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File: | include/hpp/core/path-optimization/linear-constraint.hh |
Date: | 2024-08-10 11:29:48 |
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1 | // Copyright (c) 2017, Joseph Mirabel | ||
2 | // Authors: Joseph Mirabel (joseph.mirabel@laas.fr) | ||
3 | // | ||
4 | |||
5 | // Redistribution and use in source and binary forms, with or without | ||
6 | // modification, are permitted provided that the following conditions are | ||
7 | // met: | ||
8 | // | ||
9 | // 1. Redistributions of source code must retain the above copyright | ||
10 | // notice, this list of conditions and the following disclaimer. | ||
11 | // | ||
12 | // 2. Redistributions in binary form must reproduce the above copyright | ||
13 | // notice, this list of conditions and the following disclaimer in the | ||
14 | // documentation and/or other materials provided with the distribution. | ||
15 | // | ||
16 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | ||
17 | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | ||
18 | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | ||
19 | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT | ||
20 | // HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | ||
21 | // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT | ||
22 | // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, | ||
23 | // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY | ||
24 | // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT | ||
25 | // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE | ||
26 | // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH | ||
27 | // DAMAGE. | ||
28 | |||
29 | #ifndef HPP_CORE_PATH_OPTIMIZATION_SPLINE_GRADIENT_BASED_LINEAR_CONSTRAINT_HH | ||
30 | #define HPP_CORE_PATH_OPTIMIZATION_SPLINE_GRADIENT_BASED_LINEAR_CONSTRAINT_HH | ||
31 | |||
32 | #include <hpp/core/fwd.hh> | ||
33 | #include <hpp/util/debug.hh> | ||
34 | |||
35 | namespace hpp { | ||
36 | namespace core { | ||
37 | namespace pathOptimization { | ||
38 | /// A linear constraint \f$ J \times x = b \f$ | ||
39 | struct LinearConstraint { | ||
40 | 75 | LinearConstraint(size_type inputSize, size_type outputSize) | |
41 |
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75 | : J(outputSize, inputSize), b(outputSize), xSol(inputSize) { |
42 |
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75 | J.setZero(); |
43 |
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75 | b.setZero(); |
44 | 75 | } | |
45 | |||
46 | ~LinearConstraint(); | ||
47 | |||
48 | void concatenate(const LinearConstraint& oc) { | ||
49 | assert(oc.J.cols() == J.cols()); | ||
50 | J.conservativeResize(J.rows() + oc.J.rows(), J.cols()); | ||
51 | J.bottomRows(oc.J.rows()) = oc.J; | ||
52 | b.conservativeResize(b.rows() + oc.b.rows()); | ||
53 | b.tail(oc.b.rows()) = oc.b; | ||
54 | } | ||
55 | |||
56 | /// Compute one solution and a base of the kernel of matrix J. | ||
57 | /// rank is also updated. | ||
58 | /// \param check If true, checks whether the constraint is feasible. | ||
59 | /// \return whether the constraint is feasible | ||
60 | /// (alwys true when check is false) | ||
61 | bool decompose(bool check = false, bool throwIfNotValid = false); | ||
62 | |||
63 | /// Compute rank of the constraint using a LU decomposition | ||
64 | 18 | void computeRank() { | |
65 |
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18 | if (J.size() == 0) |
66 | 15 | rank = 0; | |
67 | else { | ||
68 |
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3 | Eigen::FullPivLU<matrix_t> lu(J); |
69 |
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3 | rank = lu.rank(); |
70 | 3 | } | |
71 | 18 | } | |
72 | |||
73 | /// Reduced constraint into the set of solutions of this constraint. | ||
74 | /// \param[in] lc the full constraint | ||
75 | /// \param[out] lcr the reduced constraint | ||
76 | /// \return if computeRank, returns true if the reduced constraint is full | ||
77 | /// rank. | ||
78 | /// if not computeRank, returns true. | ||
79 | /// \note rank is computed using computeRank method. | ||
80 | 33 | bool reduceConstraint(const LinearConstraint& lc, LinearConstraint& lcr, | |
81 | bool computeRank = true) const { | ||
82 |
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33 | lcr.J.noalias() = lc.J * PK; |
83 |
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33 | lcr.b.noalias() = lc.b - lc.J * xStar; |
84 | |||
85 | // Decompose | ||
86 |
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33 | if (computeRank) { |
87 | 18 | lcr.computeRank(); | |
88 | 18 | return lcr.rank == std::min(lcr.J.rows(), lcr.J.cols()); | |
89 | } else | ||
90 | 15 | return true; | |
91 | } | ||
92 | |||
93 | /// Compute the unique solution derived from v into \ref xSol. | ||
94 | /// \f$ xSol \gets x^* + PK \times v \f$ | ||
95 | /// \param v an element of the kernel of matrix \ref J. | ||
96 | /// \retval this->xSol | ||
97 | 18 | void computeSolution(const vector_t& v) { | |
98 |
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18 | xSol.noalias() = xStar + PK * v; |
99 | #ifdef HPP_DEBUG | ||
100 | isSatisfied(xSol); | ||
101 | #endif // HPP_DEBUG | ||
102 | 18 | } | |
103 | |||
104 | /// Returns \f$ ( J \times x - b ).isZero (threshold) \f$ | ||
105 | bool isSatisfied(const vector_t& x, | ||
106 | const value_type& threshold = | ||
107 | Eigen::NumTraits<value_type>::dummy_precision()) { | ||
108 | vector_t err(J * x - b); | ||
109 | if (err.isZero(threshold)) return true; | ||
110 | hppDout(error, "constraints could not be satisfied: " << err.norm() << '\n' | ||
111 | << err); | ||
112 | return false; | ||
113 | } | ||
114 | |||
115 | 18 | void addRows(const std::size_t& nbRows) { | |
116 |
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18 | if (nbRows > 0) { |
117 | 18 | J.conservativeResize(J.rows() + nbRows, J.cols()); | |
118 | 18 | b.conservativeResize(b.rows() + nbRows); | |
119 | |||
120 |
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18 | J.bottomRows(nbRows).setZero(); |
121 | } | ||
122 | 18 | } | |
123 | |||
124 | /// \name Model | ||
125 | /// \{ | ||
126 | matrix_t J; | ||
127 | vector_t b; | ||
128 | /// \} | ||
129 | |||
130 | /// \name Data | ||
131 | /// Solutions are \f$ \left\{ x^* + PK \times v, v \in | ||
132 | /// \mathbb{R}^{nCols(J) - rank} \right\} \f$ | ||
133 | /// \{ | ||
134 | |||
135 | /// Rank of \ref J | ||
136 | size_type rank; | ||
137 | |||
138 | /// Projector onto \f$ kernel(J) \f$ | ||
139 | matrix_t PK; | ||
140 | /// \f$ x^* \f$ is a particular solution. | ||
141 | vector_t xStar, xSol; | ||
142 | |||
143 | /// \} | ||
144 | }; | ||
145 | } // namespace pathOptimization | ||
146 | } // namespace core | ||
147 | } // namespace hpp | ||
148 | |||
149 | #endif // HPP_CORE_PATH_OPTIMIZATION_SPLINE_GRADIENT_BASED_LINEAR_CONSTRAINT_HH | ||
150 |