# Source code for bob.measure.plot

```#!/usr/bin/env python
# vim: set fileencoding=utf-8 :
# Mon 23 May 2011 14:36:14 CEST
import numpy
import warnings

[docs]def log_values(min_step=-4, counts_per_step=4):
"""Computes log-scaled values between :math:`10^{M}` and 1

This function computes log-scaled values between :math:`10^{M}` and 1
(including), where :math:`M` is the ``min_ste`` argument, which needs to be a
negative integer.  The integral ``counts_per_step`` value defines how many
values between two adjacent powers of 10 will be created.  The total number
of values will be ``-min_step * counts_per_step + 1``.

Parameters:

min_step (:py:class:`int`, optional): The power of 10 that will be the
minimum value.  E.g., the default ``-4`` will result in the first number
to be :math:`10^{-4}` = ``0.00001`` or ``0.01%``

counts_per_step (:py:class:`int`, optional): The number of values that will
be put between two adjacent powers of 10.  With the default value ``4``
(and default values of ``min_step``), we will get ``log_list ==
1e-4``, ``log_list == 1e-3``, ..., ``log_list == 1``.

Returns:

:py:class:`list`: A list of logarithmically scaled values between
:math:`10^{M}` and 1.

"""

import math
return [math.pow(10., i * 1. / counts_per_step) for i in range(min_step * counts_per_step, 0)] + [1.]

def _semilogx(x, y, **kwargs):
# remove points were x is 0
x, y = numpy.asarray(x), numpy.asarray(y)
zero_index = x == 0
x = x[~zero_index]
y = y[~zero_index]
from matplotlib import pyplot
return pyplot.semilogx(x, y, **kwargs)

[docs]def roc(negatives, positives, npoints=2000, CAR=None, min_far=-8, tpr=False, semilogx=False, **kwargs):
"""Plots Receiver Operating Characteristic (ROC) curve.

This method will call ``matplotlib`` to plot the ROC curve for a system which
contains a particular set of negatives (impostors) and positives (clients)
scores. We use the standard :py:func:`matplotlib.pyplot.plot` command. All
parameters passed with exception of the three first parameters of this method
will be directly passed to the plot command.

The plot will represent the false-alarm on the horizontal axis and the
false-rejection on the vertical axis.  The values for the axis will be
computed using :py:func:`bob.measure.roc`.

.. note::

This function does not initiate and save the figure instance, it only
issues the plotting command. You are the responsible for setting up and
saving the figure as you see fit.

Parameters
----------
negatives : array
1D float array that contains the scores of the
"negative" (noise, non-class) samples of your classifier. See
(:py:func:`bob.measure.roc`)

positives : array
1D float array that contains the scores of the
"positive" (signal, class) samples of your classifier. See
(:py:func:`bob.measure.roc`)

npoints : :py:class:`int`, optional
The number of points for the plot. See
(:py:func:`bob.measure.roc`)

min_far : float, optional
The minimum value of FPR and FNR that is used for ROC computations.

tpr : bool, optional
If True, will plot TPR (TPR = 1 - FNR) on the y-axis instead of FNR.

semilogx : bool, optional
If True, will use pyplot.semilogx to plot the ROC curve.

CAR : :py:class:`bool`, optional
If set to ``True``, it will plot the CPR
(CAR) over FPR in using :py:func:`matplotlib.pyplot.semilogx`, otherwise the
FPR over FNR linearly using :py:func:`matplotlib.pyplot.plot`.

**kwargs
Extra plotting parameters, which are
passed directly to :py:func:`matplotlib.pyplot.plot`.

Returns
-------
object
`list` of :py:class:`matplotlib.lines.Line2D`: The lines that
were added as defined by the return value of
:py:func`matplotlib.pyplot.plot`.
"""
if CAR is not None:
warnings.warn('CAR argument is deprecated. Please use TPR and semilogx arguments instead.', DeprecationWarning)
tpr = semilogx = CAR

from matplotlib import pyplot
from . import roc as calc
fpr, fnr = calc(negatives, positives, npoints, min_far=min_far)

if tpr:
fnr = 1 - fnr  # plot tpr instead of fnr

if not semilogx:
return pyplot.plot(fpr, fnr, **kwargs)
else:
return _semilogx(fpr, fnr, **kwargs)

[docs]def roc_for_far(negatives, positives, far_values=log_values(), CAR=True,
**kwargs):
"""Plots the ROC curve for the given list of False Positive Rates (FAR).

This method will call ``matplotlib`` to plot the ROC curve for a system which
contains a particular set of negatives (impostors) and positives (clients)
scores. We use the standard :py:func:`matplotlib.pyplot.semilogx` command.
All parameters passed with exception of the three first parameters of this
method will be directly passed to the plot command.

The plot will represent the False Positive Rate (FPR) on the horizontal
axis and the Correct Positive Rate (CPR) on the vertical axis.  The values
for the axis will be computed using :py:func:`bob.measure.roc_for_far`.

.. note::

This function does not initiate and save the figure instance, it only
issues the plotting command. You are the responsible for setting up and
saving the figure as you see fit.

Parameters:

negatives (array): 1D float array that contains the scores of the
"negative" (noise, non-class) samples of your classifier. See
(:py:func:`bob.measure.roc`)

positives (array): 1D float array that contains the scores of the
"positive" (signal, class) samples of your classifier. See
(:py:func:`bob.measure.roc`)

far_values (:py:class:`list`, optional): The values for the FPR, where the
CPR (CAR) should be plotted; each value should be in range [0,1].

CAR (:py:class:`bool`, optional): If set to ``True``, it will plot the CPR
(CAR) over FPR in using :py:func:`matplotlib.pyplot.semilogx`, otherwise the
FPR over FNR linearly using :py:func:`matplotlib.pyplot.plot`.

kwargs (:py:class:`dict`, optional): Extra plotting parameters, which are
passed directly to :py:func:`matplotlib.pyplot.plot`.

Returns:

:py:class:`list` of :py:class:`matplotlib.lines.Line2D`: The lines that
were added as defined by the return value of
:py:func:`matplotlib.pyplot.semilogx`.

"""

from matplotlib import pyplot
from . import roc_for_far as calc
out = calc(negatives, positives, far_values)
if not CAR:
return pyplot.plot(out[0, :], out[1, :], **kwargs)
else:
return _semilogx(out[0, :], (1 - out[1, :]), **kwargs)

[docs]def precision_recall_curve(negatives, positives, npoints=2000, **kwargs):
"""Plots a Precision-Recall curve.

This method will call ``matplotlib`` to plot the precision-recall curve for a
system which contains a particular set of ``negatives`` (impostors) and
``positives`` (clients) scores. We use the standard
:py:func:`matplotlib.pyplot.plot` command. All parameters passed with
exception of the three first parameters of this method will be directly
passed to the plot command.

.. note::

This function does not initiate and save the figure instance, it only
issues the plotting command. You are the responsible for setting up and
saving the figure as you see fit.

Parameters:

negatives (array): 1D float array that contains the scores of the
"negative" (noise, non-class) samples of your classifier. See
(:py:func:`bob.measure.precision_recall_curve`)

positives (array): 1D float array that contains the scores of the
"positive" (signal, class) samples of your classifier. See
(:py:func:`bob.measure.precision_recall_curve`)

npoints (:py:class:`int`, optional): The number of points for the plot. See
(:py:func:`bob.measure.precision_recall_curve`)

kwargs (:py:class:`dict`, optional): Extra plotting parameters, which are
passed directly to :py:func:`matplotlib.pyplot.plot`.

Returns:

:py:class:`list` of :py:class:`matplotlib.lines.Line2D`: The lines that
were added as defined by the return value of
:py:func:`matplotlib.pyplot.plot`.

"""

from matplotlib import pyplot
from . import precision_recall_curve as calc
out = calc(negatives, positives, npoints)
return pyplot.plot(100.0 * out[0, :], 100.0 * out[1, :], **kwargs)

[docs]def epc(dev_negatives, dev_positives, test_negatives, test_positives,
npoints=100, **kwargs):
"""Plots Expected Performance Curve (EPC) as defined in the paper:

Bengio, S., Keller, M., Mariéthoz, J. (2004). The Expected Performance Curve.
International Conference on Machine Learning ICML Workshop on ROC Analysis in
Machine Learning, 136(1), 1963–1966. IDIAP RR. Available:
http://eprints.pascal-network.org/archive/00000670/

This method will call ``matplotlib`` to plot the EPC curve for a system which
contains a particular set of negatives (impostors) and positives (clients)
for both the development and test sets. We use the standard
:py:func:`matplotlib.pyplot.plot` command. All parameters passed with
exception of the five first parameters of this method will be directly passed
to the plot command.

The plot will represent the minimum HTER on the vertical axis and the cost on
the horizontal axis.

.. note::

This function does not initiate and save the figure instance, it only
issues the plotting commands. You are the responsible for setting up and
saving the figure as you see fit.

Parameters:

dev_negatives (array): 1D float array that contains the scores of the
"negative" (noise, non-class) samples of your classifier, from the
development set. See (:py:func:`bob.measure.epc`)

dev_positives (array): 1D float array that contains the scores of the
"positive" (signal, class) samples of your classifier, from the
development set. See (:py:func:`bob.measure.epc`)

test_negatives (array): 1D float array that contains the scores of the
"negative" (noise, non-class) samples of your classifier, from the test
set. See (:py:func:`bob.measure.epc`)

test_positives (array): 1D float array that contains the scores of the
"positive" (signal, class) samples of your classifier, from the test set.
See (:py:func:`bob.measure.epc`)

npoints (:py:class:`int`, optional): The number of points for the plot. See
(:py:func:`bob.measure.epc`)

kwargs (:py:class:`dict`, optional): Extra plotting parameters, which are
passed directly to :py:func:`matplotlib.pyplot.plot`.

Returns:

:py:class:`list` of :py:class:`matplotlib.lines.Line2D`: The lines that
were added as defined by the return value of
:py:func:`matplotlib.pyplot.plot`.

"""

from matplotlib import pyplot
from . import epc as calc

out = calc(dev_negatives, dev_positives, test_negatives, test_positives,
npoints)
return pyplot.plot(out[0, :], 100.0 * out[1, :], **kwargs)

[docs]def det(negatives, positives, npoints=2000, min_far=-8, **kwargs):
"""Plots Detection Error Trade-off (DET) curve as defined in the paper:

Martin, A., Doddington, G., Kamm, T., Ordowski, M., & Przybocki, M. (1997).
The DET curve in assessment of detection task performance. Fifth European
Conference on Speech Communication and Technology (pp. 1895-1898). Available:

This method will call ``matplotlib`` to plot the DET curve(s) for a system
which contains a particular set of negatives (impostors) and positives
(clients) scores. We use the standard :py:func:`matplotlib.pyplot.plot`
command. All parameters passed with exception of the three first parameters
of this method will be directly passed to the plot command.

The plot will represent the false-alarm on the horizontal axis and the
false-rejection on the vertical axis.

This method is strongly inspired by the NIST implementation for Matlab,
called DETware, version 2.1 and available for download at the NIST website:

.. note::

This function does not initiate and save the figure instance, it only
issues the plotting commands. You are the responsible for setting up and
saving the figure as you see fit.

.. note::

If you wish to reset axis zooming, you must use the Gaussian scale rather
than the visual marks showed at the plot, which are just there for
displaying purposes. The real axis scale is based on
:py:func:`bob.measure.ppndf`.  For example, if you wish to set the x and y
axis to display data between 1% and 40% here is the recipe:

.. code-block:: python

import bob.measure
from matplotlib import pyplot
bob.measure.plot.det(...) #call this as many times as you need
#AFTER you plot the DET curve, just set the axis in this way:
pyplot.axis([bob.measure.ppndf(k/100.0) for k in (1, 40, 1, 40)])

We provide a convenient way for you to do the above in this module. So,
optionally, you may use the :py:func:`bob.measure.plot.det_axis` method
like this:

.. code-block:: python

import bob.measure
bob.measure.plot.det(...)
# please note we convert percentage values in det_axis()
bob.measure.plot.det_axis([1, 40, 1, 40])

Parameters:

negatives (array): 1D float array that contains the scores of the
"negative" (noise, non-class) samples of your classifier. See
(:py:func:`bob.measure.det`)

positives (array): 1D float array that contains the scores of the
"positive" (signal, class) samples of your classifier. See
(:py:func:`bob.measure.det`)

npoints (:py:class:`int`, optional): The number of points for the plot. See
(:py:func:`bob.measure.det`)

axisfontsize (:py:class:`str`, optional): The size to be used by
x/y-tick-labels to set the font size on the axis

kwargs (:py:class:`dict`, optional): Extra plotting parameters, which are
passed directly to :py:func:`matplotlib.pyplot.plot`.

Returns:

:py:class:`list` of :py:class:`matplotlib.lines.Line2D`: The lines that
were added as defined by the return value of
:py:func:`matplotlib.pyplot.plot`.

"""

# these are some constants required in this method
desiredTicks = [
"0.000001", "0.000002", "0.000005",
"0.00001", "0.00002", "0.00005",
"0.0001", "0.0002", "0.0005",
"0.001", "0.002", "0.005",
"0.01", "0.02", "0.05",
"0.1", "0.2", "0.4", "0.6", "0.8", "0.9",
"0.95", "0.98", "0.99",
"0.995", "0.998", "0.999",
"0.9995", "0.9998", "0.9999",
"0.99995", "0.99998", "0.99999"
]

desiredLabels = [
"0.0001", "0.0002", "0.0005",
"0.001", "0.002", "0.005",
"0.01", "0.02", "0.05",
"0.1", "0.2", "0.5",
"1", "2", "5",
"10", "20", "40", "60", "80", "90",
"95", "98", "99",
"99.5", "99.8", "99.9",
"99.95", "99.98", "99.99",
"99.995", "99.998", "99.999"
]

# this will actually do the plotting
from matplotlib import pyplot
from . import det as calc
from . import ppndf

out = calc(negatives, positives, npoints, min_far)
retval = pyplot.plot(out[0, :], out[1, :], **kwargs)

# now the trick: we must plot the tick marks by hand using the PPNDF method
pticks = ppndf(numpy.array(desiredTicks, dtype=float))
ax = pyplot.gca()  # and finally we set our own tick marks
ax.set_xticks(pticks)
ax.set_xticklabels(desiredLabels)
ax.set_yticks(pticks)
ax.set_yticklabels(desiredLabels)

return retval

[docs]def det_axis(v, **kwargs):
"""Sets the axis in a DET plot.

This method wraps the :py:func:`matplotlib.pyplot.axis` by calling
:py:func:`bob.measure.ppndf` on the values passed by the user so they are
meaningful in a DET plot as performed by :py:func:`bob.measure.plot.det`.

Parameters:

v (``sequence``): A sequence (list, tuple, array or the like) containing
the X and Y limits in the order ``(xmin, xmax, ymin, ymax)``. Expected
values should be in percentage (between 0 and 100%).  If ``v`` is not a
list or tuple that contains 4 numbers it is passed without further
inspection to :py:func:`matplotlib.pyplot.axis`.

kwargs (:py:class:`dict`, optional): Extra plotting parameters, which are
passed directly to :py:func:`matplotlib.pyplot.axis`.

Returns:

object: Whatever is returned by :py:func:`matplotlib.pyplot.axis`.

"""

import logging
logger = logging.getLogger("bob.measure")

from matplotlib import pyplot
from . import ppndf

# treat input
try:
tv = list(v)  # normal input
if len(tv) != 4:
raise IndexError
tv = [ppndf(float(k) / 100) for k in tv]
cur = pyplot.axis()

# limits must be within bounds
if tv < cur:
logger.warn("Readjusting xmin: the provided value is out of bounds")
tv = cur
if tv > cur:
logger.warn("Readjusting xmax: the provided value is out of bounds")
tv = cur
if tv < cur:
logger.warn("Readjusting ymin: the provided value is out of bounds")
tv = cur
if tv > cur:
logger.warn("Readjusting ymax: the provided value is out of bounds")
tv = cur

except:
tv = v

return pyplot.axis(tv, **kwargs)

[docs]def cmc(cmc_scores, logx=True, **kwargs):
"""Plots the (cumulative) match characteristics and returns the maximum rank.

This function plots a CMC curve using the given CMC scores (:py:class:`list`:
A list of tuples, where each tuple contains the
``negative`` and ``positive`` scores for one probe of the database).

Parameters:

cmc_scores (array): 1D float array containing the CMC values (See
:py:func:`bob.measure.cmc`)

logx (:py:class:`bool`, optional): If set (the default), plots the rank
axis in logarithmic scale using :py:func:`matplotlib.pyplot.semilogx` or
in linear scale using :py:func:`matplotlib.pyplot.plot`

kwargs (:py:class:`dict`, optional): Extra plotting parameters, which are
passed directly to :py:func:`matplotlib.pyplot.plot`.

Returns:

int: The number of classes (clients) in the given scores.

"""

from matplotlib import pyplot
from . import cmc as calc

out = calc(cmc_scores)

if logx:
_semilogx(range(1, len(out) + 1), out, **kwargs)
else:
pyplot.plot(range(1, len(out) + 1), out, **kwargs)

return len(out)

[docs]def detection_identification_curve(cmc_scores, far_values=log_values(), rank=1, logx=True, **kwargs):
"""Plots the Detection & Identification curve over the FPR

This curve is designed to be used in an open set identification protocol, and
defined in Chapter 14.1 of [LiJain2005]_.  It requires to have at least one
open set probe item, i.e., with no corresponding gallery, such that the
positives for that pair are ``None``.

The detection and identification curve first computes FPR thresholds based on
the out-of-set probe scores (negative scores).  For each probe item, the
**maximum** negative score is used.  Then, it plots the detection and
identification rates for those thresholds, which are based on the in-set
probe scores only. See [LiJain2005]_ for more details.

.. [LiJain2005] **Stan Li and Anil K. Jain**, *Handbook of Face Recognition*, Springer, 2005

Parameters:

cmc_scores (array): 1D float array containing the CMC values (See
:py:func:`bob.measure.cmc`)

rank (:py:class:`int`, optional): The rank for which the curve should be
plotted

far_values (:py:class:`list`, optional): The values for the FPR (FAR), where the
CPR (CAR) should be plotted; each value should be in range [0,1].

logx (:py:class:`bool`, optional): If set (the default), plots the rank
axis in logarithmic scale using :py:func:`matplotlib.pyplot.semilogx` or
in linear scale using :py:func:`matplotlib.pyplot.plot`

kwargs (:py:class:`dict`, optional): Extra plotting parameters, which are
passed directly to :py:func:`matplotlib.pyplot.plot`.

Returns:

:py:class:`list` of :py:class:`matplotlib.lines.Line2D`: The lines that
were added as defined by the return value of
:py:func:`matplotlib.pyplot.plot`.

"""

import numpy
import math
from matplotlib import pyplot
from . import far_threshold, detection_identification_rate

# for each probe, for which no positives exists, get the highest negative
# score; and sort them to compute the FAR thresholds
negatives = sorted(max(neg) for neg, pos in cmc_scores if (
pos is None or not numpy.array(pos).size) and neg is not None)
if not negatives:
raise ValueError(
"There need to be at least one pair with only negative scores")

# compute thresholds based on FAR values
thresholds = [far_threshold(negatives, [], v, True) for v in far_values]

# compute detection and identification rate based on the thresholds for
# the given rank
rates = [detection_identification_rate(cmc_scores, t, rank)
if not math.isnan(t) else numpy.nan for t in thresholds]

# plot curve
if logx:
return _semilogx(far_values, rates, **kwargs)
else:
return pyplot.plot(far_values, rates, **kwargs)
```