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| 1 | +/* |
| 2 | + For more information, please see: http://software.sci.utah.edu |
| 3 | +
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| 4 | + The MIT License |
| 5 | +
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| 6 | + Copyright (c) 2015 Scientific Computing and Imaging Institute, |
| 7 | + University of Utah. |
| 8 | +
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| 9 | +
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| 10 | + Permission is hereby granted, free of charge, to any person obtaining a |
| 11 | + copy of this software and associated documentation files (the "Software"), |
| 12 | + to deal in the Software without restriction, including without limitation |
| 13 | + the rights to use, copy, modify, merge, publish, distribute, sublicense, |
| 14 | + and/or sell copies of the Software, and to permit persons to whom the |
| 15 | + Software is furnished to do so, subject to the following conditions: |
| 16 | +
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| 17 | + The above copyright notice and this permission notice shall be included |
| 18 | + in all copies or substantial portions of the Software. |
| 19 | +
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| 20 | + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS |
| 21 | + OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| 22 | + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL |
| 23 | + THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
| 24 | + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING |
| 25 | + FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER |
| 26 | + DEALINGS IN THE SOFTWARE. |
| 27 | +*/ |
| 28 | + |
| 29 | +// File : SolveInverseProblemWithTikhonov.cc |
| 30 | +// Author : Jaume Coll-Font, Moritz Dannhauer, Ayla Khan, Dan White |
| 31 | +// Date : September 06th, 2017 (last update) |
| 32 | + |
| 33 | +#include <boost/bind.hpp> |
| 34 | +#include <boost/lexical_cast.hpp> |
| 35 | + |
| 36 | +#include <Core/Algorithms/Legacy/Inverse/TikhonovAlgoAbstractBase.h> |
| 37 | +#include <Core/Algorithms/Legacy/Inverse/SolveInverseProblemWithStandardTikhonovImpl.h> |
| 38 | + |
| 39 | +#include <Core/Datatypes/Matrix.h> |
| 40 | +#include <Core/Datatypes/DenseMatrix.h> |
| 41 | +#include <Core/Datatypes/DenseColumnMatrix.h> |
| 42 | +#include <Core/Datatypes/SparseRowMatrix.h> |
| 43 | +#include <Core/Datatypes/MatrixTypeConversions.h> |
| 44 | + |
| 45 | +#include <Core/Algorithms/Base/AlgorithmPreconditions.h> |
| 46 | + |
| 47 | +#include <Core/Logging/LoggerInterface.h> |
| 48 | +#include <Core/Utils/Exception.h> |
| 49 | + |
| 50 | +using namespace SCIRun; |
| 51 | +using namespace SCIRun::Core; |
| 52 | +using namespace SCIRun::Core::Datatypes; |
| 53 | +using namespace SCIRun::Core::Logging; |
| 54 | +using namespace SCIRun::Core::Algorithms; |
| 55 | +using namespace SCIRun::Core::Algorithms::Inverse; |
| 56 | + |
| 57 | + |
| 58 | +///////////////////////// |
| 59 | +///////// compute Inverse solution |
| 60 | + DenseMatrix SolveInverseProblemWithStandardTikhonovImpl::computeInverseSolution( double lambda, bool inverseCalculation) const |
| 61 | + { |
| 62 | + //............................ |
| 63 | + // OPERATIONS PERFORMED IN THIS SECTION: |
| 64 | + // The description of these operations is general and applies to underdetermined or overdetermined equations depending on the definition given to M1, M2, M3 and y (look at the selection of underdetermined or overdetermined for details) |
| 65 | + //............................ |
| 66 | + // |
| 67 | + // G = (M1 + lambda^2 * M2) |
| 68 | + // b = G^-1 * y |
| 69 | + // x = M3 * b |
| 70 | + // |
| 71 | + // A^-1 = M3 * G^-1 * M4 |
| 72 | + //........................................................................................................... |
| 73 | + const int sizeB = M1.ncols(); |
| 74 | + const int sizeSolution = M3.nrows(); |
| 75 | + const int numTimeSamples = y.ncols(); |
| 76 | + DenseMatrix inverseG(sizeB,sizeB); |
| 77 | + |
| 78 | + DenseMatrix b(sizeB); |
| 79 | + DenseMatrix solution(sizeSolution,numTimeSamples); |
| 80 | + DenseMatrix G; |
| 81 | + |
| 82 | + G = M1 + lambda * lambda * M2; |
| 83 | + |
| 84 | + b = G.lu().solve(y).eval(); |
| 85 | + |
| 86 | + solution = M3 * b; |
| 87 | + |
| 88 | + // if (inverseCalculation) |
| 89 | + // { |
| 90 | + // inverseG = G.inverse().eval(); |
| 91 | + // inverseMatrix_.reset( new DenseMatrix( (M3 * inverseG) * M4) ); |
| 92 | + // } |
| 93 | + // inverseSolution_.reset(new DenseMatrix(solution)); |
| 94 | + return solution; |
| 95 | + } |
| 96 | +//////// fi compute inverse solution |
| 97 | +//////////////////////// |
| 98 | + |
| 99 | +/////// precomputeInverseMatrices |
| 100 | +/////////////// |
| 101 | + void SolveInverseProblemWithStandardTikhonovImpl::preAlocateInverseMatrices(const SCIRun::Core::Datatypes::DenseMatrix& forwardMatrix_, const SCIRun::Core::Datatypes::DenseMatrix& measuredData_ , const SCIRun::Core::Datatypes::DenseMatrix& sourceWeighting_, const SCIRun::Core::Datatypes::DenseMatrix& sensorWeighting_, const int regularizationChoice_, const int regularizationSolutionSubcase_, const int regularizationResidualSubcase_) |
| 102 | + { |
| 103 | + |
| 104 | + // TODO: use DimensionMismatch exception where appropriate |
| 105 | + // DIMENSION CHECK!! |
| 106 | + const int M = forwardMatrix_.nrows(); |
| 107 | + const int N = forwardMatrix_.ncols(); |
| 108 | + |
| 109 | + // PREALOCATE VARIABLES and MATRICES |
| 110 | + DenseMatrix forward_transpose = forwardMatrix_.transpose(); |
| 111 | + |
| 112 | + // get Parameters |
| 113 | + // auto regularizationChoice_ = get(regularizationChoice).toInt(); |
| 114 | + // auto regularizationChoice_ = get(regularizationSolutionSubcase).toInt(); |
| 115 | + // auto regularizationResidualSubcase_ = get(regularizationResidualSubcase).toInt(); |
| 116 | + |
| 117 | + // select underdetermined case if user decides so or the option is set to automatic and number of measurements is smaller than number of unknowns. |
| 118 | + if ( ( (M < N) && (regularizationChoice_ == TikhonovAlgoAbstractBase::automatic) ) || (regularizationChoice_ == TikhonovAlgoAbstractBase::underdetermined)) |
| 119 | + { |
| 120 | + //UNDERDETERMINED CASE |
| 121 | + //......................................................................... |
| 122 | + // OPERATE ON DATA: |
| 123 | + // Compute X = (R^T * R)^-1 * A^T (A * (R^T*R)^-1 * A^T + LAMBDA * LAMBDA * (C^T*C)^-1 ) * Y |
| 124 | + // X = M3 * G^-1 * (M4) * Y |
| 125 | + // Will set: |
| 126 | + // M1 = A * (R^T*R)^-1 * A^T |
| 127 | + // M2 = (C^T*C)^-1 |
| 128 | + // M3 = (R * R^T)^-1 * A^T |
| 129 | + // M4 = identity |
| 130 | + // y = measuredData |
| 131 | + //.........................M1,................................................ |
| 132 | + |
| 133 | + DenseMatrix RRtr(N,N); |
| 134 | + DenseMatrix iRRtr(N,N); |
| 135 | + DenseMatrix CCtr(M,M); |
| 136 | + DenseMatrix iCCtr(M,M); |
| 137 | + |
| 138 | + // DEFINITIONS AND PREALOCATION OF SOURCE REGULARIZATION MATRIX 'R' |
| 139 | + // if R does not exist, set as identity of size equal to N (columns of fwd matrix) |
| 140 | + if (true)//(&sourceWeighting_==NULL) |
| 141 | + { |
| 142 | + RRtr = DenseMatrix::Identity(N, N); |
| 143 | + iRRtr = RRtr; |
| 144 | + } |
| 145 | + else |
| 146 | + { |
| 147 | + |
| 148 | + // if provided the non-squared version of R |
| 149 | + if( regularizationSolutionSubcase_ == TikhonovAlgoAbstractBase::solution_constrained ) |
| 150 | + { |
| 151 | + RRtr = sourceWeighting_.transpose() * sourceWeighting_; |
| 152 | + } |
| 153 | + // otherwise, if the source regularization is provided as the squared version (RR^T) |
| 154 | + else if ( regularizationSolutionSubcase_ == TikhonovAlgoAbstractBase::solution_constrained_squared ) |
| 155 | + { |
| 156 | + RRtr = sourceWeighting_; |
| 157 | + } |
| 158 | + |
| 159 | + // check if squared regularization matrix is invertible |
| 160 | + auto LURRtr = RRtr.fullPivLu(); |
| 161 | + if ( !LURRtr.isInvertible() ) |
| 162 | + { |
| 163 | + |
| 164 | + THROW_ALGORITHM_INPUT_ERROR_SIMPLE("Regularization matrix in the source space is not invertible."); |
| 165 | + } |
| 166 | + |
| 167 | + // COMPUTE inverse |
| 168 | + iRRtr = LURRtr.inverse().eval(); |
| 169 | + |
| 170 | + } |
| 171 | + |
| 172 | + |
| 173 | + // DEFINITIONS AND PREALOCATIONS OF MEASUREMENTS COVARIANCE MATRIX 'C' |
| 174 | + // if C does not exist, set as identity of size equal to M (rows of fwd matrix) |
| 175 | + if (true)//(&sensorWeighting_==NULL) |
| 176 | + { |
| 177 | + CCtr = DenseMatrix::Identity(M, M); |
| 178 | + iCCtr = CCtr; |
| 179 | + |
| 180 | + } |
| 181 | + else |
| 182 | + { |
| 183 | + // if measurement covariance matrix provided in non-squared form |
| 184 | + if (regularizationResidualSubcase_ == TikhonovAlgoAbstractBase::residual_constrained) |
| 185 | + { |
| 186 | + // check that the matrix is of appropriate size (equal number of rows as rows in fwd matrix) |
| 187 | + if(M != sensorWeighting_.ncols()) |
| 188 | + { |
| 189 | + CCtr = sensorWeighting_.transpose() * sensorWeighting_; |
| 190 | + } |
| 191 | + } |
| 192 | + // otherwise if the source covariance matrix is provided in squared form |
| 193 | + else if ( regularizationResidualSubcase_ == TikhonovAlgoAbstractBase::residual_constrained_squared ) |
| 194 | + { |
| 195 | + CCtr = sensorWeighting_; |
| 196 | + } |
| 197 | + |
| 198 | + // check if squared regularization matrix is invertible |
| 199 | + auto LUCCtr = CCtr.fullPivLu(); |
| 200 | + if ( !LUCCtr.isInvertible() ) |
| 201 | + { |
| 202 | + THROW_ALGORITHM_INPUT_ERROR_SIMPLE("Residual covariance matrix is not invertible."); |
| 203 | + } |
| 204 | + iCCtr = LUCCtr.inverse().eval(); |
| 205 | + |
| 206 | + |
| 207 | + |
| 208 | + } |
| 209 | + |
| 210 | + // DEFINE M1 = (A * (R^T*R)^-1 * A^T MATRIX FOR FASTER COMPUTATION |
| 211 | + DenseMatrix RAtr = iRRtr * forward_transpose; |
| 212 | + M1 = forwardMatrix_ * RAtr; |
| 213 | + |
| 214 | + // DEFINE M2 = (C^TC)^-1 |
| 215 | + M2 = iCCtr; |
| 216 | + |
| 217 | + // DEFINE M3 = (R^TR)^-1 * A^T |
| 218 | + M3 = RAtr; |
| 219 | + |
| 220 | + // DEFINE M4 = identity (size of number of measurements) |
| 221 | + M4 = DenseMatrix::Identity(M, N); |
| 222 | + |
| 223 | + // DEFINE measurement vector |
| 224 | + y = measuredData_; |
| 225 | + |
| 226 | + |
| 227 | + |
| 228 | + } |
| 229 | + //OVERDETERMINED CASE, |
| 230 | + //similar procedure as underdetermined case (documentation comments similar, see above) |
| 231 | + else if ( ( (regularizationChoice_ == TikhonovAlgoAbstractBase::automatic) && (M>=N) ) || (regularizationChoice_ == TikhonovAlgoAbstractBase::overdetermined) ) |
| 232 | + { |
| 233 | + //......................................................................... |
| 234 | + // OPERATE ON DATA: |
| 235 | + // Computes X = (A^T * C^T * C * A + LAMBDA * LAMBDA * R^T * R) * A^T * C^T * C * Y |
| 236 | + // X = (M3) * G^-1 * M4 * Y |
| 237 | + //......................................................................... |
| 238 | + // Will set: |
| 239 | + // M1 = A * C^T*C * A^T |
| 240 | + // M2 = R^T*R |
| 241 | + // M3 = identity |
| 242 | + // M4 = A^TC^TC |
| 243 | + // y = A * C^T*C * measuredData |
| 244 | + //......................................................................... |
| 245 | + |
| 246 | + |
| 247 | + // prealocations |
| 248 | + DenseMatrix RtrR(N,N); |
| 249 | + DenseMatrix CtrC(M,M); |
| 250 | + |
| 251 | + |
| 252 | + // DEFINITIONS AND PREALOCATION OF SOURCE REGULARIZATION MATRIX 'R' |
| 253 | + |
| 254 | + // if R does not exist, set as identity of size equal to N (columns of fwd matrix) |
| 255 | + if (true)//(&sourceWeighting_==NULL) |
| 256 | + { |
| 257 | + RtrR = DenseMatrix::Identity(N, N); |
| 258 | + } |
| 259 | + else |
| 260 | + { |
| 261 | + // if provided the non-squared version of R |
| 262 | + if( regularizationSolutionSubcase_ == TikhonovAlgoAbstractBase::solution_constrained ) |
| 263 | + { |
| 264 | + RtrR = sourceWeighting_.transpose() * sourceWeighting_; |
| 265 | + } |
| 266 | + // otherwise, if the source regularization is provided as the squared version (RR^T) |
| 267 | + else if ( regularizationSolutionSubcase_ == TikhonovAlgoAbstractBase::solution_constrained_squared ) |
| 268 | + { |
| 269 | + RtrR = sourceWeighting_; |
| 270 | + } |
| 271 | + } |
| 272 | + |
| 273 | + |
| 274 | + // DEFINITIONS AND PREALOCATIONS OF MEASUREMENTS COVARIANCE MATRIX 'C' |
| 275 | + // if C does not exist, set as identity of size equal to M (rows of fwd matrix) |
| 276 | + if (true)//(&sensorWeighting_==NULL) |
| 277 | + { |
| 278 | + CtrC = DenseMatrix::Identity(M, M); |
| 279 | + } |
| 280 | + else |
| 281 | + { |
| 282 | + // if measurement covariance matrix provided in non-squared form |
| 283 | + if (regularizationResidualSubcase_ == TikhonovAlgoAbstractBase::residual_constrained) |
| 284 | + { |
| 285 | + CtrC = sensorWeighting_.transpose() * sensorWeighting_; |
| 286 | + } |
| 287 | + // otherwise if the source covariance matrix is provided in squared form |
| 288 | + else if ( regularizationResidualSubcase_ == TikhonovAlgoAbstractBase::residual_constrained_squared ) |
| 289 | + { |
| 290 | + CtrC = sensorWeighting_; |
| 291 | + } |
| 292 | + |
| 293 | + } |
| 294 | + |
| 295 | + // DEFINE M1 = (A * (R*R^T)^-1 * A^T MATRIX FOR FASTER COMPUTATION |
| 296 | + DenseMatrix CtrCA = CtrC * (forwardMatrix_); |
| 297 | + M1 = forward_transpose * CtrCA; |
| 298 | + |
| 299 | + // DEFINE M2 = (CC^T)^-1 |
| 300 | + M2 = RtrR; |
| 301 | + |
| 302 | + // DEFINE M3 = identity (size of number of measurements) |
| 303 | + M3 = DenseMatrix::Identity(N, N); |
| 304 | + |
| 305 | + // DEFINT M4 = A^T* C^T * C |
| 306 | + M4 = CtrCA.transpose(); |
| 307 | + |
| 308 | + // DEFINE measurement vector |
| 309 | + y = CtrCA.transpose() * measuredData_; |
| 310 | + |
| 311 | + } |
| 312 | + |
| 313 | + } |
| 314 | +//////// End of prealocation of matrices |
| 315 | +//////////// |
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