loglog and semilogx/y#

The logarithmic axis is used so often that there are a sethelper functions, that do the same thing:semilogy,semilogx, andloglog.

fig,axs=plt.subplot_mosaic([['linear','linear-log'],['log-linear','log-log']],layout='constrained')x=np.arange(0,3*np.pi,0.1)y=2*np.sin(x)+3ax=axs['linear']ax.plot(x,y)ax.set_xlabel('linear')ax.set_ylabel('linear')ax.set_title('plot(x, y)')ax=axs['linear-log']ax.semilogy(x,y)ax.set_xlabel('linear')ax.set_ylabel('log')ax.set_title('semilogy(x, y)')ax=axs['log-linear']ax.semilogx(x,y)ax.set_xlabel('log')ax.set_ylabel('linear')ax.set_title('semilogx(x, y)')ax=axs['log-log']ax.loglog(x,y)ax.set_xlabel('log')ax.set_ylabel('log')ax.set_title('loglog(x, y)')

Other built-in scales#

There are other scales that can be used. The list of registeredscales can be returned fromscale.get_scale_names:

print(mscale.get_scale_names())

['asinh', 'function', 'functionlog', 'linear', 'log', 'logit', 'symlog']

fig,axs=plt.subplot_mosaic([['asinh','symlog'],['log','logit']],layout='constrained')x=np.arange(0,1000)forname,axinaxs.items():ifnamein['asinh','symlog']:yy=x-np.mean(x)elifnamein['logit']:yy=(x-np.min(x))yy=yy/np.max(np.abs(yy))else:yy=xax.plot(yy,yy)ax.set_yscale(name)ax.set_title(name)

Optional arguments for scales#

Some of the default scales have optional arguments. These aredocumented in the API reference for the respective scales atscale. One can change the base of the logarithmbeing plotted (eg 2 below) or the linear threshold rangefor'symlog'.

fig,axs=plt.subplot_mosaic([['log','symlog']],layout='constrained',figsize=(6.4,3))forname,axinaxs.items():ifnamein['log']:ax.plot(x,x)ax.set_yscale('log',base=2)ax.set_title('log base=2')else:ax.plot(x-np.mean(x),x-np.mean(x))ax.set_yscale('symlog',linthresh=100)ax.set_title('symlog linthresh=100')

Arbitrary function scales#

Users can define a full scale class and pass that toset_xscaleandset_yscale (seeCustom scale). A short cut for thisis to use the 'function' scale, and pass as extra arguments aforward andaninverse function. The following performs aMercator transform to the y-axis.

# Function Mercator transformdefforward(a):a=np.deg2rad(a)returnnp.rad2deg(np.log(np.abs(np.tan(a)+1.0/np.cos(a))))definverse(a):a=np.deg2rad(a)returnnp.rad2deg(np.arctan(np.sinh(a)))t=np.arange(0,170.0,0.1)s=t/2.fig,ax=plt.subplots(layout='constrained')ax.plot(t,s,'-',lw=2)ax.set_yscale('function',functions=(forward,inverse))ax.set_title('function: Mercator')ax.grid(True)ax.set_xlim(0,180)ax.yaxis.set_minor_formatter(NullFormatter())ax.yaxis.set_major_locator(FixedLocator(np.arange(0,90,10)))

What is a "scale"?#

A scale is an object that gets attached to an axis. The class documentationis atscale.set_xscale andset_yscaleset the scale on the respective Axis objects. You can determine the scaleon an axis withget_scale:

fig,ax=plt.subplots(layout='constrained',figsize=(3.2,3))ax.semilogy(x,x)print(ax.xaxis.get_scale())print(ax.yaxis.get_scale())

linearlog

Setting a scale does three things. First it defines a transform on the axisthat maps between data values to position along the axis. This transform canbe accessed viaget_transform:

print(ax.yaxis.get_transform())

LogTransform(base=10, nonpositive='clip')

Transforms on the axis are a relatively low-level concept, but is one of theimportant roles played byset_scale.

Setting the scale also sets default tick locators (ticker) and tickformatters appropriate for the scale. An axis with a 'log' scale has aLogLocator to pick ticks at decade intervals, and aLogFormatter to use scientific notation on the decades.

print('X axis')print(ax.xaxis.get_major_locator())print(ax.xaxis.get_major_formatter())print('Y axis')print(ax.yaxis.get_major_locator())print(ax.yaxis.get_major_formatter())

X axis<matplotlib.ticker.AutoLocator object at 0x7f49d8a180e0><matplotlib.ticker.ScalarFormatter object at 0x7f49d8a1ab40>Y axis<matplotlib.ticker.LogLocator object at 0x7f49d906f8c0><matplotlib.ticker.LogFormatterSciNotation object at 0x7f49d8ce7c50>

Total running time of the script: (0 minutes 5.469 seconds)

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