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<section id="nep-12-missing-data-functionality-in-numpy">
<span id="nep12"></span><h1><a class="toc-backref" href="#id1" role="doc-backlink">NEP 12 — Missing data functionality in NumPy</a><a class="headerlink" href="#nep-12-missing-data-functionality-in-numpy" title="Link to this heading">#</a></h1>
<dl class="field-list simple">
<dt class="field-odd">Author<span class="colon">:</span></dt>
<dd class="field-odd"><p>Mark Wiebe <<a class="reference external" href="mailto:mwwiebe%40gmail.com">mwwiebe<span>@</span>gmail<span>.</span>com</a>></p>
</dd>
<dt class="field-even">Copyright<span class="colon">:</span></dt>
<dd class="field-even"><p>Copyright 2011 by Enthought, Inc</p>
</dd>
<dt class="field-odd">License<span class="colon">:</span></dt>
<dd class="field-odd"><p>CC By-SA 3.0 (<a class="reference external" href="https://creativecommons.org/licenses/by-sa/3.0/">https://creativecommons.org/licenses/by-sa/3.0/</a>)</p>
</dd>
<dt class="field-even">Date<span class="colon">:</span></dt>
<dd class="field-even"><p>2011-06-23</p>
</dd>
<dt class="field-odd">Status<span class="colon">:</span></dt>
<dd class="field-odd"><p>Deferred</p>
</dd>
</dl>
<section id="table-of-contents">
<h2><a class="toc-backref" href="#id2" role="doc-backlink">Table of contents</a><a class="headerlink" href="#table-of-contents" title="Link to this heading">#</a></h2>
<nav class="contents" id="contents">
<p class="topic-title">Contents</p>
<ul class="simple">
<li><p><a class="reference internal" href="#nep-12-missing-data-functionality-in-numpy" id="id1">NEP 12 — Missing data functionality in NumPy</a></p>
<ul>
<li><p><a class="reference internal" href="#table-of-contents" id="id2">Table of contents</a></p></li>
<li><p><a class="reference internal" href="#abstract" id="id3">Abstract</a></p></li>
<li><p><a class="reference internal" href="#definition-of-missing-data" id="id4">Definition of missing data</a></p>
<ul>
<li><p><a class="reference internal" href="#unknown-yet-existing-data-na" id="id5">Unknown yet existing data (NA)</a></p></li>
<li><p><a class="reference internal" href="#data-that-doesn-t-exist-or-is-being-skipped-ignore" id="id6">Data that doesn’t exist or is being skipped (IGNORE)</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#implementation-techniques-for-missing-values" id="id7">Implementation techniques for missing values</a></p>
<ul>
<li><p><a class="reference internal" href="#bit-patterns-signalling-missing-values-bitpattern" id="id8">Bit patterns signalling missing values (bitpattern)</a></p></li>
<li><p><a class="reference internal" href="#boolean-masks-signalling-missing-values-mask" id="id9">Boolean masks signalling missing values (mask)</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#glossary-of-terms" id="id10">Glossary of terms</a></p></li>
<li><p><a class="reference internal" href="#missing-values-as-seen-in-python" id="id11">Missing values as seen in Python</a></p>
<ul>
<li><p><a class="reference internal" href="#working-with-missing-values" id="id12">Working with missing values</a></p></li>
<li><p><a class="reference internal" href="#accessing-a-boolean-mask" id="id13">Accessing a boolean mask</a></p></li>
<li><p><a class="reference internal" href="#creating-na-masked-arrays" id="id14">Creating NA-masked arrays</a></p></li>
<li><p><a class="reference internal" href="#na-masks-when-constructing-from-lists" id="id15">Na-masks when constructing from lists</a></p></li>
<li><p><a class="reference internal" href="#mask-implementation-details" id="id16">Mask implementation details</a></p></li>
<li><p><a class="reference internal" href="#new-ndarray-methods" id="id17">New ndarray methods</a></p></li>
<li><p><a class="reference internal" href="#element-wise-ufuncs-with-missing-values" id="id18">Element-wise ufuncs with missing values</a></p></li>
<li><p><a class="reference internal" href="#reduction-ufuncs-with-missing-values" id="id19">Reduction ufuncs with missing values</a></p></li>
<li><p><a class="reference internal" href="#parameterized-na-data-types" id="id20">Parameterized NA data types</a></p></li>
<li><p><a class="reference internal" href="#future-expansion-to-multi-na-payloads" id="id21">Future expansion to multi-NA payloads</a></p></li>
<li><p><a class="reference internal" href="#differences-with-numpy-ma" id="id22">Differences with numpy.ma</a></p></li>
<li><p><a class="reference internal" href="#boolean-indexing" id="id23">Boolean indexing</a></p></li>
<li><p><a class="reference internal" href="#pep-3118" id="id24">PEP 3118</a></p></li>
<li><p><a class="reference internal" href="#cython" id="id25">Cython</a></p></li>
<li><p><a class="reference internal" href="#hard-masks" id="id26">Hard masks</a></p></li>
<li><p><a class="reference internal" href="#shared-masks" id="id27">Shared masks</a></p></li>
<li><p><a class="reference internal" href="#interaction-with-pre-existing-c-api-usage" id="id28">Interaction with pre-existing C API usage</a></p>
<ul>
<li><p><a class="reference internal" href="#numpy-documentation-how-to-extend-numpy" id="id29">NumPy documentation - how to extend NumPy</a></p></li>
<li><p><a class="reference internal" href="#tutorial-from-cython-website" id="id30">Tutorial from Cython website</a></p></li>
<li><p><a class="reference internal" href="#numerical-python-jpl-website" id="id31">Numerical Python - JPL website</a></p></li>
</ul>
</li>
</ul>
</li>
<li><p><a class="reference internal" href="#c-implementation-details" id="id32">C implementation details</a></p>
<ul>
<li><p><a class="reference internal" href="#mask-binary-format" id="id33">Mask binary format</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#c-iterator-api-changes-iteration-with-masks" id="id34">C iterator API changes: iteration with masks</a></p>
<ul>
<li><p><a class="reference internal" href="#iterator-mask-features" id="id35">Iterator mask features</a></p></li>
<li><p><a class="reference internal" href="#iterator-na-array-features" id="id36">Iterator NA-array features</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#rejected-alternative" id="id37">Rejected alternative</a></p>
<ul>
<li><p><a class="reference internal" href="#parameterized-data-type-which-adds-additional-memory-for-the-na-flag" id="id38">Parameterized data type which adds additional memory for the NA flag</a></p></li>
</ul>
</li>
<li><p><a class="reference internal" href="#acknowledgments" id="id39">Acknowledgments</a></p></li>
</ul>
</li>
</ul>
</nav>
</section>
<section id="abstract">
<h2><a class="toc-backref" href="#id3" role="doc-backlink">Abstract</a><a class="headerlink" href="#abstract" title="Link to this heading">#</a></h2>
<p>Users interested in dealing with missing data within NumPy are generally
pointed to the masked array subclass of the ndarray, known
as ‘numpy.ma’. This class has a number of users who depend strongly
on its capabilities, but people who are accustomed to the deep integration
of the missing data placeholder “NA” in the R project and others who
find the programming interface challenging or inconsistent tend not
to use it.</p>
<p>This NEP proposes to integrate a mask-based missing data solution
into NumPy, with an additional bitpattern-based missing data solution
that can be implemented concurrently or later integrating seamlessly
with the mask-based solution.</p>
<p>The mask-based solution and the bitpattern-based solutions in this
proposal offer the exact same missing value abstraction, with several
differences in performance, memory overhead, and flexibility.</p>
<p>The mask-based solution is more flexible, supporting all behaviors of the
bitpattern-based solution, but leaving the hidden values untouched
whenever an element is masked.</p>
<p>The bitpattern-based solution requires less memory, is bit-level
compatible with the 64-bit floating point representation used in R, but
does not preserve the hidden values and in fact requires stealing at
least one bit pattern from the underlying dtype to represent the missing
value NA.</p>
<p>Both solutions are generic in the sense that they can be used with
custom data types very easily, with no effort in the case of the masked
solution, and with the requirement that a bit pattern to sacrifice be
chosen in the case of the bitpattern solution.</p>
</section>
<section id="definition-of-missing-data">
<h2><a class="toc-backref" href="#id4" role="doc-backlink">Definition of missing data</a><a class="headerlink" href="#definition-of-missing-data" title="Link to this heading">#</a></h2>
<p>In order to be able to develop an intuition about what computation
will be done by various NumPy functions, a consistent conceptual
model of what a missing element means must be applied.
Ferreting out the behaviors people need or want when they are working
with “missing data” seems to be tricky, but I believe that it boils
down to two different ideas, each of which is internally self-consistent.</p>
<p>One of them, the “unknown yet existing data” interpretation, can be applied
rigorously to all computations, while the other makes sense for
some statistical operations like standard deviation but not for
linear algebra operations like matrix product.
Thus, making “unknown yet existing data” be the default interpretation
is superior, providing a consistent model across all computations,
and for those operations where the other interpretation makes sense,
an optional parameter “skipna=” can be added.</p>
<p>For people who want the other interpretation to be default, a mechanism
proposed elsewhere for customizing subclass ufunc behavior with a
_numpy_ufunc_ member function would allow a subclass with a different
default to be created.</p>
<section id="unknown-yet-existing-data-na">
<h3><a class="toc-backref" href="#id5" role="doc-backlink">Unknown yet existing data (NA)</a><a class="headerlink" href="#unknown-yet-existing-data-na" title="Link to this heading">#</a></h3>
<p>This is the approach taken in the R project, defining a missing element
as something which does have a valid value which isn’t known, or is
NA (not available). This proposal adopts this behavior as the
default for all operations involving missing values.</p>
<p>In this interpretation, nearly any computation with a missing input produces
a missing output. For example, ‘sum(a)’ would produce a missing value
if ‘a’ contained just one missing element. When the output value does
not depend on one of the inputs, it is reasonable to output a value
that is not NA, such as logical_and(NA, False) == False.</p>
<p>Some more complex arithmetic operations, such as matrix products, are
well defined with this interpretation, and the result should be
the same as if the missing values were NaNs. Actually implementing
such things to the theoretical limit is probably not worth it,
and in many cases either raising an exception or returning all
missing values may be preferred to doing precise calculations.</p>
</section>
<section id="data-that-doesn-t-exist-or-is-being-skipped-ignore">
<h3><a class="toc-backref" href="#id6" role="doc-backlink">Data that doesn’t exist or is being skipped (IGNORE)</a><a class="headerlink" href="#data-that-doesn-t-exist-or-is-being-skipped-ignore" title="Link to this heading">#</a></h3>
<p>Another useful interpretation is that the missing elements should be
treated as if they didn’t exist in the array, and the operation should
do its best to interpret what that means according to the data
that’s left. In this case, ‘mean(a)’ would compute the mean of just
the values that are available, adjusting both the sum and count it
uses based on which values are missing. To be consistent, the mean of
an array of all missing values must produce the same result as the
mean of a zero-sized array without missing value support.</p>
<p>This kind of data can arise when conforming sparsely sampled data
into a regular sampling pattern, and is a useful interpretation to
use when attempting to get best-guess answers for many statistical queries.</p>
<p>In R, many functions take a parameter “na.rm=T” which means to treat
the data as if the NA values are not part of the data set. This proposal
defines a standard parameter “skipna=True” for this same purpose.</p>
</section>
</section>
<section id="implementation-techniques-for-missing-values">
<h2><a class="toc-backref" href="#id7" role="doc-backlink">Implementation techniques for missing values</a><a class="headerlink" href="#implementation-techniques-for-missing-values" title="Link to this heading">#</a></h2>
<p>In addition to there being two different interpretations of missing values,
there are two different commonly used implementation techniques for
missing values. While there are some differing default behaviors between
existing implementations of the techniques, I believe that the design
choices made in a new implementation must be made based on their merits,
not by rote copying of previous designs.</p>
<p>Both masks and bitpatterns have different strong and weak points,
depending on the application context. This NEP thus proposes to implement
both. To enable the writing of generic “missing value” code which does
not have to worry about whether the arrays it is using have taken one
or the other approach, the missing value semantics will be identical
for the two implementations.</p>
<section id="bit-patterns-signalling-missing-values-bitpattern">
<h3><a class="toc-backref" href="#id8" role="doc-backlink">Bit patterns signalling missing values (bitpattern)</a><a class="headerlink" href="#bit-patterns-signalling-missing-values-bitpattern" title="Link to this heading">#</a></h3>
<p>One or more patterns of bits, for example a NaN with
a particular payload, are chosen to represent the missing value
placeholder NA.</p>
<p>A consequence of this approach is that assigning NA changes the bits
holding the value, so that value is gone.</p>
<p>Additionally, for some types such as integers, a good and proper value
must be sacrificed to enable this functionality.</p>
</section>
<section id="boolean-masks-signalling-missing-values-mask">
<h3><a class="toc-backref" href="#id9" role="doc-backlink">Boolean masks signalling missing values (mask)</a><a class="headerlink" href="#boolean-masks-signalling-missing-values-mask" title="Link to this heading">#</a></h3>
<p>A mask is a parallel array of booleans, either one byte per element or
one bit per element, allocated alongside the existing array data. In this
NEP, the convention is chosen that True means the element is valid
(unmasked), and False means the element is NA.</p>
<p>By taking care when writing any C algorithm that works with values
and masks together, it is possible to have the memory for a value
that is masked never be written to. This feature allows multiple
simultaneous views of the same data with different choices of what
is missing, a feature requested by many people on the mailing list.</p>
<p>This approach places no limitations on the values of the underlying
data type, it may take on any binary pattern without affecting the
NA behavior.</p>
</section>
</section>
<section id="glossary-of-terms">
<h2><a class="toc-backref" href="#id10" role="doc-backlink">Glossary of terms</a><a class="headerlink" href="#glossary-of-terms" title="Link to this heading">#</a></h2>
<p>Because the above discussions of the different concepts and their
relationships are tricky to understand, here are more succinct
definitions of the terms used in this NEP.</p>
<dl class="simple">
<dt>NA (Not Available/Propagate)</dt><dd><p>A placeholder for a value which is unknown to computations. That
value may be temporarily hidden with a mask, may have been lost
due to hard drive corruption, or gone for any number of reasons.
For sums and products this means to produce NA if any of the inputs
are NA. This is the same as NA in the R project.</p>
</dd>
<dt>IGNORE (Ignore/Skip)</dt><dd><p>A placeholder which should be treated by computations as if no value does
or could exist there. For sums, this means act as if the value
were zero, and for products, this means act as if the value were one.
It’s as if the array were compressed in some fashion to not include
that element.</p>
</dd>
<dt>bitpattern</dt><dd><p>A technique for implementing either NA or IGNORE, where a particular
set of bit patterns are chosen from all the possible bit patterns of the
value’s data type to signal that the element is NA or IGNORE.</p>
</dd>
<dt>mask</dt><dd><p>A technique for implementing either NA or IGNORE, where a
boolean or enum array parallel to the data array is used to signal
which elements are NA or IGNORE.</p>
</dd>
<dt>numpy.ma</dt><dd><p>The existing implementation of a particular form of masked arrays,
which is part of the NumPy codebase.</p>
</dd>
<dt>Python API</dt><dd><p>All the interface mechanisms that are exposed to Python code
for using missing values in NumPy. This API is designed to be
Pythonic and fit into the way NumPy works as much as possible.</p>
</dd>
<dt>C API</dt><dd><p>All the implementation mechanisms exposed for CPython extensions
written in C that want to support NumPy missing value support.
This API is designed to be as natural as possible in C, and
is usually prioritizes flexibility and high performance.</p>
</dd>
</dl>
</section>
<section id="missing-values-as-seen-in-python">
<h2><a class="toc-backref" href="#id11" role="doc-backlink">Missing values as seen in Python</a><a class="headerlink" href="#missing-values-as-seen-in-python" title="Link to this heading">#</a></h2>
<section id="working-with-missing-values">
<h3><a class="toc-backref" href="#id12" role="doc-backlink">Working with missing values</a><a class="headerlink" href="#working-with-missing-values" title="Link to this heading">#</a></h3>
<p>NumPy will gain a global singleton called numpy.NA, similar to None,
but with semantics reflecting its status as a missing value. In particular,
trying to treat it as a boolean will raise an exception, and comparisons
with it will produce numpy.NA instead of True or False. These basics are
adopted from the behavior of the NA value in the R project. To dig
deeper into the ideas, <a class="reference external" href="https://en.wikipedia.org/wiki/Ternary_logic#Kleene_logic">https://en.wikipedia.org/wiki/Ternary_logic#Kleene_logic</a>
provides a starting point.</p>
<p>For example,:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">NA</span><span class="p">,</span> <span class="mf">7.0</span><span class="p">],</span> <span class="n">maskna</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="go">array([1., 2., NA, 7.], maskna=True)</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">NA</span><span class="p">,</span> <span class="mf">7.0</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="s1">'NA'</span><span class="p">)</span>
<span class="go">array([1., 2., NA, 7.], dtype='NA[<f8]')</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">NA</span><span class="p">,</span> <span class="mf">7.0</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="s1">'NA[f4]'</span><span class="p">)</span>
<span class="go">array([1., 2., NA, 7.], dtype='NA[<f4]')</span>
</pre></div>
</div>
<p>produce arrays with values [1.0, 2.0, <inaccessible>, 7.0] /
mask [Exposed, Exposed, Hidden, Exposed], and
values [1.0, 2.0, <NA bitpattern>, 7.0] for the masked and
NA dtype versions respectively.</p>
<p>The np.NA singleton may accept a dtype= keyword parameter, indicating
that it should be treated as an NA of a particular data type. This is also
a mechanism for preserving the dtype in a NumPy scalar-like fashion.
Here’s what this looks like:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">NA</span><span class="p">,</span> <span class="mf">7.0</span><span class="p">],</span> <span class="n">maskna</span><span class="o">=</span><span class="kc">True</span><span class="p">))</span>
<span class="go">NA(dtype='<f8')</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">NA</span><span class="p">,</span> <span class="mf">7.0</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="s1">'NA[f8]'</span><span class="p">))</span>
<span class="go">NA(dtype='NA[<f8]')</span>
</pre></div>
</div>
<p>Assigning a value to an array always causes that element to not be NA,
transparently unmasking it if necessary. Assigning numpy.NA to the array
masks that element or assigns the NA bitpattern for the particular dtype.
In the mask-based implementation, the storage behind a missing value may never
be accessed in any way, other than to unmask it by assigning its value.</p>
<p>To test if a value is missing, the function “np.isna(arr[0])” will
be provided. One of the key reasons for the NumPy scalars is to allow
their values into dictionaries.</p>
<p>All operations which write to masked arrays will not affect the value
unless they also unmask that value. This allows the storage behind
masked elements to still be relied on if they are still accessible
from another view which doesn’t have them masked. For example, the
following was run on the missingdata work-in-progress branch:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">a</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="gp">>>> </span><span class="n">b</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">maskna</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">b</span>
<span class="go">array([1, 2], maskna=True)</span>
<span class="gp">>>> </span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">NA</span>
<span class="gp">>>> </span><span class="n">b</span>
<span class="go">array([NA, 2], maskna=True)</span>
<span class="gp">>>> </span><span class="n">a</span>
<span class="go">array([1, 2])</span>
<span class="gp">>>> </span><span class="c1"># The underlying number 1 value in 'a[0]' was untouched</span>
</pre></div>
</div>
<p>Copying values between the mask-based implementation and the
bitpattern implementation will transparently do the correct thing,
turning the bitpattern into a masked value, or a masked value
into the bitpattern where appropriate. The one exception is
if a valid value in a masked array happens to have the NA bitpattern,
copying this value to the NA form of the dtype will cause it to
become NA as well.</p>
<p>When operations are done between arrays with NA dtypes and masked arrays,
the result will be masked arrays. This is because in some cases the
NA dtypes cannot represent all the values in the masked array, so
going to masked arrays is the only way to preserve all aspects of the data.</p>
<p>If np.NA or masked values are copied to an array without support for
missing values enabled, an exception will be raised. Adding a mask to
the target array would be problematic, because then having a mask
would be a “viral” property consuming extra memory and reducing
performance in unexpected ways.</p>
<p>By default, the string “NA” will be used to represent missing values
in str and repr outputs. A global configuration will allow
this to be changed, exactly extending the way nan and inf are treated.
The following works in the current draft implementation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="n">maskna</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">a</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">NA</span>
<span class="gp">>>> </span><span class="n">a</span>
<span class="go">array([0, 1, 2, NA, 4, 5], maskna=True)</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">set_printoptions</span><span class="p">(</span><span class="n">nastr</span><span class="o">=</span><span class="s1">'blah'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">a</span>
<span class="go">array([0, 1, 2, blah, 4, 5], maskna=True)</span>
</pre></div>
</div>
<p>For floating point numbers, Inf and NaN are separate concepts from
missing values. If a division by zero occurs in an array with default
missing value support, an unmasked Inf or NaN will be produced. To
mask those values, a further ‘a[np.logical_not(a.isfinite(a))] = np.NA’
can achieve that. For the bitpattern approach, the parameterized
dtype(‘NA[f8,InfNan]’) described in a later section can be used to get
these semantics without the extra manipulation.</p>
<p>A manual loop through a masked array like:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">5.</span><span class="p">,</span> <span class="n">maskna</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">a</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">NA</span>
<span class="gp">>>> </span><span class="n">a</span>
<span class="go">array([ 0., 1., 2., NA, 4.], maskna=True)</span>
<span class="gp">>>> </span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">a</span><span class="p">)):</span>
<span class="gp">... </span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="gp">...</span>
<span class="go">__main__:2: RuntimeWarning: divide by zero encountered in log</span>
<span class="gp">>>> </span><span class="n">a</span>
<span class="go">array([ -inf, 0. , 0.69314718, NA, 1.38629436], maskna=True)</span>
</pre></div>
</div>
<p>works even with masked values, because ‘a[i]’ returns an NA object
with a data type associated, that can be treated properly by the ufuncs.</p>
</section>
<section id="accessing-a-boolean-mask">
<h3><a class="toc-backref" href="#id13" role="doc-backlink">Accessing a boolean mask</a><a class="headerlink" href="#accessing-a-boolean-mask" title="Link to this heading">#</a></h3>
<p>The mask used to implement missing data in the masked approach is not
accessible from Python directly. This is partially due to differing
opinions on whether True in the mask should mean “missing” or “not missing”
Additionally, exposing the mask directly would preclude a potential
space optimization, where a bit-level instead of a byte-level mask
is used to get a factor of eight memory usage improvement.</p>
<p>To access a mask directly, there are two functions provided. They
work equivalently for both arrays with masks and NA bit
patterns, so they are specified in terms of NA and available values
instead of masked and unmasked values. The functions are
‘np.isna’ and ‘np.isavail’, which test for NA or available values
respectively.</p>
</section>
<section id="creating-na-masked-arrays">
<h3><a class="toc-backref" href="#id14" role="doc-backlink">Creating NA-masked arrays</a><a class="headerlink" href="#creating-na-masked-arrays" title="Link to this heading">#</a></h3>
<p>The usual way to create an array with an NA mask is to pass the keyword
parameter maskna=True to one of the constructors. Most functions that
create a new array take this parameter, and produce an NA-masked
array with all its elements exposed when the parameter is set to True.</p>
<p>There are also two flags which indicate and control the nature of the mask
used in masked arrays. These flags can be used to add a mask, or ensure
the mask isn’t a view into another array’s mask.</p>
<p>First is ‘arr.flags.maskna’, which is True for all masked arrays and
may be set to True to add a mask to an array which does not have one.</p>
<p>Second is ‘arr.flags.ownmaskna’, which is True if the array owns the
memory to the mask, and False if the array has no mask, or has a view
into the mask of another array. If this is set to True in a masked
array, the array will create a copy of the mask so that further modifications
to the mask will not affect the original mask from which the view was taken.</p>
</section>
<section id="na-masks-when-constructing-from-lists">
<h3><a class="toc-backref" href="#id15" role="doc-backlink">Na-masks when constructing from lists</a><a class="headerlink" href="#na-masks-when-constructing-from-lists" title="Link to this heading">#</a></h3>
<p>The initial design of NA-mask construction was to make all construction
fully explicit. This turns out to be unwieldy when working interactively
with NA-masked arrays, and having an object array be created instead of
an NA-masked array can be very surprising.</p>
<p>Because of this, the design has been changed to enable an NA-mask whenever
creating an array from lists which have an NA object in them. There could
be some debate of whether one should create NA-masks or NA-bitpatterns
by default, but due to the time constraints it was only feasible to tackle
NA-masks, and extending the NA-mask support more fully throughout NumPy seems
much more reasonable than starting another system and ending up with two
incomplete systems.</p>
</section>
<section id="mask-implementation-details">
<h3><a class="toc-backref" href="#id16" role="doc-backlink">Mask implementation details</a><a class="headerlink" href="#mask-implementation-details" title="Link to this heading">#</a></h3>
<p>The memory ordering of the mask will always match the ordering of
the array it is associated with. A Fortran-style array will have a
Fortran-style mask, etc.</p>
<p>When a view of an array with a mask is taken, the view will have
a mask which is also a view of the mask in the original
array. This means unmasking values in views will also unmask them
in the original array, and if a mask is added to an array, it will
not be possible to ever remove that mask except to create a new array
copying the data but not the mask.</p>
<p>It is still possible to temporarily treat an array with a mask without
giving it one, by first creating a view of the array and then adding a
mask to that view. A data set can be viewed with multiple different
masks simultaneously, by creating multiple views, and giving each view
a mask.</p>
</section>
<section id="new-ndarray-methods">
<h3><a class="toc-backref" href="#id17" role="doc-backlink">New ndarray methods</a><a class="headerlink" href="#new-ndarray-methods" title="Link to this heading">#</a></h3>
<p>New functions added to the numpy namespace are:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">isna</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="p">[</span><span class="n">IMPLEMENTED</span><span class="p">]</span>
<span class="n">Returns</span> <span class="n">a</span> <span class="n">boolean</span> <span class="n">array</span> <span class="k">with</span> <span class="kc">True</span> <span class="n">wherever</span> <span class="n">the</span> <span class="n">array</span> <span class="ow">is</span> <span class="n">masked</span>
<span class="ow">or</span> <span class="n">matches</span> <span class="n">the</span> <span class="n">NA</span> <span class="n">bitpattern</span><span class="p">,</span> <span class="ow">and</span> <span class="kc">False</span> <span class="n">elsewhere</span>
<span class="n">np</span><span class="o">.</span><span class="n">isavail</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="n">Returns</span> <span class="n">a</span> <span class="n">boolean</span> <span class="n">array</span> <span class="k">with</span> <span class="kc">False</span> <span class="n">wherever</span> <span class="n">the</span> <span class="n">array</span> <span class="ow">is</span> <span class="n">masked</span>
<span class="ow">or</span> <span class="n">matches</span> <span class="n">the</span> <span class="n">NA</span> <span class="n">bitpattern</span><span class="p">,</span> <span class="ow">and</span> <span class="kc">True</span> <span class="n">elsewhere</span>
</pre></div>
</div>
<p>New functions added to the ndarray are:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">arr</span><span class="o">.</span><span class="n">copy</span><span class="p">(</span><span class="o">...</span><span class="p">,</span> <span class="n">replacena</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">NA</span><span class="p">)</span>
<span class="n">Modification</span> <span class="n">to</span> <span class="n">the</span> <span class="n">copy</span> <span class="n">function</span> <span class="n">which</span> <span class="n">replaces</span> <span class="n">NA</span> <span class="n">values</span><span class="p">,</span>
<span class="n">either</span> <span class="n">masked</span> <span class="ow">or</span> <span class="k">with</span> <span class="n">the</span> <span class="n">NA</span> <span class="n">bitpattern</span><span class="p">,</span> <span class="k">with</span> <span class="n">the</span> <span class="s1">'replacena='</span>
<span class="n">parameter</span> <span class="n">supplied</span><span class="o">.</span> <span class="n">When</span> <span class="s1">'replacena'</span> <span class="n">isn</span><span class="s1">'t NA, the copied</span>
<span class="n">array</span> <span class="ow">is</span> <span class="n">unmasked</span> <span class="ow">and</span> <span class="n">has</span> <span class="n">the</span> <span class="s1">'NA'</span> <span class="n">part</span> <span class="n">stripped</span> <span class="kn">from</span><span class="w"> </span><span class="nn">the</span>
<span class="n">parameterized</span> <span class="n">dtype</span> <span class="p">(</span><span class="s1">'NA[f8]'</span> <span class="n">becomes</span> <span class="n">just</span> <span class="s1">'f8'</span><span class="p">)</span><span class="o">.</span>
<span class="n">The</span> <span class="n">default</span> <span class="k">for</span> <span class="n">replacena</span> <span class="ow">is</span> <span class="n">chosen</span> <span class="n">to</span> <span class="n">be</span> <span class="n">np</span><span class="o">.</span><span class="n">NA</span> <span class="n">instead</span> <span class="n">of</span> <span class="kc">None</span><span class="p">,</span>
<span class="n">because</span> <span class="n">it</span> <span class="n">may</span> <span class="n">be</span> <span class="n">desirable</span> <span class="n">to</span> <span class="n">replace</span> <span class="n">NA</span> <span class="k">with</span> <span class="kc">None</span> <span class="ow">in</span> <span class="n">an</span>
<span class="n">NA</span><span class="o">-</span><span class="n">masked</span> <span class="nb">object</span> <span class="n">array</span><span class="o">.</span>
<span class="n">For</span> <span class="n">future</span> <span class="n">multi</span><span class="o">-</span><span class="n">NA</span> <span class="n">support</span><span class="p">,</span> <span class="s1">'replacena'</span> <span class="n">could</span> <span class="n">accept</span> <span class="n">a</span> <span class="n">dictionary</span>
<span class="n">mapping</span> <span class="n">the</span> <span class="n">NA</span> <span class="n">payload</span> <span class="n">to</span> <span class="n">the</span> <span class="n">value</span> <span class="n">to</span> <span class="n">substitute</span> <span class="k">for</span> <span class="n">that</span>
<span class="n">particular</span> <span class="n">NA</span><span class="o">.</span> <span class="n">NAs</span> <span class="k">with</span> <span class="n">payloads</span> <span class="ow">not</span> <span class="n">appearing</span> <span class="ow">in</span> <span class="n">the</span> <span class="n">dictionary</span>
<span class="n">would</span> <span class="n">remain</span> <span class="k">as</span> <span class="n">NA</span> <span class="n">unless</span> <span class="n">a</span> <span class="s1">'default'</span> <span class="n">key</span> <span class="n">was</span> <span class="n">also</span> <span class="n">supplied</span><span class="o">.</span>
<span class="n">Both</span> <span class="n">the</span> <span class="n">parameter</span> <span class="n">to</span> <span class="n">replacena</span> <span class="ow">and</span> <span class="n">the</span> <span class="n">values</span> <span class="ow">in</span> <span class="n">the</span> <span class="n">dictionaries</span>
<span class="n">can</span> <span class="n">be</span> <span class="n">either</span> <span class="n">scalars</span> <span class="ow">or</span> <span class="n">arrays</span> <span class="n">which</span> <span class="n">get</span> <span class="n">broadcast</span> <span class="n">onto</span> <span class="s1">'arr'</span><span class="o">.</span>
<span class="n">arr</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">maskna</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> <span class="p">[</span><span class="n">IMPLEMENTED</span><span class="p">]</span>
<span class="n">This</span> <span class="ow">is</span> <span class="n">a</span> <span class="n">shortcut</span> <span class="k">for</span>
<span class="o">>>></span> <span class="n">a</span> <span class="o">=</span> <span class="n">arr</span><span class="o">.</span><span class="n">view</span><span class="p">()</span>
<span class="o">>>></span> <span class="n">a</span><span class="o">.</span><span class="n">flags</span><span class="o">.</span><span class="n">maskna</span> <span class="o">=</span> <span class="kc">True</span>
<span class="n">arr</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">ownmaskna</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> <span class="p">[</span><span class="n">IMPLEMENTED</span><span class="p">]</span>
<span class="n">This</span> <span class="ow">is</span> <span class="n">a</span> <span class="n">shortcut</span> <span class="k">for</span>
<span class="o">>>></span> <span class="n">a</span> <span class="o">=</span> <span class="n">arr</span><span class="o">.</span><span class="n">view</span><span class="p">()</span>
<span class="o">>>></span> <span class="n">a</span><span class="o">.</span><span class="n">flags</span><span class="o">.</span><span class="n">maskna</span> <span class="o">=</span> <span class="kc">True</span>
<span class="o">>>></span> <span class="n">a</span><span class="o">.</span><span class="n">flags</span><span class="o">.</span><span class="n">ownmaskna</span> <span class="o">=</span> <span class="kc">True</span>
</pre></div>
</div>
</section>
<section id="element-wise-ufuncs-with-missing-values">
<h3><a class="toc-backref" href="#id18" role="doc-backlink">Element-wise ufuncs with missing values</a><a class="headerlink" href="#element-wise-ufuncs-with-missing-values" title="Link to this heading">#</a></h3>
<p>As part of the implementation, ufuncs and other operations will
have to be extended to support masked computation. Because this
is a useful feature in general, even outside the context of
a masked array, in addition to working with masked arrays ufuncs
will take an optional ‘where=’ parameter which allows the use
of boolean arrays to choose where a computation should be done.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">b</span><span class="p">,</span> <span class="n">where</span><span class="o">=</span><span class="p">(</span><span class="n">a</span> <span class="o">></span> <span class="n">threshold</span><span class="p">))</span>
</pre></div>
</div>
<p>A benefit of having this ‘where=’ parameter is that it provides a way
to temporarily treat an object with a mask without ever creating a
masked array object. In the example above, this would only do the
add for the array elements with True in the ‘where’ clause, and neither
‘a’ nor ‘b’ need to be masked arrays.</p>
<p>If the ‘out’ parameter isn’t specified, use of the ‘where=’ parameter
will produce an array with a mask as the result, with missing values
for everywhere the ‘where’ clause had the value False.</p>
<p>For boolean operations, the R project special cases logical_and and
logical_or so that logical_and(NA, False) is False, and
logical_or(NA, True) is True. On the other hand, 0 * NA isn’t 0, but
here the NA could represent Inf or NaN, in which case 0 * the backing
value wouldn’t be 0 anyway.</p>
<p>For NumPy element-wise ufuncs, the design won’t support this ability
for the mask of the output to depend simultaneously on the mask and
the value of the inputs. The NumPy 1.6 nditer, however, makes it
fairly easy to write standalone functions which look and feel just
like ufuncs, but deviate from their behavior. The functions logical_and
and logical_or can be moved into standalone function objects which are
backwards compatible with the current ufuncs.</p>
</section>
<section id="reduction-ufuncs-with-missing-values">
<h3><a class="toc-backref" href="#id19" role="doc-backlink">Reduction ufuncs with missing values</a><a class="headerlink" href="#reduction-ufuncs-with-missing-values" title="Link to this heading">#</a></h3>
<p>Reduction operations like ‘sum’, ‘prod’, ‘min’, and ‘max’ will operate
consistently with the idea that a masked value exists, but its value
is unknown.</p>
<p>An optional parameter ‘skipna=’ will be added to those functions
which can interpret it appropriately to do the operation as if just
the unmasked values existed.</p>
<p>With ‘skipna=True’, when all the input values are masked,
‘sum’ and ‘prod’ will produce the additive and multiplicative identities
respectively, while ‘min’ and ‘max’ will produce masked values.
Statistics operations which require a count, like ‘mean’ and ‘std’
will also use the unmasked value counts for their calculations if
‘skipna=True’, and produce masked values when all the inputs are masked.</p>