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Commit98184f4

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Merge pull request#21178 from rwpenney/feature/asinh-scale
Add asinh axis scaling (*smooth* symmetric logscale)
2 parentsdaaa231 +e43cbfd commit98184f4

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‎doc/api/colors_api.rst‎

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:toctree: _as_gen/
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:template: autosummary.rst
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AsinhNorm
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BoundaryNorm
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Colormap
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CenteredNorm
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New axis scale ``asinh`` (experimental)
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---------------------------------------
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The new ``asinh`` axis scale offers an alternative to ``symlog`` that
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smoothly transitions between the quasi-linear and asymptotically logarithmic
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regions of the scale. This is based on an arcsinh transformation that
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allows plotting both positive and negative values that span many orders
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of magnitude.
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..plot::
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import matplotlib.pyplot as plt
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import numpy as np
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fig, (ax0, ax1) = plt.subplots(1, 2, sharex=True)
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x = np.linspace(-3, 6, 100)
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ax0.plot(x, x)
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ax0.set_yscale('symlog')
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ax0.grid()
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ax0.set_title('symlog')
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ax1.plot(x, x)
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ax1.set_yscale('asinh')
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ax1.grid()
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ax1.set_title(r'$sinh^{-1}$')
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for p in (-2, 2):
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for ax in (ax0, ax1):
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c = plt.Circle((p, p), radius=0.5, fill=False,
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color='red', alpha=0.8, lw=3)
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ax.add_patch(c)
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"""
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==================================
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Colormap NormalizationsSymlognorm
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Colormap NormalizationsSymLogNorm
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==================================
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Demonstration of using norm to map colormaps onto data in non-linear ways.
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.. redirect-from:: /gallery/userdemo/colormap_normalization_symlognorm
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"""
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###############################################################################
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# Synthetic dataset consisting of two humps, one negative and one positive,
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# the positive with 8-times the amplitude.
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# Linearly, the negative hump is almost invisible,
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# and it is very difficult to see any detail of its profile.
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# With the logarithmic scaling applied to both positive and negative values,
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# it is much easier to see the shape of each hump.
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#
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# See `~.colors.SymLogNorm`.
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importnumpyasnp
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importmatplotlib.pyplotasplt
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importmatplotlib.colorsascolors
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"""
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SymLogNorm: two humps, one negative and one positive, The positive
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with 5-times the amplitude. Linearly, you cannot see detail in the
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negative hump. Here we logarithmically scale the positive and
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negative data separately.
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Note that colorbar labels do not come out looking very good.
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"""
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defrbf(x,y):
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return1.0/ (1+5* ((x**2)+ (y**2)))
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N=100
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N=200
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gain=8
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X,Y=np.mgrid[-3:3:complex(0,N),-2:2:complex(0,N)]
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Z1=np.exp(-X**2-Y**2)
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Z2=np.exp(-(X-1)**2- (Y-1)**2)
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Z= (Z1-Z2)*2
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Z1=rbf(X+0.5,Y+0.5)
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Z2=rbf(X-0.5,Y-0.5)
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Z=gain*Z1-Z2
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shadeopts= {'cmap':'PRGn','shading':'gouraud'}
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colormap='PRGn'
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lnrwidth=0.5
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fig,ax=plt.subplots(2,1)
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fig,ax=plt.subplots(2,1,sharex=True,sharey=True)
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pcm=ax[0].pcolormesh(X,Y,Z,
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norm=colors.SymLogNorm(linthresh=0.03,linscale=0.03,
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vmin=-1.0,vmax=1.0,base=10),
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cmap='RdBu_r',shading='nearest')
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norm=colors.SymLogNorm(linthresh=lnrwidth,linscale=1,
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vmin=-gain,vmax=gain,base=10),
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**shadeopts)
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fig.colorbar(pcm,ax=ax[0],extend='both')
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ax[0].text(-2.5,1.5,'symlog')
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pcm=ax[1].pcolormesh(X,Y,Z,cmap='RdBu_r',vmin=-np.max(Z),
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shading='nearest')
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pcm=ax[1].pcolormesh(X,Y,Z,vmin=-gain,vmax=gain,
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**shadeopts)
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fig.colorbar(pcm,ax=ax[1],extend='both')
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ax[1].text(-2.5,1.5,'linear')
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###############################################################################
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# In order to find the best visualization for any particular dataset,
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# it may be necessary to experiment with multiple different color scales.
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# As well as the `~.colors.SymLogNorm` scaling, there is also
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# the option of using `~.colors.AsinhNorm` (experimental), which has a smoother
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# transition between the linear and logarithmic regions of the transformation
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# applied to the data values, "Z".
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# In the plots below, it may be possible to see contour-like artifacts
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# around each hump despite there being no sharp features
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# in the dataset itself. The ``asinh`` scaling shows a smoother shading
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# of each hump.
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fig,ax=plt.subplots(2,1,sharex=True,sharey=True)
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pcm=ax[0].pcolormesh(X,Y,Z,
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norm=colors.SymLogNorm(linthresh=lnrwidth,linscale=1,
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vmin=-gain,vmax=gain,base=10),
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**shadeopts)
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fig.colorbar(pcm,ax=ax[0],extend='both')
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ax[0].text(-2.5,1.5,'symlog')
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pcm=ax[1].pcolormesh(X,Y,Z,
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norm=colors.AsinhNorm(linear_width=lnrwidth,
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vmin=-gain,vmax=gain),
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**shadeopts)
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fig.colorbar(pcm,ax=ax[1],extend='both')
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ax[1].text(-2.5,1.5,'asinh')
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plt.show()

‎examples/scales/asinh_demo.py‎

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"""
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============
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Asinh Demo
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============
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Illustration of the `asinh <.scale.AsinhScale>` axis scaling,
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which uses the transformation
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.. math::
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a\\rightarrow a_0\\sinh^{-1} (a / a_0)
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For coordinate values close to zero (i.e. much smaller than
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the "linear width" :math:`a_0`), this leaves values essentially unchanged:
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.. math::
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a\\rightarrow a + {\\cal O}(a^3)
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but for larger values (i.e. :math:`|a|\\gg a_0`, this is asymptotically
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.. math::
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a\\rightarrow a_0\\, {\\rm sgn}(a)\\ln |a| + {\\cal O}(1)
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As with the `symlog <.scale.SymmetricalLogScale>` scaling,
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this allows one to plot quantities
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that cover a very wide dynamic range that includes both positive
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and negative values. However, ``symlog`` involves a transformation
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that has discontinuities in its gradient because it is built
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from *separate* linear and logarithmic transformations.
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The ``asinh`` scaling uses a transformation that is smooth
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for all (finite) values, which is both mathematically cleaner
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and reduces visual artifacts associated with an abrupt
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transition between linear and logarithmic regions of the plot.
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.. note::
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`.scale.AsinhScale` is experimental, and the API may change.
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See `~.scale.AsinhScale`, `~.scale.SymmetricalLogScale`.
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"""
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importnumpyasnp
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importmatplotlib.pyplotasplt
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# Prepare sample values for variations on y=x graph:
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x=np.linspace(-3,6,500)
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###############################################################################
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# Compare "symlog" and "asinh" behaviour on sample y=x graph,
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# where there is a discontinuous gradient in "symlog" near y=2:
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fig1=plt.figure()
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ax0,ax1=fig1.subplots(1,2,sharex=True)
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ax0.plot(x,x)
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ax0.set_yscale('symlog')
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ax0.grid()
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ax0.set_title('symlog')
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ax1.plot(x,x)
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ax1.set_yscale('asinh')
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ax1.grid()
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ax1.set_title('asinh')
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###############################################################################
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# Compare "asinh" graphs with different scale parameter "linear_width":
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fig2=plt.figure(constrained_layout=True)
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axs=fig2.subplots(1,3,sharex=True)
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forax, (a0,base)inzip(axs, ((0.2,2), (1.0,0), (5.0,10))):
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ax.set_title('linear_width={:.3g}'.format(a0))
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ax.plot(x,x,label='y=x')
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ax.plot(x,10*x,label='y=10x')
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ax.plot(x,100*x,label='y=100x')
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ax.set_yscale('asinh',linear_width=a0,base=base)
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ax.grid()
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ax.legend(loc='best',fontsize='small')
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###############################################################################
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# Compare "symlog" and "asinh" scalings
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# on 2D Cauchy-distributed random numbers,
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# where one may be able to see more subtle artifacts near y=2
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# due to the gradient-discontinuity in "symlog":
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fig3=plt.figure()
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ax=fig3.subplots(1,1)
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r=3*np.tan(np.random.uniform(-np.pi/2.02,np.pi/2.02,
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size=(5000,)))
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th=np.random.uniform(0,2*np.pi,size=r.shape)
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ax.scatter(r*np.cos(th),r*np.sin(th),s=4,alpha=0.5)
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ax.set_xscale('asinh')
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ax.set_yscale('symlog')
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ax.set_xlabel('asinh')
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ax.set_ylabel('symlog')
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ax.set_title('2D Cauchy random deviates')
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ax.set_xlim(-50,50)
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ax.set_ylim(-50,50)
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ax.grid()
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plt.show()
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###############################################################################
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#
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# .. admonition:: References
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#
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# - `matplotlib.scale.AsinhScale`
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# - `matplotlib.ticker.AsinhLocator`
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# - `matplotlib.scale.SymmetricalLogScale`

‎examples/scales/symlog_demo.py‎

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fig.tight_layout()
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plt.show()
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###############################################################################
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# It should be noted that the coordinate transform used by ``symlog``
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# has a discontinuous gradient at the transition between its linear
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# and logarithmic regions. The ``asinh`` axis scale is an alternative
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# technique that may avoid visual artifacts caused by these disconinuities.
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###############################################################################
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#
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# .. admonition:: References
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#
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# - `matplotlib.scale.SymmetricalLogScale`
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# - `matplotlib.ticker.SymmetricalLogLocator`
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# - `matplotlib.scale.AsinhScale`

‎lib/matplotlib/colors.py‎

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self._scale.linthresh=value
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@make_norm_from_scale(
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scale.AsinhScale,
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init=lambdalinear_width=1,vmin=None,vmax=None,clip=False:None)
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classAsinhNorm(Normalize):
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"""
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The inverse hyperbolic sine scale is approximately linear near
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the origin, but becomes logarithmic for larger positive
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or negative values. Unlike the `SymLogNorm`, the transition between
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these linear and logarithmic regions is smooth, which may reduce
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the risk of visual artifacts.
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.. note::
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This API is provisional and may be revised in the future
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based on early user feedback.
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Parameters
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----------
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linear_width : float, default: 1
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The effective width of the linear region, beyond which
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the transformation becomes asymptotically logarithmic
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"""
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@property
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deflinear_width(self):
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returnself._scale.linear_width
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@linear_width.setter
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deflinear_width(self,value):
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self._scale.linear_width=value
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classPowerNorm(Normalize):
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"""
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Linearly map a given value to the 0-1 range and then apply

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