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Commit 92c41731 authored by Jonathan Juhl's avatar Jonathan Juhl
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Delete Knee_Locater.py

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import numpy as np
from scipy import interpolate
from scipy.signal import argrelextrema
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
import warnings
from typing import Tuple, Optional, Iterable
class KneeLocator(object):
def __init__(
self,
x: Iterable[float],
y: Iterable[float],
S: float = 1.0,
curve: str = "concave",
direction: str = "increasing",
interp_method: str = "interp1d",
online: bool = False,
):
"""
Once instantiated, this class attempts to find the point of maximum
curvature on a line. The knee is accessible via the `.knee` attribute.
:param x: x values.
:param y: y values.
:param S: Sensitivity, original paper suggests default of 1.0
:param curve: If 'concave', algorithm will detect knees. If 'convex', it
will detect elbows.
:param direction: one of {"increasing", "decreasing"}
:param interp_method: one of {"interp1d", "polynomial"}
:param online: Will correct old knee points if True, will return first knee if False
"""
# Step 0: Raw Input
self.x = np.array(x)
self.y = np.array(y)
self.curve = curve
self.direction = direction
self.N = len(self.x)
self.S = S
self.all_knees = set()
self.all_norm_knees = set()
self.all_knees_y = []
self.all_norm_knees_y = []
self.online = online
# Step 1: fit a smooth line
if interp_method == "interp1d":
uspline = interpolate.interp1d(self.x, self.y)
self.Ds_y = uspline(self.x)
elif interp_method == "polynomial":
pn_model = PolynomialFeatures(7)
xpn = pn_model.fit_transform(self.x.reshape(-1, 1))
regr_model = LinearRegression()
regr_model.fit(xpn, self.y)
self.Ds_y = regr_model.predict(
pn_model.fit_transform(self.x.reshape(-1, 1))
)
else:
warnings.warn(
"{} is an invalid interp_method parameter, use either 'interp1d' or 'polynomial'".format(
interp_method
)
)
return
# Step 2: normalize values
self.x_normalized = self.__normalize(self.x)
self.y_normalized = self.__normalize(self.Ds_y)
# Step 3: Calculate the Difference curve
self.x_normalized, self.y_normalized = self.transform_xy(
self.x_normalized, self.y_normalized, self.direction, self.curve
)
# normalized difference curve
self.y_difference = self.y_normalized - self.x_normalized
self.x_difference = self.x_normalized.copy()
# Step 4: Identify local maxima/minima
# local maxima
self.maxima_indices = argrelextrema(self.y_difference, np.greater_equal)[0]
self.x_difference_maxima = self.x_difference[self.maxima_indices]
self.y_difference_maxima = self.y_difference[self.maxima_indices]
# local minima
self.minima_indices = argrelextrema(self.y_difference, np.less_equal)[0]
self.x_difference_minima = self.x_difference[self.minima_indices]
self.y_difference_minima = self.y_difference[self.minima_indices]
# Step 5: Calculate thresholds
self.Tmx = self.y_difference_maxima - (
self.S * np.abs(np.diff(self.x_normalized).mean())
)
# Step 6: find knee
self.knee, self.norm_knee = self.find_knee()
# Step 7: If we have a knee, extract data about it
self.knee_y = self.norm_knee_y = None
if self.knee:
self.knee_y = self.y[self.x == self.knee][0]
self.norm_knee_y = self.y_normalized[self.x_normalized == self.norm_knee][0]
@staticmethod
def __normalize(a: Iterable[float]) -> Iterable[float]:
"""normalize an array
:param a: The array to normalize
"""
return (a - min(a)) / (max(a) - min(a))
@staticmethod
def transform_xy(
x: Iterable[float], y: Iterable[float], direction: str, curve: str
) -> Tuple[Iterable[float], Iterable[float]]:
"""transform x and y to concave, increasing based on given direction and curve"""
# convert elbows to knees
if curve == "convex":
x = x.max() - x
y = y.max() - y
# flip decreasing functions to increasing
if direction == "decreasing":
y = np.flip(y, axis=0)
if curve == "convex":
x = np.flip(x, axis=0)
y = np.flip(y, axis=0)
return x, y
def find_knee(self,):
"""This function finds and sets the knee value and the normalized knee value. """
if not self.maxima_indices.size:
warnings.warn(
"No local maxima found in the difference curve\n"
"The line is probably not polynomial, try plotting\n"
"the difference curve with plt.plot(knee.x_difference, knee.y_difference)\n"
"Also check that you aren't mistakenly setting the curve argument",
RuntimeWarning,
)
return None, None
# placeholder for which threshold region i is located in.
maxima_threshold_index = 0
minima_threshold_index = 0
# traverse the difference curve
for i, x in enumerate(self.x_difference):
# skip points on the curve before the the first local maxima
if i < self.maxima_indices[0]:
continue
j = i + 1
# reached the end of the curve
if x == 1.0:
break
# if we're at a local max, increment the maxima threshold index and continue
if (self.maxima_indices == i).any():
threshold = self.Tmx[maxima_threshold_index]
threshold_index = i
maxima_threshold_index += 1
# values in difference curve are at or after a local minimum
if (self.minima_indices == i).any():
threshold = 0.0
minima_threshold_index += 1
if self.y_difference[j] < threshold:
if self.curve == "convex":
if self.direction == "decreasing":
knee = self.x[threshold_index]
norm_knee = self.x_normalized[threshold_index]
else:
knee = self.x[-(threshold_index + 1)]
norm_knee = self.x_normalized[-(threshold_index + 1)]
elif self.curve == "concave":
if self.direction == "decreasing":
knee = self.x[-(threshold_index + 1)]
norm_knee = self.x_normalized[-(threshold_index + 1)]
else:
knee = self.x[threshold_index]
norm_knee = self.x_normalized[threshold_index]
# add the y value at the knee
y_at_knee = self.y[self.x == knee][0]
y_norm_at_knee = self.y_normalized[self.x_normalized == norm_knee][0]
if knee not in self.all_knees:
self.all_knees_y.append(y_at_knee)
self.all_norm_knees_y.append(y_norm_at_knee)
# now add the knee
self.all_knees.add(knee)
self.all_norm_knees.add(norm_knee)
# if detecting in offline mode, return the first knee found
if self.online is False:
return knee, norm_knee
if self.all_knees == set():
warnings.warn("No knee/elbow found")
return None, None
return knee, norm_knee
def plot_knee_normalized(self, figsize: Optional[Tuple[int, int]] = None):
"""Plot the normalized curve, the difference curve (x_difference, y_normalized) and the knee, if it exists.
:param figsize: Optional[Tuple[int, int]
The figure size of the plot. Example (12, 8)
:return: NoReturn
"""
import matplotlib.pyplot as plt
if figsize is None:
figsize = (6, 6)
plt.figure(figsize=figsize)
plt.title("Normalized Knee Point")
plt.plot(self.x_normalized, self.y_normalized, "b", label="normalized curve")
plt.plot(self.x_difference, self.y_difference, "r", label="difference curve")
plt.xticks(
np.arange(self.x_normalized.min(), self.x_normalized.max() + 0.1, 0.1)
)
plt.yticks(
np.arange(self.y_difference.min(), self.y_normalized.max() + 0.1, 0.1)
)
plt.vlines(
self.norm_knee,
plt.ylim()[0],
plt.ylim()[1],
linestyles="--",
label="knee/elbow",
)
plt.legend(loc="best")
def plot_knee(self, figsize: Optional[Tuple[int, int]] = None):
"""
Plot the curve and the knee, if it exists
:param figsize: Optional[Tuple[int, int]
The figure size of the plot. Example (12, 8)
:return: NoReturn
"""
import matplotlib.pyplot as plt
if figsize is None:
figsize = (6, 6)
plt.figure(figsize=figsize)
plt.title("Knee Point")
plt.plot(self.x, self.y, "b", label="data")
plt.vlines(
self.knee, plt.ylim()[0], plt.ylim()[1], linestyles="--", label="knee/elbow"
)
plt.legend(loc="best")
# Niceties for users working with elbows rather than knees
@property
def elbow(self):
return self.knee
@property
def norm_elbow(self):
return self.norm_knee
@property
def elbow_y(self):
return self.knee_y
@property
def norm_elbow_y(self):
return self.norm_knee_y
@property
def all_elbows(self):
return self.all_knees
@property
def all_norm_elbows(self):
return self.all_norm_knees
@property
def all_elbows_y(self):
return self.all_knees_y
@property
def all_norm_elbows_y(self):
return self.all_norm_knees_y
\ No newline at end of file
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