.html#numpy.choose" title="numpy.choose"><code class="xref py py-func docutils literal notranslate"><span class="pre">choose</span></code></a>,
<a class="reference internal" href="generated/numpy.clip.html#numpy.clip" title="numpy.clip"><code class="xref py py-func docutils literal notranslate"><span class="pre">clip</span></code></a>, <a class="reference internal" href="generated/numpy.compress.html#numpy.compress" title="numpy.compress"><code class="xref py py-func docutils literal notranslate"><span class="pre">compress</span></code></a>, <a class="reference internal" href="generated/numpy.copy.html#numpy.copy" title="numpy.copy"><code class="xref py py-func docutils literal notranslate"><span class="pre">copy</span></code></a>, <a class="reference internal" href="generated/numpy.cumprod.html#numpy.cumprod" title="numpy.cumprod"><code class="xref py py-func docutils literal notranslate"><span class="pre">cumprod</span></code></a>,
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<a class="reference internal" href="generated/numpy.transpose.html#numpy.transpose" title="numpy.transpose"><code class="xref py py-func docutils literal notranslate"><span class="pre">transpose</span></code></a>, <a class="reference internal" href="generated/numpy.var.html#numpy.var" title="numpy.var"><code class="xref py py-func docutils literal notranslate"><span class="pre">var</span></code></a>.</p>
<section id="array-conversion">
<h3>Array conversion<a class="headerlink" href="#array-conversion" title="Link to this heading">#</a></h3>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.item.html#numpy.ndarray.item" title="numpy.ndarray.item"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.item</span></code></a>(*args)</p></td>
<td><p>Copy an element of an array to a standard Python scalar and return it.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.tolist.html#numpy.ndarray.tolist" title="numpy.ndarray.tolist"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.tolist</span></code></a>()</p></td>
<td><p>Return the array as an <code class="docutils literal notranslate"><span class="pre">a.ndim</span></code>-levels deep nested list of Python scalars.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.tobytes.html#numpy.ndarray.tobytes" title="numpy.ndarray.tobytes"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.tobytes</span></code></a>([order])</p></td>
<td><p>Construct Python bytes containing the raw data bytes in the array.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.tofile.html#numpy.ndarray.tofile" title="numpy.ndarray.tofile"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.tofile</span></code></a>(fid[, sep, format])</p></td>
<td><p>Write array to a file as text or binary (default).</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.dump.html#numpy.ndarray.dump" title="numpy.ndarray.dump"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.dump</span></code></a>(file)</p></td>
<td><p>Dump a pickle of the array to the specified file.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.dumps.html#numpy.ndarray.dumps" title="numpy.ndarray.dumps"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.dumps</span></code></a>()</p></td>
<td><p>Returns the pickle of the array as a string.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.astype.html#numpy.ndarray.astype" title="numpy.ndarray.astype"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.astype</span></code></a>(dtype[, order, casting, ...])</p></td>
<td><p>Copy of the array, cast to a specified type.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.byteswap.html#numpy.ndarray.byteswap" title="numpy.ndarray.byteswap"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.byteswap</span></code></a>([inplace])</p></td>
<td><p>Swap the bytes of the array elements</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.copy.html#numpy.ndarray.copy" title="numpy.ndarray.copy"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.copy</span></code></a>([order])</p></td>
<td><p>Return a copy of the array.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.view.html#numpy.ndarray.view" title="numpy.ndarray.view"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.view</span></code></a>([dtype][, type])</p></td>
<td><p>New view of array with the same data.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.getfield.html#numpy.ndarray.getfield" title="numpy.ndarray.getfield"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.getfield</span></code></a>(dtype[, offset])</p></td>
<td><p>Returns a field of the given array as a certain type.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.setflags.html#numpy.ndarray.setflags" title="numpy.ndarray.setflags"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.setflags</span></code></a>([write, align, uic])</p></td>
<td><p>Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.fill.html#numpy.ndarray.fill" title="numpy.ndarray.fill"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.fill</span></code></a>(value)</p></td>
<td><p>Fill the array with a scalar value.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="shape-manipulation">
<h3>Shape manipulation<a class="headerlink" href="#shape-manipulation" title="Link to this heading">#</a></h3>
<p>For reshape, resize, and transpose, the single tuple argument may be
replaced with <code class="docutils literal notranslate"><span class="pre">n</span></code> integers which will be interpreted as an n-tuple.</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.reshape.html#numpy.ndarray.reshape" title="numpy.ndarray.reshape"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.reshape</span></code></a>(shape, /, *[, order, copy])</p></td>
<td><p>Returns an array containing the same data with a new shape.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.resize.html#numpy.ndarray.resize" title="numpy.ndarray.resize"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.resize</span></code></a>(new_shape[, refcheck])</p></td>
<td><p>Change shape and size of array in-place.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.transpose.html#numpy.ndarray.transpose" title="numpy.ndarray.transpose"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.transpose</span></code></a>(*axes)</p></td>
<td><p>Returns a view of the array with axes transposed.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.swapaxes.html#numpy.ndarray.swapaxes" title="numpy.ndarray.swapaxes"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.swapaxes</span></code></a>(axis1, axis2)</p></td>
<td><p>Return a view of the array with <em class="xref py py-obj">axis1</em> and <em class="xref py py-obj">axis2</em> interchanged.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.flatten.html#numpy.ndarray.flatten" title="numpy.ndarray.flatten"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.flatten</span></code></a>([order])</p></td>
<td><p>Return a copy of the array collapsed into one dimension.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.ndarray.ravel.html#numpy.ndarray.ravel" title="numpy.ndarray.ravel"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.ravel</span></code></a>([order])</p></td>
<td><p>Return a flattened array.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.ndarray.squeeze.html#numpy.ndarray.squeeze" title="numpy.ndarray.squeeze"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndarray.squeeze</span></code></a>([axis])</p></td>
<td><p>Remove axes of length one from <em class="xref py py-obj">a</em>.</p></td>