1 | /*
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2 | * Licensed to the Apache Software Foundation (ASF) under one or more
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3 | * contributor license agreements. See the NOTICE file distributed with
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4 | * this work for additional information regarding copyright ownership.
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5 | * The ASF licenses this file to You under the Apache License, Version 2.0
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6 | * (the "License"); you may not use this file except in compliance with
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7 | * the License. You may obtain a copy of the License at
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8 | *
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9 | * http://www.apache.org/licenses/LICENSE-2.0
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10 | *
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11 | * Unless required by applicable law or agreed to in writing, software
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12 | * distributed under the License is distributed on an "AS IS" BASIS,
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13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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14 | * See the License for the specific language governing permissions and
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15 | * limitations under the License.
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16 | */
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17 | package agents.anac.y2019.harddealer.math3.fitting.leastsquares;
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18 |
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19 | import agents.anac.y2019.harddealer.math3.linear.RealMatrix;
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20 | import agents.anac.y2019.harddealer.math3.linear.RealVector;
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21 | import agents.anac.y2019.harddealer.math3.optim.OptimizationProblem;
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22 |
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23 | /**
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24 | * The data necessary to define a non-linear least squares problem.
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25 | * <p>
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26 | * Includes the observed values, computed model function, and
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27 | * convergence/divergence criteria. Weights are implicit in {@link
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28 | * Evaluation#getResiduals()} and {@link Evaluation#getJacobian()}.
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29 | * </p>
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30 | * <p>
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31 | * Instances are typically either created progressively using a {@link
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32 | * LeastSquaresBuilder builder} or created at once using a {@link LeastSquaresFactory
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33 | * factory}.
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34 | * </p>
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35 | * @see LeastSquaresBuilder
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36 | * @see LeastSquaresFactory
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37 | * @see LeastSquaresAdapter
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38 | *
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39 | * @since 3.3
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40 | */
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41 | public interface LeastSquaresProblem extends OptimizationProblem<LeastSquaresProblem.Evaluation> {
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42 |
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43 | /**
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44 | * Gets the initial guess.
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45 | *
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46 | * @return the initial guess values.
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47 | */
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48 | RealVector getStart();
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49 |
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50 | /**
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51 | * Get the number of observations (rows in the Jacobian) in this problem.
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52 | *
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53 | * @return the number of scalar observations
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54 | */
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55 | int getObservationSize();
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56 |
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57 | /**
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58 | * Get the number of parameters (columns in the Jacobian) in this problem.
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59 | *
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60 | * @return the number of scalar parameters
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61 | */
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62 | int getParameterSize();
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63 |
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64 | /**
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65 | * Evaluate the model at the specified point.
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66 | *
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67 | *
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68 | * @param point the parameter values.
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69 | * @return the model's value and derivative at the given point.
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70 | * @throws agents.anac.y2019.harddealer.math3.exception.TooManyEvaluationsException
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71 | * if the maximal number of evaluations (of the model vector function) is
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72 | * exceeded.
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73 | */
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74 | Evaluation evaluate(RealVector point);
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75 |
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76 | /**
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77 | * An evaluation of a {@link LeastSquaresProblem} at a particular point. This class
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78 | * also computes several quantities derived from the value and its Jacobian.
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79 | */
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80 | public interface Evaluation {
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81 |
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82 | /**
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83 | * Get the covariance matrix of the optimized parameters. <br/> Note that this
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84 | * operation involves the inversion of the <code>J<sup>T</sup>J</code> matrix,
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85 | * where {@code J} is the Jacobian matrix. The {@code threshold} parameter is a
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86 | * way for the caller to specify that the result of this computation should be
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87 | * considered meaningless, and thus trigger an exception.
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88 | *
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89 | *
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90 | * @param threshold Singularity threshold.
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91 | * @return the covariance matrix.
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92 | * @throws agents.anac.y2019.harddealer.math3.linear.SingularMatrixException
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93 | * if the covariance matrix cannot be computed (singular problem).
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94 | */
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95 | RealMatrix getCovariances(double threshold);
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96 |
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97 | /**
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98 | * Get an estimate of the standard deviation of the parameters. The returned
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99 | * values are the square root of the diagonal coefficients of the covariance
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100 | * matrix, {@code sd(a[i]) ~= sqrt(C[i][i])}, where {@code a[i]} is the optimized
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101 | * value of the {@code i}-th parameter, and {@code C} is the covariance matrix.
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102 | *
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103 | *
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104 | * @param covarianceSingularityThreshold Singularity threshold (see {@link
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105 | * #getCovariances(double) computeCovariances}).
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106 | * @return an estimate of the standard deviation of the optimized parameters
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107 | * @throws agents.anac.y2019.harddealer.math3.linear.SingularMatrixException
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108 | * if the covariance matrix cannot be computed.
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109 | */
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110 | RealVector getSigma(double covarianceSingularityThreshold);
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111 |
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112 | /**
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113 | * Get the normalized cost. It is the square-root of the sum of squared of
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114 | * the residuals, divided by the number of measurements.
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115 | *
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116 | * @return the cost.
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117 | */
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118 | double getRMS();
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119 |
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120 | /**
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121 | * Get the weighted Jacobian matrix.
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122 | *
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123 | * @return the weighted Jacobian: W<sup>1/2</sup> J.
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124 | * @throws agents.anac.y2019.harddealer.math3.exception.DimensionMismatchException
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125 | * if the Jacobian dimension does not match problem dimension.
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126 | */
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127 | RealMatrix getJacobian();
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128 |
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129 | /**
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130 | * Get the cost.
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131 | *
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132 | * @return the cost.
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133 | * @see #getResiduals()
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134 | */
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135 | double getCost();
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136 |
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137 | /**
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138 | * Get the weighted residuals. The residual is the difference between the
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139 | * observed (target) values and the model (objective function) value. There is one
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140 | * residual for each element of the vector-valued function. The raw residuals are
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141 | * then multiplied by the square root of the weight matrix.
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142 | *
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143 | * @return the weighted residuals: W<sup>1/2</sup> K.
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144 | * @throws agents.anac.y2019.harddealer.math3.exception.DimensionMismatchException
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145 | * if the residuals have the wrong length.
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146 | */
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147 | RealVector getResiduals();
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148 |
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149 | /**
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150 | * Get the abscissa (independent variables) of this evaluation.
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151 | *
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152 | * @return the point provided to {@link #evaluate(RealVector)}.
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153 | */
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154 | RealVector getPoint();
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155 | }
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156 | }
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