1 /*
2 * Licensed to the Hipparchus project 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 Hipparchus project 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 * https://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.hipparchus.optim.nonlinear.vector.constrained;
18
19 import org.hipparchus.exception.LocalizedCoreFormats;
20 import org.hipparchus.exception.MathIllegalArgumentException;
21 import org.hipparchus.linear.Array2DRowRealMatrix;
22 import org.hipparchus.linear.ArrayRealVector;
23 import org.hipparchus.linear.RealMatrix;
24 import org.hipparchus.linear.RealVector;
25 import org.hipparchus.util.MathUtils;
26
27 /** Given P, Q, d, implements \(\frac{1}{2}x^T P X + Q^T x + d\).
28 * The gradient is P x + Q^T, and the Hessian is P
29 * @since 3.1
30 */
31 public class QuadraticFunction extends TwiceDifferentiableFunction {
32
33 /** Square matrix of weights for quadratic terms. */
34 private final RealMatrix p;
35
36 /** Vector of weights for linear terms. */
37 private final RealVector q;
38
39 /** Constant term. */
40 private final double d;
41
42 /** Dimension of the vector. */
43 private final int n;
44
45 /** Construct quadratic function \(\frac{1}{2}x^T P X + Q^T x + d\).
46 * @param p square matrix of weights for quadratic terms.
47 * Typically expected to be positive definite or positive semi-definite.
48 * @param q vector of weights for linear terms.
49 * @param d constant term
50 */
51 public QuadraticFunction(RealMatrix p, RealVector q, double d) {
52 this.n = q.getDimension();
53 if (n < 1) {
54 throw new MathIllegalArgumentException(LocalizedCoreFormats.INSUFFICIENT_DIMENSION, d, 1);
55 }
56 MathUtils.checkDimension(p.getRowDimension(), n);
57 this.p = p.copy();
58 this.q = q.copy();
59 this.d = d;
60 }
61
62 /** Construct quadratic function \(\frac{1}{2}x^T P X + Q^T x + d\).
63 * @param h square matrix of weights for quadratic terms.
64 * Typically expected to be positive definite or positive semi-definite.
65 * @param c vector of weights for linear terms.
66 * @param d constant term
67 */
68 public QuadraticFunction(double[][] h, double[] c, double d) {
69 this(new Array2DRowRealMatrix(h), new ArrayRealVector(c), d);
70 }
71
72 /** Get square matrix of weights for quadratic terms.
73 * @return square matrix of weights for quadratic terms
74 */
75 public RealMatrix getP() {
76 return this.p;
77 }
78
79 /** Get vector of weights for linear terms.
80 * @return vector of weights for linear terms
81 */
82 public RealVector getQ() {
83 return this.q;
84 }
85
86 /** Get constant term.
87 * @return constant term
88 */
89 public double getD() {
90 return d;
91 }
92
93 /** {@inheritDoc} */
94 @Override
95 public int dim() {
96 return n;
97 }
98
99 /** {@inheritDoc} */
100 @Override
101 public double value(final RealVector x) {
102 return 0.5 * p.operate(x).dotProduct(x) + q.dotProduct(x) + d;
103 }
104
105 /** {@inheritDoc} */
106 @Override
107 public RealVector gradient(final RealVector x) {
108 return p.operate(x).add(q);
109 }
110
111 /** {@inheritDoc} */
112 @Override
113 public RealMatrix hessian(final RealVector x) {
114 return p.copy();
115 }
116
117 }