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# Colormap Normalizations

Demonstration of using norm to map colormaps onto data in non-linear ways.

    import numpy as np
    import matplotlib.pyplot as plt
    import matplotlib.colors as colors
    from matplotlib.mlab import bivariate_normal

    '''
    Lognorm: Instead of pcolor log10(Z1) you can have colorbars that have
    the exponential labels using a norm.
    '''
    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')

    '''
    PowerNorm: Here a power-law trend in X partially obscures a rectified
    sine wave in Y. We can remove the power law using a PowerNorm.
    '''
    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')

    '''
    SymLogNorm: two humps, one negative and one positive, The positive
    with 5-times the amplitude. Linearly, you cannot see detail in the
    negative hump.  Here we logarithmically scale the positive and
    negative data separately.

    Note that colorbar labels do not come out looking very good.
    '''

    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')

    '''
    Custom Norm: An example with a customized normalization.  This one
    uses the example above, and normalizes the negative data differently
    from the positive.
    '''
    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

    # Example of making your own norm.  Also see matplotlib.colors.
    # From Joe Kington: This one gives two different linear ramps:

    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')

    '''
    BoundaryNorm: For this one you provide the boundaries for your colors,
    and the Norm puts the first color in between the first pair, the
    second color between the second pair, etc.
    '''

    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')

    plt.show()

Total running time of the script: ( 0 minutes 1.079 seconds)

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