# Custom scale Matplotlib

Custom scale

Create a custom scale, by implementing the scaling use for latitude data in a Mercator Projection.

from __future__ import unicode_literals

import numpy as np

from numpy import ma

from matplotlib import scale as mscale

from matplotlib import transforms as mtransforms

from matplotlib.ticker import Formatter, FixedLocator

from matplotlib import rcParams

# BUG: this example fails with any other setting of axisbelow

rcParams[‘axes.axisbelow’] = False

class MercatorLatitudeScale(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.

source:

http://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,

# “gca().set_yscale(“mercator”)“ would be used to select this

# scale.

name = ‘mercator’

def __init__(self, axis, **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.

“””

mscale.ScaleBase.__init__(self)

thresh = kwargs.pop(“thresh”, np.radians(85))

if thresh >= np.pi / 2.0:

raise ValueError(“thresh must be less than pi/2”)

self.thresh = thresh

def get_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.

“””

return self.MercatorLatitudeTransform(self.thresh)

def set_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 “ticker.py“.

In our case, the Mercator example uses a fixed locator from

-90 to 90 degrees and a custom formatter class to put convert

the radians to degrees and put a degree symbol after the

value::

“””

class DegreeFormatter(Formatter):

def __call__(self, x, pos=None):

return “%d\N{DEGREE SIGN}” % np.degrees(x)

axis.set_major_locator(FixedLocator(

np.radians(np.arange(-90, 90, 10))))

axis.set_major_formatter(DegreeFormatter())

axis.set_minor_formatter(DegreeFormatter())

def limit_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.

“””

return max(vmin, -self.thresh), min(vmax, self.thresh)

class MercatorLatitudeTransform(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 = 1

output_dims = 1

is_separable = True

has_inverse = True

def __init__(self, thresh):

mtransforms.Transform.__init__(self)

self.thresh = thresh

def transform_non_affine(self, a):

“””

This transform takes an Nx1 “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. Importantly, the

“transform“ method *must* return an array that is 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)

if masked.mask.any():

return ma.log(np.abs(ma.tan(masked) + 1.0 / ma.cos(masked)))

else:

return np.log(np.abs(np.tan(a) + 1.0 / np.cos(a)))

def inverted(self):

“””

Override this method so matplotlib knows how to get the

inverse transform for this transform.

“””

return MercatorLatitudeScale.InvertedMercatorLatitudeTransform(

self.thresh)

class InvertedMercatorLatitudeTransform(mtransforms.Transform):

input_dims = 1

output_dims = 1

is_separable = True

has_inverse = True

def __init__(self, thresh):

mtransforms.Transform.__init__(self)

self.thresh = thresh

def transform_non_affine(self, a):

return np.arctan(np.sinh(a))

def inverted(self):

return MercatorLatitudeScale.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__’:

import matplotlib.pyplot as plt

t = np.arange(-180.0, 180.0, 0.1)

s = np.radians(t)/2.

plt.plot(t, s, ‘-‘, lw=2)

plt.gca().set_yscale(‘mercator’)

plt.xlabel(‘Longitude’)

plt.ylabel(‘Latitude’)

plt.title(‘Mercator: Projection of the Oppressor’)

plt.grid(True)

plt.show()