From 1aacddede591ce98b266813f6ee175f002bd1964 Mon Sep 17 00:00:00 2001 From: yucheng Date: Fri, 15 Apr 2022 17:23:21 +0800 Subject: [PATCH 1/3] add AutoPiecewiseLinFit class --- pwlf/autopwlf.py | 232 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 232 insertions(+) create mode 100644 pwlf/autopwlf.py diff --git a/pwlf/autopwlf.py b/pwlf/autopwlf.py new file mode 100644 index 0000000..03203f4 --- /dev/null +++ b/pwlf/autopwlf.py @@ -0,0 +1,232 @@ +import re +import pwlf +import numpy as np +from sympy import Symbol +from sympy.utilities import lambdify +from collections import defaultdict +from scipy.optimize import rosen, differential_evolution +from utils.io import * + +class AutoPiecewiseLinFit(object): + + def __init__(self, x, y) -> None: + r""" + Automatically determine number of segments to do piecewise linear fit, + and apply bounds to speed up convergence. + Parameters + ---------- + x : array_like + The x or independent data point locations as list or 1 dimensional + numpy array. + y : array_like + The y or dependent data point locations as list or 1 dimensional + numpy array. + Attributes + ---------- + n : int + number of segment + bounds : array_like + Bounds for each breakpoint location within the optimization. This + should have the shape of (n_segments, 2). + slopes : ndarray(1-D) + The slope of each ling segment as a 1-D numpy array. + intercepts : ndarray (1-D) + The y-intercept of each line segment as a 1-D numpy array. + my_pwlf : PiecewiseLinFit + Piecewise linear fit model, which is callable. + source code https://github.com/cjekel/piecewise_linear_fit_py/blob/master/pwlf/pwlf.py + Methods + ------- + fit_curve_and_guess(degree=16, lb=10, ub=10) + Fit a polynomial function first then extract roots + piecewise_fit(lin_num: int = None, use_bound=True) + Fit a continuous piecewise linear function for a specified number + of line segments. + parse_model() + Format a lambda expression y = k*x + b and return it + cal_slopes() + Calculate the slopes of the lines after a piecewise linear + function has been fitted. + model_error() + Evaluate model piecewise, which format as + (start, end): [mean of vertical distance, mean of y_data value, number of y_data on this segment] + Examples + -------- + Initialize for x, y data + >>> my_pwlf = AutoPiecewiseLinFit(x, y) + Guess number of segment first + >>> n = my_pwlf.fit_curve_and_guess() + Fit model with bounds specific + >>> fit_1.piecewise_fit(n, use_bound=True) + Calculate slopes and intercepts + >>> fit_1.cal_slopes() + Evalute model + >>> fit_1.model_error() + """ + + + if not all(isinstance(n, (int, float)) for n in x) or \ + not all(isinstance(n, (int, float)) for n in y): + raise ValueError("input x and y should by int or float") + + x, y = self._switch_to_np_array(x), self._switch_to_np_array(y) + self.x_data, self.y_data = x, y + + + @staticmethod + def _switch_to_np_array(input_): + if isinstance(input_, np.ndarray) is False: + input_ = np.array(input_) + return input_ + + + @staticmethod + def _unpack_expr(func): + r""" + Extract piecewise model's parameters. + Parameters + ---------- + func : callable object + Model function + + Returns + ------- + k : int + Slope + b : int + Intercept + """ + text = func.__doc__ + l = re.findall(r'return .*\n', text)[0] + l = re.split(r' |\n', l)[1:-1] + if len(l) == 3: + if '*x' in l[0]: + k, b = eval(l[0].split('*')[0]), eval(l[1]+l[2]) + elif '*' in l[2]: + k, b = eval(l[1]+l[2].split('*')[0]), eval(l[0]) + elif len(l) == 4: + if '*x' in l[1]: + k, b = eval(l[0]+l[1].split('*')[0]), eval(l[2]+l[3]) + elif '*x' in l[3]: + k, b = eval(l[2]+l[3].split('*')[0]), eval(l[0]+l[1]) + return k, b + + def fit_curve_and_guess(self, degree=16, lb=10, ub=10) -> int: + r""" + Guess lines number by using curve fit then extract roots. + Then initize bounds with roots-lb and roots+ub, which can + speed up convergence. + Parameters + ---------- + degree : int + Polynomial degree to fit curve + lb : int + Lower bound + ub : int + Up bound + Returns + ------- + guess : int + The guess of piecewise lines number. + """ + + coeff = np.polyfit(self.x_data, self.y_data, degree) + f = np.poly1d(coeff) + f_d = np.polyder(f, 1) + xroot = np.roots(f_d) + xroot = list(filter(lambda x : x.imag == 0, xroot)) + xroot = list(filter(lambda x : x >= self.x_data.min() and x <= self.x_data.max(), xroot)) + self.n = len(xroot)+1 + self.bounds = np.zeros([self.n-1, 2]) + for i, e in enumerate(xroot): + self.bounds[i][0] = e.real-lb + self.bounds[i][1] = e.real+ub + return self.n + + def piecewise_fit(self, lin_num: int = None, use_bound=True) -> None: + r""" + Use pwlf.fit() to fit model. + Parameters + ---------- + lin_num : None, or int + Default lin_num=None, automatically infer segment number. + use_bound : bool, optional + Defalut True, use bounds to speed up convergence + """ + my_pwlf = pwlf.PiecewiseLinFit(self.x_data, self.y_data) + if use_bound == True: + if lin_num is None: + my_pwlf.fit(self.n, bounds=self.bounds, workers=-1, updating='deferred') + else: + my_pwlf.fit(lin_num, bounds=self.bounds, workers=-1, updating='deferred') + else: + if lin_num is None: + my_pwlf.fit(self.n, workers=-1, updating='deferred') + else: + my_pwlf.fit(lin_num, workers=-1, updating='deferred') + break_predict = my_pwlf.predict(my_pwlf.fit_breaks) + self.slopes = my_pwlf.calc_slopes() + self.intercepts = break_predict[0:-1] - self.slopes * my_pwlf.fit_breaks[0:-1] + self.my_pwlf = my_pwlf + + def parse_model(self) -> dict: + r""" + Format a lambda expression y = k*x + b and return it + + Returns + ------- + model : dict + Mapping (start point, end point) to linear function + """ + x = Symbol('x') + breaks = self.my_pwlf.fit_breaks + model = dict() + for i, (k, b) in enumerate(zip(self.slopes, self.intercepts)): + expr = k * x + b + f = lambdify(x, expr, 'numpy') + model[(breaks[i], breaks[i+1])] = f + return model + + def cal_slopes(self) -> defaultdict: + r""" + Calculate the slopes and intercepts of the lines after a piecewise linear + function has been fitted. + Returns + ------- + model_params : defaultdict + Mapping (start point, end point) to [slope, intercept] + """ + model = self.parse_model() + model_params = defaultdict(list) + for key, val in model.items(): + k, v = self._unpack_expr(val) + model_params[key].extend([k, v]) + return model_params + + def model_error(self) -> defaultdict: + r""" + Evaluate model piecewise, which format as + (start, end): [mean of vertical distance, mean of y_data value, number of y_data on this segment] + Returns + ------- + model_error_piecewise : defaultdict + """ + def vert_dist(func, x, y): + k, b = self._unpack_expr(func) + d = abs(k*x - y + b) / np.sqrt(k**2+1) + return d + + model = self.parse_model() + model_error_piecewise = defaultdict(list) + tmp = defaultdict(list) + for x, y in zip(self.x_data, self.y_data): + for k, func in model.items(): + if k[0] <= x and x < k[1]: + model_error_piecewise[k].append(vert_dist(func, x, y)**2) + tmp[k].append(y); break + model_error_piecewise = {k:[np.mean(v), np.mean(tmp[k]), len(v)] for k, v in model_error_piecewise.items()} + return model_error_piecewise + + def piecewise_fit_fast(self): + # TODO : Further improve computation speed by restricting break points to int + return \ No newline at end of file From bcb481b0c8785b4d4519f23b9ca086e04bebb457 Mon Sep 17 00:00:00 2001 From: yucheng Date: Tue, 26 Apr 2022 15:59:53 +0800 Subject: [PATCH 2/3] [update]Add an example and some comments --- polyfit_deg_3.png | Bin 0 -> 65493 bytes polyfit_deg_4.png | Bin 0 -> 66122 bytes polyfit_deg_5.png | Bin 0 -> 65588 bytes polyfit_deg_6.png | Bin 0 -> 66262 bytes polyfit_deg_7.png | Bin 0 -> 65642 bytes polyfit_deg_8.png | Bin 0 -> 65657 bytes polyfit_deg_9.png | Bin 0 -> 65645 bytes pwlf/autopwlf.py | 62 ++++++++++++++++++++++++++++++++++++++++++++-- 8 files changed, 60 insertions(+), 2 deletions(-) create mode 100644 polyfit_deg_3.png create mode 100644 polyfit_deg_4.png create mode 100644 polyfit_deg_5.png create mode 100644 polyfit_deg_6.png create mode 100644 polyfit_deg_7.png create mode 100644 polyfit_deg_8.png create mode 100644 polyfit_deg_9.png diff --git a/polyfit_deg_3.png b/polyfit_deg_3.png new file mode 100644 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piecewise_fit_fast(self): # TODO : Further improve computation speed by restricting break points to int - return \ No newline at end of file + return + +if __name__ == "__main__": + ## complex dataset + # x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74] + # y1 = [50.69, 50.63, 50.01, 50.22, 49.63, 47.62, 48.5, 48.71, 48.35, 49.05, 48.15, 49.05, 49.23, 49.85, 49.76, 49.34, 48.02, 48.58, 49.01, 49.7, 51.37, 51.82, 51.85, 50.9, 51.0, 50.77, 49.21, 51.35, 51.71, 51.62, 51.71, 52.76, 51.2, 50.22, 51.07, 51.46, 52.06, 51.76, 51.22, 50.83, 50.02, 49.81, 49.8, 50.24, 49.47, 49.73, 48.7, 46.76, 45.48, 44.39, 44.7, 44.45, 42.15, 39.45, 42.58, 44.51, 46.17, 44.81, 45.53, 45.76, 45.77, 45.18, 45.05, 45.01, 46.23, 46.8, 47.1, 47.39, 46.86, 47.18, 45.9, 45.7, 45.75, 42.1, 41.1] + # y2 = [6.02, 6.0, 5.98, 5.99, 6.02, 5.95, 6.01, 6.02, 6.0, 5.99, 5.96, 5.96, 5.99, 6.0, 6.02, 6.05, 6.04, 6.08, 6.13, 6.2, 6.33, 6.41, 6.51, 6.53, 6.54, 6.54, 6.52, 6.57, 6.59, 6.63, 6.64, 6.7, 6.7, 6.69, 6.72, 6.73, 6.74, 6.75, 6.73, 6.74, 6.73, 6.71, 6.71, 6.73, 6.73, 6.73, 6.71, 6.65, 6.61, 6.59, 6.58, 6.57, 6.56, 6.57, 6.57, 6.59, 6.7, 6.7, 6.73, 6.76, 6.78, 6.77, 6.78, 6.78, 6.79, 6.76, 6.74, 6.72, 6.72, 6.73, 6.72, 6.66, 6.69, 6.57, 6.47] + """ a simple dataset """ + x = np.arange(0, 4*np.pi, 0.1) + y = np.sin(x) + """ + coeff is parameter of polyfit model. + One degree polynomial model y = a_1*x + a_0 + >>> x = np.linspace(-5, 5, 100) + >>> y = 4 * x + 1.5 + >>> noise_y = y + np.random.randn(y.shape[-1]) * 2.5 + >>> p = plt.plot(x, noise_y, 'rx') + >>> p = plt.plot(x, y, 'b:') + >>> coeff = polyfit(x, noise_y, 1) + >>> print(coeff) + >>> [3.93921315 1.59379469] -> [a_1, a_0] + """ + coeff = np.polyfit(x, y, deg=9) + """ + poly1d assemble coeff to polynomial model + >>> f = poly1d(coeff) + >>> print(f) + >>> 3.939 x + 1.594 + """ + f = np.poly1d(coeff) + """np.polyder is a tool that return the derivative of the specified order of a polynomial.""" + f_d = np.polyder(f, 1) + """ + np.roots return the roots of a polynomial with coefficients given in p. + here xroot are [-27.02577916 8.46877068 4.36903767] + when increasing degree to deg=9, results contain imaginary roots: + [12.83124078+1.06520938j 12.83124078-1.06520938j 10.98184655+0.j + 7.86313591+0.j 4.70268776+0.j 1.58653459+0.j + -0.28007017+1.04758677j -0.28007017-1.04758677j] + """ + xroot = np.roots(f_d) + """ + but we just need xroot between x.min() and x.max() + after filter, xroot are [8.468770676220245, 4.369037674890286] + """ + min, max = x.min(), x.max() + xroot = list(filter(lambda x : (x >= min and x < max), xroot)) + yroot = np.sin(xroot) + fit_1 = AutoPiecewiseLinFit(x, y) + n_1 = fit_1.fit_curve_and_guess() + fit_1.piecewise_fit(n_1) + model = fit_1.parse_model() + x_hat = [key for key, _ in model.items() for key in key] + y_hat = [value(key) for key, value in model.items() for key in key] + fig, axes = plt.subplots(1, 1, figsize=(12, 8)) + axes.plot(x,y) + axes.scatter(xroot, yroot, color='red') + axes.plot(x_hat, y_hat, color='green') + plt.savefig('polyfit_deg_9.png') \ No newline at end of file From 8513dc458628e5f6bdaee4232ab3219cd722bbbf Mon Sep 17 00:00:00 2001 From: yucheng Date: Wed, 27 Apr 2022 20:49:32 +0800 Subject: [PATCH 3/3] [fix]fixed problem that degree parameter not apply on fit_curve_and_guess() function --- polyfit_deg_3.png | Bin 65493 -> 61997 bytes polyfit_deg_4.png | Bin 66122 -> 61976 bytes polyfit_deg_5.png | Bin 65588 -> 66251 bytes polyfit_deg_6.png | Bin 66262 -> 65590 bytes polyfit_deg_7.png | Bin 65642 -> 65647 bytes polyfit_deg_8.png | Bin 65657 -> 66337 bytes polyfit_deg_9.png | Bin 65645 -> 65645 bytes pwlf/autopwlf.py | 42 +++++++++++++++++++++++------------------- 8 files changed, 23 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zioSk7FmoEDo)Q7|8ejRQOMeFDccZ*JJJ_zLpPAw4=Eeq$bKs>@U7!nn4jpm=or)6w z|5rG$X7lmT-dDEq`Eg)j@tV7gbxp*^rj5zR&5ErA|1ShJ>^s!Kwcroaw~fHNaUh`1 zmvznm{j%0#3_u|9B;U4IwpDPmz<&?M$$bAyMHw3sV-^UNDgkfYW?=Ai1)fRkl+XkK DX)S@L diff --git a/pwlf/autopwlf.py b/pwlf/autopwlf.py index a8fed70..b265244 100644 --- a/pwlf/autopwlf.py +++ b/pwlf/autopwlf.py @@ -237,10 +237,12 @@ def piecewise_fit_fast(self): # y1 = [50.69, 50.63, 50.01, 50.22, 49.63, 47.62, 48.5, 48.71, 48.35, 49.05, 48.15, 49.05, 49.23, 49.85, 49.76, 49.34, 48.02, 48.58, 49.01, 49.7, 51.37, 51.82, 51.85, 50.9, 51.0, 50.77, 49.21, 51.35, 51.71, 51.62, 51.71, 52.76, 51.2, 50.22, 51.07, 51.46, 52.06, 51.76, 51.22, 50.83, 50.02, 49.81, 49.8, 50.24, 49.47, 49.73, 48.7, 46.76, 45.48, 44.39, 44.7, 44.45, 42.15, 39.45, 42.58, 44.51, 46.17, 44.81, 45.53, 45.76, 45.77, 45.18, 45.05, 45.01, 46.23, 46.8, 47.1, 47.39, 46.86, 47.18, 45.9, 45.7, 45.75, 42.1, 41.1] # y2 = [6.02, 6.0, 5.98, 5.99, 6.02, 5.95, 6.01, 6.02, 6.0, 5.99, 5.96, 5.96, 5.99, 6.0, 6.02, 6.05, 6.04, 6.08, 6.13, 6.2, 6.33, 6.41, 6.51, 6.53, 6.54, 6.54, 6.52, 6.57, 6.59, 6.63, 6.64, 6.7, 6.7, 6.69, 6.72, 6.73, 6.74, 6.75, 6.73, 6.74, 6.73, 6.71, 6.71, 6.73, 6.73, 6.73, 6.71, 6.65, 6.61, 6.59, 6.58, 6.57, 6.56, 6.57, 6.57, 6.59, 6.7, 6.7, 6.73, 6.76, 6.78, 6.77, 6.78, 6.78, 6.79, 6.76, 6.74, 6.72, 6.72, 6.73, 6.72, 6.66, 6.69, 6.57, 6.47] """ a simple dataset """ + x = np.arange(0, 4*np.pi, 0.1) y = np.sin(x) - """ - coeff is parameter of polyfit model. + deg = 9 # number of degree + + """ coeff is parameter of polyfit model. One degree polynomial model y = a_1*x + a_0 >>> x = np.linspace(-5, 5, 100) >>> y = 4 * x + 1.5 @@ -249,36 +251,38 @@ def piecewise_fit_fast(self): >>> p = plt.plot(x, y, 'b:') >>> coeff = polyfit(x, noise_y, 1) >>> print(coeff) - >>> [3.93921315 1.59379469] -> [a_1, a_0] - """ - coeff = np.polyfit(x, y, deg=9) - """ - poly1d assemble coeff to polynomial model + >>> [3.93921315 1.59379469] -> [a_1, a_0]""" + + coeff = np.polyfit(x, y, deg=deg) + + """poly1d assemble coeff to polynomial model >>> f = poly1d(coeff) >>> print(f) - >>> 3.939 x + 1.594 - """ + >>> 3.939 x + 1.594""" + f = np.poly1d(coeff) + """np.polyder is a tool that return the derivative of the specified order of a polynomial.""" + f_d = np.polyder(f, 1) - """ - np.roots return the roots of a polynomial with coefficients given in p. + + """np.roots return the roots of a polynomial with coefficients given in p. here xroot are [-27.02577916 8.46877068 4.36903767] when increasing degree to deg=9, results contain imaginary roots: [12.83124078+1.06520938j 12.83124078-1.06520938j 10.98184655+0.j 7.86313591+0.j 4.70268776+0.j 1.58653459+0.j - -0.28007017+1.04758677j -0.28007017-1.04758677j] - """ + -0.28007017+1.04758677j -0.28007017-1.04758677j] """ + xroot = np.roots(f_d) - """ - but we just need xroot between x.min() and x.max() - after filter, xroot are [8.468770676220245, 4.369037674890286] - """ + + """but we just need xroot between x.min() and x.max() + after filter, xroot are [8.468770676220245, 4.369037674890286]""" + min, max = x.min(), x.max() xroot = list(filter(lambda x : (x >= min and x < max), xroot)) yroot = np.sin(xroot) fit_1 = AutoPiecewiseLinFit(x, y) - n_1 = fit_1.fit_curve_and_guess() + n_1 = fit_1.fit_curve_and_guess(degree=deg) fit_1.piecewise_fit(n_1) model = fit_1.parse_model() x_hat = [key for key, _ in model.items() for key in key] @@ -287,4 +291,4 @@ def piecewise_fit_fast(self): axes.plot(x,y) axes.scatter(xroot, yroot, color='red') axes.plot(x_hat, y_hat, color='green') - plt.savefig('polyfit_deg_9.png') \ No newline at end of file + plt.savefig(f'polyfit_deg_{deg}.png') \ No newline at end of file