├── docs
    ├── Global.md
    ├── _config.yml
    └── index.md
├── prinpy
    ├── __init__.py
    ├── glob.py
    └── local.py
├── .gitignore
├── setup.py
├── LICENSE
├── README.md
└── prinPy quickstart.ipynb


/docs/Global.md:
--------------------------------------------------------------------------------
1 | 


--------------------------------------------------------------------------------
/prinpy/__init__.py:
--------------------------------------------------------------------------------
1 | 


--------------------------------------------------------------------------------
/docs/_config.yml:
--------------------------------------------------------------------------------
1 | theme: jekyll-theme-minimal


--------------------------------------------------------------------------------
/.gitignore:
--------------------------------------------------------------------------------
1 | #checkpoints
2 | .ipynb_checkpoints/
3 | __pycache__/
4 | build/
5 | dist/
6 | prinpy.egg-info/
7 | 


--------------------------------------------------------------------------------
/docs/index.md:
--------------------------------------------------------------------------------
1 | # prinPy Documentation
2 | Welcome to the prinPy documentation!
3 | 
4 | This site is under construction.
5 | 


--------------------------------------------------------------------------------
/setup.py:
--------------------------------------------------------------------------------
 1 | from setuptools import setup
 2 | 
 3 | with open("README.md", 'r') as f:
 4 |     long_description = f.read()
 5 | 
 6 | setup(
 7 |     name = 'prinpy',
 8 |     version = '0.0.3.1',
 9 |     license = "MIT",
10 |     description = "A package for fitting principal curves in Python",
11 |     author = "https://github.com/artusoma/",
12 |     author_email = 'artusoma1@gmail.com',
13 |     url = 'https://github.com/artusoma/prinPy', 
14 |     packages = ["prinpy"],
15 |     long_description = long_description,
16 |     long_description_content_type='text/markdown',
17 |     install_requires = ['numpy',
18 |                         'matplotlib',
19 |                         'scipy',
20 |                         'keras',
21 |                         'tensorflow',
22 |                         ],
23 | )


--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
 1 | MIT License
 2 | 
 3 | Copyright (c) 2020 artusoma
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | [![Downloads](https://pepy.tech/badge/prinpy)](https://pepy.tech/project/prinpy)
 2 | # prinPy
 3 | `pip install prinpy`<br>
 4 | <br>
 5 | Inspired by [this R package](https://github.com/rcannood/princurve), prinPy brings principal curves to Python. 
 6 | 
 7 | ## What prinPy does
 8 | PrinPy has local and global algorithms for computing principal curves. 
 9 | 
10 | ## What is a Principal Curve?
11 | A principal curve is a smooth n-dimensional curve that passes through the middle of a dataset. Principal curves are a dimensionality reduction tool analogous to a nonlinear principal component. PCs have uses in GPS data, image recognition, bioinformatics, and so much more. 
12 | 
13 | ### Local Algorithms
14 | Local algorithms work on a step-by-step basis. Starting at one end of the curve, it will attempt to make segments that meet an acceptable error threshold as it moves from one end of the curve to the other. Once the algorithm can connect the current point to the end point, the algorithm terminates and a curve is interpolated through the segments. PrinPy currently has two local algorithms:
15 | 
16 | 1. CLPC-g (Greedy Constraint Local Principal Curve)<sup>1</sup>
17 | 2. CLPC-s (One-Dimensional Search Constraint Local Principal Curve)<sup>1</sup>
18 | 
19 | CLPC-g will be faster and is fine for simpler curves. CLPS-s has the potential to be much more accurate at the expense of speed for more difficult curves. After fitting a curve, prinPy has the ability to project to the curve.
20 | 
21 | ### Global Algorithms
22 | Global algorithms, unlike local algorithms, are more like minimization problems. Given a dataset, a global algorithm might make an initial guess at a principal curve and adjust it from there. 
23 | 
24 | The sole global algorithm as of now performs nonlinear principal component analysis. The global algorithm, called NLPCA in this package, is a neural network implementation.<sup>2</sup> This algorithm works by creating an autoassociative neural network with a "bottle-neck" layer which forces the network to learn the most important features of the data. 
25 | 
26 | **Which one should I use?** <br>
27 | The local algorithms will be better for tightly bunched data, such as digit recogniition or GPS data. The global algorithm is better suited for "clouds" of data or sparsely represented data.
28 | 
29 | ## Quick-Start
30 | View the quickstart notebook [here](https://github.com/artusoma/prinPy/blob/master/prinPy%20quickstart.ipynb). Docs will be coming soon!
31 | 
32 | ```python
33 | # Example of local PC fitting
34 | cl = CLPCG() # Create solver
35 | 
36 | # CLPCG.fit() fits the principal curve. takes x_data, y_data,
37 | # and the min allowed error for each step. e_min is acheived 
38 | # through trial and error, but 1/4 to 1/2 data error is what authors
39 | # recommend.
40 | cl.fit(xdata, ydata, e_max = .1) 
41 | cl.plot()       # plots curve, optional axes can be passed
42 | 
43 | # Reconstruct curve
44 | tcks = cl.spline_ticks    # get spline ticks
45 | xy = scipy.interpolate.splev(np.linspace(0,1,100), self.spline_ticks)
46 | ```
47 | 
48 | ## References
49 | \[1\] Dewang Chen, Jiateng Yin, Shiying Yang, Lingxi Li, Peter Pudney,
50 | Constraint local principal curve: Concept, algorithms and applications,
51 | Journal of Computational and Applied Mathematics,
52 | Volume 298,
53 | 2016,
54 | Pages 222-235,
55 | ISSN 0377-0427,
56 | https://doi.org/10.1016/j.cam.2015.11.041.
57 | 
58 | \[2\] Mark Kramer, Nonlinear Principal Component Analysis Using
59 | Autoassociative Neural Networks 
60 | 


--------------------------------------------------------------------------------
/prinpy/glob.py:
--------------------------------------------------------------------------------
  1 | '''
  2 | This is the global module that contains principal curve and nonlinear
  3 | principal component analysis algorithms that work to optimize a line
  4 | over an entire dataset. Additionally, these algorithms should work
  5 | in space greater than 2-dimensions.
  6 | '''
  7 | 
  8 | # General libraries
  9 | import numpy as np
 10 | 
 11 | # ML libraries
 12 | import tensorflow as tf
 13 | import keras
 14 | from keras.models import Model
 15 | from keras.layers import Dense, Input, LeakyReLU
 16 | from keras import optimizers
 17 | import keras.backend as k
 18 | 
 19 | # Preprocessing
 20 | from sklearn.preprocessing import MinMaxScaler, StandardScaler
 21 | 
 22 | 
 23 | def orth_dist(y_true, y_pred):
 24 |     '''
 25 |     Loss function for the NLPCA NN. Returns the sum of the orthogonal
 26 |     distance from the output tensor to the real tensor.
 27 |     '''
 28 |     loss = tf.math.reduce_sum((y_true - y_pred)**2)
 29 |     return loss
 30 | 
 31 | 
 32 | class NLPCA(object):
 33 |     '''This is a global solver for principal curves that uses neural networks.
 34 | 
 35 |     Attributes:
 36 |         None
 37 |     '''
 38 |     def __init__(self):
 39 |         self.fit_points = None
 40 |         self.model = None
 41 |         self.intermediate_layer_model = None
 42 | 
 43 |     def fit(self, data, epochs = 500, nodes = 25, lr = .01, verbose = 0):
 44 |         '''This method creates a model and will fit it to the given m x n 
 45 |         dimensional data.
 46 | 
 47 |         Args:
 48 |             data (np array): A numpy array of shape (m,n), where m is the 
 49 |                 number of points and n is the number of dimensions. 
 50 |             epochs (int): Number of epochs to train neural network, defaults
 51 |                 to 500.
 52 |             nodes (int): Number of nodes for the construction layers. Defaults
 53 |                 to 25. The more complex the curve, the higher this number
 54 |                 should be.
 55 |             lr (float): Learning rate for backprop. Defaults to .01
 56 |             verbose (0 or 1): Verbose = 0 mutes the training text from Keras.
 57 |                 Defaults to 0.
 58 | 
 59 |         Returns:   
 60 |             None
 61 |         '''
 62 |         num_dim = data.shape[1] # get number of dimensions for pts
 63 | 
 64 |         # create models, base and intermediate
 65 |         model = self.create_model(num_dim, nodes = nodes, lr = lr)
 66 |         bname = model.layers[2].name        # bottle-neck layer name
 67 | 
 68 |         # The itermediate model gets the output of the bottleneck layer, 
 69 |         # which acts as the projection layer.
 70 |         self.intermediate_layer_model = Model(inputs=model.input,
 71 |                                         outputs=model.get_layer(bname).output)
 72 | 
 73 |         # Fit the model and set the instances self.model to model
 74 |         model.fit(data, data, epochs = epochs, verbose = verbose)
 75 |         self.model = model
 76 | 
 77 |         return
 78 | 
 79 |     def project(self, data):
 80 |         '''The project function will project the points to the curve generated
 81 |         by the fit function. Given back is the projection index of the original
 82 |         data and a sorted version of the original data. 
 83 | 
 84 |         Args:
 85 |             data (np array): m x n array to project to the curve
 86 | 
 87 |         Returns:
 88 |             proj (array): A one-dimension array that contains the projection
 89 |                 index for each point in data.
 90 |             all_sorted (array): A m x n+1 array that contains data sorted by 
 91 |                 its projection index, along with the index. 
 92 |         '''
 93 |         pts = self.model.predict(data)
 94 |         proj = self.intermediate_layer_model.predict(data)
 95 | 
 96 |         self.fit_points = pts
 97 |         
 98 |         all = np.concatenate([pts, proj], axis = 1)
 99 |         all_sorted = all[all[:,2].argsort()]
100 |         
101 |         return proj, all_sorted
102 | 
103 |     def create_model(self, num_dim, nodes, lr):
104 |         '''Creates a tf model.
105 | 
106 |         Args:
107 |             num_dim (int): How many dimensions the input space is
108 |             nodes (int): How many nodes for the construction layers
109 |             lr (float): Learning rate of backpropigation
110 | 
111 |         Returns: 
112 |             model (object): Keras Model
113 |         '''
114 |         # Create layers:
115 |         # Function G
116 |         input = Input(shape = (num_dim,)) #input layer
117 |         mapping = Dense(nodes, activation = 'sigmoid')(input)   #mapping layer
118 |         bottle = Dense(1, activation = 'sigmoid')(mapping) #bottle-neck layer
119 | 
120 |         # Function H
121 |         demapping = Dense(nodes, activation = 'sigmoid')(bottle)   #mapping layer
122 |         output = Dense(num_dim)(demapping)   #output layer
123 | 
124 |         # Connect and compile model:
125 |         model = Model(inputs = input, outputs = output)
126 |         gradient_descent = optimizers.adam(learning_rate=lr)
127 |         model.compile(loss = orth_dist, optimizer = gradient_descent)
128 | 
129 |         return model
130 | 
131 |     def preprocess(self, data):
132 |         '''Converts individual arrays into a singular m x n array, where
133 |         m is the number of observations and n is the number of dimensions.
134 |         Normalizes the data for faster training.
135 | 
136 |         Args:
137 |             data (list): List of arrays of points. For example, if you have
138 |                 data for x, y, and z stored in arrays x_, y_, and z_, pass
139 |                 in [x_, y_, z_]
140 |         
141 |         Returns:
142 |             data_comb (array): A single m x n, where each column 
143 |                 is MinMaxScaled and normed.
144 |         '''
145 |         data_lists = []
146 | 
147 |         scale = MinMaxScaler(feature_range=(-1,1))
148 |         norm = StandardScaler()
149 |         for arr in data:   
150 |             normed = norm.fit_transform(arr.reshape(-1,1))
151 |             scaled = scale.fit_transform(normed.reshape(-1,1))
152 |             data_lists.append(scaled)
153 |         
154 |         return np.concatenate(data_lists, axis = 1)


--------------------------------------------------------------------------------
/prinpy/local.py:
--------------------------------------------------------------------------------
  1 | '''
  2 | These are local algorithms. These work on a per-step basis. Starting
  3 | at one point, the algorithm attempts to choose the next best point, 
  4 | and so on until the end is reached.
  5 | '''
  6 | 
  7 | # Import some modules
  8 | import numpy as np
  9 | import matplotlib.pyplot as plt
 10 | import scipy.optimize as op
 11 | import scipy.interpolate
 12 | 
 13 | 
 14 | def distg(pts, v1, v2):
 15 |     '''
 16 |     Returns the minimum of points from line and points from vertex
 17 |     pts: points to calulate distance from
 18 |     v1: vertex j
 19 |     v2: vertex j+1
 20 |     '''
 21 |     D1 = np.linalg.norm(v2 - pts, axis = 1)
 22 |     D2 = np.abs(np.cross(v2-v1, v1-pts)) / np.linalg.norm(v2-v1)
 23 | 
 24 |     error_t = [np.min([i,j]) for i,j in zip(D1, D2)]
 25 | 
 26 |     return sum(error_t)/len(error_t)
 27 | 
 28 | def points_in(pts, r1, p):
 29 |     '''
 30 |     Gets points in r1 from p
 31 |     '''
 32 |     distances = np.linalg.norm(p - pts, axis = 1)
 33 |     return pts[(distances < (r1))]
 34 | 
 35 | def points_out(pts, r1, p):
 36 |     '''
 37 |     Gets points out r1 from p
 38 |     '''
 39 |     distances = np.linalg.norm(p - pts, axis = 1)
 40 |     return pts[(distances > r1)]
 41 | 
 42 | def points_btw(pts, r1, r2, p):
 43 |     '''
 44 |     Gets points between r1 < r2 from p
 45 |     '''
 46 |     distances = np.linalg.norm(p - pts, axis = 1)
 47 |     return pts[(distances < r2) & (distances > r1)]
 48 | 
 49 | def reset(x,y):
 50 |     dat = np.concatenate([x.reshape(-1,1), y.reshape(-1,1)], axis = 1)
 51 |     return dat, [dat[0,:]]
 52 | 
 53 | def proj_min(X, tck, pt):
 54 |     '''
 55 |     Finds the distance X along the PC where pt has the shortest
 56 |     projection distance. 
 57 |     '''
 58 |     loc_ = scipy.interpolate.splev(X, tck)
 59 |     return np.linalg.norm(loc_ - pt)
 60 | 
 61 | class CLPCG:
 62 |     def __init__(self):
 63 |         self.fit_points = []
 64 |         self.spline_ticks = None
 65 |     
 66 |     def points(self, x, y, e_max = .2, fmin_error = False):
 67 |         '''Implements CLPC-greedy algorithm. 
 68 | 
 69 |         Args:
 70 |             x (array): x-data to fit
 71 |             y (array): y-data to fit
 72 |             e_max (flat): Max allowed error. If not met, another point P will 
 73 |                 be addedto the curve. Authors suggest 1/4 to 1/2 of 
 74 |                 measurement error. Defaults to .2
 75 | 
 76 |         Returns:   
 77 |             points (array): collection of points that construct the straight 
 78 |             line segments.
 79 |         '''
 80 |          # Combine x,y and sort
 81 |         data = np.concatenate([x.reshape(-1,1), y.reshape(-1,1)], axis = 1)
 82 | 
 83 |         points = []      # points of principal curve
 84 |         points.append(data[0,:])     # Append first point
 85 |         pe = data[-1,:] # end point
 86 | 
 87 |         while 1:
 88 |             pt_found = False 
 89 | 
 90 |             # Start drawing circle
 91 |             rl = 0 # lower radius bound
 92 |             rt = 2 * np.linalg.norm(pe - points[-1]) # upper bound
 93 | 
 94 |             # First, attempt to connect to end point.
 95 |             # Connecting to the end point with acceptable ei is the 
 96 |             # termination condition.
 97 |             rend = np.linalg.norm(pe - points[-1])
 98 |             in_c = points_in(data, rend, points[-1]) #get pts inside circle
 99 |             try:
100 |                 e_end = distg(in_c, points[-1], pe) # calculate error to end pt
101 |             except ZeroDivisionError: # successfully terminates, weird case
102 |                 break
103 | 
104 |             if e_end <= e_max:
105 |                 points.append(pe)
106 |                 break
107 | 
108 |             while not pt_found: # point with acceptable error not found
109 |                 # begin draw circle with radius ri
110 |                 ri = rl + (rt - rl)/2
111 | 
112 |                 in_c = points_in(data, ri, points[-1]) #get pts inside circle
113 |                 rj = ri * .9    # Construct inner radius
114 |                 btw_c = points_btw(data, rj, ri, points[-1]) #get pts btw circle
115 |                 
116 |                 if btw_c.shape[0] == 0:  # No points s.t. rj > ||p|| > ri
117 |                     raise ValueError("e_max = %f is too small. Choose a " \
118 |                                      "larger e_max." % e_max)   
119 |                 else:
120 |                     # candidate point is mean of points in circle sector
121 |                     p2 = np.array([np.mean(btw_c[:,0]), np.mean(btw_c[:,1])])
122 |                     e_i = distg(in_c, points[-1], p2) # calculate error
123 | 
124 |                 if e_i > e_max:  # if error not acceptable, reduce size of rt
125 |                     rt = ri
126 | 
127 |                 # If error is acceptable, add p2 to points
128 |                 else:       
129 |                     data = points_out(data, ri, points[-1])
130 |                     points.append(p2)
131 |                     pt_found = True
132 | 
133 |         # transform points into an array
134 |         res_x = np.array([p[0] for p in points])
135 |         res_y = np.array([p[1] for p in points])
136 |         res = np.concatenate([res_x.reshape(-1,1), res_y.reshape(-1,1)], axis = 1)
137 | 
138 |         if res.shape[0] <= 3:
139 |             raise ValueError("Not enough points generated: Spline degre 3 with" \
140 |                               " %d points generated. Try reducing e_max" \
141 |                              % (res.shape[0]))
142 | 
143 |         self.fit_points = res
144 |         return res
145 | 
146 |     def fit(self, x, y, e_max = .2, fmin_error = False):
147 |         '''
148 |         Calculates principal curve ticks
149 | 
150 |         Args: same as points
151 | 
152 |         Returns: 
153 |             None
154 |         '''
155 |         res = self.points(x, y, e_max, fmin_error)
156 |         tck, u = scipy.interpolate.splprep(res.T, s = 0)
157 |         self.spline_ticks = tck
158 | 
159 |         return
160 | 
161 |     def plot(self, ax = None):
162 |         '''
163 |         Plots the curve to a MPL axes object.
164 | 
165 |         Args:
166 |             ax (object): Optional set of ax to plot to. If None, a set of ax
167 |                 will be created. 
168 |         '''
169 |         if ax == None:
170 |             fig, ax = plt.subplots()
171 |         xy = scipy.interpolate.splev(np.linspace(0,1,100), self.spline_ticks)
172 |         ax.plot(xy[0], xy[1], c = 'black')
173 |         return
174 | 
175 |     def project(self, x, y):
176 |         '''
177 |         Projects points x,y to principal curve calculated by calc_pc
178 |         Args:
179 |             x (array): x-data to project
180 |             y (array): y-data to project
181 |         Returns:
182 |             proj (array): Projecton index of points onto curve between (0,1)
183 |         '''
184 |         # for each point min distance to curve
185 |         data = np.concatenate([x.reshape(-1,1), y.reshape(-1,1)], axis = 1)
186 | 
187 |         proj = []
188 |         for p in data:
189 |             proj_dist = op.minimize(
190 |                     proj_min,
191 |                     x0 = [.5],
192 |                     args = (self.spline_ticks, p),
193 |                     method = 'Powell'
194 |                     ).x
195 |             proj.append(proj_dist)
196 |         return proj
197 | 
198 | # Functions specific to the search alg, namely finding the 
199 | # error line and the function we search with/minimize
200 | def to_min_error(theta, pts, v1, r1):
201 |     v2 = np.array([v1[0]+r1*np.cos(theta[0]), v1[1]+r1*np.sin(theta[0])])
202 |     D1 = np.linalg.norm(v2 - pts, axis = 1)
203 |     D2 = np.abs(np.cross(v2-v1, v1-pts)) / np.linalg.norm(v2-v1)
204 | 
205 |     error_t = [np.min([i,j]) for i,j in zip(D1, D2)]
206 | 
207 |     return sum(error_t)/len(error_t)
208 | 
209 | def error_line(theta, c, r1):
210 |     p2 = np.array([c[0]+r1*np.cos(theta), c[1]+r1*np.sin(theta)])
211 |     return p2
212 | 
213 | def point_dist(pts, v1, v2):
214 |     '''
215 |     Tells CLPCS if it should invert direction of best fit line
216 |     v1: vertex j
217 |     v2: vertex j+1
218 |     '''
219 |     D1 = np.linalg.norm(v2 - pts, axis = 1)
220 |     return sum(D1)/len(D1)
221 | 
222 | class CLPCS:
223 |     def __init__(self):
224 |         self.fit_points = []
225 |         self.spline_ticks = None
226 |     
227 |     def points(self, x, y, e_max = .2, rl = 0):
228 |         '''Implements CLPC one dimensional search algorithm
229 | 
230 |         Args:
231 |             x (array): x-data to fit
232 |             y (array): y-data to fit
233 |             e_max (flat): Max allowed error. If not met, another point P will 
234 |                 be addedto the curve. Authors suggest 1/4 to 1/2 of 
235 |                 measurement error. Defaults to .2
236 | 
237 |         Returns:   
238 |             points (array): collection of points that construct the straight 
239 |             line segments.
240 |         '''
241 |         # Combine x,y and sort
242 |         data = np.concatenate([x.reshape(-1,1), y.reshape(-1,1)], axis = 1)
243 | 
244 |         points = []      # points of principal curve
245 |         points.append(data[0,:])     # Append first point
246 |         pe = data[-1,:] # end point
247 | 
248 |         while 1:
249 |             pt_found = False
250 | 
251 |             # Start drawing circle
252 |             rt = 2 * np.linalg.norm(pe - points[-1]) # upper bound
253 | 
254 |             # First, attempt to connect to end point.
255 |             # Connecting to the end point with acceptable ei is the 
256 |             # termination condition.
257 |             rend = np.linalg.norm(pe - points[-1])
258 |             in_c = points_in(data, rend, points[-1]) #get pts inside circle
259 |             try:
260 |                 e_end = distg(in_c, points[-1], pe) # calculate error to end pt
261 |             except ZeroDivisionError: # successfully terminates, weird case
262 |                 break
263 | 
264 |             if e_end <= e_max:
265 |                 points.append(pe)
266 |                 break
267 | 
268 |             while not pt_found:
269 |                 ri = rl + (rt - rl)/2
270 | 
271 |                 # Get points inside circle
272 |                 in_c = points_in(data, ri, points[-1])
273 |                 
274 |                 if in_c.shape[0] == 0:  # No points are in circle
275 |                     raise ValueError("e_max = %f is too small. Choose a " \
276 |                                     "smaller e_max." % e_max)   
277 |                     
278 |                 else:
279 |                     # find min error
280 |                     theta = op.minimize(
281 |                         to_min_error,
282 |                         x0 = [0],
283 |                         args = (in_c, points[-1], ri),
284 |                         method = 'Powell'
285 |                         ).x
286 |                     p2 = error_line(theta, points[-1], ri) 
287 |                     e_i = distg(in_c, points[-1], p2) # calculate error
288 |                     p_error = point_dist(in_c, points[-1], p2)
289 | 
290 |                     # Try to invert p2 and check error. This is because
291 |                     # the optimzation alg can fail to account for the fact
292 |                     # that p2 could be closer to points than drawing other dir
293 |                     theta_inv = np.pi + theta
294 |                     p2_inv = error_line(theta_inv, points[-1], ri)
295 |                     p_error_inv = point_dist(in_c, points[-1], p2_inv)
296 | 
297 |                     if p_error_inv < p_error: p2 = p2_inv
298 | 
299 |                 if e_i >= e_max:
300 |                     rt = ri
301 |                 else:
302 |                     data = points_out(data, ri, points[-1])
303 |                     points.append(p2)
304 | 
305 |                     pt_found = True
306 |             
307 |         res_x = np.array([p[0] for p in points])
308 |         res_y = np.array([p[1] for p in points])
309 |         res = np.concatenate([res_x.reshape(-1,1), res_y.reshape(-1,1)], axis = 1)
310 |         return res
311 | 
312 |     def fit(self, x, y, e_max = .2, rl = 0):
313 |         '''
314 |         Calculates principal curve ticks
315 |         Args: same as fit_points
316 | 
317 |         Returns: 
318 |             None
319 |         '''
320 |         res = self.points(x, y, e_max, rl)
321 |         tck, u = scipy.interpolate.splprep(res.T, s = 0)
322 |         self.spline_ticks = tck
323 |         return
324 | 
325 |     def plot(self, ax = None, **kwargs):
326 |         '''
327 |         Plots the curve to a MPL axes object.
328 |         Args:
329 |             ax (object): Optional set of ax to plot to. If None, a 
330 |                 set of ax will be created. 
331 |         '''
332 |         if ax == None:
333 |             fig, ax = plt.subplots()
334 |         xy = scipy.interpolate.splev(np.linspace(0,1,100), self.spline_ticks)
335 |         ax.plot(xy[0], xy[1], c = 'black', **kwargs)
336 |         return
337 | 
338 |     def project(self, x, y):
339 |         '''
340 |         Projects points x,y to principal curve calculated by calc_pc
341 |         Args:
342 |             x (array): x-data to project
343 |             y (array): y-data to project
344 |         Returns:
345 |             proj (array): projections of points onto curve between (0,1)
346 |         '''
347 |         # for each point min distance to curve
348 |         data = np.concatenate([x.reshape(-1,1), y.reshape(-1,1)], axis = 1)
349 | 
350 |         proj = []
351 |         for p in data:
352 |             proj_dist = op.minimize(
353 |                     proj_min,
354 |                     x0 = [.5],
355 |                     args = (self.spline_ticks, p),
356 |                     method = 'Powell'
357 |                     ).x
358 |             proj.append(proj_dist)
359 |         return proj
360 | 


--------------------------------------------------------------------------------
/prinPy quickstart.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# prinPy Quickstart Guide"
  8 |    ]
  9 |   },
 10 |   {
 11 |    "cell_type": "markdown",
 12 |    "metadata": {},
 13 |    "source": [
 14 |     "prinPy has global and local algorithms. "
 15 |    ]
 16 |   },
 17 |   {
 18 |    "cell_type": "markdown",
 19 |    "metadata": {},
 20 |    "source": [
 21 |     "## 1. Local Algorithms"
 22 |    ]
 23 |   },
 24 |   {
 25 |    "cell_type": "code",
 26 |    "execution_count": 75,
 27 |    "metadata": {},
 28 |    "outputs": [],
 29 |    "source": [
 30 |     "from prinpy.local import CLPCG\n",
 31 |     "\n",
 32 |     "# Some other modules\n",
 33 |     "import numpy as np\n",
 34 |     "import matplotlib.pyplot as plt\n",
 35 |     "import seaborn as sns; sns.set()\n",
 36 |     "import timeit"
 37 |    ]
 38 |   },
 39 |   {
 40 |    "cell_type": "markdown",
 41 |    "metadata": {},
 42 |    "source": [
 43 |     "### Generate Test Data"
 44 |    ]
 45 |   },
 46 |   {
 47 |    "cell_type": "code",
 48 |    "execution_count": 2,
 49 |    "metadata": {},
 50 |    "outputs": [],
 51 |    "source": [
 52 |     "theta = np.linspace(0,np.pi*3, 1000)\n",
 53 |     "r = np.linspace(0,1,1000) ** .5\n",
 54 |     "\n",
 55 |     "x_data = r * np.cos(theta) + np.random.normal(scale = .02, size = 1000)\n",
 56 |     "y_data = r * np.sin(theta) + np.random.normal(scale = .02, size = 1000)"
 57 |    ]
 58 |   },
 59 |   {
 60 |    "cell_type": "markdown",
 61 |    "metadata": {},
 62 |    "source": [
 63 |     "### Plot"
 64 |    ]
 65 |   },
 66 |   {
 67 |    "cell_type": "code",
 68 |    "execution_count": 3,
 69 |    "metadata": {},
 70 |    "outputs": [
 71 |     {
 72 |      "data": {
 73 |       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAD4CAYAAADhNOGaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nO29e3RU15ng+9sGl4OEgyWhEBsEEkIWkdOOYss2wSYYA0noZiD3jnHsXrmteJLB6dtxWE4mKybhJp2EHrs7y80lub3aZnriyP1wbDzTCU3CSgOWbbCCbeHgl2IhFRKIR+NCEsSoFAqJff84tY92HZ0qlahSqR7fby2tqjpnn6qt89jf/r79PZTWGkEQBKFwuWKyOyAIgiBMLiIIBEEQChwRBIIgCAWOCAJBEIQCRwSBIAhCgTN1sjtwOcycOVNXVlZOdjcEQRByioMHD57RWpd7t+ekIKisrKS1tXWyuyEIgpBTKKWO+m1Pi2lIKfUTpdR7Sqm34+xXSqkfKaU6lVJvKqVusvY1KqU6on+N6eiPIAiCkDzpWiP4KfCZBPtXATXRv/XA3wMopUqB7wK3AbcC31VKlaSpT4IgCEISpEUQaK1fAvoSNFkLPKUdDgDXKKWuBT4N7NZa92mt+4HdJBYogiAIQprJlNfQbKDH+nw8ui3edkEQBCFDZEoQKJ9tOsH20V+g1HqlVKtSqjUUCqW1c4IgCIVMpgTBcaDC+jwHOJlg+yi01tu01g1a64by8lHeT4IgCMJlkilBsAP4s6j30CLgnNb6FPBr4FNKqZLoIvGnotsEQRCEDJGWOAKl1NPAncBMpdRxHE+gKwG01o8DvwL+GOgEwsD90X19SqkfAK9Fv+r7WutEi86CIAhCmkmLINBa3zfGfg38RZx9PwF+ko5+CEI66RuIsL21h3UNFZQWBya7O4IwYUiuISHv6RuI8MSLQfoGIuM6bntrD4/sepftrT1jN04zl9tnQbgccjLFhCCMBzOgAzywtDrp49Y1VMS8psp4NIzL7bMgXA4iCIS853IH9NLiAA8srXZn58maiOIN+MkM7ubYFXWzLqvPgnA5iGlIyAsSmVLMgF5aHIhp5z0m3nfYJqJkTDamfVNLd0zbdQ0VbFy1MGZw936fOXbzzja33RMvBgmGzif8Xb9+iXlJSBbRCIS8IFlTit0uHBlm694OwpFhHlp5vbvvwJFeHrun3p3N2xqF3+/Ys/g9bafd2Xw4MhTT1gikRP1e11DBgSO9NLeH3LUJ06fm9pDv79r9CkeGKQpMidtXQfBDBIGQNYzXS8duP5b5p28gQlNLN4ORITYsr2FdQwVNLV3Rvdo91h6EzeBpD+DrGioIR4YIR4bpG4hQWhyIESDN7SFXkPSHI7x5/By3VJbyxItBbqks5cfPd7BpdR0lRc5xt1SWsqy23BUepcUBHrun3v2/DCvqZrFo/ml3W99AhK8/e8gVDma7ET7hyDCg3f/1cs+xUBiIIBCyBr9ZbaLByjvjHUsT2Lq3A4CNqxZGtyo2LF9A4+IqYGQQbmrpihnovYNnUWAqj+x6l6LAFHcWD0QH87aY2bwZqJvbQ1SXFxMMDQBtLJpfxiO73mVZbTnN7SEWzT9N9dLpbj/s/8W8N/vN/9PcHmJZbbnbL0e4dbNh+QJAs3VvJxtXLRz3OgWMCE7QNC6uivkOESb5hwgCISMkM3h4Z7WQeLAazyKwM5N3ZsnGbLJ1b4crFOzFYHugX9dQETPztgd+82oP3Ilm816NwN433kVhuw/mfNr/07qGCooCU1nXUBFXcwqGzrN5ZxubVtdRXT495vttwVkUmBpzHcTklH8oJ9Yrt2hoaNBSoSy3eOLFII/sepeNqxaOOXgkmo0mOuZyzUpmYDN989u3rLY8Zt0gEyTzP9ltAN/25tyb/8G029cRYn9nL8tqy3ny/ltHfa9oBPmHUuqg1rrBu100AiEjjGf27gwujmkD4KGVtTH7/Qai8bhmmuNsu7/9Gm+f+a1MDYTJ/E/JmMfWNVSwr+MMze0hmlq6KQpM4ZFd77J+yXyunHIFm1bXjTqmtDjAQyuvjytoRBPIL0QQCBnBHlz9BtLR25wM5YMXL43y4bcHv1sqS/nGc2/w//xJ3SjXTC/xBlY/b55E+zJlGklGePq18Z7L0uIAN8+7hv2dZzCmMfuY7a09lDQEfIWan5fVvo4QP7rvpowLRmHiEEEgpEy8gd3xylE0Lq4cc8GyqaWLrXs7CUeGeGhlLY2LKykKTKH3/AUe2fUuvecjlE0PjLJzr3u8hWBogB/8so29X78zYT/TFSmc7ojjeCQSUIna+J3fxsVV7pqBfYwxG9ltbVbUzeLAkV5W1M1ix6ETAOzv7I3xqhpLMCZjvhImFxEEQsqMePsMuYONs9jY6baxvYD8B1IV82oGqy27DwPQduoc+zt7gVgTyA/v/hjfeO4Nfnj3x8bsZzIDazKk63smCr/zG6/PYwm1PW2nXa8mx7tKYWsVyXyHLSgAWWjOQkQQCCkz4u0z7D7k6xoq6D0foe3UOQYjQ64Hih1YZaduMBqAdzAx202wlnf/TfNKxtQECo3xCKqx2noHeVug2zP98Xp3SeqM7EIEgZASXrXfHijKpgfcWbw3sAmSW+i0Byrbj17IDInMSJezQB+vbSJXVmHiEUEgJGSshcBEg7kdqbukpnzU8ZmytQvpwXu9konm9sZgeNNxmPtq8862aLu2Ua6swsQjgkAYhZ8fPfjP5BINBvHSJQi5RTwT0FhmJW/0s9nml47DcWFt83VlFSYeEQTCKOzB3zvQ+7kmJhoMEu2XCNXcIFkT0OMvBnnnxDm+/9mPUl0+3TcGI146jgeWVosmMImIIBBi6BuIEI4Ms2H5glGuhhA7o0s10lZMQ7lBMtdpe2sP2146AsDmnY55x28SYLzGtrf2sGl1HTfOORGT10mYHEQQCDHY+Wq8D6YREncsKIuJUr1cn/Bsd8MUHJK5TusaKugdiPDOiXNjmndsDcObwE+YHNIiCJRSnwG2AlOAf9BaP+rZvwVYFv1YBHxIa31NdN8w8FZ03zGt9Zp09EkYH/YiXjgyTDgyNGqWZoTEhuULWFJTnnRyOCH/KS0O8K0//khSbb0aht/9ligg0SARzekjZUGglJoC/B2wEjgOvKaU2qG1bjNttNYPWe0fBD5ufcWg1ro+1X4Il0/fQISvPv1b9neecVNAO7O0qaO8gMyr8SMH5Ss0BCEeXg3D735LFJBoEuK1dvfxcnAkyFC4fNKhEdwKdGqtjwAopX4GrAXa4rS/D/huGn5XGAeJZk/bW3uieWjALxeNwfsAOymb/YWGICRLvICzcGQIE8nsjV8wAYq2R5Jw+aRDEMwGeqzPx4Hb/BoqpeYBVcDz1uYPKKVagSHgUa31z+Mcux5YDzB37tw0dLuwSOT5YefqNymHkw0QkgVfIVXiLSqbrLN9AxGKAlNZUTeLJ14MuuZL0Kypny15jNJAOgSB8tkWr8jBvcBzWutha9tcrfVJpdR84Hml1Fta6+CoL9R6G7ANnHoEqXa60BjLDdSbcjjeg+QVKLLgK0w0ZsJhB6c9tPJ6IDbaGSSP0eWSDkFwHLCng3OAk3Ha3gv8hb1Ba30y+npEKfUCzvrBKEEgpBc/DSEZf3HRAIRMY0com/rOJkeV5DFKD1ek4TteA2qUUlVKqQDOYL/D20gpVQuUAL+xtpUopa6Kvp8J3E78tQVhnJikbmam/8iud9ne2jMqVsC09W7zw2gAonoLmcKOUH7snnr2tJ1272X7frTf2/e+MDYpawRa6yGl1FeAX+O4j/5Ea/2OUur7QKvW2giF+4Cf6djamB8BnlBKXcIRSo/a3kZCasSLEPaLFUgUPyAIk4nXW83+HM+cKVHr40NqFucx8R6S5CqECUL2Y9YINiyviXExlWym/sSrWZwO05CQ5fSHY9VkO8zf3iYmHyHXWNdQwcZVCzEupl9/9hB9AxF2HDpJc3uIHYfiLVcKNiIIcpBk7Z9GPd68sy3mIbH3bW/tSfgdgpDNmAnMmvrZVJcXu0nsjONia3ffqOdE1g9GI7mGcpBk7Z+JMj2K94+QT+xpO00wNBATYPbm8XMx97xB1g9GI2sEOUKiAuDJ2PdlDUDIZ8az7lXIz4KsEeQ4tinHa8/3uoY+8WKQYOj8qHUBWQMQ8hW/+9u7zTwbwKg1skJHTEM5QiJTjtc19JFd7/L0q8fo7g0Tjgy7UZiCkM/EK4NpsGtp3DjnGjdfkV1CsxC1BBCNIOuxZzHxZvT2zGddQwXLasvp7g1H9+ae6U8QLgevc4TXEcI8G06aCs3GVQtHldAsVOcJ0QiynGTLBNqzmcfuqaeppRuTRE4QCgHbOWLR/NO+2XPNszEYGcbJcxl7rPeYQtEURBBkOX43qPfm9EsEJ+YgodCwEyBWL/UPIjOp041ZyKRPj5c80fts5atgEEGQ5fjdoN6bU1xBBSF57LTr8Z4Ze73BHAP563oqgiAH8Q78kgpaEMaHX61te7bf1NLF1r2dhCNDbl0EyN/suyIIJpFEamYwdJ5v/e+3AM1//z9vpKQokNAjQhCE5Ig3q7e3j5RZiS23kq+TLhEEk0giNXPzzjZe6epz3y+aX+a6vpniHPl4QwrCRBNvVu/dbrSGQkAEwSSSSM3ctLqOcMTRCDatrqOkyJn9x/OIEAQhObyzelszt7cbExEoGhdXjorih/wpjSmCYBJJpGZWl0/nmQc+EbNtLI8IQRDGTyJT0da9nYCjHTywtNpjPsqf0pgiCARBKGgSmYrCkSFAjWqTb6UxRRBkkHxVKwUhl4mnmTvxOLU+RyQ+LheRFBMZpKmlm0d2vUtTS/eokPZg6Dz3P/kqwdD5Se6lIBQu8ZI2GvI1FYVoBBlFu69eFXPzzraoN1AbT95/6+R0TxAKHDsxnZ93nsQRCOPGGyfQuLiKosBU97N9g21aXQe0RV8FQZgMzLrA4MVL3DhnBusaKkY9x/liDrJJi2lIKfUZpVS7UqpTKfWwz/4vKKVCSqlD0b8vWfsalVId0b/GdPQnW/CqkYlqAlSXT+fJ+2+NKbQtJfUEIbM4uYimsu2lIxQFpsbk8rLNQX0DEbbsbmfL7sN58XymrBEopaYAfwesBI4Drymldmit2zxNn9Faf8VzbCnwXaABx25yMHpsf6r9mkzi5Snx7h9roThf85oIQjYTz0PIfo5NCgoYcS3NZdJhGroV6NRaHwFQSv0MWAt4BYEfnwZ2a637osfuBj4DPJ2Gfk0a8fKUGOIN8F4Bka/2SEHIZrzmH39zkJN64o4FM1lRN4snXgzmtAdgOgTBbMBeQj8O3ObT7j8rpT4JHAYe0lr3xDl2tt+PKKXWA+sB5s6dm4ZuTwx9AxEOHHFSQwxevOQ7+483wPulk871mYYg5CONiyvdFBT5oLmnQxAon23eslj/Bjyttb6glPoy0ATcleSxzkattwHbwClef/ndnVi2t/a4OYKmXXmF700Sb4AXDUAQcgP7GTZprcORIfoGIjmpFaRDEBwH7JFrDnDSbqC17rU+/g/gr61j7/Qc+0Ia+jRp2LnO7epgyQzuogEIQu5hit08sutdt9BNrpEOr6HXgBqlVJVSKgDcC+ywGyilrrU+rgF+F33/a+BTSqkSpVQJ8KnotpymKDCFxsVVlBYHEnoKCbmBn/eWeHQVDslc63UNFW4N5Fy8N1IWBFrrIeArOAP474BntdbvKKW+r5RaE232VaXUO0qpN4CvAl+IHtsH/ABHmLwGfN8sHOcq8SIPc/HmEBz8rmm+RpgKo0nmWtsTPpNB4KtP/zZnnve0BJRprX8F/Mqz7TvW+43AxjjH/gT4STr6MRkk4+nTNxDh688ekjoCWYT3uiVy6U2UaKxQi50XEsmu3Zlr3z9wAYD9nWdoaummcXFl0vfaZCGRxSmSjKfP9tYemttDLKstl4XgScL78NnXbV1DBX/+Twd5pauP3oEI3/rjj8Qc63dNky12bn67qaUbs27k9/DbsSdSgS67SHbtzlz7OxbMdLft63iPg0f72N/pLJN6U1lny6RQBEGK2B4Drx/t58fPd7BpdV1MhLA9o5CHO/P4aWT2NbE9vd7o6WfL7na8xUjsgRxGMsf2hyNs3tnGg3fV8Fp3H7dUlnLHgpn0nr/gepA4ee073P7YaUYMY+W4EbIfc0+tqJvFd3/xNvs7e3n92DkA7lhQljBAbbIRQZAitsfAzjdPEQwN4E0cJ95AmcNP7Y6nkYUjwzS1dLGmfja95yO0nTpH3bUz3IjRg0f7+dF9H6eppTtmIAfF1r0dhCPDtHb38XKwl64zA3T3hllWW87+zjPs7zzDtMBUHlp5vTtZ6B+4wC8OnaS7N8yBI708dk/9qNgSU4HOL0gpG00Kwgj2c/6j+26iqaWbA0fO8EpXPzfPK3GvWTaOByII0oB5iG+pLHU1AiFz2GYVk8U1HBmiKDCVFXWz6B2IcHt1GZtW18UIB3tw/9affMT9rkM9/bza3c/+zjPRBcKRsJWDR/upu/aD0U+aG2bP4OVgL5+sKee+W6exom4WF4ed2eBvgmcAJ/jooZXXc/+Tr9LdG6a0+Eqa20Nsb+3hgaXVowb46qXTeeLF4CjzQTaaFAR/nFoG1xMMXcfmnW2sqfeNk80aRBCMk7EWGSWFdObxmlWW1ZYDikd2vctLh0O8HHTss3vaTrtlPtc1VLCvw5m5/+LQSdbUz6a6fDqlxQHq55bwanc/t1WVxmgQB4/2s7+zl5vnlbquggBlxQHXtl9SFOBH993kmqJe7e53c9E0fqKS14/1M7P4SirLiuk9f4Fg6LwrvA4c6WXT6jr2tJ32zVO1om4WB470uvuE7GdP22ma20Msmu/ce9mq1YkgGCdm0DEzznBk2DUTmJDzbLrAucTlPiTG9DIYGaLmQ1czLTCFNfXXURSYQu9AhJeDva6N1rH3OwXJv7f2BtY/1UowNMDmnW08dk+9owFoRwNYNL/U7cdDK2vj9u+BpdWjZvCP3VPv/o4ZzJt+0825wSHODQ4BYV4/dpaO987T3B6iurzYrUfhXSMwv3uif5Dm9hCd773KT/+Lk6k2WwcWwcG7HpCtWp0IgnFiLmg4Mswju95lw/IFbFy1kHBkKCsvcC6R6CFJNOA5nzXb9nVxx4Iy9nf2urPwvoEIZVG33tLiAFt2H47JGrntzxrYvNOpA2F+f8PympgZv/078frlncH7lTnctLqOcOQtLg4P89HZ11BSdCVr6mdz45yTDEaGWL5Q8YeLw9xeXRYz6zdrFBUl0wDo6R9k805nHcrWhuw1ByE7yVatTgTBODGxAk0tXWxYXhPjWWK8QYTLI5FvvjG12JoXjHjvmLRVddfOYElNecyAbA/eg5EhAG6rKhllzitpGFm4TXZA9bqhJpqdV5dP55kHPuH+T9tbeygpcpwNtu7tcIUYjJix+gYitHY7Hk3lVwcovzrAlVOmsGl1HX0DEcIRR3DYaw5C9uCd3BhTEbRlleAWQXAZOAuNnWxctTCrPQFyjUS++SO2f+0+WEDUTDcMwPolVUwbwzw3LeDc8ovmz/TVLMZ7Db1uqMlqhV4BAtB7PsL+zl5urx5xNWxq6eblYC+VZUW8fuwcG1ctdL/7iReDbN3bwfpPzicw9Yqsm2UK/jUNzFpWNgluEQRJYpsmbqkspbq8mFsqSye7W3lDMpG9K+pm8cyrPdyxYMR0sq/jDL8JnuHV7n6W1ZbT3B7izeNn3UVX7/fZ6YPTgTcLpf2aCG9siWvGmj5ixuobiHDwqKMNfKpuFmXTr/KNbg5HhmIWJIXswa+2gVmLyibrgQiCJLFncAeO9BIMDfDj5zvESyhNjFWsxw7SAcd0Eo4Msb/TcdFcVlvu1n2Ot+gKE6u5jee7k4lW3t7aw/7OXpbVlvPlOxf4ajAr6mbxnZ+/zfpPzvetr2sjC8vZgS34s6WgjQiCJHBssUNsWF7jagTH+sI8eFfNZHctb/DOps2gFY4MsXVvJweO9LpC4I4FM6PrNN3Rz2WuvdXMtkxgVjbNusaLrQnFG8C/8/O3XffY0uKA671k1lLs2JY9bafFoSGLyCYPIhEESeBdE9je2kMwNMBr3X3cNK9ksruX9Yw1E7X3A2zZ3c7Bo2fZ33mGOxbMZMPyBa53jZ2vZ039da4ZyG+tJtfNJOZ/8QsuM5iAthtmz3AnLOs/Od+NeK4sK6K7N8zF4Xf40X0fB7IrtUE+YlKSDEaGmBaY6jqUeMmmVBMiCJIgmWLWQnwSedbEegQN8ebxc65Jp7q8mP2dZ1hSM5Pq8uk8tPL6mO/1BuvkK/b95hWqX15a7brHmgnLvNIijvaFua2qlMjQMN29UHft1eLQkCG8UetvHj/r6yFkX4/xZMOdCEQQJEGiCyaMTSLPGuMRdFtVqZuH57aqEq6cMoWvrbye17r74grcQhHI9v3n1Q7sfSvqZvFsVFs1/LbnHBUl0zjUc5Zg6HxMMkRhYrADHNtO/T6hh9CICXTYFR6TkaFUBME48V4gEQzjI55W9dLhEN29YarLi1k0v4yteztZUjMz4UNQiDPcRMJvT9tpgqEBVyMA7cYm9PQP8p2fv80//9dFGe5x4WHyDMFos6eXkSDGBTFBjJme5IggGCe5EjI+GcQTit60HObcGY+JB5ZWuwnjNq2uiwZZSXCeH4mEnzMTHWLw4iXeOXGOl4NOTMJNc6/h9WNnuWH2DEC02kwy1mQlXor6TE9yRBCQ2oNRKOaJZIgnFE1Y/eDFS2zdGxsMZtpWl0+PccUtdKF6OTgp0aeyda+TJiMw9Qqa20NsWF7Dp2/4sO/kZaxoaGFiyRatVgQByc3qve6Mpm22XMhswHZ33LL7MMbDxyzq3jhnBhuW19B7PgJo1x1XSB/eiYkpqGMP9Ha+G9FoM0/fQITHX+jkjePn+NicGb4xIplGBAHJzeqbWrrYureT9Uvm+yYkE0bYcehkjNeEqeplcjRt23cEgI2rFgJkTVBNPuCdmJiiSUWBqe6alkl7bcdZyP2cOba39rBtXxcAr3T1UTb9qkkXwlek40uUUp9RSrUrpTqVUg/77P+aUqpNKfWmUmqvUmqetW9YKXUo+rcjHf0ZL+bhSTwQOUnNpkWzWsqgNRozu2zt7uO2KpN+Q3nOr3MeTVpoc4xTAEZIN+saKti4aqFb8ayppYvm9hB3LCgjHE3AZ65D30BkkntbGKxrqODWSif+6NbKkqwQwkprPXarRF+g1BTgMLASOA68BtyntW6z2iwDXtFah5VSfw7cqbX+XHTfea31uHzaGhoadGtra0r9joffekEyxccLGb8KYRuWL/CtzTvZ/tL5TLxzacdqbFheA2g3YM9oZY/sepdlteVZlREzn7GfGb+cWBOFUuqg1rrBuz0dGsGtQKfW+ojWOgL8DFhrN9BaN2utw9GPB4A5afjdCcFvhmoCRIoCU2OEwxMvBgtuFuX3fze1dPHIrnd55tVj3DjnGtYvqcIUZIkXROONBJbBJ3XiaVcmVqO6vJil15dHK62doaJkGif6w24pz+b2EF9/9lDB3dOZxhbYJu3HZGvE6VgjmA3Y/8Vx4LYE7b8I7LI+f0Ap1QoMAY9qrX/ud5BSaj2wHmDu3LkpdTgRfjlv7DxDhkJdZPOLozh49CwAbafeZ3/nGTcLqCkOI2SGePZ+O/XxN557ww046+kf5KkDxwBivIyyKT1yPuL12gpHhghHhgmGzmdUO7BJhyBQPtt87U1Kqc8DDcBSa/NcrfVJpdR84Hml1Fta6+CoL9R6G7ANHNNQ6t32xy8DpLf2ABSu26hfHMX+zjOUFl/Jl+6oYknNTDfhm7FLi9knM8TzYDPJ+Ix56OMVM3jv/QuUFV/Jwg/P4OS5P7Cm/joaF1dmXXrkfMT7DJm0Km8eP+ubMTcTpMM0dByw75w5wElvI6XUCuDbwBqt9QWzXWt9Mvp6BHgB+Hga+pQUtpnDvA+GzrNl92G27G6nbyDiLrZ5Hw4xaTisa6iguryYvoGL/MN+xxOipCjgVmPKBrVXGBEGG1ctpPiqKzlx9g+8eeJ9QucvsL/zDHvaTrvV98zCcaGaPycae+ywiy5tWl03aR6J6dAIXgNqlFJVwAngXuBP7QZKqY8DTwCf0Vq/Z20vAcJa6wtKqZnA7cDfpKFPSWGraIBb+9VIZeNyJ2ryCH5Rwj+8+2N847k3mD+zKGaft46vMLmYAWhF3Sy+9b/fQmvNg3fVsGh+mau92TlvgII0f2YSk5cItDuBmgxSFgRa6yGl1FeAXwNTgJ9ord9RSn0faNVa7wB+CEwHtiulAI5prdcAHwGeUEpdwtFOHrW9jSYar4pmEkXVzLqaaVdeIQOYD/a5soVoMDTA6huvY+OqhTH7ZADJPqrLp7Nofilb93by4uH3eGhlrZvMzpvzBkSQTzQjJiFFUWBKxj2JIE0BZVrrXwG/8mz7jvV+RZzjWoA/SkcfLge/4Jutezti6sIWOl6XRHPOgqHzHDzaR+/5CJ+7NTZfSt9AJK3lIIWJwFnaO3i03zWBAu4gBNmT/iCf8avHbVslMnX+JbLYwl7B7xuIJPR/LxTieUftOHSC/Z1O1bCy6aPrssoAkt00Lq50Z6JNLV2umc9c796BCB2n32fT6jpJXT2B2KahNfWzXZNqpqvriSCwMEm7nJD8KaO8h/Ld3OEn7MyNGo4Mxbi3eSOEhdyitDjAptV1XBx+h30dZ3j92FnCkWEaF1cCTlpwpwRmm9TlnkCcMWckDYidhTeTE04RBB7iaQWF4C7qJ+zsG9UJROrl6VeP8Zf/6QbX00EihHMPk3Nof+cZd1t/eOQarqibxXd/8Q4VJdPYsvtw3HKLQurYY4tx8c20ABZBwOiZsJ9WUAjmjkQBSQC95yPs7+yluzfMD37ZRjA04JaJLASNKZ8wtunKsiJKiwO8fuwswffO89RvjtJ7PkLHe+9Td90H2faSkyBQggPTi3fMMed20+o6oC36mjkKWhDESy1dCLN/PxIFJJkoYtC0nXp/VBnJQj1nuYBffqdwZMitXra2/jo+fcOHqZ11Nf/x+z/QerSX14+dIzJ0iQ3LF1Szl6EAACAASURBVGDShQjpw88Nu7Q4MKouR6YoaEFgLsafLZpHdXkxt1Q6GTMLYfafLN7kWHbu9Jvmlbjt5JxlL351orfu7WTD8hqW1JS7g9D9T75KMDRARck07lgwk++tvUEWiicIPzfsRDWNJ9rkWtCCwK6XGwwN8OPnO3jsnnqaWroAVfB2UTtr5WS4tAnpwU9rM54qZtuW3YepKJlGZVkR3b1hPr9ongiBCcTWshO5WmfK5FqQgsCWst56uWa2BGIX9Ya/Z9qlTUgPXm3NdgB48/g5amZd7a4F2OnDhYnHe228GnimovMLUhB4paxtlytpCEQLdhS2XbRvIOKmJ37wrhp2HDpJnFyCQpYTzy3YaHldZ5xspLdXl7GmfjY7Dp2gqaW74DXiicavJoGphLivI8T+zl4OHOnNSI2IghQEiRY2S4sDPLSyNtNdyipskxAA/94e9SkHUDy08vpJ65swfppautm6t4NwZJiHVl7vDkDGQ6W5PcTt1WU0VJay49AJ0YgzhJmQ2mZXE59Td+0MQEUD/ron/JkrKEHgNQkJo7GFgLEXD13S3FZVwitd/YhWkIvomFcjGPZ1nOF7a29g0fzTbrK59Z+cz+3VZdwwe0ZBa8SZwE7rYZtdTb6h7/z87WjLiX/mCkoQeAtCSADUaLzrAqb05B0LZrJh+QK3EL2QOzQurvLY/Z2BZX/nGZ54MUh1+XTW1F9HUWAK4cgQLwd7CUy9IibATJ6R9GOvD1QvHVmYf2BpNU+8GOTlYC/Lassz8swVlCCwTUJjrcYXaqSsfY68BU2W1MwsqHORL3gXJBsXV/HUb47SH77Iv71xksGLl4CRinOmUIoxG5l9QubwPocTTUEJAvuBsNUyvypaEinrYISBVK7KD8wEZ8s99Xxt+yH6Bi6yrLbcvbbmeje1dDMYGebGOWIimgwyHZeTjgplOYk50fGqaK2om8Wy2nLXfatQ8BZAL1TNKN/oG4iwZXc7X336tzyy613aT7/Pnq/dycZVC0d5pRj30m37jlAUmCrXPQPYFRInoypcQWkENrbrFozWDPa0naa5PeTm0slX7IEeIBwZYsPympiaxKIZ5T7OArHjDXR7ddmoHDdeJGVIZvF6EGXKbdRQsILAO8CZCk3mc6E8CN5ynVv3drJx1UJPGmr/Gg1CbtA3EOHg0T738w2zZ7C9tYdbKkv58fMdvjUHJGXIxGNPwmxTtVmb2d7aI4VpJhrvQL+ibhYHjvS6GkKhPAh+As9+X1ocYDByiW37jnDgSC9///mbRRhkMd4gpVsqS/nGc28QDA0w55ppzC6ZBtqpRVxdXkwwNIDUHJgcRhLPDbtpJuw1mnBkKGOTr4IVBN6B3piCoC2jKtlk4z0PfsKv7dQ5AF7p6svoLEVIjN/6jdfEYGJBSoqu5PjZQY6fHWTR/FI2rloYoxEImcc2x9rWCG+xGuPNNZFrdWkRBEqpzwBbcYrX/4PW+lHP/quAp4CbgV7gc1rr7ui+jcAXgWHgq1rrX6ejT+PFDrkvtMHOL7+JXTz7aytrOd5/iE/WlOe9qSyXsAd9M3nxBimd6B+ku/co/+nG6ygpvpLBi5cYjAwDisqZxaIJTCKxieem+mrlmVqrS1kQKKWmAH8HrASOA68ppXZordusZl8E+rXWC5RS9wJ/DXxOKVUH3AvcAFwH7FFKXa+1Hk61X+PFdpOM51KaL3hnF95ZpClTGI4M0bi4ih8/30F3b5j7bp2Wl+cjGxjvjK9vIELv+QtUlhXR3B7i688ecoWBHaTUNxBhdsk0qyj9SO2NwYvDfOuPPzKR/5aQBGOZoU39iPWfnD9h5qJ0uI/eCnRqrY9orSPAz4C1njZrgabo++eA5UopFd3+M631Ba11F9AZ/b5JZcehk74upfmC10V0XUMFG1ctZNPqOjauWsgNs2cAMHjxkhtMZvuaC+nHe028GPdC41a4vbWHbfu66O4NU1Eyjeb2EI+/EBx1nNESNu9si84oFZVlRQC8c+LchP0/wvjwu77mfjAZkTtOv8/WvZ0TMi6lwzQ0G7B7dhy4LV4brfWQUuocUBbdfsBz7Ow09OmyMCd/w/IFbFy1MG8HPq/a6TeLnHblFW6N4mW15QW1bjIZeK9JPK3NVLRaUTfLzZJ74MgZevoHaT3ay/1PvjrKC8hOG7Km/joGI0O0nXqf7629YTL+VcGDN8ljPK9Fb06idJIOQaB8tnmzJMVrk8yxzhcotR5YDzB37tzx9M+XeKl5zWs+D3qJVNFg6Dybd7ZR86GrRQhkEO818dqEjVfb4MVLbN3rbG9cXMX21h6++ZmP8OPnOzg3eJHm9hAXh9/mn760yP0ub2qVbfu62LhqoRSemUTs8ccW1PEyIvvlJEon6RAExwG793OAk3HaHFdKTQVmAH1JHguA1nobsA2goaEh5XR8fosvheIyGo++gQjrn2olGBrg4vAlVysSIZB5vDNC49V245wZ7nUx97AR1o+/EOT1Y2ejKYxH8Eutkq/abq7gTYBpXr3eX5CZQM50CILXgBqlVBVwAmfx9089bXYAjcBvgLuB57XWWim1A/gXpdTf4iwW1wCvpqFPYyIPhDPwN7V0MRi5xLTAFEATDA1QXV7M99Z+VGaMk4h3UuI3WHg93b58ZzVl0wMJ7+lCn+xkC3agJowe7E050UzFEqQsCKI2/68Av8ZxH/2J1vodpdT3gVat9Q7gfwL/qJTqxNEE7o0e+45S6lmgDRgC/iJTHkOF9kD4VUOyy3ICbFheI1pAlmK7GtoebXZCwEK7p3MZJ1ZgajRWYHQBIL9YgokkLXEEWutfAb/ybPuO9f4PwLo4x/4V8Ffp6IcQH79qSGZWYjQCv9KEknQuu/CaDGTwz13iOQhkul4xFHBkcaHhVw3JLssZDJ3n688e4sG7anitu2+UtwpI0rlsQEya+UM8BwF7sia5hoS0Yt90JQ2BUbN8U4nsWF84mn+msJLv5QqiAeQv8UpXZgIRBAWI3yx/0+o6IkNvM7tkGtfOmFZwyfcEIZNkm8lVBEEB4jfLry6fzievL3cFxJ62/K7DIAiTid9krKmli617O9nXEWJ/Z2/MvolGBEEB4p3lu26kFy+xfkkV0zwJsARBSB2/+gOxz5kTX1t37QyW1JRnNOeZCIICxRvZaNxIN65aKKYgQZgAvFrAuoYKmlq6AU3j4ioaF1fG1CXwFsuaSEQQFCjeyEaTt0Y0AUGYGPxSS2/d2wHgxgrECyKcaEQQFBjeWs1eN1JBECYGv2jx3oEI75w45z6PidpPJOlIQy3kEEYT2NN22g1IMtGqwdD5mFS4giCkH/O8AZQVB3g52ButFTF5iEZQYPipm95AFm8NVUEQ0oddq3gwMsQdC2b6agSZRARBgeGnbnoDWewaqmYxWYSCIKQHu1bxtn1dwOS7a4sgEEblOw+GzvPm8XPcUlk6qmCGIAjjxxtAZhIIOky+k4YIggJjrEL1MJL7HpAylYKQBmwvvRV1s9i8s41Nq+uyxklDBEGB4V0P8EtwZaphPXhXDYvml4lZSBBSxF6bM1r2xeG3WVJTnhXPlwiCAsO7HuCX4MpoBIvml4k5SBDSgG1+3bS6DmijorTIXTR+aOX1k9o/EQQFhl/9U+8ilV09KRPVkQQhH/GuCzipXLoBzWP31NPU0hVtmXLl3ZQRQSDEYG5eUGzd28HBo/3cPO8aGhdXiUAQhHHgTSnhjSRuXFxFUZbk9RJBUIAkSoFrbt4NyxewrLac5vYQ+zvPZKRcniDkE96YHVOHGHTWlRYVQVCAeGcqJvsoKNbUXweM3LxGlc2GWYsg5DrZGqgpgqAA8c5UTB50YFQh7clexBKEXMXPNJStZV9TEgRKqVLgGaAS6Abu0Vr3e9rUA38PfBAYBv5Ka/1MdN9PgaXAuWjzL2itD6XSJ2FsRqukTh70OxbMlJm/IKQJP9OQ/ZpNKK0vf8VaKfU3QJ/W+lGl1MNAidb6m5421wNaa92hlLoOOAh8RGt9NioIdmqtnxvP7zY0NOjW1tbL7rcQS7aVzRMEYWJQSh3UWjd4t6eafXQt0BR93wR81ttAa31Ya90RfX8SeA8oT/F3hQmkbyDClt3tbNl9WDKRCsI4ycVsvqmuEczSWp8C0FqfUkp9KFFjpdStQAAIWpv/Sin1HWAv8LDW+kKcY9cD6wHmzp2bYrcFm5FsiE5xmtbuPl4OOjVT7TUD0RwEYWzM87Sv4wz7O88QjgzTuLgyJrVLtj1DYwoCpdQe4MM+u749nh9SSl0L/CPQqLW+FN28EfgPHOGwDfgm8H2/47XW26JtaGhomPwIjDxiJBvisOvnfGtlCZ+odtYMjAAIR4bcReVsW+wShGzBPE8n+gfZ33mGwcgwj78YZNtLR/inA0fp6R8EsusZGtM0pLVeobX+qM/fL4DT0QHeDPTv+X2HUuqDwC+BTVrrA9Z3n9IOF4AngVvT8U8J46O0OBC9eTW3VZUCEJg6hcbFlZQWB9wZzmDkEstqyyc9d7ogZCN2wZl1DRUEQ+cBmBa4gndOOP4wPf2D3LGgjHBkKKtMRqmahnYAjcCj0ddfeBsopQLAvwJPaa23e/ZdGzUpKZz1hbdT7I9wmZgC9huWL6AoMIXm9hDbW3vcItvgaAxODqLJzZ0uCNmI7R4K8HKwl2W15TQurmJN/Wy+8/O3uWH2DKZdOYWtezuyKkgzVUHwKPCsUuqLwDFgHYBSqgH4stb6S8A9wCeBMqXUF6LHGTfRf1ZKleP4Lx4Cvpxif4TLxK+wttfNbU39dW5AjCAIsZjI4XBkiDX1s91tpcUBSosD/PN/XQQ4mkO2PUcpuY9OFuI+mjn6BiJu2txlteU8dk99Vi1yCUI28cSLQR7Z9S4bVy3Mmtm+TTz3UYksFlzsVBNmfeDxFzppbg9x3YwP0NweoqmlW6KNBSEO2Rw0lggRBIKLWSeAkZwo/952GoApV6hoq9zTIAUhU2RTIrnxIIJAcDF1CEwN1e2tPXT3hqkuL+aHd3+M17r74s50JMZAKDS8ZV+9934uPRMiCASX0uJATA1VW80tLQ5w07wSwP8Gz+aEWoIwEXjLvkLsvd/U0s3WvR1ZUYFsLEQQCHEx8QXxBv1wZMgtrJGrtlFBuFy8ZV/te79vIEJrd1/0U/abU0UQCAnxm+nbcQX2PtEEhHzH1oYNJUWj1wW2t/bExBFkOyIIhFHYN7vfTN8siGWjP7QgTCS2OejGOdewdW8Hz7b2sO3PGqguHwmy9JpVs51Us48KeYi52be39riDvt/NbJuOsilcXhAminUNFW4J19buPirLigiGBti8sy2mXaLnJhsRQSCMYl1DBRtXLXQTznlT6pptRnN4ZNe7NLV05UzKXUEYD/b9Xloc4LF76llWW87LwV4+dPVV3LFgJg/eVZPT97+YhoRR2L7QJlLS9owA3LWBeOsFgpAveNfJjDAwEfcbVy3kte6+nL7/RRAICUnkGbGibhZNLd30D0RoP/0+65dUyXqBkHfEWyd77J76UQvHuXr/S64hYdyM1CcYqV8AsKy2nCfvl0zigpCtTFSpSqFA8FsXAM36JfO5ae413FZVwqbVdTHtBCGXKaR7WUxDQlLYdlJbVd7e2sPrx86ycdVCqsun899/2ca2fV30nr/At/6kbjK7LAiXTTB0nvVPtRIMDXDgSG/crLu5lEYiESIIhKTw+kV7g8vMa9up9wH497bTfPnOBTn9cAiFy+adbQRDA5QWX0lze4ivP3vIVxjkS2oVEQRCUsTLqmhv7xuIUHft1RzvD9PdG3YrnAlCrrFpdR3QxoN31fC3uw/T3B7iq0//lu+tvYEdh05gUrXnS2oVEQRC2mhq6WLbvi7WL6mibPpV7sORL+qzUDhUl093HR9unncN+zvPsL/zDJt3trlu1EWBKXmTWkUEgZA08QZ0s30wcgmAaVYtVrvC2UuHQzRUlrpFbwQhFxjJFaRYU38dN85xNIJc1wJsRBAISRPPHmq2b1he40Yk2/ua20NUlxfzcrCXl4O97kzKIBqDkI3Y96Wdnt1+ny+IIBCSJp49NFGCLTsg7ZlXj9F26n1uqSzliReDbnu/tNYiEISJwG/S4d02Eicz5FbsywfzTyJSEgRKqVLgGaAS6Abu0Vr3+7QbBt6KfjymtV4T3V4F/AwoBV4H/i+tdf477eYoySwYJ9pXNv0q9nd2cercIMHQgGsqWlN/HSBpKoSJx0+rtTOKmmjheBpuvpKqRvAwsFdr/ahS6uHo52/6tBvUWtf7bP9rYIvW+mdKqceBLwJ/n2KfhCxlXUOFm7PIz1Qkaa2FiWCstOrrGip46XCI5vYQD/7L63z/sx91txeKZpqqIFgL3Bl93wS8gL8gGIVSSgF3AX9qHf+XiCDIO+wH0cy4VtTNct3wzEOZq4W/hezGLhnZuLiScGSYx1/oZFpgquu40FBZ6k5M9rSdLrj7MFVBMEtrfQpAa31KKfWhOO0+oJRqBYaAR7XWPwfKgLNa66Fom+PA7Hg/pJRaD6wHmDt3bordFjKJVx03D1k+LroJ2Yh2X7e39sTkxzLaaOPiSrdNIWqkYwoCpdQe4MM+u749jt+Zq7U+qZSaDzyvlHoL+L1Pu7gZ8LTW24Bt4CSdG8dvC5PMirpZHDjSy4q6We62voEITS3dgKZxcZWvO2ohqebCxOG4fypAs6JuFuHIMIORIaZFHRPA0UazvcD8RDKmINBar4i3Tyl1Wil1bVQbuBZ4L853nIy+HlFKvQB8HPhfwDVKqalRrWAOcPIy/gchy9nTdprm9hCL5p+meqlTzs+emRVZcQcQq8o/tPJ6EQxCSpQWBygKTOGRXe+y881To8pKCqmbhnYAjcCj0ddfeBsopUqAsNb6glJqJnA78Ddaa62UagbuxvEc8j1eyH3iLdCFI8PYqvhIYNowAIORIZ54MVhQbnxC6vhNHNY1VPBsa49bVlLSpceSUj0CpVQZ8CwwFzgGrNNa9ymlGoAva62/pJRaDDwBXMJJe/3/aq3/Z/T4+Yy4j/4W+LzW+sJYvyv1CPITUw3t9uoyGipLAdi6t4MNy2tcbyLRCISxMPfRxlULYyYOwdB5Nu9sY9PquoLVCOLVI5DCNELWYKejMP7bYhISEpEoQKx21tX84Jdt/PDuj3HTvJJJ7ml2IIVphKyntDjAptV13F5dRm+0GIipEWvwFgvpG4iwZfdhtuxuL4gCIoVKvCIxxiNte2uP2864J39t+yGCoQG+8dwbk9HlnEJSTAhZxZ62064/d9vJ33PzvGtivIq8rqiJFp2F/MF73c2Af0tlKctqy12PNDtKuG/gIqXFV/LDuz8mDgdjIIJAyCqcReQhDh4966b+tQd478Kz36KzkB8kigg2nmV3LJjJ/s4zrkeandtq0fzT7sBv1g1AHA78EEEgZBWlxYGo33cXddd9kGlXXhEzwHujj532lWxv7aE/LLO+fCJeIKKDs7Z5cXiYDctrfKPTjaty30CEcGSYDcsXyGQhDrJGIGQdjrmnk47T748KNvOjqaWbR3a9yxd/+lqMvRgKqwB5vrGuoSIm6Zt9LRsXV7GstpxXuvopCkxJeI8Y82FRYKpMEOIgGoGQddjJ6bzlLp2I5C5MqUDnwXZmh929YZbVlo+qhyAmgdzDNgsBbNnd7poLwbmWJm/VWLP8fCknOZGIIBCyjtLiQNyH3GgLhqLAFNbUmxRValT1MxkEcouRWgDDMTmBzDW3BX2ySQolmeHYiCAQspJ4D69ZTB68eIkDR87wSlc/4ciQJLDLAeIVgFlRN4s9bafduBETVLhheY1b0Oi2qlI+VnENX47eE3ZhIyF1ZI1AyCmc5GC1lBUHeKXL1EBSgH+MwdefPRSzbhAMnef+J18lGDof872yljDx2D7/9rXZvLPN3b6uoYJlteW8HOwFNJt3trFtXxevdPVRVhyIqWhnrwUJqSEagZCT2G6jJoWwX4xBc3vINSf0DURY/1QrwdAAEJtvRtYSkudyffJtM11TSzfN7SHuWDCTTavrYlw9jVkwHBmOtinj5nmlvq7DQnoQQSDkJH5pg+MNFLYveTA0QHV5MZtW18Ucu6JuFi8dDtE7ECEYOs+OQyfxS5FtU6hBSmMJzXjnJdbc5yzw3zzvGqrLp7uunnY7u2Jd/O8R0oEIAiFnGGvg9YsxsD97BYOdhGzHoRNuRHPH6fdpbg8Bo6OV7T4UqhYx1ow8mfPSuLiKIqsegB8y4GcOEQRCzpDqwOsdWDbvbIsO+G3cOOcaANdUceMcRyNYUTcrZmHS7kO8ATGbNYXL7Zv3uEQJAY3ZLhwZom8gErMwbNrLIJ9diCAQcoZ02YZNLEJFSZE78JcUOcVLjAeLcUP1piZIZvBvauli697OGG+mdAqHVL4rWWHq9eix3TnN+ov3e+x+mUIwbx4/59r8/XIFZaOwLEREEAg5Q7pmkXYswsZVC93c9A8srR418PuV2QxHhtwym3ZMgznOeDH1D1zk/idfZdPqOva0nU44cCYaDL3tUtGMvIIsXh/s5G3N7SE2LF8QE+XrN+v3akt2UKCdA0iKDWUfIgiEgsPEIoAaNbM3+8KRYfoGIuw4dILm9hA3zjnBQytrY4TIhuU1MYOjOb4/HOHN42dpP/0+r3T1AW08dk89QIypKdkB3TvAhiNDMfl1xoNXmMbrg/nuW6IFgtbUz44p5mKXfzS2/t6BCLdXl7GibpabUhza3M+2oPU7d8LkIYJAKDhMLEK8fUWBqdEBbgpmdm9ebSFizEf2orOZGTe3h1i/pIqiwJQYD6VnXu1h274jhCND0eR6Y5u67Fm4EUQbVy30tb374ZjCut2C7Xb0tZ+pyzYLmXUUu950vH5te+kIADsOneShldf71qr2LtgL2YEIAkHw4B0cjQsjxAoRE4S2r+NMNAeOE5vgN9iZmfC80qLor6hxp0gwWTTXL6kiHBkmGDrPd37+Ni8HexOuR9g1G+z/x7TxekWZKnHGtOPN3+Ttl/lf93WE2N/pBIL5nUfvMUL2IIJAEDx4B6t4A5cxq6xfUsWVU5Q78/cb7Gyb+bLacjcIDhKvFXjdVbfu7WBZbbk7UDumJwDlm6fHLHAbYVVZVsQtlaXuYG/ajBw75PbRG+g11jn70X03xawHyKCfO4ggEITLJFkzhxlk4w2s8ez0fQMRHvyX190ZvzElmaIre393GoB5pUVuTQbH/h67sOsM0h93B/8fP98xaqY/cmwNG5YvABQlRaMH8kRCSwb+3CUlQaCUKgWeASqBbuAerXW/p80yYIu1aSFwr9b650qpnwJLgXPRfV/QWh9KpU+CkCmSHfj83Elt4rmkNrV0R3PugNeUVNIQoPf8BQJTp/C9tTe4vv3me/wGaePG6a3e5e2DEQpFgSmjPJy82oaQH6SqETwM7NVaP6qUejj6+Zt2A611M1APruDoBP7davINrfVzKfZDELIY5XmNxStQzKA7GBkC4I4FZTGmJHBm8Nv2dcW4v44lmPyqd/nt8xNM8bQNIT9IVRCsBe6Mvm8CXsAjCDzcDezSWodT/F1ByBkaF1fGLDiPhW2mMYOuX/Su/ZpO4q1xmFfx9sk/lNb68g9W6qzW+hrrc7/WuiRB++eBv9Va74x+/inwCeACsBd4WGt9Ic6x64H1AHPnzr356NGjl91vQchmLifqViJ1hWRQSh3UWjd4t49Zj0AptUcp9bbP39pxduBa4I+AX1ubN+KsGdwClJJAm9Bab9NaN2itG8rLy8fz04KQU5gZ+XgGdMnRL6TCmKYhrfWKePuUUqeVUtdqrU9FB/r3EnzVPcC/aq0vWt99Kvr2glLqSeC/JdlvQRAsJEe/kAqpVijbATRG3zcCv0jQ9j7gaXtDVHiglFLAZ4G3U+yPIBQkl6NFCIIhVUHwKLBSKdUBrIx+RinVoJT6B9NIKVUJVAAveo7/Z6XUW8BbwExgc4r9EQRBEMZJSl5DWuteYLnP9lbgS9bnbmC2T7u7Uvl9QRAEIXWkeL0gCEKBI4JAEAShwBFBIAiCUOCIIBAEQShwRBAIgiAUOCmlmJgslFIhIF05JmYCZ9L0XROB9C91sr2P0r/UyPb+Qfb0cZ7WelRqhpwUBOlEKdXql3sjW5D+pU6291H6lxrZ3j/I/j6KaUgQBKHAEUEgCIJQ4IgggG2T3YExkP6lTrb3UfqXGtneP8jyPhb8GoEgCEKhIxqBIAhCgSOCQBAEocApCEGglFqnlHpHKXVJKRXXhUsp9RmlVLtSqlMp9bC1vUop9YpSqkMp9YxSKq1J35VSpUqp3dHv362UGlXuUym1TCl1yPr7g1Lqs9F9P1VKdVn76jPdv2i7YasPO6zt2XD+6pVSv4neB28qpT5n7Zuw8xfvnrL2XxU9J53Rc1Rp7dsY3d6ulPp0uvo0zv59TSnVFj1ne5VS86x9vtc7w/37glIqZPXjS9a+xug90aGUavQem6H+bbH6dlgpddbaN+HnL2m01nn/B3wEqAVeABritJkCBIH5QAB4A6iL7nsWuDf6/nHgz9Pcv7/BqdcM8DDw12O0LwX6gKLo558Cd0/g+Uuqf8D5ONsn/fwB1wM10ffXAaeAayby/CW6p6w2/zfwePT9vcAz0fd10fZXAVXR75kyCf1bZt1nf276l+h6Z7h/XwD+P59jS4Ej0deS6PuSTPfP0/5B4CeZOn/j+SsIjUBr/TutdfsYzW4FOrXWR7TWEeBnwFqllALuAp6LtmvCqaaWTtZGvzfZ778b2KW1Dqe5H/EYb/9csuX8aa0Pa607ou9P4pRVneji1773lKeN3ffngOXRc7YW+JnW+oLWugvojH5fRvuntW627rMDwJw09yGl/iXg08BurXWf1rof2A18ZpL7N6pKY7ZQEIIgSWYDduXv49FtZcBZrfWQZ3s6maWj9Zujrx8ao/29jL6h/iqqvm9Rw1tW1AAAAytJREFUSl01Sf37gFKqVSl1wJityMLzp5S6FWcGF7Q2T8T5i3dP+baJnqNzOOcsmWMz0T+bLwK7rM9+13sy+vefo9fuOaWUKdqcVecvalKrAp63Nk/0+UualCqUZRNKqT3Ah312fVtrnaiWsvsVPtt0gu3jIlH/xvk91wJ/BPza2rwR+A+cwW0b8E3g+5PQv7la65NKqfnA88opQ/p7n3aTff7+EWjUWl+Kbk75/MX7OZ9t3v99Qu+7MUj6N5RSnwcagKXW5lHXW2sd9Dt+Avv3b8DTWusLSqkv42hXdyV5bCb6Z7gXeE5rPWxtm+jzlzR5Iwi01itS/IrjOHWVDXOAkziJoq5RSk2NztjM9rT1Tyl1Wil1rdb6VHSgei/BV90D/KvW+qL13aeiby8opZ4E/ttk9C9qckFrfUQp9QLwceB/kSXnTyn1QeCXwCat9QHru1M+f3GId0/5tTmulJoKzMBZ/0nm2Ez0D6XUChyBu1RrfcFsj3O90zmQjdk/7ZTLNfwP4K+tY+/0HPtCGvuWVP8s7gX+wt6QgfOXNGIaGuE1oEY5Hi4BnAu3QzurOs04dnmARiAZDWM87Ih+bzLfP8rOGB38jD3+s8Dbme6fUqrEmFSUUjOB24G2bDl/0Wv6r8BTWuvtnn0Tdf5876kEfb8beD56znYA90a9iqqAGuDVNPUr6f4ppT4OPAGs0Vq/Z233vd6T0L9rrY9rgN9F3/8a+FS0nyXAp4jVojPSv2gfa3EWrH9jbcvE+UueyV6tzsQf8H/gSO8LwGng19Ht1wG/str9MXAYRyp/29o+H+ch7AS2A1eluX9lwF6gI/paGt3eAPyD1a4SOAFc4Tn+eeAtnAHsn4Dpme4fsDjahzeir1/MpvMHfB64CByy/uon+vz53VM4Zqc10fcfiJ6Tzug5mm8d++3oce3Aqgl6Nsbq357oM2PO2Y6xrneG+/cI8E60H83AQuvY/xI9r53A/ZPRv+jnvwQe9RyXkfOX7J+kmBAEQShwxDQkCIJQ4IggEARBKHBEEAiCIBQ4IggEQRAKHBEEgiAIBY4IAkEQhAJHBIEgCEKB8/8DyZONAhUQo28AAAAASUVORK5CYII=\n",
 74 |       "text/plain": [
 75 |        "<Figure size 432x288 with 1 Axes>"
 76 |       ]
 77 |      },
 78 |      "metadata": {
 79 |       "needs_background": "light"
 80 |      },
 81 |      "output_type": "display_data"
 82 |     }
 83 |    ],
 84 |    "source": [
 85 |     "plt.scatter(x_data, y_data, s = 1)\n",
 86 |     "plt.show()"
 87 |    ]
 88 |   },
 89 |   {
 90 |    "cell_type": "markdown",
 91 |    "metadata": {},
 92 |    "source": [
 93 |     "### Fit Principal Curve with Local Algorithms"
 94 |    ]
 95 |   },
 96 |   {
 97 |    "cell_type": "code",
 98 |    "execution_count": 4,
 99 |    "metadata": {},
100 |    "outputs": [
101 |     {
102 |      "name": "stdout",
103 |      "output_type": "stream",
104 |      "text": [
105 |       "Took 0.214514 seconds\n"
106 |      ]
107 |     }
108 |    ],
109 |    "source": [
110 |     "cl = CLPCG()  # Create CLPCG object\n",
111 |     "\n",
112 |     "# the fit() method calculates the principal curve\n",
113 |     "# e_max is determined through trial and error as of\n",
114 |     "# now, but aim for about 1/2 data error and adjust from\n",
115 |     "# there. \n",
116 |     "start = timeit.default_timer()\n",
117 |     "\n",
118 |     "cl.fit(x_data, y_data, e_max = .03)  # CLPCG.fit() to fit PC\n",
119 |     "\n",
120 |     "stop = timeit.default_timer()\n",
121 |     "\n",
122 |     "print(\"Took %f seconds\" % (stop - start))"
123 |    ]
124 |   },
125 |   {
126 |    "cell_type": "code",
127 |    "execution_count": 76,
128 |    "metadata": {},
129 |    "outputs": [
130 |     {
131 |      "data": {
132 |       "text/plain": [
133 |        "<matplotlib.collections.PathCollection at 0x1ded4b31608>"
134 |       ]
135 |      },
136 |      "execution_count": 76,
137 |      "metadata": {},
138 |      "output_type": "execute_result"
139 |     },
140 |     {
141 |      "data": {
142 |       "image/png": "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\n",
143 |       "text/plain": [
144 |        "<Figure size 432x288 with 1 Axes>"
145 |       ]
146 |      },
147 |      "metadata": {},
148 |      "output_type": "display_data"
149 |     }
150 |    ],
151 |    "source": [
152 |     "fig, ax = plt.subplots()\n",
153 |     "ax.scatter(x_data, y_data, s = 3, alpha = .7)\n",
154 |     "cl.plot(ax)     # .plot will display the fit curve.\n",
155 |     "                # you can optionally pass in a matplotlib ax\n",
156 |     "pts = cl.fit_points   # fitted points with PC that spline is passed through\n",
157 |     "ax.scatter(pts[:,0], pts[:,1], s = 40, c = 'green')"
158 |    ]
159 |   },
160 |   {
161 |    "cell_type": "code",
162 |    "execution_count": 6,
163 |    "metadata": {},
164 |    "outputs": [],
165 |    "source": [
166 |     "# .proj will return a projection index for each point\n",
167 |     "proj = cl.project(x_data, y_data) \n",
168 |     "print(proj[:5])"
169 |    ]
170 |   },
171 |   {
172 |    "cell_type": "code",
173 |    "execution_count": 10,
174 |    "metadata": {},
175 |    "outputs": [
176 |     {
177 |      "name": "stdout",
178 |      "output_type": "stream",
179 |      "text": [
180 |       "[0.         0.         0.         0.         0.02700805 0.04754636\n",
181 |       " 0.09041594 0.12945787 0.18449046 0.22115265 0.2495283  0.30794099\n",
182 |       " 0.36219516 0.4034585  0.45169821 0.50868772 0.57010873 0.63433081\n",
183 |       " 0.69801242 0.75620144 0.80715538 0.89094181 1.         1.\n",
184 |       " 1.         1.        ]\n",
185 |       "[[ 0.01447173  0.01714681]\n",
186 |       " [ 0.06537318 -0.00911538]\n",
187 |       " [ 0.17175084  0.04210127]\n",
188 |       " [ 0.21407512  0.16854487]\n",
189 |       " [ 0.05238058  0.39507542]]\n"
190 |      ]
191 |     }
192 |    ],
193 |    "source": [
194 |     "# additionally, you can get spline ticks or fit points:\n",
195 |     "tck = cl.spline_ticks\n",
196 |     "fit_pts = cl.fit_points\n",
197 |     "\n",
198 |     "print(tck[0])\n",
199 |     "print(fit_pts[:5])"
200 |    ]
201 |   },
202 |   {
203 |    "cell_type": "markdown",
204 |    "metadata": {},
205 |    "source": [
206 |     "## 2. Global"
207 |    ]
208 |   },
209 |   {
210 |    "cell_type": "code",
211 |    "execution_count": 13,
212 |    "metadata": {},
213 |    "outputs": [],
214 |    "source": [
215 |     "# NLPCA is the global alg\n",
216 |     "from prinpy.glob import NLPCA"
217 |    ]
218 |   },
219 |   {
220 |    "cell_type": "code",
221 |    "execution_count": 54,
222 |    "metadata": {},
223 |    "outputs": [],
224 |    "source": [
225 |     "# Generate some test data\n",
226 |     "t = np.linspace(0, 1, 1000) + np.random.normal(scale = .1, size = 1000)\n",
227 |     "x = 5*np.cos(t) + np.random.normal(scale = .1, size = 1000)\n",
228 |     "y = np.sin(t) + np.random.normal(scale = .1, size = 1000)"
229 |    ]
230 |   },
231 |   {
232 |    "cell_type": "code",
233 |    "execution_count": 77,
234 |    "metadata": {},
235 |    "outputs": [
236 |     {
237 |      "data": {
238 |       "text/plain": [
239 |        "<matplotlib.collections.PathCollection at 0x1ded4ba5a48>"
240 |       ]
241 |      },
242 |      "execution_count": 77,
243 |      "metadata": {},
244 |      "output_type": "execute_result"
245 |     },
246 |     {
247 |      "data": {
248 |       "image/png": "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\n",
249 |       "text/plain": [
250 |        "<Figure size 432x288 with 1 Axes>"
251 |       ]
252 |      },
253 |      "metadata": {},
254 |      "output_type": "display_data"
255 |     }
256 |    ],
257 |    "source": [
258 |     "plt.scatter(x, y, s = 1)"
259 |    ]
260 |   },
261 |   {
262 |    "cell_type": "code",
263 |    "execution_count": 65,
264 |    "metadata": {},
265 |    "outputs": [],
266 |    "source": [
267 |     "# create solver\n",
268 |     "pca = NLPCA()\n",
269 |     "\n",
270 |     "# transform data for better training with the \n",
271 |     "# neural net using built in preprocessor\n",
272 |     "data_new = pca.preprocess( [x,y] )\n",
273 |     "\n",
274 |     "# fit the data\n",
275 |     "pca.fit(data_new, epochs = 150, nodes = 15, lr = .01, verbose = 0)\n",
276 |     "\n",
277 |     "# project the current data. This returns a projection\n",
278 |     "# index for each point and points to plot the curve\n",
279 |     "proj, curve_pts = pca.project(data_new)"
280 |    ]
281 |   },
282 |   {
283 |    "cell_type": "code",
284 |    "execution_count": 81,
285 |    "metadata": {},
286 |    "outputs": [
287 |     {
288 |      "data": {
289 |       "text/plain": [
290 |        "[<matplotlib.lines.Line2D at 0x1ded36f4208>]"
291 |       ]
292 |      },
293 |      "execution_count": 81,
294 |      "metadata": {},
295 |      "output_type": "execute_result"
296 |     },
297 |     {
298 |      "data": {
299 |       "image/png": "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\n",
300 |       "text/plain": [
301 |        "<Figure size 432x288 with 1 Axes>"
302 |       ]
303 |      },
304 |      "metadata": {},
305 |      "output_type": "display_data"
306 |     }
307 |    ],
308 |    "source": [
309 |     "plt.scatter(data_new[:,0], \n",
310 |     "            data_new[:,1], \n",
311 |     "            s = 5, \n",
312 |     "            c = proj.reshape(-1), \n",
313 |     "            cmap = 'viridis')\n",
314 |     "plt.plot(curve_pts[:,0], \n",
315 |     "         curve_pts[:,1], \n",
316 |     "         color = 'black',\n",
317 |     "         linewidth = '2.5')"
318 |    ]
319 |   }
320 |  ],
321 |  "metadata": {
322 |   "kernelspec": {
323 |    "display_name": "Python 3",
324 |    "language": "python",
325 |    "name": "python3"
326 |   },
327 |   "language_info": {
328 |    "codemirror_mode": {
329 |     "name": "ipython",
330 |     "version": 3
331 |    },
332 |    "file_extension": ".py",
333 |    "mimetype": "text/x-python",
334 |    "name": "python",
335 |    "nbconvert_exporter": "python",
336 |    "pygments_lexer": "ipython3",
337 |    "version": "3.7.6"
338 |   }
339 |  },
340 |  "nbformat": 4,
341 |  "nbformat_minor": 4
342 | }
343 | 


--------------------------------------------------------------------------------