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| 1 | // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- | ||
| 2 | // vi: set et ts=4 sw=4 sts=4: | ||
| 3 | // | ||
| 4 | // SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | /*! | ||
| 8 | * \file | ||
| 9 | * \ingroup Core | ||
| 10 | * \brief Implements tabulation for a two-dimensional function. | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_TABULATED_2D_FUNCTION_HH | ||
| 13 | #define DUMUX_TABULATED_2D_FUNCTION_HH | ||
| 14 | |||
| 15 | #include <vector> | ||
| 16 | #include <cassert> | ||
| 17 | #include <algorithm> | ||
| 18 | |||
| 19 | namespace Dumux { | ||
| 20 | |||
| 21 | /*! | ||
| 22 | * \ingroup Core | ||
| 23 | * \brief Implements tabulation for a two-dimensional function. | ||
| 24 | * | ||
| 25 | * This class can be used to tabulate a two dimensional function | ||
| 26 | * \f$f(x, y)\f$ over the range \f$[x_{min}, x_{max}] \times [y_{min}, | ||
| 27 | * y_{max}]\f$. For this, the ranges of the \f$x\f$ and \f$y\f$ axes are | ||
| 28 | * divided into \f$m\f$ and \f$n\f$ sub-intervals and the values of | ||
| 29 | * \f$f(x_i, y_j)\f$ need to be provided. Here, \f$x_i\f$ and | ||
| 30 | * \f$y_j\f$ are the largest positions of the \f$i\f$-th and | ||
| 31 | * \f$j\f$-th interval. Between these sampling points this tabulation | ||
| 32 | * class uses linear interpolation. | ||
| 33 | */ | ||
| 34 | template<class Scalar> | ||
| 35 | class Tabulated2DFunction | ||
| 36 | { | ||
| 37 | public: | ||
| 38 | /*! | ||
| 39 | * \brief Default constructor. | ||
| 40 | */ | ||
| 41 | Tabulated2DFunction() | ||
| 42 | { }; | ||
| 43 | |||
| 44 | /*! | ||
| 45 | * \brief Constructor where the tabulation parameters are already | ||
| 46 | * provided. | ||
| 47 | */ | ||
| 48 | Tabulated2DFunction(Scalar xMin, Scalar xMax, int m, | ||
| 49 | Scalar yMin, Scalar yMax, int n) | ||
| 50 | { | ||
| 51 | resize(xMin, xMax, m, yMin, yMax, n); | ||
| 52 | }; | ||
| 53 | |||
| 54 | /*! | ||
| 55 | * \brief Resize the tabulation to a new range. | ||
| 56 | * | ||
| 57 | * \note _All_ previously specified sampling points become invalid | ||
| 58 | * after calling this method. You have to supply new ones. | ||
| 59 | */ | ||
| 60 | void resize(Scalar xMin, Scalar xMax, int m, | ||
| 61 | Scalar yMin, Scalar yMax, int n) | ||
| 62 | { | ||
| 63 | 2 | samples_.resize(m*n); | |
| 64 | |||
| 65 | 6 | m_ = m; | |
| 66 | 6 | n_ = n; | |
| 67 | |||
| 68 | 6 | xMin_ = xMin; | |
| 69 | 6 | xMax_ = xMax; | |
| 70 | |||
| 71 | 6 | yMin_ = yMin; | |
| 72 | 2 | yMax_ = yMax; | |
| 73 | } | ||
| 74 | |||
| 75 | /*! | ||
| 76 | * \brief Return the position on the x-axis of the i-th interval. | ||
| 77 | */ | ||
| 78 | 200 | Scalar iToX(int i) const | |
| 79 | { | ||
| 80 |
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200 | assert(0 <= i && i < m_); |
| 81 | |||
| 82 | 200 | return xMin_ + i*(xMax_ - xMin_)/(m_ - 1); | |
| 83 | } | ||
| 84 | |||
| 85 | /*! | ||
| 86 | * \brief Return the position on the y-axis of the j-th interval. | ||
| 87 | */ | ||
| 88 | 40000 | Scalar jToY(int j) const | |
| 89 | { | ||
| 90 |
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40000 | assert(0 <= j && j < n_); |
| 91 | |||
| 92 | 40000 | return yMin_ + j*(yMax_ - yMin_)/(n_ - 1); | |
| 93 | } | ||
| 94 | |||
| 95 | /*! | ||
| 96 | * \brief Return the interval index of a given position on the x-axis. | ||
| 97 | * | ||
| 98 | * This method returns a *floating point* number. The integer part | ||
| 99 | * should be interpreted as interval, the decimal places are the | ||
| 100 | * position of the x value between the i-th and the (i+1)-th | ||
| 101 | * sample point. | ||
| 102 | */ | ||
| 103 | Scalar xToI(Scalar x) const | ||
| 104 | { | ||
| 105 | 44292 | return (x - xMin_)/(xMax_ - xMin_)*(m_ - 1); | |
| 106 | } | ||
| 107 | |||
| 108 | |||
| 109 | /*! | ||
| 110 | * \brief Return the interval index of a given position on the y-axis. | ||
| 111 | * | ||
| 112 | * This method returns a *floating point* number. The integer part | ||
| 113 | * should be interpreted as interval, the decimal places are the | ||
| 114 | * position of the y value between the j-th and the (j+1)-th | ||
| 115 | * sample point. | ||
| 116 | */ | ||
| 117 | Scalar yToJ(Scalar y) const | ||
| 118 | { | ||
| 119 | 44292 | return (y - yMin_)/(yMax_ - yMin_)*(n_ - 1); | |
| 120 | } | ||
| 121 | |||
| 122 | |||
| 123 | /*! | ||
| 124 | * \brief Get the value of the sample point which is at the | ||
| 125 | * intersection of the \f$i\f$-th interval of the x-Axis | ||
| 126 | * and the \f$j\f$-th of the y-Axis. | ||
| 127 | */ | ||
| 128 | 177168 | Scalar getSamplePoint(int i, int j) const | |
| 129 | { | ||
| 130 |
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177168 | assert(0 <= i && i < m_); |
| 131 |
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177168 | assert(0 <= j && j < n_); |
| 132 | |||
| 133 | 354336 | return samples_[j*m_ + i]; | |
| 134 | } | ||
| 135 | |||
| 136 | /*! | ||
| 137 | * \brief Set the value of the sample point which is at the | ||
| 138 | * intersection of the \f$i\f$-th interval of the x-Axis | ||
| 139 | * and the \f$j\f$-th of the y-Axis. | ||
| 140 | */ | ||
| 141 | 120000 | void setSamplePoint(int i, int j, Scalar value) | |
| 142 | { | ||
| 143 |
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120000 | assert(0 <= i && i < m_); |
| 144 |
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120000 | assert(0 <= j && j < n_); |
| 145 | |||
| 146 | 240000 | samples_[j*m_ + i] = value; | |
| 147 | 120000 | } | |
| 148 | |||
| 149 | /*! | ||
| 150 | * \brief Return an interpolated value. | ||
| 151 | */ | ||
| 152 | 44292 | Scalar get(Scalar x, Scalar y) const | |
| 153 | { | ||
| 154 | 88584 | Scalar alpha = xToI(x); | |
| 155 | 88584 | Scalar beta = yToJ(y); | |
| 156 | |||
| 157 | using std::clamp; | ||
| 158 |
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44292 | int i = clamp(static_cast<int>(alpha), 0, m_ - 2); |
| 159 |
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44292 | int j = clamp(static_cast<int>(beta), 0, n_ - 2); |
| 160 | |||
| 161 | 44292 | alpha -= i; | |
| 162 | 44292 | beta -= j; | |
| 163 | |||
| 164 | // bi-linear interpolation | ||
| 165 | 44292 | Scalar s1 = getSamplePoint(i, j)*(1.0 - alpha) + getSamplePoint(i + 1, j)*alpha; | |
| 166 | 44292 | Scalar s2 = getSamplePoint(i, j + 1)*(1.0 - alpha) + getSamplePoint(i + 1, j + 1)*alpha; | |
| 167 | 44292 | return s1*(1.0 - beta) + s2*beta; | |
| 168 | } | ||
| 169 | |||
| 170 | /*! | ||
| 171 | * \brief The () operator | ||
| 172 | * | ||
| 173 | * This is just a convenience alias for get(x,y); | ||
| 174 | */ | ||
| 175 | Scalar operator()(Scalar x, Scalar y) const | ||
| 176 | 44292 | { return get(x, y); } | |
| 177 | |||
| 178 | private: | ||
| 179 | // the vector which contains the values of the sample points | ||
| 180 | // f(x_i, y_j). don't use this directly, use getSamplePoint(i,j) | ||
| 181 | // instead! | ||
| 182 | std::vector<Scalar> samples_; | ||
| 183 | |||
| 184 | // the number of sample points in x direction | ||
| 185 | int m_; | ||
| 186 | |||
| 187 | // the number of sample points in y direction | ||
| 188 | int n_; | ||
| 189 | |||
| 190 | // the range of the tabulation on the x axis | ||
| 191 | Scalar xMin_; | ||
| 192 | Scalar xMax_; | ||
| 193 | |||
| 194 | // the range of the tabulation on the y axis | ||
| 195 | Scalar yMin_; | ||
| 196 | Scalar yMax_; | ||
| 197 | |||
| 198 | }; | ||
| 199 | |||
| 200 | } // end namespace Dumux | ||
| 201 | |||
| 202 | #endif | ||
| 203 |