importnumpyasnpfromnumpyimportmafrommatplotlibimportscaleasmscalefrommatplotlibimporttransformsasmtransformsfrommatplotlib.tickerimportFixedLocator,FuncFormatterclassMercatorLatitudeScale(mscale.ScaleBase):"""    Scales data in range -pi/2 to pi/2 (-90 to 90 degrees) using    the system used to scale latitudes in a Mercator__ projection.    The scale function:      ln(tan(y) + sec(y))    The inverse scale function:      atan(sinh(y))    Since the Mercator scale tends to infinity at +/- 90 degrees,    there is user-defined threshold, above and below which nothing    will be plotted.  This defaults to +/- 85 degrees.    __ https://en.wikipedia.org/wiki/Mercator_projection    """# The scale class must have a member ``name`` that defines the string used# to select the scale.  For example, ``ax.set_yscale("mercator")`` would be# used to select this scale.name='mercator'def__init__(self,axis,*,thresh=np.deg2rad(85),**kwargs):"""        Any keyword arguments passed to ``set_xscale`` and ``set_yscale`` will        be passed along to the scale's constructor.        thresh: The degree above which to crop the data.        """super().__init__(axis)ifthresh>=np.pi/2:raiseValueError("thresh must be less than pi/2")self.thresh=threshdefget_transform(self):"""        Override this method to return a new instance that does the        actual transformation of the data.        The MercatorLatitudeTransform class is defined below as a        nested class of this one.        """returnself.MercatorLatitudeTransform(self.thresh)defset_default_locators_and_formatters(self,axis):"""        Override to set up the locators and formatters to use with the        scale.  This is only required if the scale requires custom        locators and formatters.  Writing custom locators and        formatters is rather outside the scope of this example, but        there are many helpful examples in :mod:`.ticker`.        In our case, the Mercator example uses a fixed locator from -90 to 90        degrees and a custom formatter to convert the radians to degrees and        put a degree symbol after the value.        """fmt=FuncFormatter(lambdax,pos=None:f"{np.degrees(x):.0f}\N{DEGREE SIGN}")axis.set(major_locator=FixedLocator(np.radians(range(-90,90,10))),major_formatter=fmt,minor_formatter=fmt)deflimit_range_for_scale(self,vmin,vmax,minpos):"""        Override to limit the bounds of the axis to the domain of the        transform.  In the case of Mercator, the bounds should be        limited to the threshold that was passed in.  Unlike the        autoscaling provided by the tick locators, this range limiting        will always be adhered to, whether the axis range is set        manually, determined automatically or changed through panning        and zooming.        """returnmax(vmin,-self.thresh),min(vmax,self.thresh)classMercatorLatitudeTransform(mtransforms.Transform):# There are two value members that must be defined.# ``input_dims`` and ``output_dims`` specify number of input# dimensions and output dimensions to the transformation.# These are used by the transformation framework to do some# error checking and prevent incompatible transformations from# being connected together.  When defining transforms for a# scale, which are, by definition, separable and have only one# dimension, these members should always be set to 1.input_dims=output_dims=1def__init__(self,thresh):mtransforms.Transform.__init__(self)self.thresh=threshdeftransform_non_affine(self,a):"""            This transform takes a numpy array and returns a transformed copy.            Since the range of the Mercator scale is limited by the            user-specified threshold, the input array must be masked to            contain only valid values.  Matplotlib will handle masked arrays            and remove the out-of-range data from the plot.  However, the            returned array *must* have the same shape as the input array, since            these values need to remain synchronized with values in the other            dimension.            """masked=ma.masked_where((a<-self.thresh)|(a>self.thresh),a)ifmasked.mask.any():returnma.log(np.abs(ma.tan(masked)+1/ma.cos(masked)))else:returnnp.log(np.abs(np.tan(a)+1/np.cos(a)))definverted(self):"""            Override this method so Matplotlib knows how to get the            inverse transform for this transform.            """returnMercatorLatitudeScale.InvertedMercatorLatitudeTransform(self.thresh)classInvertedMercatorLatitudeTransform(mtransforms.Transform):input_dims=output_dims=1def__init__(self,thresh):mtransforms.Transform.__init__(self)self.thresh=threshdeftransform_non_affine(self,a):returnnp.arctan(np.sinh(a))definverted(self):returnMercatorLatitudeScale.MercatorLatitudeTransform(self.thresh)# Now that the Scale class has been defined, it must be registered so# that Matplotlib can find it.mscale.register_scale(MercatorLatitudeScale)if__name__=='__main__':importmatplotlib.pyplotaspltt=np.arange(-180.0,180.0,0.1)s=np.radians(t)/2.plt.plot(t,s,'-',lw=2)plt.yscale('mercator')plt.xlabel('Longitude')plt.ylabel('Latitude')plt.title('Mercator projection')plt.grid(True)plt.show()

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