1 /*
2  * Licensed to the Apache Software Foundation (ASF) under one or more
3  * contributor license agreements.  See the NOTICE file distributed with
4  * this work for additional information regarding copyright ownership.
5  * The ASF licenses this file to You under the Apache License, Version 2.0
6  * (the "License"); you may not use this file except in compliance with
7  * the License.  You may obtain a copy of the License at
8  *
9  *      http://www.apache.org/licenses/LICENSE-2.0
10  *
11  * Unless required by applicable law or agreed to in writing, software
12  * distributed under the License is distributed on an "AS IS" BASIS,
13  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14  * See the License for the specific language governing permissions and
15  * limitations under the License.
16  */
17 package org.apache.commons.math3.optim.nonlinear.vector.jacobian;
18 
19 import java.util.ArrayList;
20 
21 import org.apache.commons.math3.analysis.MultivariateVectorFunction;
22 import org.apache.commons.math3.analysis.MultivariateMatrixFunction;
23 import org.apache.commons.math3.util.MathUtils;
24 import org.apache.commons.math3.util.FastMath;
25 import org.apache.commons.math3.optim.nonlinear.vector.ModelFunction;
26 import org.apache.commons.math3.optim.nonlinear.vector.ModelFunctionJacobian;
27 
28 /**
29  * Class that models a circle.
30  * The parameters of problem are:
31  * <ul>
32  *  <li>the x-coordinate of the circle center,</li>
33  *  <li>the y-coordinate of the circle center,</li>
34  *  <li>the radius of the circle.</li>
35  * </ul>
36  * The model functions are:
37  * <ul>
38  *  <li>for each triplet (cx, cy, r), the (x, y) coordinates of a point on the
39  *   corresponding circle.</li>
40  * </ul>
41  */
42 @Deprecated
43 class CircleProblem {
44     /** Cloud of points assumed to be fitted by a circle. */
45     private final ArrayList<double[]> points;
46     /** Error on the x-coordinate of the points. */
47     private final double xSigma;
48     /** Error on the y-coordinate of the points. */
49     private final double ySigma;
50     /** Number of points on the circumference (when searching which
51         model point is closest to a given "observation". */
52     private final int resolution;
53 
54     /**
55      * @param xError Assumed error for the x-coordinate of the circle points.
56      * @param yError Assumed error for the y-coordinate of the circle points.
57      * @param searchResolution Number of points to try when searching the one
58      * that is closest to a given "observed" point.
59      */
CircleProblem(double xError, double yError, int searchResolution)60     public CircleProblem(double xError,
61                          double yError,
62                          int searchResolution) {
63         points = new ArrayList<double[]>();
64         xSigma = xError;
65         ySigma = yError;
66         resolution = searchResolution;
67     }
68 
69     /**
70      * @param xError Assumed error for the x-coordinate of the circle points.
71      * @param yError Assumed error for the y-coordinate of the circle points.
72      */
CircleProblem(double xError, double yError)73     public CircleProblem(double xError,
74                          double yError) {
75         this(xError, yError, 500);
76     }
77 
addPoint(double px, double py)78     public void addPoint(double px, double py) {
79         points.add(new double[] { px, py });
80     }
81 
target()82     public double[] target() {
83         final double[] t = new double[points.size() * 2];
84         for (int i = 0; i < points.size(); i++) {
85             final double[] p = points.get(i);
86             final int index = i * 2;
87             t[index] = p[0];
88             t[index + 1] = p[1];
89         }
90 
91         return t;
92     }
93 
weight()94     public double[] weight() {
95         final double wX = 1 / (xSigma * xSigma);
96         final double wY = 1 / (ySigma * ySigma);
97         final double[] w = new double[points.size() * 2];
98         for (int i = 0; i < points.size(); i++) {
99             final int index = i * 2;
100             w[index] = wX;
101             w[index + 1] = wY;
102         }
103 
104         return w;
105     }
106 
getModelFunction()107     public ModelFunction getModelFunction() {
108         return new ModelFunction(new MultivariateVectorFunction() {
109                 public double[] value(double[] params) {
110                     final double cx = params[0];
111                     final double cy = params[1];
112                     final double r = params[2];
113 
114                     final double[] model = new double[points.size() * 2];
115 
116                     final double deltaTheta = MathUtils.TWO_PI / resolution;
117                     for (int i = 0; i < points.size(); i++) {
118                         final double[] p = points.get(i);
119                         final double px = p[0];
120                         final double py = p[1];
121 
122                         double bestX = 0;
123                         double bestY = 0;
124                         double dMin = Double.POSITIVE_INFINITY;
125 
126                         // Find the angle for which the circle passes closest to the
127                         // current point (using a resolution of 100 points along the
128                         // circumference).
129                         for (double theta = 0; theta <= MathUtils.TWO_PI; theta += deltaTheta) {
130                             final double currentX = cx + r * FastMath.cos(theta);
131                             final double currentY = cy + r * FastMath.sin(theta);
132                             final double dX = currentX - px;
133                             final double dY = currentY - py;
134                             final double d = dX * dX + dY * dY;
135                             if (d < dMin) {
136                                 dMin = d;
137                                 bestX = currentX;
138                                 bestY = currentY;
139                             }
140                         }
141 
142                         final int index = i * 2;
143                         model[index] = bestX;
144                         model[index + 1] = bestY;
145                     }
146 
147                     return model;
148                 }
149             });
150     }
151 
152     public ModelFunctionJacobian getModelFunctionJacobian() {
153         return new ModelFunctionJacobian(new MultivariateMatrixFunction() {
154                 public double[][] value(double[] point) {
155                     return jacobian(point);
156                 }
157         });
158     }
159 
160     private double[][] jacobian(double[] params) {
161         final double[][] jacobian = new double[points.size() * 2][3];
162 
163         for (int i = 0; i < points.size(); i++) {
164             final int index = i * 2;
165             // Partial derivative wrt x-coordinate of center.
166             jacobian[index][0] = 1;
167             jacobian[index + 1][0] = 0;
168             // Partial derivative wrt y-coordinate of center.
169             jacobian[index][1] = 0;
170             jacobian[index + 1][1] = 1;
171             // Partial derivative wrt radius.
172             final double[] p = points.get(i);
173             jacobian[index][2] = (p[0] - params[0]) / params[2];
174             jacobian[index + 1][2] = (p[1] - params[1]) / params[2];
175         }
176 
177         return jacobian;
178     }
179 }
180