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performance_diagrams.py
performance_diagrams.py 11.79 KiB
"""Methods for plotting performance diagram."""
import numpy
import matplotlib.colors
import matplotlib.pyplot as pyplot
DEFAULT_LINE_COLOUR = numpy.array([228, 26, 28], dtype=float) / 255
DEFAULT_LINE_WIDTH = 3
DEFAULT_BIAS_LINE_COLOUR = numpy.full(3, 152. / 255)
DEFAULT_BIAS_LINE_WIDTH = 2
LEVELS_FOR_CSI_CONTOURS = numpy.linspace(0, 1, num=11, dtype=float)
LEVELS_FOR_BIAS_CONTOURS = numpy.array(
[0.25, 0.5, 0.75, 1., 1.5, 2., 3., 5.])
BIAS_STRING_FORMAT = '%.2f'
BIAS_LABEL_PADDING_PX = 10
FIGURE_WIDTH_INCHES = 10
FIGURE_HEIGHT_INCHES = 10
FONT_SIZE = 20
pyplot.rc('font', size=FONT_SIZE)
pyplot.rc('axes', titlesize=FONT_SIZE)
pyplot.rc('axes', labelsize=FONT_SIZE)
pyplot.rc('xtick', labelsize=FONT_SIZE)
pyplot.rc('ytick', labelsize=FONT_SIZE)
pyplot.rc('legend', fontsize=FONT_SIZE)
pyplot.rc('figure', titlesize=FONT_SIZE)
def _get_sr_pod_grid(success_ratio_spacing=0.01, pod_spacing=0.01):
"""Creates grid in SR-POD (success ratio / probability of detection) space.
M = number of rows (unique POD values) in grid
N = number of columns (unique success ratios) in grid
:param success_ratio_spacing: Spacing between grid cells in adjacent
columns.
:param pod_spacing: Spacing between grid cells in adjacent rows.
:return: success_ratio_matrix: M-by-N numpy array of success ratios.
Success ratio increases with column index.
:return: pod_matrix: M-by-N numpy array of POD values. POD decreases with
row index.
"""
num_success_ratios = 1 + int(numpy.ceil(1. / success_ratio_spacing))
num_pod_values = 1 + int(numpy.ceil(1. / pod_spacing))
unique_success_ratios = numpy.linspace(0., 1., num=num_success_ratios)
unique_pod_values = numpy.linspace(0., 1., num=num_pod_values)[::-1]
return numpy.meshgrid(unique_success_ratios, unique_pod_values)
def _csi_from_sr_and_pod(success_ratio_array, pod_array):
"""Computes CSI (critical success index) from success ratio and POD.
POD = probability of detection
:param success_ratio_array: numpy array (any shape) of success ratios.
:param pod_array: numpy array (same shape) of POD values.
:return: csi_array: numpy array (same shape) of CSI values.
"""
return (success_ratio_array ** -1 + pod_array ** -1 - 1.) ** -1
def _bias_from_sr_and_pod(success_ratio_array, pod_array):
"""Computes frequency bias from success ratio and POD.
POD = probability of detection
:param success_ratio_array: numpy array (any shape) of success ratios.
:param pod_array: numpy array (same shape) of POD values.
:return: frequency_bias_array: numpy array (same shape) of frequency biases.
"""
return pod_array / success_ratio_array
def _get_csi_colour_scheme():
"""Returns colour scheme for CSI (critical success index).
:return: colour_map_object: Colour scheme (instance of
`matplotlib.colors.ListedColormap`).
:return: colour_norm_object: Instance of `matplotlib.colors.BoundaryNorm`,
defining the scale of the colour map.
"""
this_colour_map_object = pyplot.cm.Blues
this_colour_norm_object = matplotlib.colors.BoundaryNorm(
LEVELS_FOR_CSI_CONTOURS, this_colour_map_object.N)
rgba_matrix = this_colour_map_object(this_colour_norm_object(
LEVELS_FOR_CSI_CONTOURS))
colour_list = [
rgba_matrix[i, ..., :-1] for i in range(rgba_matrix.shape[0])
]
colour_map_object = matplotlib.colors.ListedColormap(colour_list)
colour_map_object.set_under(numpy.array([1, 1, 1]))
colour_norm_object = matplotlib.colors.BoundaryNorm(
LEVELS_FOR_CSI_CONTOURS, colour_map_object.N)
return colour_map_object, colour_norm_object
def _add_colour_bar(
axes_object, colour_map_object, values_to_colour, min_colour_value,
max_colour_value, colour_norm_object=None,
orientation_string='vertical', extend_min=True, extend_max=True,
fraction_of_axis_length=1., font_size=FONT_SIZE):
"""Adds colour bar to existing axes.
:param axes_object: Existing axes (instance of
`matplotlib.axes._subplots.AxesSubplot`).
:param colour_map_object: Colour scheme (instance of
`matplotlib.pyplot.cm`).
:param values_to_colour: numpy array of values to colour.
:param min_colour_value: Minimum value in colour map.
:param max_colour_value: Max value in colour map.
:param colour_norm_object: Instance of `matplotlib.colors.BoundaryNorm`,
defining the scale of the colour map. If `colour_norm_object is None`,
will assume that scale is linear.
:param orientation_string: Orientation of colour bar ("vertical" or
"horizontal").
:param extend_min: Boolean flag. If True, the bottom of the colour bar will
have an arrow. If False, it will be a flat line, suggesting that lower
values are not possible.
:param extend_max: Same but for top of colour bar.
:param fraction_of_axis_length: Fraction of axis length (y-axis if
orientation is "vertical", x-axis if orientation is "horizontal")
occupied by colour bar.
:param font_size: Font size for labels on colour bar.
:return: colour_bar_object: Colour bar (instance of
`matplotlib.pyplot.colorbar`) created by this method.
"""
if colour_norm_object is None:
colour_norm_object = matplotlib.colors.Normalize(
vmin=min_colour_value, vmax=max_colour_value, clip=False)
scalar_mappable_object = pyplot.cm.ScalarMappable(
cmap=colour_map_object, norm=colour_norm_object)
scalar_mappable_object.set_array(values_to_colour)
if extend_min and extend_max:
extend_string = 'both'
elif extend_min:
extend_string = 'min'
elif extend_max:
extend_string = 'max'
else:
extend_string = 'neither'
if orientation_string == 'horizontal':
padding = 0.075
else:
padding = 0.05
colour_bar_object = pyplot.colorbar(
ax=axes_object, mappable=scalar_mappable_object,
orientation=orientation_string, pad=padding, extend=extend_string,
shrink=fraction_of_axis_length)
colour_bar_object.ax.tick_params(labelsize=font_size)
return colour_bar_object
def get_points_in_perf_diagram(observed_labels, forecast_probabilities):
"""Creates points for performance diagram.
E = number of examples
T = number of binarization thresholds
:param observed_labels: length-E numpy array of class labels (integers in
0...1).
:param forecast_probabilities: length-E numpy array with forecast
probabilities of label = 1.
:return: pod_by_threshold: length-T numpy array of POD (probability of
detection) values.
:return: success_ratio_by_threshold: length-T numpy array of success ratios.
"""
assert numpy.all(numpy.logical_or(
observed_labels == 0, observed_labels == 1
))
assert numpy.all(numpy.logical_and(
forecast_probabilities >= 0, forecast_probabilities <= 1
))
observed_labels = observed_labels.astype(int)
binarization_thresholds = numpy.linspace(0, 1, num=1001, dtype=float)
num_thresholds = len(binarization_thresholds)
pod_by_threshold = numpy.full(num_thresholds, numpy.nan)
success_ratio_by_threshold = numpy.full(num_thresholds, numpy.nan)
for k in range(num_thresholds):
these_forecast_labels = (
forecast_probabilities >= binarization_thresholds[k]
).astype(int)
this_num_hits = numpy.sum(numpy.logical_and(
these_forecast_labels == 1, observed_labels == 1
))
this_num_false_alarms = numpy.sum(numpy.logical_and(
these_forecast_labels == 1, observed_labels == 0
))
this_num_misses = numpy.sum(numpy.logical_and(
these_forecast_labels == 0, observed_labels == 1
))
try:
pod_by_threshold[k] = (
float(this_num_hits) / (this_num_hits + this_num_misses)
)
except ZeroDivisionError:
pass
try:
success_ratio_by_threshold[k] = (
float(this_num_hits) / (this_num_hits + this_num_false_alarms)
)
except ZeroDivisionError:
pass
pod_by_threshold = numpy.array([1.] + pod_by_threshold.tolist() + [0.])
success_ratio_by_threshold = numpy.array(
[0.] + success_ratio_by_threshold.tolist() + [1.]
)
return pod_by_threshold, success_ratio_by_threshold
def plot_performance_diagram(
observed_labels, forecast_probabilities,
line_colour=DEFAULT_LINE_COLOUR, line_width=DEFAULT_LINE_WIDTH,
bias_line_colour=DEFAULT_BIAS_LINE_COLOUR,
bias_line_width=DEFAULT_BIAS_LINE_WIDTH, axes_object=None):
"""Plots performance diagram.
E = number of examples
:param observed_labels: length-E numpy array of class labels (integers in
0...1).
:param forecast_probabilities: length-E numpy array with forecast
probabilities of label = 1.
:param line_colour: Colour (in any format accepted by `matplotlib.colors`).
:param line_width: Line width (real positive number).
:param bias_line_colour: Colour of contour lines for frequency bias.
:param bias_line_width: Width of contour lines for frequency bias.
:param axes_object: Will plot on these axes (instance of
`matplotlib.axes._subplots.AxesSubplot`). If `axes_object is None`,
will create new axes.
:return: pod_by_threshold: See doc for `get_points_in_perf_diagram`.
detection) values.
:return: success_ratio_by_threshold: Same.
"""
pod_by_threshold, success_ratio_by_threshold = get_points_in_perf_diagram(
observed_labels=observed_labels,
forecast_probabilities=forecast_probabilities)
if axes_object is None:
_, axes_object = pyplot.subplots(
1, 1, figsize=(FIGURE_WIDTH_INCHES, FIGURE_HEIGHT_INCHES)
)
success_ratio_matrix, pod_matrix = _get_sr_pod_grid()
csi_matrix = _csi_from_sr_and_pod(success_ratio_matrix, pod_matrix)
frequency_bias_matrix = _bias_from_sr_and_pod(
success_ratio_matrix, pod_matrix)
this_colour_map_object, this_colour_norm_object = _get_csi_colour_scheme()
pyplot.contourf(
success_ratio_matrix, pod_matrix, csi_matrix, LEVELS_FOR_CSI_CONTOURS,
cmap=this_colour_map_object, norm=this_colour_norm_object, vmin=0.,
vmax=1., axes=axes_object)
colour_bar_object = _add_colour_bar(
axes_object=axes_object, colour_map_object=this_colour_map_object,
colour_norm_object=this_colour_norm_object,
values_to_colour=csi_matrix, min_colour_value=0.,
max_colour_value=1., orientation_string='vertical',
extend_min=False, extend_max=False)
colour_bar_object.set_label('CSI (critical success index)')
bias_colour_tuple = ()
for _ in range(len(LEVELS_FOR_BIAS_CONTOURS)):
bias_colour_tuple += (bias_line_colour,)
bias_contour_object = pyplot.contour(
success_ratio_matrix, pod_matrix, frequency_bias_matrix,
LEVELS_FOR_BIAS_CONTOURS, colors=bias_colour_tuple,
linewidths=bias_line_width, linestyles='dashed', axes=axes_object)
pyplot.clabel(
bias_contour_object, inline=True, inline_spacing=BIAS_LABEL_PADDING_PX,
fmt=BIAS_STRING_FORMAT, fontsize=FONT_SIZE)
nan_flags = numpy.logical_or(
numpy.isnan(success_ratio_by_threshold), numpy.isnan(pod_by_threshold)
)
if not numpy.all(nan_flags):
real_indices = numpy.where(numpy.invert(nan_flags))[0]
axes_object.plot(
success_ratio_by_threshold[real_indices],
pod_by_threshold[real_indices], color=line_colour,
linestyle='solid', linewidth=line_width)
axes_object.set_xlabel('Success ratio (1 - FAR)')
axes_object.set_ylabel('POD (probability of detection)')
axes_object.set_xlim(0., 1.)
axes_object.set_ylim(0., 1.)
return pod_by_threshold, success_ratio_by_threshold