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<li><a class="reference internal" href="#">Colormap Normalization</a><ul>
<li><a class="reference internal" href="#logarithmic">Logarithmic</a></li>
<li><a class="reference internal" href="#symmetric-logarithmic">Symmetric logarithmic</a></li>
<li><a class="reference internal" href="#power-law">Power-law</a></li>
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<div class="section" id="colormap-normalization">
<span id="colormapnorm-tutorial"></span><h1>Colormap Normalization<a class="headerlink" href="#colormap-normalization" title="Permalink to this headline">¶</a></h1>
<p>Objects that use colormaps by default linearly map the colors in the
colormap from data values <em>vmin</em> to <em>vmax</em>. For example:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">pcolormesh</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="n">Z</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=-</span><span class="mf">1.</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mf">1.</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'RdBu_r'</span><span class="p">)</span>
</pre></div>
</div>
<p>will map the data in <em>Z</em> linearly from -1 to +1, so <em>Z=0</em> will
give a color at the center of the colormap <em>RdBu_r</em> (white in this
case).</p>
<p>Matplotlib does this mapping in two steps, with a normalization from
[0,1] occurring first, and then mapping onto the indices in the
colormap. Normalizations are classes defined in the
<a class="reference internal" href="../api/colors_api.html#module-matplotlib.colors" title="matplotlib.colors"><code class="xref py py-func docutils literal"><span class="pre">matplotlib.colors()</span></code></a> module. The default, linear normalization is
<a class="reference internal" href="../api/colors_api.html#matplotlib.colors.Normalize" title="matplotlib.colors.Normalize"><code class="xref py py-func docutils literal"><span class="pre">matplotlib.colors.Normalize()</span></code></a>.</p>
<p>Artists that map data to color pass the arguments <em>vmin</em> and <em>vmax</em> to
construct a <a class="reference internal" href="../api/colors_api.html#matplotlib.colors.Normalize" title="matplotlib.colors.Normalize"><code class="xref py py-func docutils literal"><span class="pre">matplotlib.colors.Normalize()</span></code></a> instance, then call it:</p>
<div class="highlight-ipython"><div class="highlight"><pre><span class="gp">In [1]: </span><span class="kn">import</span> <span class="nn">matplotlib</span> <span class="kn">as</span> <span class="nn">mpl</span>
<span class="gp">In [2]: </span><span class="n">norm</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">colors</span><span class="o">.</span><span class="n">Normalize</span><span class="p">(</span><span class="n">vmin</span><span class="o">=-</span><span class="mf">1.</span><span class="p">,</span><span class="n">vmax</span><span class="o">=</span><span class="mf">1.</span><span class="p">)</span>
<span class="gp">In [3]: </span><span class="n">norm</span><span class="p">(</span><span class="mf">0.</span><span class="p">)</span>
<span class="gh">Out[3]: </span><span class="go">0.5</span>
</pre></div>
</div>
<p>However, there are sometimes cases where it is useful to map data to
colormaps in a non-linear fashion.</p>
<div class="section" id="logarithmic">
<h2>Logarithmic<a class="headerlink" href="#logarithmic" title="Permalink to this headline">¶</a></h2>
<p>One of the most common transformations is to plot data by taking
its logarithm (to the base-10). This transformation is useful to
display changes across disparate scales. Using <code class="xref py py-func docutils literal"><span class="pre">colors.LogNorm()</span></code>
normalizes the data via <img src="../_images/mathmpl/math-4f1ee0d2b3.png" style="position: relative; bottom: -7px"/>. In the example below,
there are two bumps, one much smaller than the other. Using
<code class="xref py py-func docutils literal"><span class="pre">colors.LogNorm()</span></code>, the shape and location of each bump can clearly
be seen:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="sd">"""</span>
<span class="sd">Demonstration of using norm to map colormaps onto data in non-linear ways.</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">matplotlib.colors</span> <span class="kn">as</span> <span class="nn">colors</span>
<span class="kn">from</span> <span class="nn">matplotlib.mlab</span> <span class="kn">import</span> <span class="n">bivariate_normal</span>
<span class="sd">'''</span>
<span class="sd">Lognorm: Instead of pcolor log10(Z1) you can have colorbars that have</span>
<span class="sd">the exponential labels using a norm.</span>
<span class="sd">'''</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mgrid</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span> <span class="o">-</span><span class="mi">2</span><span class="p">:</span><span class="mi">2</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">)]</span>
<span class="c1"># A low hump with a spike coming out of the top right. Needs to have</span>
<span class="c1"># z/colour axis on a log scale so we see both hump and spike. linear</span>
<span class="c1"># scale only shows the spike.</span>
<span class="n">Z1</span> <span class="o">=</span> <span class="n">bivariate_normal</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="mf">0.1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">)</span> <span class="o">+</span> \
<span class="mf">0.1</span> <span class="o">*</span> <span class="n">bivariate_normal</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="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">)</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">pcolor</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="n">Z1</span><span class="p">,</span>
<span class="n">norm</span><span class="o">=</span><span class="n">colors</span><span class="o">.</span><span class="n">LogNorm</span><span class="p">(</span><span class="n">vmin</span><span class="o">=</span><span class="n">Z1</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">vmax</span><span class="o">=</span><span class="n">Z1</span><span class="o">.</span><span class="n">max</span><span class="p">()),</span>
<span class="n">cmap</span><span class="o">=</span><span class="s1">'PuBu_r'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">pcm</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'max'</span><span class="p">)</span>
<span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">pcolor</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="n">Z1</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'PuBu_r'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">pcm</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'max'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<p>(<a class="reference external" href="../users/plotting/examples/colormap_normalizations_lognorm.py">Source code</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_lognorm.png">png</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_lognorm.hires.png">hires.png</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_lognorm.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/colormap_normalizations_lognorm.png" src="../_images/colormap_normalizations_lognorm.png" />
</div>
</div>
<div class="section" id="symmetric-logarithmic">
<h2>Symmetric logarithmic<a class="headerlink" href="#symmetric-logarithmic" title="Permalink to this headline">¶</a></h2>
<p>Similarly, it sometimes happens that there is data that is positive
and negative, but we would still like a logarithmic scaling applied to
both. In this case, the negative numbers are also scaled
logarithmically, and mapped to smaller numbers; e.g., if <code class="xref py py-obj docutils literal"><span class="pre">vmin=-vmax</span></code>,
then they the negative numbers are mapped from 0 to 0.5 and the
positive from 0.5 to 1.</p>
<p>Since the logarithm of values close to zero tends toward infinity, a
small range around zero needs to be mapped linearly. The parameter
<em>linthresh</em> allows the user to specify the size of this range
(-<em>linthresh</em>, <em>linthresh</em>). The size of this range in the colormap is
set by <em>linscale</em>. When <em>linscale</em> == 1.0 (the default), the space used
for the positive and negative halves of the linear range will be equal
to one decade in the logarithmic range.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="sd">"""</span>
<span class="sd">Demonstration of using norm to map colormaps onto data in non-linear ways.</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">matplotlib.colors</span> <span class="kn">as</span> <span class="nn">colors</span>
<span class="kn">from</span> <span class="nn">matplotlib.mlab</span> <span class="kn">import</span> <span class="n">bivariate_normal</span>
<span class="sd">"""</span>
<span class="sd">SymLogNorm: two humps, one negative and one positive, The positive</span>
<span class="sd">with 5-times the amplitude. Linearly, you cannot see detail in the</span>
<span class="sd">negative hump. Here we logarithmically scale the positive and</span>
<span class="sd">negative data separately.</span>
<span class="sd">Note that colorbar labels do not come out looking very good.</span>
<span class="sd">"""</span>
<span class="n">N</span><span class="o">=</span><span class="mi">100</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mgrid</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span> <span class="o">-</span><span class="mi">2</span><span class="p">:</span><span class="mi">2</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">)]</span>
<span class="n">Z1</span> <span class="o">=</span> <span class="p">(</span><span class="n">bivariate_normal</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="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span> \
<span class="o">-</span> <span class="mf">0.4</span> <span class="o">*</span> <span class="p">(</span><span class="n">bivariate_normal</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="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span>
<span class="n">Z1</span> <span class="o">=</span> <span class="n">Z1</span><span class="o">/</span><span class="mf">0.03</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</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="n">Z1</span><span class="p">,</span>
<span class="n">norm</span><span class="o">=</span><span class="n">colors</span><span class="o">.</span><span class="n">SymLogNorm</span><span class="p">(</span><span class="n">linthresh</span><span class="o">=</span><span class="mf">0.03</span><span class="p">,</span> <span class="n">linscale</span><span class="o">=</span><span class="mf">0.03</span><span class="p">,</span>
<span class="n">vmin</span><span class="o">=-</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mf">1.0</span><span class="p">),</span>
<span class="n">cmap</span><span class="o">=</span><span class="s1">'RdBu_r'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">pcm</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'both'</span><span class="p">)</span>
<span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</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="n">Z1</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'RdBu_r'</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=-</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">Z1</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">pcm</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'both'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<p>(<a class="reference external" href="../users/plotting/examples/colormap_normalizations_symlognorm.py">Source code</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_symlognorm.png">png</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_symlognorm.hires.png">hires.png</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_symlognorm.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/colormap_normalizations_symlognorm.png" src="../_images/colormap_normalizations_symlognorm.png" />
</div>
</div>
<div class="section" id="power-law">
<h2>Power-law<a class="headerlink" href="#power-law" title="Permalink to this headline">¶</a></h2>
<p>Sometimes it is useful to remap the colors onto a power-law
relationship (i.e. <img src="../_images/mathmpl/math-5ad2665eea.png" style="position: relative; bottom: -7px"/>, where <img src="../_images/mathmpl/math-ae65c1de79.png" style="position: relative; bottom: -7px"/> is the
power). For this we use the <code class="xref py py-func docutils literal"><span class="pre">colors.PowerNorm()</span></code>. It takes as an
argument <em>gamma</em> (<em>gamma</em> == 1.0 will just yield the default linear
normalization):</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">There should probably be a good reason for plotting the data using
this type of transformation. Technical viewers are used to linear
and logarithmic axes and data transformations. Power laws are less
common, and viewers should explicitly be made aware that they have
been used.</p>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="sd">"""</span>
<span class="sd">Demonstration of using norm to map colormaps onto data in non-linear ways.</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">matplotlib.colors</span> <span class="kn">as</span> <span class="nn">colors</span>
<span class="kn">from</span> <span class="nn">matplotlib.mlab</span> <span class="kn">import</span> <span class="n">bivariate_normal</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mgrid</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span> <span class="o">-</span><span class="mi">2</span><span class="p">:</span><span class="mi">2</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">)]</span>
<span class="sd">'''</span>
<span class="sd">PowerNorm: Here a power-law trend in X partially obscures a rectified</span>
<span class="sd">sine wave in Y. We can remove the power law using a PowerNorm.</span>
<span class="sd">'''</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mgrid</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">3</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span> <span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">)]</span>
<span class="n">Z1</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">Y</span> <span class="o">*</span> <span class="mf">10.</span><span class="p">))</span> <span class="o">*</span> <span class="n">X</span><span class="o">**</span><span class="p">(</span><span class="mf">2.</span><span class="p">)</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</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="n">Z1</span><span class="p">,</span> <span class="n">norm</span><span class="o">=</span><span class="n">colors</span><span class="o">.</span><span class="n">PowerNorm</span><span class="p">(</span><span class="n">gamma</span><span class="o">=</span><span class="mf">1.</span><span class="o">/</span><span class="mf">2.</span><span class="p">),</span>
<span class="n">cmap</span><span class="o">=</span><span class="s1">'PuBu_r'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">pcm</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'max'</span><span class="p">)</span>
<span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</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="n">Z1</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'PuBu_r'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">pcm</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'max'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<p>(<a class="reference external" href="../users/plotting/examples/colormap_normalizations_power.py">Source code</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_power.png">png</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_power.hires.png">hires.png</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_power.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/colormap_normalizations_power.png" src="../_images/colormap_normalizations_power.png" />
</div>
</div>
<div class="section" id="discrete-bounds">
<h2>Discrete bounds<a class="headerlink" href="#discrete-bounds" title="Permalink to this headline">¶</a></h2>
<p>Another normaization that comes with matplolib is
<code class="xref py py-func docutils literal"><span class="pre">colors.BoundaryNorm()</span></code>. In addition to <em>vmin</em> and <em>vmax</em>, this
takes as arguments boundaries between which data is to be mapped. The
colors are then linearly distributed between these “bounds”. For
instance:</p>
<div class="highlight-ipython"><div class="highlight"><pre><span class="gp">In [4]: </span><span class="kn">import</span> <span class="nn">matplotlib.colors</span> <span class="kn">as</span> <span class="nn">colors</span>
<span class="gp">In [5]: </span><span class="n">bounds</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="o">-</span><span class="mf">0.25</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.125</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="gp">In [6]: </span><span class="n">norm</span> <span class="o">=</span> <span class="n">colors</span><span class="o">.</span><span class="n">BoundaryNorm</span><span class="p">(</span><span class="n">boundaries</span><span class="o">=</span><span class="n">bounds</span><span class="p">,</span> <span class="n">ncolors</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
<span class="gp">In [7]: </span><span class="k">print</span><span class="p">(</span><span class="n">norm</span><span class="p">([</span><span class="o">-</span><span class="mf">0.2</span><span class="p">,</span><span class="o">-</span><span class="mf">0.15</span><span class="p">,</span><span class="o">-</span><span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">,</span> <span class="mf">0.99</span><span class="p">]))</span>
<span class="go">[0 0 1 2 3 3]</span>
</pre></div>
</div>
<p>Note unlike the other norms, this norm returns values from 0 to <em>ncolors</em>-1.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="sd">"""</span>
<span class="sd">Demonstration of using norm to map colormaps onto data in non-linear ways.</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">matplotlib.colors</span> <span class="kn">as</span> <span class="nn">colors</span>
<span class="kn">from</span> <span class="nn">matplotlib.mlab</span> <span class="kn">import</span> <span class="n">bivariate_normal</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mgrid</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span> <span class="o">-</span><span class="mi">2</span><span class="p">:</span><span class="mi">2</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">)]</span>
<span class="n">Z1</span> <span class="o">=</span> <span class="p">(</span><span class="n">bivariate_normal</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="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span> \
<span class="o">-</span> <span class="mf">0.4</span> <span class="o">*</span> <span class="p">(</span><span class="n">bivariate_normal</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="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span>
<span class="n">Z1</span> <span class="o">=</span> <span class="n">Z1</span><span class="o">/</span><span class="mf">0.03</span>
<span class="sd">'''</span>
<span class="sd">BoundaryNorm: For this one you provide the boundaries for your colors,</span>
<span class="sd">and the Norm puts the first color in between the first pair, the</span>
<span class="sd">second color between the second pair, etc.</span>
<span class="sd">'''</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
<span class="c1"># even bounds gives a contour-like effect</span>
<span class="n">bounds</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="n">norm</span> <span class="o">=</span> <span class="n">colors</span><span class="o">.</span><span class="n">BoundaryNorm</span><span class="p">(</span><span class="n">boundaries</span><span class="o">=</span><span class="n">bounds</span><span class="p">,</span> <span class="n">ncolors</span><span class="o">=</span><span class="mi">256</span><span class="p">)</span>
<span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</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="n">Z1</span><span class="p">,</span>
<span class="n">norm</span><span class="o">=</span><span class="n">norm</span><span class="p">,</span>
<span class="n">cmap</span><span class="o">=</span><span class="s1">'RdBu_r'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">pcm</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'both'</span><span class="p">,</span> <span class="n">orientation</span><span class="o">=</span><span class="s1">'vertical'</span><span class="p">)</span>
<span class="c1"># uneven bounds changes the colormapping:</span>
<span class="n">bounds</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="o">-</span><span class="mf">0.25</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.125</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="n">norm</span> <span class="o">=</span> <span class="n">colors</span><span class="o">.</span><span class="n">BoundaryNorm</span><span class="p">(</span><span class="n">boundaries</span><span class="o">=</span><span class="n">bounds</span><span class="p">,</span> <span class="n">ncolors</span><span class="o">=</span><span class="mi">256</span><span class="p">)</span>
<span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</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="n">Z1</span><span class="p">,</span> <span class="n">norm</span><span class="o">=</span><span class="n">norm</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'RdBu_r'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">pcm</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'both'</span><span class="p">,</span> <span class="n">orientation</span><span class="o">=</span><span class="s1">'vertical'</span><span class="p">)</span>
<span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</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="n">Z1</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'RdBu_r'</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=-</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">Z1</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">pcm</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'both'</span><span class="p">,</span> <span class="n">orientation</span><span class="o">=</span><span class="s1">'vertical'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<p>(<a class="reference external" href="../users/plotting/examples/colormap_normalizations_bounds.py">Source code</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_bounds.png">png</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_bounds.hires.png">hires.png</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_bounds.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/colormap_normalizations_bounds.png" src="../_images/colormap_normalizations_bounds.png" />
</div>
</div>
<div class="section" id="custom-normalization-two-linear-ranges">
<h2>Custom normalization: Two linear ranges<a class="headerlink" href="#custom-normalization-two-linear-ranges" title="Permalink to this headline">¶</a></h2>
<p>It is possible to define your own normalization. In the following
example, we modify <code class="xref py py-func docutils literal"><span class="pre">colors:SymLogNorm()</span></code> to use different linear
maps for the negative data values and the positive. (Note that this
example is simple, and does not validate inputs or account for complex
cases such as masked data)</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p>This may appear soon as <code class="xref py py-func docutils literal"><span class="pre">colors.OffsetNorm()</span></code>.</p>
<p class="last">As above, non-symmetric mapping of data to color is non-standard
practice for quantitative data, and should only be used advisedly. A
practical example is having an ocean/land colormap where the land and
ocean data span different ranges.</p>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="sd">"""</span>
<span class="sd">Demonstration of using norm to map colormaps onto data in non-linear ways.</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">matplotlib.colors</span> <span class="kn">as</span> <span class="nn">colors</span>
<span class="kn">from</span> <span class="nn">matplotlib.mlab</span> <span class="kn">import</span> <span class="n">bivariate_normal</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">100</span>
<span class="sd">'''</span>
<span class="sd">Custom Norm: An example with a customized normalization. This one</span>
<span class="sd">uses the example above, and normalizes the negative data differently</span>
<span class="sd">from the positive.</span>
<span class="sd">'''</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mgrid</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span> <span class="o">-</span><span class="mi">2</span><span class="p">:</span><span class="mi">2</span><span class="p">:</span><span class="nb">complex</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">)]</span>
<span class="n">Z1</span> <span class="o">=</span> <span class="p">(</span><span class="n">bivariate_normal</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="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span> \
<span class="o">-</span> <span class="mf">0.4</span> <span class="o">*</span> <span class="p">(</span><span class="n">bivariate_normal</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="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span>
<span class="n">Z1</span> <span class="o">=</span> <span class="n">Z1</span><span class="o">/</span><span class="mf">0.03</span>
<span class="c1"># Example of making your own norm. Also see matplotlib.colors.</span>
<span class="c1"># From Joe Kington: This one gives two different linear ramps:</span>
<span class="k">class</span> <span class="nc">MidpointNormalize</span><span class="p">(</span><span class="n">colors</span><span class="o">.</span><span class="n">Normalize</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">midpoint</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">clip</span><span class="o">=</span><span class="bp">False</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">midpoint</span> <span class="o">=</span> <span class="n">midpoint</span>
<span class="n">colors</span><span class="o">.</span><span class="n">Normalize</span><span class="o">.</span><span class="n">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vmin</span><span class="p">,</span> <span class="n">vmax</span><span class="p">,</span> <span class="n">clip</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">,</span> <span class="n">clip</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="c1"># I'm ignoring masked values and all kinds of edge cases to make a</span>
<span class="c1"># simple example...</span>
<span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">vmin</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">midpoint</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">vmax</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">ma</span><span class="o">.</span><span class="n">masked_array</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">value</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="c1">#####</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</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="n">Z1</span><span class="p">,</span>
<span class="n">norm</span><span class="o">=</span><span class="n">MidpointNormalize</span><span class="p">(</span><span class="n">midpoint</span><span class="o">=</span><span class="mf">0.</span><span class="p">),</span>
<span class="n">cmap</span><span class="o">=</span><span class="s1">'RdBu_r'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">pcm</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'both'</span><span class="p">)</span>
<span class="n">pcm</span> <span class="o">=</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</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="n">Z1</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'RdBu_r'</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=-</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">Z1</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">pcm</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'both'</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<p>(<a class="reference external" href="../users/plotting/examples/colormap_normalizations_custom.py">Source code</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_custom.png">png</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_custom.hires.png">hires.png</a>, <a class="reference external" href="../users/plotting/examples/colormap_normalizations_custom.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../_images/colormap_normalizations_custom.png" src="../_images/colormap_normalizations_custom.png" />
</div>
</div>
</div>
</div>
</div>
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