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<h1>Source code for numpy</h1><div class="highlight"><pre>
<span></span><span class="sd">"""</span>
<span class="sd">NumPy</span>
<span class="sd">=====</span>
<span class="sd">Provides</span>
<span class="sd"> 1. An array object of arbitrary homogeneous items</span>
<span class="sd"> 2. Fast mathematical operations over arrays</span>
<span class="sd"> 3. Linear Algebra, Fourier Transforms, Random Number Generation</span>
<span class="sd">How to use the documentation</span>
<span class="sd">----------------------------</span>
<span class="sd">Documentation is available in two forms: docstrings provided</span>
<span class="sd">with the code, and a loose standing reference guide, available from</span>
<span class="sd">`the NumPy homepage <https://www.scipy.org>`_.</span>
<span class="sd">We recommend exploring the docstrings using</span>
<span class="sd">`IPython <https://ipython.org>`_, an advanced Python shell with</span>
<span class="sd">TAB-completion and introspection capabilities. See below for further</span>
<span class="sd">instructions.</span>
<span class="sd">The docstring examples assume that `numpy` has been imported as `np`::</span>
<span class="sd"> >>> import numpy as np</span>
<span class="sd">Code snippets are indicated by three greater-than signs::</span>
<span class="sd"> >>> x = 42</span>
<span class="sd"> >>> x = x + 1</span>
<span class="sd">Use the built-in ``help`` function to view a function's docstring::</span>
<span class="sd"> >>> help(np.sort)</span>
<span class="sd"> ... # doctest: +SKIP</span>
<span class="sd">For some objects, ``np.info(obj)`` may provide additional help. This is</span>
<span class="sd">particularly true if you see the line "Help on ufunc object:" at the top</span>
<span class="sd">of the help() page. Ufuncs are implemented in C, not Python, for speed.</span>
<span class="sd">The native Python help() does not know how to view their help, but our</span>
<span class="sd">np.info() function does.</span>
<span class="sd">To search for documents containing a keyword, do::</span>
<span class="sd"> >>> np.lookfor('keyword')</span>
<span class="sd"> ... # doctest: +SKIP</span>
<span class="sd">General-purpose documents like a glossary and help on the basic concepts</span>
<span class="sd">of numpy are available under the ``doc`` sub-module::</span>
<span class="sd"> >>> from numpy import doc</span>
<span class="sd"> >>> help(doc)</span>
<span class="sd"> ... # doctest: +SKIP</span>
<span class="sd">Available subpackages</span>
<span class="sd">---------------------</span>
<span class="sd">doc</span>
<span class="sd"> Topical documentation on broadcasting, indexing, etc.</span>
<span class="sd">lib</span>
<span class="sd"> Basic functions used by several sub-packages.</span>
<span class="sd">random</span>
<span class="sd"> Core Random Tools</span>
<span class="sd">linalg</span>
<span class="sd"> Core Linear Algebra Tools</span>
<span class="sd">fft</span>
<span class="sd"> Core FFT routines</span>
<span class="sd">polynomial</span>
<span class="sd"> Polynomial tools</span>
<span class="sd">testing</span>
<span class="sd"> NumPy testing tools</span>
<span class="sd">f2py</span>
<span class="sd"> Fortran to Python Interface Generator.</span>
<span class="sd">distutils</span>
<span class="sd"> Enhancements to distutils with support for</span>
<span class="sd"> Fortran compilers support and more.</span>
<span class="sd">Utilities</span>
<span class="sd">---------</span>
<span class="sd">test</span>
<span class="sd"> Run numpy unittests</span>
<span class="sd">show_config</span>
<span class="sd"> Show numpy build configuration</span>
<span class="sd">dual</span>
<span class="sd"> Overwrite certain functions with high-performance Scipy tools</span>
<span class="sd">matlib</span>
<span class="sd"> Make everything matrices.</span>
<span class="sd">__version__</span>
<span class="sd"> NumPy version string</span>
<span class="sd">Viewing documentation using IPython</span>
<span class="sd">-----------------------------------</span>
<span class="sd">Start IPython with the NumPy profile (``ipython -p numpy``), which will</span>
<span class="sd">import `numpy` under the alias `np`. Then, use the ``cpaste`` command to</span>
<span class="sd">paste examples into the shell. To see which functions are available in</span>
<span class="sd">`numpy`, type ``np.<TAB>`` (where ``<TAB>`` refers to the TAB key), or use</span>
<span class="sd">``np.*cos*?<ENTER>`` (where ``<ENTER>`` refers to the ENTER key) to narrow</span>
<span class="sd">down the list. To view the docstring for a function, use</span>
<span class="sd">``np.cos?<ENTER>`` (to view the docstring) and ``np.cos??<ENTER>`` (to view</span>
<span class="sd">the source code).</span>
<span class="sd">Copies vs. in-place operation</span>
<span class="sd">-----------------------------</span>
<span class="sd">Most of the functions in `numpy` return a copy of the array argument</span>
<span class="sd">(e.g., `np.sort`). In-place versions of these functions are often</span>
<span class="sd">available as array methods, i.e. ``x = np.array([1,2,3]); x.sort()``.</span>
<span class="sd">Exceptions to this rule are documented.</span>
<span class="sd">"""</span>
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span><span class="p">,</span> <span class="n">absolute_import</span><span class="p">,</span> <span class="n">print_function</span>
<span class="kn">import</span> <span class="nn">sys</span>
<span class="kn">import</span> <span class="nn">warnings</span>
<span class="kn">from</span> <span class="nn">._globals</span> <span class="kn">import</span> <span class="n">ModuleDeprecationWarning</span><span class="p">,</span> <span class="n">VisibleDeprecationWarning</span>
<span class="kn">from</span> <span class="nn">._globals</span> <span class="kn">import</span> <span class="n">_NoValue</span>
<span class="c1"># We first need to detect if we're being called as part of the numpy setup</span>
<span class="c1"># procedure itself in a reliable manner.</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">__NUMPY_SETUP__</span>
<span class="k">except</span> <span class="ne">NameError</span><span class="p">:</span>
<span class="n">__NUMPY_SETUP__</span> <span class="o">=</span> <span class="kc">False</span>
<span class="k">if</span> <span class="n">__NUMPY_SETUP__</span><span class="p">:</span>
<span class="n">sys</span><span class="o">.</span><span class="n">stderr</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="s1">'Running from numpy source directory.</span><span class="se">\n</span><span class="s1">'</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">try</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">numpy.__config__</span> <span class="kn">import</span> <span class="n">show</span> <span class="k">as</span> <span class="n">show_config</span>
<span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span>
<span class="n">msg</span> <span class="o">=</span> <span class="s2">"""Error importing numpy: you should not try to import numpy from</span>
<span class="s2"> its source directory; please exit the numpy source tree, and relaunch</span>
<span class="s2"> your python interpreter from there."""</span>
<span class="k">raise</span> <span class="ne">ImportError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
<span class="kn">from</span> <span class="nn">.version</span> <span class="kn">import</span> <span class="n">git_revision</span> <span class="k">as</span> <span class="n">__git_revision__</span>
<span class="kn">from</span> <span class="nn">.version</span> <span class="kn">import</span> <span class="n">version</span> <span class="k">as</span> <span class="n">__version__</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'ModuleDeprecationWarning'</span><span class="p">,</span>
<span class="s1">'VisibleDeprecationWarning'</span><span class="p">]</span>
<span class="c1"># Allow distributors to run custom init code</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">_distributor_init</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">core</span>
<span class="kn">from</span> <span class="nn">.core</span> <span class="kn">import</span> <span class="o">*</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">compat</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">lib</span>
<span class="c1"># FIXME: why have numpy.lib if everything is imported here??</span>
<span class="kn">from</span> <span class="nn">.lib</span> <span class="kn">import</span> <span class="o">*</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">linalg</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">fft</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">polynomial</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">random</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">ctypeslib</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">ma</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">matrixlib</span> <span class="k">as</span> <span class="n">_mat</span>
<span class="kn">from</span> <span class="nn">.matrixlib</span> <span class="kn">import</span> <span class="o">*</span>
<span class="kn">from</span> <span class="nn">.compat</span> <span class="kn">import</span> <span class="n">long</span>
<span class="c1"># Make these accessible from numpy name-space</span>
<span class="c1"># but not imported in from numpy import *</span>
<span class="c1"># TODO[gh-6103]: Deprecate these</span>
<span class="k">if</span> <span class="n">sys</span><span class="o">.</span><span class="n">version_info</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">>=</span> <span class="mi">3</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">builtins</span> <span class="kn">import</span> <span class="nb">bool</span><span class="p">,</span> <span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">,</span> <span class="nb">complex</span><span class="p">,</span> <span class="nb">object</span><span class="p">,</span> <span class="nb">str</span>
<span class="n">unicode</span> <span class="o">=</span> <span class="nb">str</span>
<span class="k">else</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">__builtin__</span> <span class="kn">import</span> <span class="nb">bool</span><span class="p">,</span> <span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">,</span> <span class="nb">complex</span><span class="p">,</span> <span class="nb">object</span><span class="p">,</span> <span class="n">unicode</span><span class="p">,</span> <span class="nb">str</span>
<span class="kn">from</span> <span class="nn">.core</span> <span class="kn">import</span> <span class="nb">round</span><span class="p">,</span> <span class="nb">abs</span><span class="p">,</span> <span class="nb">max</span><span class="p">,</span> <span class="nb">min</span>
<span class="c1"># now that numpy modules are imported, can initialize limits</span>
<span class="n">core</span><span class="o">.</span><span class="n">getlimits</span><span class="o">.</span><span class="n">_register_known_types</span><span class="p">()</span>
<span class="n">__all__</span><span class="o">.</span><span class="n">extend</span><span class="p">([</span><span class="s1">'__version__'</span><span class="p">,</span> <span class="s1">'show_config'</span><span class="p">])</span>
<span class="n">__all__</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">core</span><span class="o">.</span><span class="n">__all__</span><span class="p">)</span>
<span class="n">__all__</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">_mat</span><span class="o">.</span><span class="n">__all__</span><span class="p">)</span>
<span class="n">__all__</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">lib</span><span class="o">.</span><span class="n">__all__</span><span class="p">)</span>
<span class="n">__all__</span><span class="o">.</span><span class="n">extend</span><span class="p">([</span><span class="s1">'linalg'</span><span class="p">,</span> <span class="s1">'fft'</span><span class="p">,</span> <span class="s1">'random'</span><span class="p">,</span> <span class="s1">'ctypeslib'</span><span class="p">,</span> <span class="s1">'ma'</span><span class="p">])</span>
<span class="c1"># These are added by `from .core import *` and `core.__all__`, but we</span>
<span class="c1"># overwrite them above with builtins we do _not_ want to export.</span>
<span class="n">__all__</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="s1">'long'</span><span class="p">)</span>
<span class="n">__all__</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="s1">'unicode'</span><span class="p">)</span>
<span class="c1"># Remove things that are in the numpy.lib but not in the numpy namespace</span>
<span class="c1"># Note that there is a test (numpy/tests/test_public_api.py:test_numpy_namespace)</span>
<span class="c1"># that prevents adding more things to the main namespace by accident.</span>
<span class="c1"># The list below will grow until the `from .lib import *` fixme above is</span>
<span class="c1"># taken care of</span>
<span class="n">__all__</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="s1">'Arrayterator'</span><span class="p">)</span>
<span class="k">del</span> <span class="n">Arrayterator</span>
<span class="c1"># Filter out Cython harmless warnings</span>
<span class="n">warnings</span><span class="o">.</span><span class="n">filterwarnings</span><span class="p">(</span><span class="s2">"ignore"</span><span class="p">,</span> <span class="n">message</span><span class="o">=</span><span class="s2">"numpy.dtype size changed"</span><span class="p">)</span>
<span class="n">warnings</span><span class="o">.</span><span class="n">filterwarnings</span><span class="p">(</span><span class="s2">"ignore"</span><span class="p">,</span> <span class="n">message</span><span class="o">=</span><span class="s2">"numpy.ufunc size changed"</span><span class="p">)</span>
<span class="n">warnings</span><span class="o">.</span><span class="n">filterwarnings</span><span class="p">(</span><span class="s2">"ignore"</span><span class="p">,</span> <span class="n">message</span><span class="o">=</span><span class="s2">"numpy.ndarray size changed"</span><span class="p">)</span>
<span class="c1"># oldnumeric and numarray were removed in 1.9. In case some packages import</span>
<span class="c1"># but do not use them, we define them here for backward compatibility.</span>
<span class="n">oldnumeric</span> <span class="o">=</span> <span class="s1">'removed'</span>
<span class="n">numarray</span> <span class="o">=</span> <span class="s1">'removed'</span>
<span class="k">if</span> <span class="n">sys</span><span class="o">.</span><span class="n">version_info</span><span class="p">[:</span><span class="mi">2</span><span class="p">]</span> <span class="o">>=</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">7</span><span class="p">):</span>
<span class="c1"># Importing Tester requires importing all of UnitTest which is not a</span>
<span class="c1"># cheap import Since it is mainly used in test suits, we lazy import it</span>
<span class="c1"># here to save on the order of 10 ms of import time for most users</span>
<span class="c1">#</span>
<span class="c1"># The previous way Tester was imported also had a side effect of adding</span>
<span class="c1"># the full `numpy.testing` namespace</span>
<span class="c1">#</span>
<span class="c1"># module level getattr is only supported in 3.7 onwards</span>
<span class="c1"># https://www.python.org/dev/peps/pep-0562/</span>
<span class="k">def</span> <span class="fm">__getattr__</span><span class="p">(</span><span class="n">attr</span><span class="p">):</span>
<span class="k">if</span> <span class="n">attr</span> <span class="o">==</span> <span class="s1">'testing'</span><span class="p">:</span>
<span class="kn">import</span> <span class="nn">numpy.testing</span> <span class="k">as</span> <span class="nn">testing</span>
<span class="k">return</span> <span class="n">testing</span>
<span class="k">elif</span> <span class="n">attr</span> <span class="o">==</span> <span class="s1">'Tester'</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">.testing</span> <span class="kn">import</span> <span class="n">Tester</span>
<span class="k">return</span> <span class="n">Tester</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">AttributeError</span><span class="p">(</span><span class="s2">"module </span><span class="si">{!r}</span><span class="s2"> has no attribute "</span>
<span class="s2">"</span><span class="si">{!r}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="vm">__name__</span><span class="p">,</span> <span class="n">attr</span><span class="p">))</span>
<span class="k">def</span> <span class="fm">__dir__</span><span class="p">():</span>
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span> <span class="o">+</span> <span class="p">[</span><span class="s1">'Tester'</span><span class="p">,</span> <span class="s1">'testing'</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># We don't actually use this ourselves anymore, but I'm not 100% sure that</span>
<span class="c1"># no-one else in the world is using it (though I hope not)</span>
<span class="kn">from</span> <span class="nn">.testing</span> <span class="kn">import</span> <span class="n">Tester</span>
<span class="c1"># Pytest testing</span>
<span class="kn">from</span> <span class="nn">numpy._pytesttester</span> <span class="kn">import</span> <span class="n">PytestTester</span>
<span class="n">test</span> <span class="o">=</span> <span class="n">PytestTester</span><span class="p">(</span><span class="vm">__name__</span><span class="p">)</span>
<span class="k">del</span> <span class="n">PytestTester</span>
<span class="k">def</span> <span class="nf">_sanity_check</span><span class="p">():</span>
<span class="sd">"""</span>
<span class="sd"> Quick sanity checks for common bugs caused by environment.</span>
<span class="sd"> There are some cases e.g. with wrong BLAS ABI that cause wrong</span>
<span class="sd"> results under specific runtime conditions that are not necessarily</span>
<span class="sd"> achieved during test suite runs, and it is useful to catch those early.</span>
<span class="sd"> See https://github.com/numpy/numpy/issues/8577 and other</span>
<span class="sd"> similar bug reports.</span>
<span class="sd"> """</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">x</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="n">dtype</span><span class="o">=</span><span class="n">float32</span><span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">abs</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">-</span> <span class="mf">2.0</span><span class="p">)</span> <span class="o"><</span> <span class="mf">1e-5</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">AssertionError</span><span class="p">()</span>
<span class="k">except</span> <span class="ne">AssertionError</span><span class="p">:</span>
<span class="n">msg</span> <span class="o">=</span> <span class="p">(</span><span class="s2">"The current Numpy installation (</span><span class="si">{!r}</span><span class="s2">) fails to "</span>
<span class="s2">"pass simple sanity checks. This can be caused for example "</span>
<span class="s2">"by incorrect BLAS library being linked in, or by mixing "</span>
<span class="s2">"package managers (pip, conda, apt, ...). Search closed "</span>
<span class="s2">"numpy issues for similar problems."</span><span class="p">)</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="n">msg</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="vm">__file__</span><span class="p">))</span>
<span class="n">_sanity_check</span><span class="p">()</span>
<span class="k">del</span> <span class="n">_sanity_check</span>
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