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<div class="section" id="module-colour.algebra.interpolation">
<span id="colour-algebra-interpolation-module"></span><h1>colour.algebra.interpolation Module<a class="headerlink" href="#module-colour.algebra.interpolation" title="Permalink to this headline">¶</a></h1>
<div class="section" id="interpolation">
<h2>Interpolation<a class="headerlink" href="#interpolation" title="Permalink to this headline">¶</a></h2>
<p>Defines classes for interpolating variables.</p>
<ul class="simple">
<li><a class="reference internal" href="#colour.algebra.interpolation.LinearInterpolator1d" title="colour.algebra.interpolation.LinearInterpolator1d"><tt class="xref py py-class docutils literal"><span class="pre">LinearInterpolator1d</span></tt></a>: 1-D function linear interpolation.</li>
<li><a class="reference internal" href="#colour.algebra.interpolation.SpragueInterpolator" title="colour.algebra.interpolation.SpragueInterpolator"><tt class="xref py py-class docutils literal"><span class="pre">SpragueInterpolator</span></tt></a>: 1-D function fifth-order polynomial
interpolation.</li>
</ul>
<dl class="class">
<dt id="colour.algebra.interpolation.LinearInterpolator1d">
<em class="property">class </em><tt class="descclassname">colour.algebra.interpolation.</tt><tt class="descname">LinearInterpolator1d</tt><big>(</big><em>x=None</em>, <em>y=None</em><big>)</big><a class="reference internal" href="_modules/colour/algebra/interpolation.html#LinearInterpolator1d"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#colour.algebra.interpolation.LinearInterpolator1d" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <tt class="xref py py-class docutils literal"><span class="pre">object</span></tt></p>
<p>Linearly interpolates a 1-D function.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>x</strong> (<em>ndarray</em>) – Independent <span class="math">\(x\)</span> variable values corresponding with <span class="math">\(y\)</span>
variable.</li>
<li><strong>y</strong> (<em>ndarray</em>) – Dependent and already known <span class="math">\(y\)</span> variable values to
interpolate.</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="colour.algebra.interpolation.LinearInterpolator1d.__call__">
<tt class="descname">__call__</tt><big>(</big><big>)</big><a class="reference internal" href="_modules/colour/algebra/interpolation.html#LinearInterpolator1d.__call__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#colour.algebra.interpolation.LinearInterpolator1d.__call__" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<p class="rubric">Notes</p>
<p>This class is a wrapper around <em>numpy.interp</em> definition.</p>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><a class="reference internal" href="#colour.algebra.interpolation.SpragueInterpolator" title="colour.algebra.interpolation.SpragueInterpolator"><tt class="xref py py-class docutils literal"><span class="pre">SpragueInterpolator</span></tt></a></p>
</div>
<p class="rubric">Examples</p>
<p>Interpolating a single numeric variable:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">y</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="mf">5.9200</span><span class="p">,</span> <span class="mf">9.3700</span><span class="p">,</span> <span class="mf">10.8135</span><span class="p">,</span> <span class="mf">4.5100</span><span class="p">,</span> <span class="mf">69.5900</span><span class="p">,</span> <span class="mf">27.8007</span><span class="p">,</span> <span class="mf">86.0500</span><span class="p">])</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">arange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">f</span> <span class="o">=</span> <span class="n">LinearInterpolator1d</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="gp">>>> </span><span class="c"># Doctests ellipsis for Python 2.x compatibility.</span>
<span class="gp">>>> </span><span class="n">f</span><span class="p">(</span><span class="mf">0.5</span><span class="p">)</span>
<span class="go">7.64...</span>
</pre></div>
</div>
<p>Interpolating an <em>array_like</em> variable:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">f</span><span class="p">([</span><span class="mf">0.25</span><span class="p">,</span> <span class="mf">0.75</span><span class="p">])</span>
<span class="go">array([ 6.7825, 8.5075])</span>
</pre></div>
</div>
<dl class="method">
<dt>
<tt class="descname">__call__</tt><big>(</big><em>x</em><big>)</big><a class="reference internal" href="_modules/colour/algebra/interpolation.html#LinearInterpolator1d.__call__"><span class="viewcode-link">[source]</span></a></dt>
<dd><p>Evaluates the interpolating polynomial at given point(s).</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>x</strong> (<em>numeric or array_like</em>) – Point(s) to evaluate the interpolant at.</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">Interpolated value(s).</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body">float or ndarray</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="attribute">
<dt id="colour.algebra.interpolation.LinearInterpolator1d.x">
<tt class="descname">x</tt><a class="reference internal" href="_modules/colour/algebra/interpolation.html#LinearInterpolator1d.x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#colour.algebra.interpolation.LinearInterpolator1d.x" title="Permalink to this definition">¶</a></dt>
<dd><p>Property for <strong>self.__x</strong> private attribute.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">self.__x</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body">array_like</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="attribute">
<dt id="colour.algebra.interpolation.LinearInterpolator1d.y">
<tt class="descname">y</tt><a class="reference internal" href="_modules/colour/algebra/interpolation.html#LinearInterpolator1d.y"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#colour.algebra.interpolation.LinearInterpolator1d.y" title="Permalink to this definition">¶</a></dt>
<dd><p>Property for <strong>self.__y</strong> private attribute.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">self.__y</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body">array_like</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="colour.algebra.interpolation.SplineInterpolator">
<em class="property">class </em><tt class="descclassname">colour.algebra.interpolation.</tt><tt class="descname">SplineInterpolator</tt><big>(</big><em>*args</em>, <em>**kwargs</em><big>)</big><a class="reference internal" href="_modules/colour/algebra/interpolation.html#SplineInterpolator"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#colour.algebra.interpolation.SplineInterpolator" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <tt class="xref py py-class docutils literal"><span class="pre">scipy.interpolate.interpolate.interp1d</span></tt></p>
<p>Interpolates a 1-D function using cubic spline interpolation.</p>
<p class="rubric">Notes</p>
<p>This class is a wrapper around <em>scipy.interpolate.interp1d</em> class.</p>
</dd></dl>
<dl class="class">
<dt id="colour.algebra.interpolation.SpragueInterpolator">
<em class="property">class </em><tt class="descclassname">colour.algebra.interpolation.</tt><tt class="descname">SpragueInterpolator</tt><big>(</big><em>x=None</em>, <em>y=None</em><big>)</big><a class="reference internal" href="_modules/colour/algebra/interpolation.html#SpragueInterpolator"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#colour.algebra.interpolation.SpragueInterpolator" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <tt class="xref py py-class docutils literal"><span class="pre">object</span></tt></p>
<p>Constructs a fifth-order polynomial that passes through <span class="math">\(y\)</span> dependent
variable.</p>
<p>Sprague (1880) method is recommended by the <em>CIE</em> for interpolating
functions having a uniformly spaced independent variable.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>x</strong> (<em>array_like</em>) – Independent <span class="math">\(x\)</span> variable values corresponding with <span class="math">\(y\)</span>
variable.</li>
<li><strong>y</strong> (<em>array_like</em>) – Dependent and already known <span class="math">\(y\)</span> variable values to
interpolate.</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="colour.algebra.interpolation.SpragueInterpolator.__call__">
<tt class="descname">__call__</tt><big>(</big><big>)</big><a class="reference internal" href="_modules/colour/algebra/interpolation.html#SpragueInterpolator.__call__"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#colour.algebra.interpolation.SpragueInterpolator.__call__" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><a class="reference internal" href="#colour.algebra.interpolation.LinearInterpolator1d" title="colour.algebra.interpolation.LinearInterpolator1d"><tt class="xref py py-class docutils literal"><span class="pre">LinearInterpolator1d</span></tt></a></p>
</div>
<p class="rubric">Notes</p>
<p>The minimum number <span class="math">\(k\)</span> of data points required along the
interpolation axis is <span class="math">\(k=6\)</span>.</p>
<p class="rubric">References</p>
<table class="docutils footnote" frame="void" id="id1" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[1]</td><td>CIE TC 1-38. (2005). 9.2.4 Method of interpolation for uniformly
spaced independent variable. In CIE 167:2005 Recommended Practice
for Tabulating Spectral Data for Use in Colour Computations
(pp. 1–27). ISBN:978-3-901-90641-1</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id2" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[2]</td><td>Westland, S., Ripamonti, C., & Cheung, V. (2012). Interpolation
Methods. In Computational Colour Science Using MATLAB
(2nd ed., pp. 29–37). ISBN:978-0-470-66569-5</td></tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<p>Interpolating a single numeric variable:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">y</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="mf">5.9200</span><span class="p">,</span> <span class="mf">9.3700</span><span class="p">,</span> <span class="mf">10.8135</span><span class="p">,</span> <span class="mf">4.5100</span><span class="p">,</span> <span class="mf">69.5900</span><span class="p">,</span> <span class="mf">27.8007</span><span class="p">,</span> <span class="mf">86.0500</span><span class="p">])</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">arange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">f</span> <span class="o">=</span> <span class="n">SpragueInterpolator</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">f</span><span class="p">(</span><span class="mf">0.5</span><span class="p">)</span>
<span class="go">7.2185025...</span>
</pre></div>
</div>
<p>Interpolating an <em>array_like</em> variable:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">f</span><span class="p">([</span><span class="mf">0.25</span><span class="p">,</span> <span class="mf">0.75</span><span class="p">])</span>
<span class="go">array([ 6.7295161..., 7.8140625...])</span>
</pre></div>
</div>
<dl class="attribute">
<dt id="colour.algebra.interpolation.SpragueInterpolator.SPRAGUE_C_COEFFICIENTS">
<tt class="descname">SPRAGUE_C_COEFFICIENTS</tt><em class="property"> = array([[ 884, -1960, 3033, -2648, 1080, -180], [ 508, -540, 488, -367, 144, -24], [ -24, 144, -367, 488, -540, 508], [ -180, 1080, -2648, 3033, -1960, 884]])</em><a class="headerlink" href="#colour.algebra.interpolation.SpragueInterpolator.SPRAGUE_C_COEFFICIENTS" title="Permalink to this definition">¶</a></dt>
<dd><p>Defines the coefficients used to generate extra points for boundaries
interpolation.</p>
<p>SPRAGUE_C_COEFFICIENTS : array_like, (4, 6)</p>
<p class="rubric">References</p>
<table class="docutils footnote" frame="void" id="id3" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[3]</td><td>CIE TC 1-38. (2005). Table V. Values of the c-coefficients of
Equ.s 6 and 7. In CIE 167:2005 Recommended Practice for Tabulating
Spectral Data for Use in Colour Computations (p. 19).
ISBN:978-3-901-90641-1</td></tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt>
<tt class="descname">__call__</tt><big>(</big><em>x</em><big>)</big><a class="reference internal" href="_modules/colour/algebra/interpolation.html#SpragueInterpolator.__call__"><span class="viewcode-link">[source]</span></a></dt>
<dd><p>Evaluates the interpolating polynomial at given point(s).</p>
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<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>x</strong> (<em>numeric or array_like</em>) – Point(s) to evaluate the interpolant at.</td>
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<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">Interpolated value(s).</td>
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<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body">numeric or ndarray</td>
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<dt id="colour.algebra.interpolation.SpragueInterpolator.x">
<tt class="descname">x</tt><a class="reference internal" href="_modules/colour/algebra/interpolation.html#SpragueInterpolator.x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#colour.algebra.interpolation.SpragueInterpolator.x" title="Permalink to this definition">¶</a></dt>
<dd><p>Property for <strong>self.__x</strong> private attribute.</p>
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<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">self.__x</td>
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<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body">array_like</td>
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<dl class="attribute">
<dt id="colour.algebra.interpolation.SpragueInterpolator.y">
<tt class="descname">y</tt><a class="reference internal" href="_modules/colour/algebra/interpolation.html#SpragueInterpolator.y"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#colour.algebra.interpolation.SpragueInterpolator.y" title="Permalink to this definition">¶</a></dt>
<dd><p>Property for <strong>self.__y</strong> private attribute.</p>
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<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">self.__y</td>
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<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body">array_like</td>
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</dd></dl>
</dd></dl>
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