Logit scale

matplotlib · efiring · Mar 3, 2015 · Nov 3, 2014 · Mar 3, 2015 · Mar 2, 2015
commit 76840ea91d4d8a6e09b4fa1ad6fd36b2b179971e
diff --git a/doc/conf.py b/doc/conf.py
@@ -126,6 +126,7 @@
     ('color', 'Color'),
     ('text_labels_and_annotations', 'Text, labels, and annotations'),
     ('ticks_and_spines', 'Ticks and spines'),
+    ('scales', 'Axis scales'),
     ('subplots_axes_and_figures', 'Subplots, axes, and figures'),
     ('style_sheets', 'Style sheets'),
     ('specialty_plots', 'Specialty plots'),

diff --git a/doc/pyplots/pyplot_scales.py b/doc/pyplots/pyplot_scales.py
@@ -0,0 +1,43 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+# make up some data in the interval ]0, 1[
+y = np.random.normal(loc=0.5, scale=0.4, size=1000)
+y = y[(y > 0) & (y < 1)]
+y.sort()
+x = np.arange(len(y))
+
+# plot with various axes scales
+plt.figure(1)
+
+# linear
+plt.subplot(221)
+plt.plot(x, y)
+plt.yscale('linear')
+plt.title('linear')
+plt.grid(True)
+
+
+# log
+plt.subplot(222)
+plt.plot(x, y)
+plt.yscale('log')
+plt.title('log')
+plt.grid(True)
+
+
+# symmetric log
+plt.subplot(223)
+plt.plot(x, y - y.mean())
+plt.yscale('symlog', linthreshy=0.05)
+plt.title('symlog')
+plt.grid(True)
+
+# logit
+plt.subplot(223)
+plt.plot(x, y)
+plt.yscale('logit')
+plt.title('logit')
+plt.grid(True)
+
+plt.show()
diff --git a/doc/users/pyplot_tutorial.rst b/doc/users/pyplot_tutorial.rst
@@ -280,3 +280,22 @@ variety of other coordinate systems one can choose -- see
 :ref:`annotations-tutorial` and :ref:`plotting-guide-annotation` for
 details.  More examples can be found in
 :ref:`pylab_examples-annotation_demo`.
+
+
+Logarithmic and other nonlinear axis
+====================================
+
+:mod:`matplotlib.pyplot` supports not only linear axis scales, but also
+logarithmic and logit scales. This is commonly used if data spans many orders
+of magnitude. Changing the scale of an axis is easy:
+
+    plt.xscale('log')
+
+An example of four plots with the same data and different scales for the y axis
+is shown below.
+
+.. plot:: pyplots/pyplot_scales.py
+   :include-source:
+
+It is also possible to add your own scale, see :ref:`adding-new-scales` for
+details.
diff --git a/doc/users/whats_new/updated_scale.rst b/doc/users/whats_new/updated_scale.rst
@@ -0,0 +1,4 @@
+Logit Scale
+-----------
+Added support for the 'logit' axis scale, a nonlinear transformation
+`x -> log10(x / (1-x))` for data between 0 and 1 excluded.
diff --git a/examples/scales/scales.py b/examples/scales/scales.py
@@ -0,0 +1,47 @@
+"""
+Illustrate the scale transformations applied to axes, e.g. log, symlog, logit.
+"""
+import numpy as np
+import matplotlib.pyplot as plt
+
+# make up some data in the interval ]0, 1[
+y = np.random.normal(loc=0.5, scale=0.4, size=1000)
+y = y[(y > 0) & (y < 1)]
+y.sort()
+x = np.arange(len(y))
+
+# plot with various axes scales
+fig, axs = plt.subplots(2, 2)
+
+# linear
+ax = axs[0, 0]
+ax.plot(x, y)
+ax.set_yscale('linear')
+ax.set_title('linear')
+ax.grid(True)
+
+
+# log
+ax = axs[0, 1]
+ax.plot(x, y)
+ax.set_yscale('log')
+ax.set_title('log')
+ax.grid(True)
+
+
+# symmetric log
+ax = axs[1, 0]
+ax.plot(x, y - y.mean())
+ax.set_yscale('symlog', linthreshy=0.05)
+ax.set_title('symlog')
+ax.grid(True)
+
+# logit
+ax = axs[1, 1]
+ax.plot(x, y)
+ax.set_yscale('logit')
+ax.set_title('logit')
+ax.grid(True)
+
+
+plt.show()
diff --git a/lib/matplotlib/scale.py b/lib/matplotlib/scale.py
@@ -8,9 +8,9 @@
 
 from matplotlib.cbook import dedent
 from matplotlib.ticker import (NullFormatter, ScalarFormatter,
-                               LogFormatterMathtext)
+                               LogFormatterMathtext, LogitFormatter)
 from matplotlib.ticker import (NullLocator, LogLocator, AutoLocator,
-                               SymmetricalLogLocator)
+                               SymmetricalLogLocator, LogitLocator)
 from matplotlib.transforms import Transform, IdentityTransform
 from matplotlib import docstring
 
@@ -478,10 +478,111 @@ def get_transform(self):
         return self._transform
 
 
+def _mask_non_logit(a):
+    """
+    Return a Numpy masked array where all values outside ]0, 1[ are
+    masked. If all values are inside ]0, 1[, the original array is
+    returned.
+    """
+    a = a.copy()
+    mask = (a <= 0.0) | (a >= 1.0)
+    a[mask] = np.nan
+    return a
+
+
+def _clip_non_logit(a):
+    a = a.copy()
+    a[a <= 0.0] = 1e-300
+    a[a >= 1.0] = 1 - 1e-300
+    return a
+
+
+class LogitTransform(Transform):
+    input_dims = 1
+    output_dims = 1
+    is_separable = True
+    has_inverse = True
+
+    def __init__(self, nonpos):
+        Transform.__init__(self)
+        if nonpos == 'mask':
+            self._handle_nonpos = _mask_non_logit
+        else:
+            self._handle_nonpos = _clip_non_logit
+        self._nonpos = nonpos
+
+    def transform_non_affine(self, a):
+        """logit transform (base 10), masked or clipped"""
+        a = self._handle_nonpos(a)
+        if isinstance(a, ma.MaskedArray):
+            return ma.log10(1.0 * a / (1.0 - a))
+        return np.log10(1.0 * a / (1.0 - a))
+
+    def inverted(self):
+        return LogisticTransform(self._nonpos)
+
+
+class LogisticTransform(Transform):
+    input_dims = 1
+    output_dims = 1
+    is_separable = True
+    has_inverse = True
+
+    def __init__(self, nonpos='mask'):
+        Transform.__init__(self)
+        self._nonpos = nonpos
+
+    def transform_non_affine(self, a):
+        """logistic transform (base 10)"""
+        return 1.0 / (1 + 10**(-a))
+
+    def inverted(self):
+        return LogitTransform(self._nonpos)
+
+
+class LogitScale(ScaleBase):
+    """
+    Logit scale for data between zero and one, both excluded.
+
+    This scale is similar to a log scale close to zero and to one, and almost
+    linear around 0.5. It maps the interval ]0, 1[ onto ]-infty, +infty[.
+    """
+    name = 'logit'
+
+    def __init__(self, axis, nonpos='mask'):
+        """
+        *nonpos*: ['mask' | 'clip' ]
+          values beyond ]0, 1[ can be masked as invalid, or clipped to a number
+          very close to 0 or 1
+        """
+        if nonpos not in ['mask', 'clip']:
+            raise ValueError("nonposx, nonposy kwarg must be 'mask' or 'clip'")
+
+        self._transform = LogitTransform(nonpos)
+
+    def get_transform(self):
+        """
+        Return a :class:`LogitTransform` instance.
+        """
+        return self._transform
+
+    def set_default_locators_and_formatters(self, axis):
+        # ..., 0.01, 0.1, 0.5, 0.9, 0.99, ...
+        axis.set_major_locator(LogitLocator())
+        axis.set_major_formatter(LogitFormatter())
+        axis.set_minor_locator(LogitLocator(minor=True))
+        axis.set_minor_formatter(LogitFormatter())
+
+    def limit_range_for_scale(self, vmin, vmax, minpos):
+        return (vmin <= 0 and minpos or vmin,
+                vmax >= 1 and (1 - minpos) or vmax)
+
+
 _scale_mapping = {
     'linear': LinearScale,
     'log':    LogScale,
-    'symlog': SymmetricalLogScale
+    'symlog': SymmetricalLogScale,
+    'logit':  LogitScale,
     }
 
 

diff --git a/lib/matplotlib/tests/baseline_images/test_scale/logit_scales.png b/lib/matplotlib/tests/baseline_images/test_scale/logit_scales.png
diff --git a/lib/matplotlib/tests/test_scale.py b/lib/matplotlib/tests/test_scale.py
@@ -14,6 +14,20 @@ def test_log_scales():
     ax.axhline(24.1)
 
 
+@image_comparison(baseline_images=['logit_scales'], remove_text=True,
+                  extensions=['png'])
+def test_logit_scales():
+    ax = plt.subplot(111, xscale='logit')
+
+    # Typical exctinction curve for logit
+    x = np.array([0.001, 0.003, 0.01, 0.03, 0.1, 0.2, 0.3, 0.4, 0.5,
+                  0.6, 0.7, 0.8, 0.9, 0.97, 0.99, 0.997, 0.999])
+    y = 1.0 / x
+
+    ax.plot(x, y)
+    ax.grid(True)
+
+
 @cleanup
 def test_log_scatter():
     """Issue #1799"""

diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
@@ -807,6 +807,26 @@ def __call__(self, x, pos=None):
                                                          nearest_long(fx))
 
 
+class LogitFormatter(Formatter):
+    '''Probability formatter (using Math text)'''
+    def __call__(self, x, pos=None):
+        s = ''
+        if 0.01 <= x <= 0.99:
+            if x in [.01, 0.1, 0.5, 0.9, 0.99]:
+                s = '{:.2f}'.format(x)
+        elif x < 0.01:
+            if is_decade(x):
+                s = '$10^{%.0f}$' % np.log10(x)
+        elif x > 0.99:
+            if is_decade(1-x):
+                s = '$1-10^{%.0f}$' % np.log10(1-x)
+        return s
+
+    def format_data_short(self, value):
+        'return a short formatted string representation of a number'
+        return '%-12g' % value
+
+
 class EngFormatter(Formatter):
     """
     Formats axis values using engineering prefixes to represent powers of 1000,
@@ -1694,6 +1714,88 @@ def view_limits(self, vmin, vmax):
         return result
 
 
+class LogitLocator(Locator):
+    """
+    Determine the tick locations for logit axes
+    """
+
+    def __init__(self, minor=False):
+        """
+        place ticks on the logit locations
+        """
+        self.minor = minor
+
+    def __call__(self):
+        'Return the locations of the ticks'
+        vmin, vmax = self.axis.get_view_interval()
+        return self.tick_values(vmin, vmax)
+
+    def tick_values(self, vmin, vmax):
+        # dummy axis has no axes attribute
+        if hasattr(self.axis, 'axes') and self.axis.axes.name == 'polar':
+            raise NotImplementedError('Polar axis cannot be logit scaled yet')
+
+        # what to do if a window beyond ]0, 1[ is chosen
+        if vmin <= 0.0:
+            if self.axis is not None:
+                vmin = self.axis.get_minpos()
+
+            if (vmin <= 0.0) or (not np.isfinite(vmin)):
+                raise ValueError(
+                    "Data has no values in ]0, 1[ and therefore can not be "
+                    "logit-scaled.")
+
+        # NOTE: for vmax, we should query a property similar to get_minpos, but
+        # related to the maximal, less-than-one data point. Unfortunately,
+        # get_minpos is defined very deep in the BBox and updated with data,
+        # so for now we use the trick below.
+        if vmax >= 1.0:
+            if self.axis is not None:
+                vmax = 1 - self.axis.get_minpos()
+
+            if (vmax >= 1.0) or (not np.isfinite(vmax)):
+                raise ValueError(
+                    "Data has no values in ]0, 1[ and therefore can not be "
+                    "logit-scaled.")
+
+        if vmax < vmin:
+            vmin, vmax = vmax, vmin
+
+        vmin = np.log10(vmin / (1 - vmin))
+        vmax = np.log10(vmax / (1 - vmax))
+
+        decade_min = np.floor(vmin)
+        decade_max = np.ceil(vmax)
+
+        # major ticks
+        if not self.minor:
+            ticklocs = []
+            if (decade_min <= -1):
+                expo = np.arange(decade_min, min(0, decade_max + 1))
+                ticklocs.extend(list(10**expo))
+            if (decade_min <= 0) and (decade_max >= 0):
+                ticklocs.append(0.5)
+            if (decade_max >= 1):
+                expo = -np.arange(max(1, decade_min), decade_max + 1)
+                ticklocs.extend(list(1 - 10**expo))
+
+        # minor ticks
+        else:
+            ticklocs = []
+            if (decade_min <= -2):
+                expo = np.arange(decade_min, min(-1, decade_max))
+                newticks = np.outer(np.arange(2, 10), 10**expo).ravel()
+                ticklocs.extend(list(newticks))
+            if (decade_min <= 0) and (decade_max >= 0):
+                ticklocs.extend([0.2, 0.3, 0.4, 0.6, 0.7, 0.8])
+            if (decade_max >= 2):
+                expo = -np.arange(max(2, decade_min), decade_max + 1)
+                newticks = 1 - np.outer(np.arange(2, 10), 10**expo).ravel()
+                ticklocs.extend(list(newticks))
+
+        return self.raise_if_exceeds(np.array(ticklocs))
+
+
 class AutoLocator(MaxNLocator):
     def __init__(self):
         MaxNLocator.__init__(self, nbins=9, steps=[1, 2, 5, 10])