.. _sphx_glr_tutorials_colors_colormapnorms.py: Colormap Normalization ====================== Objects that use colormaps by default linearly map the colors in the colormap from data values *vmin* to *vmax*. For example:: pcm = ax.pcolormesh(x, y, Z, vmin=-1., vmax=1., cmap='RdBu_r') will map the data in *Z* linearly from -1 to +1, so *Z=0* will give a color at the center of the colormap *RdBu_r* (white in this case). 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 :func:matplotlib.colors module. The default, linear normalization is :func:matplotlib.colors.Normalize. Artists that map data to color pass the arguments *vmin* and *vmax* to construct a :func:matplotlib.colors.Normalize instance, then call it: .. ipython:: In [1]: import matplotlib as mpl In [2]: norm = mpl.colors.Normalize(vmin=-1.,vmax=1.) In [3]: norm(0.) Out[3]: 0.5 However, there are sometimes cases where it is useful to map data to colormaps in a non-linear fashion. Logarithmic ----------- 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 :func:colors.LogNorm normalizes the data via :math:log_{10}. In the example below, there are two bumps, one much smaller than the other. Using :func:colors.LogNorm, the shape and location of each bump can clearly be seen: .. code-block:: python import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as colors from matplotlib.mlab import bivariate_normal N = 100 X, Y = np.mgrid[-3:3:complex(0, N), -2:2:complex(0, N)] # A low hump with a spike coming out of the top right. Needs to have # z/colour axis on a log scale so we see both hump and spike. linear # scale only shows the spike. Z1 = bivariate_normal(X, Y, 0.1, 0.2, 1.0, 1.0) + \ 0.1 * bivariate_normal(X, Y, 1.0, 1.0, 0.0, 0.0) fig, ax = plt.subplots(2, 1) pcm = ax[0].pcolor(X, Y, Z1, norm=colors.LogNorm(vmin=Z1.min(), vmax=Z1.max()), cmap='PuBu_r') fig.colorbar(pcm, ax=ax[0], extend='max') pcm = ax[1].pcolor(X, Y, Z1, cmap='PuBu_r') fig.colorbar(pcm, ax=ax[1], extend='max') fig.show() .. image:: /tutorials/colors/images/sphx_glr_colormapnorms_001.png :align: center Symmetric logarithmic --------------------- 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 vmin=-vmax, then they the negative numbers are mapped from 0 to 0.5 and the positive from 0.5 to 1. Since the logarithm of values close to zero tends toward infinity, a small range around zero needs to be mapped linearly. The parameter *linthresh* allows the user to specify the size of this range (-*linthresh*, *linthresh*). The size of this range in the colormap is set by *linscale*. When *linscale* == 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. .. code-block:: python N = 100 X, Y = np.mgrid[-3:3:complex(0, N), -2:2:complex(0, N)] Z1 = (bivariate_normal(X, Y, 1., 1., 1.0, 1.0))**2 \ - 0.4 * (bivariate_normal(X, Y, 1.0, 1.0, -1.0, 0.0))**2 Z1 = Z1/0.03 fig, ax = plt.subplots(2, 1) pcm = ax[0].pcolormesh(X, Y, Z1, norm=colors.SymLogNorm(linthresh=0.03, linscale=0.03, vmin=-1.0, vmax=1.0), cmap='RdBu_r') fig.colorbar(pcm, ax=ax[0], extend='both') pcm = ax[1].pcolormesh(X, Y, Z1, cmap='RdBu_r', vmin=-np.max(Z1)) fig.colorbar(pcm, ax=ax[1], extend='both') fig.show() .. image:: /tutorials/colors/images/sphx_glr_colormapnorms_002.png :align: center Power-law --------- Sometimes it is useful to remap the colors onto a power-law relationship (i.e. :math:y=x^{\gamma}, where :math:\gamma is the power). For this we use the :func:colors.PowerNorm. It takes as an argument *gamma* (*gamma* == 1.0 will just yield the default linear normalization): .. note:: 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. .. code-block:: python N = 100 X, Y = np.mgrid[0:3:complex(0, N), 0:2:complex(0, N)] Z1 = (1 + np.sin(Y * 10.)) * X**(2.) fig, ax = plt.subplots(2, 1) pcm = ax[0].pcolormesh(X, Y, Z1, norm=colors.PowerNorm(gamma=1./2.), cmap='PuBu_r') fig.colorbar(pcm, ax=ax[0], extend='max') pcm = ax[1].pcolormesh(X, Y, Z1, cmap='PuBu_r') fig.colorbar(pcm, ax=ax[1], extend='max') fig.show() .. image:: /tutorials/colors/images/sphx_glr_colormapnorms_003.png :align: center Discrete bounds --------------- Another normaization that comes with matplolib is :func:colors.BoundaryNorm. In addition to *vmin* and *vmax*, this takes as arguments boundaries between which data is to be mapped. The colors are then linearly distributed between these "bounds". For instance: .. ipython:: In [2]: import matplotlib.colors as colors In [3]: bounds = np.array([-0.25, -0.125, 0, 0.5, 1]) In [4]: norm = colors.BoundaryNorm(boundaries=bounds, ncolors=4) In [5]: print(norm([-0.2,-0.15,-0.02, 0.3, 0.8, 0.99])) [0 0 1 2 3 3] Note unlike the other norms, this norm returns values from 0 to *ncolors*-1. .. code-block:: python N = 100 X, Y = np.mgrid[-3:3:complex(0, N), -2:2:complex(0, N)] Z1 = (bivariate_normal(X, Y, 1., 1., 1.0, 1.0))**2 \ - 0.4 * (bivariate_normal(X, Y, 1.0, 1.0, -1.0, 0.0))**2 Z1 = Z1/0.03 fig, ax = plt.subplots(3, 1, figsize=(8, 8)) ax = ax.flatten() # even bounds gives a contour-like effect bounds = np.linspace(-1, 1, 10) norm = colors.BoundaryNorm(boundaries=bounds, ncolors=256) pcm = ax[0].pcolormesh(X, Y, Z1, norm=norm, cmap='RdBu_r') fig.colorbar(pcm, ax=ax[0], extend='both', orientation='vertical') # uneven bounds changes the colormapping: bounds = np.array([-0.25, -0.125, 0, 0.5, 1]) norm = colors.BoundaryNorm(boundaries=bounds, ncolors=256) pcm = ax[1].pcolormesh(X, Y, Z1, norm=norm, cmap='RdBu_r') fig.colorbar(pcm, ax=ax[1], extend='both', orientation='vertical') pcm = ax[2].pcolormesh(X, Y, Z1, cmap='RdBu_r', vmin=-np.max(Z1)) fig.colorbar(pcm, ax=ax[2], extend='both', orientation='vertical') fig.show() .. image:: /tutorials/colors/images/sphx_glr_colormapnorms_004.png :align: center Custom normalization: Two linear ranges --------------------------------------- It is possible to define your own normalization. In the following example, we modify :func:colors:SymLogNorm 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) .. note:: This may appear soon as :func:colors.OffsetNorm. 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. .. code-block:: python N = 100 X, Y = np.mgrid[-3:3:complex(0, N), -2:2:complex(0, N)] Z1 = (bivariate_normal(X, Y, 1., 1., 1.0, 1.0))**2 \ - 0.4 * (bivariate_normal(X, Y, 1.0, 1.0, -1.0, 0.0))**2 Z1 = Z1/0.03 class MidpointNormalize(colors.Normalize): def __init__(self, vmin=None, vmax=None, midpoint=None, clip=False): self.midpoint = midpoint colors.Normalize.__init__(self, vmin, vmax, clip) def __call__(self, value, clip=None): # I'm ignoring masked values and all kinds of edge cases to make a # simple example... x, y = [self.vmin, self.midpoint, self.vmax], [0, 0.5, 1] return np.ma.masked_array(np.interp(value, x, y)) fig, ax = plt.subplots(2, 1) pcm = ax[0].pcolormesh(X, Y, Z1, norm=MidpointNormalize(midpoint=0.), cmap='RdBu_r') fig.colorbar(pcm, ax=ax[0], extend='both') pcm = ax[1].pcolormesh(X, Y, Z1, cmap='RdBu_r', vmin=-np.max(Z1)) fig.colorbar(pcm, ax=ax[1], extend='both') fig.show() .. image:: /tutorials/colors/images/sphx_glr_colormapnorms_005.png :align: center **Total running time of the script:** ( 0 minutes 0.813 seconds) .. only :: html .. container:: sphx-glr-footer .. container:: sphx-glr-download :download:Download Python source code: colormapnorms.py  .. container:: sphx-glr-download :download:Download Jupyter notebook: colormapnorms.ipynb  .. only:: html .. rst-class:: sphx-glr-signature Gallery generated by Sphinx-Gallery _