Python库 | pwlf-0.1.0.tar.gz

# -- coding: utf-8 -- # MIT License # # Copyright (c) 2017, 2018 Charles Jekel # # Permission is hereby granted, free of charge, to any person obtaining a copy # of this software and associated documentation files (the "Software"), to deal # in the Software without restriction, including without limitation the rights # to use, copy, modify, merge, publish, distribute, sublicense, and/or sell # copies of the Software, and to permit persons to whom the Software is # furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included in all # copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE # AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE # SOFTWARE. from __future__ import print_function # import libraris import numpy as np from scipy.optimize import differential_evolution from scipy.optimize import fmin_l_bfgs_b from pyDOE import lhs # piecewise linerar fit library class piecewise_lin_fit(object): # Initiate the libary with the supplied x and y data # where y(x). For now x and y should be 1D numpy arrays. def __init__(self, x, y): # you must supply the x and y data of which you'll be fitting # a continous piecewise linear model to where y(x) # sort the data from least x to max x orderArg = np.argsort(x) self.xData = x[orderArg] self.yData = y[orderArg] # calculate the number of data points self.nData = len(x) # set the first and last break x values to be the min and max of x self.break0 = np.min(self.xData) self.breakN = np.max(self.xData) def fitWithBreaks(self, breaks): # define a function which fits the piecewise linear function # for specified break point locations # # The function minimizes the sum of the square of the residuals for the # pair of x,y data points # # This is a port of 4-May-2004 Nikolai Golovchenko MATLAB code # see http://golovchenko.org/docs/ContinuousPiecewiseLinearFit.pdf # # Alternatively see https://www.mathworks.com/matlabcentral/fileexchange/40913-piecewise-linear-least-square-fit # # Input: # provide the location of the end points of the breaks for each line segment # # Example: if your x data exists from 0 <= x <= 1 and you want three # piecewise linear lines, an accpetable breaks would look like # breaks = [0.0, 0.3, 0.6, 1.0] # # Ouput: # The function returns the sum of the square of the residuals # # To get the parameters of the fit look for # self.paramters # # remember that the parameters that result are part of the continous function # such that: # parameters = f(breaks) self.fitBreaks = breaks numberOfParameters = len(breaks) numberOfSegments = numberOfParameters - 1 self.numberOfParameters = numberOfParameters self.numberOfSegments = numberOfSegments sepDataX, sepDataY = self.seperateData(breaks) # add the seperated data to the object self.sep_data_x = sepDataX self.sep_data_y = sepDataY # compute matricies corresponding to the system of equations A = np.zeros([numberOfParameters, numberOfParameters]) B = np.zeros(numberOfParameters) for i in range(0,numberOfParameters): if i != 0: # first sum A[i,i-1] = A[i,i-1] - sum((sepDataX[i-1] - breaks[i-1]) * (sepDataX[i-1] - breaks[i])) / ((breaks[i] - breaks[i-1]) ** 2) A[i,i] = A[i,i] + sum((sepDataX[i-1] - breaks[i-1]) ** 2) / ((breaks[i] - breaks[i-1]) ** 2) B[i] = B[i] + (sum(sepDataX[i-1] * sepDataY[i-1]) - breaks[i-1] * sum(sepDataY[i-1])) / (breaks[i] - breaks[i-1]) if i != numberOfParameters - 1: # second sum A[i,i] = A[i,i] + sum(((sepDataX[i] - breaks[i+1]) ** 2)) / ((breaks[i+1] - breaks[i]) ** 2) A[i,i+1] = A[i,i+1] - sum((sepDataX[i] - breaks[i]) * (sepDataX[i] - breaks[i+1])) / ((breaks[i+1] - breaks[i]) ** 2) B[i] = B[i] + (-sum(sepDataX[i] * sepDataY[i]) + breaks[i+1] * sum(sepDataY[i])) / (breaks[i+1] - breaks[i]) p = np.linalg.solve(A,B) yHat = [] lineSlopes = [] for i,j in enumerate(sepDataX): m = (p[i+1] - p[i])/(breaks[i+1]-breaks[i]) lineSlopes.append(m) yHat.append(m*(j-breaks[i]) + p[i]) yHat = np.concatenate(yHat) self.slopes = np.array(lineSlopes) # calculate the sum of the square of residuals e = self.yData-yHat SSr = np.dot(e.T,e) self.fitParameters = p return(SSr) def seperateData(self, breaks): # a function that seperates the data based on the breaks numberOfParameters = len(breaks) numberOfSegments = numberOfParameters - 1 self.numberOfParameters = numberOfParameters self.numberOfSegments = numberOfSegments # Seperate Data into Segments sepDataX = [[] for i in range(self.numberOfSegments)] sepDataY = [[] for i in range(self.numberOfSegments)] for i in range(0, self.numberOfSegments): dataX = [] dataY = [] if i == 0: # the first index should always be inclusive aTest = self.xData >= breaks[i] else: # the rest of the indexies should be exclusive aTest = self.xData > breaks[i] dataX = np.extract(aTest, self.xData) dataY = np.extract(aTest, self.yData) bTest = dataX <= breaks[i+1] dataX = np.extract(bTest, dataX) dataY = np.extract(bTest, dataY) sepDataX[i] = np.array(dataX) sepDataY[i] = np.array(dataY) return(sepDataX, sepDataY) def seperateDataX(self, breaks, x): # a function that seperates the data based on the breaks for given x numberOfParameters = len(breaks) numberOfSegments = numberOfParameters - 1 self.numberOfParameters = numberOfParameters self.numberOfSegments = numberOfSegments # Seperate Data into Segments sepDataX = [[] for i in range(self.numberOfSegments)] for i in range(0, self.numberOfSegments): dataX = [] if i == 0: # the first index should always be inclusive aTest = x >= breaks[i] else: # the rest of the indexies should be exclusive aTest = x > breaks[i] dataX = np.extract(aTest, x) bTest = dataX <= breaks[i+1] dataX = np.extract(bTest, dataX) sepDataX[i] = np.array(dataX) return(sepDataX) def predict(self, x, *args):#breaks, p): # a function that predicts based on the supplied x values # you can manully supply break point and determined p # yHat = predict(x) # or yHat = predict(x, p, breaks) if len(args) == 2: p = args[0] breaks = args[1] else: p = self.fitParameters breaks = self.fitBreaks # seperate the data by x on breaks sepDataX = self.seperateDataX(breaks,x) # add the seperated data to self self.sep_predict_data_x = sepDataX yHat = [] lineSlopes = [] for i,j in enumerate(sepDataX): m = (p[i+1]