| Directory: | ./ |
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| File: | include/hpp/core/path-optimization/linear-constraint.hh |
| Date: | 2024-12-13 16:14:03 |
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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 | 24 | void computeRank() { | |
| 65 |
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24 | if (J.size() == 0) |
| 66 | 15 | rank = 0; | |
| 67 | else { | ||
| 68 |
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9 | Eigen::FullPivLU<matrix_t> lu(J); |
| 69 |
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9 | rank = lu.rank(); |
| 70 | 9 | } | |
| 71 | 24 | } | |
| 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 | 39 | bool reduceConstraint(const LinearConstraint& lc, LinearConstraint& lcr, | |
| 81 | bool computeRank = true) const { | ||
| 82 |
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39 | lcr.J.noalias() = lc.J * PK; |
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39 | lcr.b.noalias() = lc.b - lc.J * xStar; |
| 84 | |||
| 85 | // Decompose | ||
| 86 |
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39 | if (computeRank) { |
| 87 | 24 | lcr.computeRank(); | |
| 88 | 24 | 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 |