1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2011 Jitse Niesen <jitse (at) maths.leeds.ac.uk> 5 // Copyright (C) 2011 Chen-Pang He <jdh8 (at) ms63.hinet.net> 6 // 7 // This Source Code Form is subject to the terms of the Mozilla 8 // Public License v. 2.0. If a copy of the MPL was not distributed 9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10 11 #ifndef EIGEN_MATRIX_LOGARITHM 12 #define EIGEN_MATRIX_LOGARITHM 13 14 #ifndef M_PI 15 #define M_PI 3.141592653589793238462643383279503L 16 #endif 17 18 namespace Eigen { 19 20 /** \ingroup MatrixFunctions_Module 21 * \class MatrixLogarithmAtomic 22 * \brief Helper class for computing matrix logarithm of atomic matrices. 23 * 24 * \internal 25 * Here, an atomic matrix is a triangular matrix whose diagonal 26 * entries are close to each other. 27 * 28 * \sa class MatrixFunctionAtomic, MatrixBase::log() 29 */ 30 template <typename MatrixType> 31 class MatrixLogarithmAtomic 32 { 33 public: 34 35 typedef typename MatrixType::Scalar Scalar; 36 // typedef typename MatrixType::Index Index; 37 typedef typename NumTraits<Scalar>::Real RealScalar; 38 // typedef typename internal::stem_function<Scalar>::type StemFunction; 39 // typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; 40 41 /** \brief Constructor. */ 42 MatrixLogarithmAtomic() { } 43 44 /** \brief Compute matrix logarithm of atomic matrix 45 * \param[in] A argument of matrix logarithm, should be upper triangular and atomic 46 * \returns The logarithm of \p A. 47 */ 48 MatrixType compute(const MatrixType& A); 49 50 private: 51 52 void compute2x2(const MatrixType& A, MatrixType& result); 53 void computeBig(const MatrixType& A, MatrixType& result); 54 int getPadeDegree(float normTminusI); 55 int getPadeDegree(double normTminusI); 56 int getPadeDegree(long double normTminusI); 57 void computePade(MatrixType& result, const MatrixType& T, int degree); 58 void computePade3(MatrixType& result, const MatrixType& T); 59 void computePade4(MatrixType& result, const MatrixType& T); 60 void computePade5(MatrixType& result, const MatrixType& T); 61 void computePade6(MatrixType& result, const MatrixType& T); 62 void computePade7(MatrixType& result, const MatrixType& T); 63 void computePade8(MatrixType& result, const MatrixType& T); 64 void computePade9(MatrixType& result, const MatrixType& T); 65 void computePade10(MatrixType& result, const MatrixType& T); 66 void computePade11(MatrixType& result, const MatrixType& T); 67 68 static const int minPadeDegree = 3; 69 static const int maxPadeDegree = std::numeric_limits<RealScalar>::digits<= 24? 5: // single precision 70 std::numeric_limits<RealScalar>::digits<= 53? 7: // double precision 71 std::numeric_limits<RealScalar>::digits<= 64? 8: // extended precision 72 std::numeric_limits<RealScalar>::digits<=106? 10: // double-double 73 11; // quadruple precision 74 75 // Prevent copying 76 MatrixLogarithmAtomic(const MatrixLogarithmAtomic&); 77 MatrixLogarithmAtomic& operator=(const MatrixLogarithmAtomic&); 78 }; 79 80 /** \brief Compute logarithm of triangular matrix with clustered eigenvalues. */ 81 template <typename MatrixType> 82 MatrixType MatrixLogarithmAtomic<MatrixType>::compute(const MatrixType& A) 83 { 84 using std::log; 85 MatrixType result(A.rows(), A.rows()); 86 if (A.rows() == 1) 87 result(0,0) = log(A(0,0)); 88 else if (A.rows() == 2) 89 compute2x2(A, result); 90 else 91 computeBig(A, result); 92 return result; 93 } 94 95 /** \brief Compute logarithm of 2x2 triangular matrix. */ 96 template <typename MatrixType> 97 void MatrixLogarithmAtomic<MatrixType>::compute2x2(const MatrixType& A, MatrixType& result) 98 { 99 using std::abs; 100 using std::ceil; 101 using std::imag; 102 using std::log; 103 104 Scalar logA00 = log(A(0,0)); 105 Scalar logA11 = log(A(1,1)); 106 107 result(0,0) = logA00; 108 result(1,0) = Scalar(0); 109 result(1,1) = logA11; 110 111 if (A(0,0) == A(1,1)) { 112 result(0,1) = A(0,1) / A(0,0); 113 } else if ((abs(A(0,0)) < 0.5*abs(A(1,1))) || (abs(A(0,0)) > 2*abs(A(1,1)))) { 114 result(0,1) = A(0,1) * (logA11 - logA00) / (A(1,1) - A(0,0)); 115 } else { 116 // computation in previous branch is inaccurate if A(1,1) \approx A(0,0) 117 int unwindingNumber = static_cast<int>(ceil((imag(logA11 - logA00) - M_PI) / (2*M_PI))); 118 Scalar y = A(1,1) - A(0,0), x = A(1,1) + A(0,0); 119 result(0,1) = A(0,1) * (Scalar(2) * numext::atanh2(y,x) + Scalar(0,2*M_PI*unwindingNumber)) / y; 120 } 121 } 122 123 /** \brief Compute logarithm of triangular matrices with size > 2. 124 * \details This uses a inverse scale-and-square algorithm. */ 125 template <typename MatrixType> 126 void MatrixLogarithmAtomic<MatrixType>::computeBig(const MatrixType& A, MatrixType& result) 127 { 128 using std::pow; 129 int numberOfSquareRoots = 0; 130 int numberOfExtraSquareRoots = 0; 131 int degree; 132 MatrixType T = A, sqrtT; 133 const RealScalar maxNormForPade = maxPadeDegree<= 5? 5.3149729967117310e-1: // single precision 134 maxPadeDegree<= 7? 2.6429608311114350e-1: // double precision 135 maxPadeDegree<= 8? 2.32777776523703892094e-1L: // extended precision 136 maxPadeDegree<=10? 1.05026503471351080481093652651105e-1L: // double-double 137 1.1880960220216759245467951592883642e-1L; // quadruple precision 138 139 while (true) { 140 RealScalar normTminusI = (T - MatrixType::Identity(T.rows(), T.rows())).cwiseAbs().colwise().sum().maxCoeff(); 141 if (normTminusI < maxNormForPade) { 142 degree = getPadeDegree(normTminusI); 143 int degree2 = getPadeDegree(normTminusI / RealScalar(2)); 144 if ((degree - degree2 <= 1) || (numberOfExtraSquareRoots == 1)) 145 break; 146 ++numberOfExtraSquareRoots; 147 } 148 MatrixSquareRootTriangular<MatrixType>(T).compute(sqrtT); 149 T = sqrtT.template triangularView<Upper>(); 150 ++numberOfSquareRoots; 151 } 152 153 computePade(result, T, degree); 154 result *= pow(RealScalar(2), numberOfSquareRoots); 155 } 156 157 /* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = float) */ 158 template <typename MatrixType> 159 int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(float normTminusI) 160 { 161 const float maxNormForPade[] = { 2.5111573934555054e-1 /* degree = 3 */ , 4.0535837411880493e-1, 162 5.3149729967117310e-1 }; 163 int degree = 3; 164 for (; degree <= maxPadeDegree; ++degree) 165 if (normTminusI <= maxNormForPade[degree - minPadeDegree]) 166 break; 167 return degree; 168 } 169 170 /* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = double) */ 171 template <typename MatrixType> 172 int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(double normTminusI) 173 { 174 const double maxNormForPade[] = { 1.6206284795015624e-2 /* degree = 3 */ , 5.3873532631381171e-2, 175 1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 }; 176 int degree = 3; 177 for (; degree <= maxPadeDegree; ++degree) 178 if (normTminusI <= maxNormForPade[degree - minPadeDegree]) 179 break; 180 return degree; 181 } 182 183 /* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = long double) */ 184 template <typename MatrixType> 185 int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(long double normTminusI) 186 { 187 #if LDBL_MANT_DIG == 53 // double precision 188 const long double maxNormForPade[] = { 1.6206284795015624e-2L /* degree = 3 */ , 5.3873532631381171e-2L, 189 1.1352802267628681e-1L, 1.8662860613541288e-1L, 2.642960831111435e-1L }; 190 #elif LDBL_MANT_DIG <= 64 // extended precision 191 const long double maxNormForPade[] = { 5.48256690357782863103e-3L /* degree = 3 */, 2.34559162387971167321e-2L, 192 5.84603923897347449857e-2L, 1.08486423756725170223e-1L, 1.68385767881294446649e-1L, 193 2.32777776523703892094e-1L }; 194 #elif LDBL_MANT_DIG <= 106 // double-double 195 const long double maxNormForPade[] = { 8.58970550342939562202529664318890e-5L /* degree = 3 */, 196 9.34074328446359654039446552677759e-4L, 4.26117194647672175773064114582860e-3L, 197 1.21546224740281848743149666560464e-2L, 2.61100544998339436713088248557444e-2L, 198 4.66170074627052749243018566390567e-2L, 7.32585144444135027565872014932387e-2L, 199 1.05026503471351080481093652651105e-1L }; 200 #else // quadruple precision 201 const long double maxNormForPade[] = { 4.7419931187193005048501568167858103e-5L /* degree = 3 */, 202 5.8853168473544560470387769480192666e-4L, 2.9216120366601315391789493628113520e-3L, 203 8.8415758124319434347116734705174308e-3L, 1.9850836029449446668518049562565291e-2L, 204 3.6688019729653446926585242192447447e-2L, 5.9290962294020186998954055264528393e-2L, 205 8.6998436081634343903250580992127677e-2L, 1.1880960220216759245467951592883642e-1L }; 206 #endif 207 int degree = 3; 208 for (; degree <= maxPadeDegree; ++degree) 209 if (normTminusI <= maxNormForPade[degree - minPadeDegree]) 210 break; 211 return degree; 212 } 213 214 /* \brief Compute Pade approximation to matrix logarithm */ 215 template <typename MatrixType> 216 void MatrixLogarithmAtomic<MatrixType>::computePade(MatrixType& result, const MatrixType& T, int degree) 217 { 218 switch (degree) { 219 case 3: computePade3(result, T); break; 220 case 4: computePade4(result, T); break; 221 case 5: computePade5(result, T); break; 222 case 6: computePade6(result, T); break; 223 case 7: computePade7(result, T); break; 224 case 8: computePade8(result, T); break; 225 case 9: computePade9(result, T); break; 226 case 10: computePade10(result, T); break; 227 case 11: computePade11(result, T); break; 228 default: assert(false); // should never happen 229 } 230 } 231 232 template <typename MatrixType> 233 void MatrixLogarithmAtomic<MatrixType>::computePade3(MatrixType& result, const MatrixType& T) 234 { 235 const int degree = 3; 236 const RealScalar nodes[] = { 0.1127016653792583114820734600217600L, 0.5000000000000000000000000000000000L, 237 0.8872983346207416885179265399782400L }; 238 const RealScalar weights[] = { 0.2777777777777777777777777777777778L, 0.4444444444444444444444444444444444L, 239 0.2777777777777777777777777777777778L }; 240 eigen_assert(degree <= maxPadeDegree); 241 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 242 result.setZero(T.rows(), T.rows()); 243 for (int k = 0; k < degree; ++k) 244 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 245 .template triangularView<Upper>().solve(TminusI); 246 } 247 248 template <typename MatrixType> 249 void MatrixLogarithmAtomic<MatrixType>::computePade4(MatrixType& result, const MatrixType& T) 250 { 251 const int degree = 4; 252 const RealScalar nodes[] = { 0.0694318442029737123880267555535953L, 0.3300094782075718675986671204483777L, 253 0.6699905217924281324013328795516223L, 0.9305681557970262876119732444464048L }; 254 const RealScalar weights[] = { 0.1739274225687269286865319746109997L, 0.3260725774312730713134680253890003L, 255 0.3260725774312730713134680253890003L, 0.1739274225687269286865319746109997L }; 256 eigen_assert(degree <= maxPadeDegree); 257 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 258 result.setZero(T.rows(), T.rows()); 259 for (int k = 0; k < degree; ++k) 260 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 261 .template triangularView<Upper>().solve(TminusI); 262 } 263 264 template <typename MatrixType> 265 void MatrixLogarithmAtomic<MatrixType>::computePade5(MatrixType& result, const MatrixType& T) 266 { 267 const int degree = 5; 268 const RealScalar nodes[] = { 0.0469100770306680036011865608503035L, 0.2307653449471584544818427896498956L, 269 0.5000000000000000000000000000000000L, 0.7692346550528415455181572103501044L, 270 0.9530899229693319963988134391496965L }; 271 const RealScalar weights[] = { 0.1184634425280945437571320203599587L, 0.2393143352496832340206457574178191L, 272 0.2844444444444444444444444444444444L, 0.2393143352496832340206457574178191L, 273 0.1184634425280945437571320203599587L }; 274 eigen_assert(degree <= maxPadeDegree); 275 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 276 result.setZero(T.rows(), T.rows()); 277 for (int k = 0; k < degree; ++k) 278 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 279 .template triangularView<Upper>().solve(TminusI); 280 } 281 282 template <typename MatrixType> 283 void MatrixLogarithmAtomic<MatrixType>::computePade6(MatrixType& result, const MatrixType& T) 284 { 285 const int degree = 6; 286 const RealScalar nodes[] = { 0.0337652428984239860938492227530027L, 0.1693953067668677431693002024900473L, 287 0.3806904069584015456847491391596440L, 0.6193095930415984543152508608403560L, 288 0.8306046932331322568306997975099527L, 0.9662347571015760139061507772469973L }; 289 const RealScalar weights[] = { 0.0856622461895851725201480710863665L, 0.1803807865240693037849167569188581L, 290 0.2339569672863455236949351719947755L, 0.2339569672863455236949351719947755L, 291 0.1803807865240693037849167569188581L, 0.0856622461895851725201480710863665L }; 292 eigen_assert(degree <= maxPadeDegree); 293 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 294 result.setZero(T.rows(), T.rows()); 295 for (int k = 0; k < degree; ++k) 296 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 297 .template triangularView<Upper>().solve(TminusI); 298 } 299 300 template <typename MatrixType> 301 void MatrixLogarithmAtomic<MatrixType>::computePade7(MatrixType& result, const MatrixType& T) 302 { 303 const int degree = 7; 304 const RealScalar nodes[] = { 0.0254460438286207377369051579760744L, 0.1292344072003027800680676133596058L, 305 0.2970774243113014165466967939615193L, 0.5000000000000000000000000000000000L, 306 0.7029225756886985834533032060384807L, 0.8707655927996972199319323866403942L, 307 0.9745539561713792622630948420239256L }; 308 const RealScalar weights[] = { 0.0647424830844348466353057163395410L, 0.1398526957446383339507338857118898L, 309 0.1909150252525594724751848877444876L, 0.2089795918367346938775510204081633L, 310 0.1909150252525594724751848877444876L, 0.1398526957446383339507338857118898L, 311 0.0647424830844348466353057163395410L }; 312 eigen_assert(degree <= maxPadeDegree); 313 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 314 result.setZero(T.rows(), T.rows()); 315 for (int k = 0; k < degree; ++k) 316 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 317 .template triangularView<Upper>().solve(TminusI); 318 } 319 320 template <typename MatrixType> 321 void MatrixLogarithmAtomic<MatrixType>::computePade8(MatrixType& result, const MatrixType& T) 322 { 323 const int degree = 8; 324 const RealScalar nodes[] = { 0.0198550717512318841582195657152635L, 0.1016667612931866302042230317620848L, 325 0.2372337950418355070911304754053768L, 0.4082826787521750975302619288199080L, 326 0.5917173212478249024697380711800920L, 0.7627662049581644929088695245946232L, 327 0.8983332387068133697957769682379152L, 0.9801449282487681158417804342847365L }; 328 const RealScalar weights[] = { 0.0506142681451881295762656771549811L, 0.1111905172266872352721779972131204L, 329 0.1568533229389436436689811009933007L, 0.1813418916891809914825752246385978L, 330 0.1813418916891809914825752246385978L, 0.1568533229389436436689811009933007L, 331 0.1111905172266872352721779972131204L, 0.0506142681451881295762656771549811L }; 332 eigen_assert(degree <= maxPadeDegree); 333 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 334 result.setZero(T.rows(), T.rows()); 335 for (int k = 0; k < degree; ++k) 336 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 337 .template triangularView<Upper>().solve(TminusI); 338 } 339 340 template <typename MatrixType> 341 void MatrixLogarithmAtomic<MatrixType>::computePade9(MatrixType& result, const MatrixType& T) 342 { 343 const int degree = 9; 344 const RealScalar nodes[] = { 0.0159198802461869550822118985481636L, 0.0819844463366821028502851059651326L, 345 0.1933142836497048013456489803292629L, 0.3378732882980955354807309926783317L, 346 0.5000000000000000000000000000000000L, 0.6621267117019044645192690073216683L, 347 0.8066857163502951986543510196707371L, 0.9180155536633178971497148940348674L, 348 0.9840801197538130449177881014518364L }; 349 const RealScalar weights[] = { 0.0406371941807872059859460790552618L, 0.0903240803474287020292360156214564L, 350 0.1303053482014677311593714347093164L, 0.1561735385200014200343152032922218L, 351 0.1651196775006298815822625346434870L, 0.1561735385200014200343152032922218L, 352 0.1303053482014677311593714347093164L, 0.0903240803474287020292360156214564L, 353 0.0406371941807872059859460790552618L }; 354 eigen_assert(degree <= maxPadeDegree); 355 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 356 result.setZero(T.rows(), T.rows()); 357 for (int k = 0; k < degree; ++k) 358 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 359 .template triangularView<Upper>().solve(TminusI); 360 } 361 362 template <typename MatrixType> 363 void MatrixLogarithmAtomic<MatrixType>::computePade10(MatrixType& result, const MatrixType& T) 364 { 365 const int degree = 10; 366 const RealScalar nodes[] = { 0.0130467357414141399610179939577740L, 0.0674683166555077446339516557882535L, 367 0.1602952158504877968828363174425632L, 0.2833023029353764046003670284171079L, 368 0.4255628305091843945575869994351400L, 0.5744371694908156054424130005648600L, 369 0.7166976970646235953996329715828921L, 0.8397047841495122031171636825574368L, 370 0.9325316833444922553660483442117465L, 0.9869532642585858600389820060422260L }; 371 const RealScalar weights[] = { 0.0333356721543440687967844049466659L, 0.0747256745752902965728881698288487L, 372 0.1095431812579910219977674671140816L, 0.1346333596549981775456134607847347L, 373 0.1477621123573764350869464973256692L, 0.1477621123573764350869464973256692L, 374 0.1346333596549981775456134607847347L, 0.1095431812579910219977674671140816L, 375 0.0747256745752902965728881698288487L, 0.0333356721543440687967844049466659L }; 376 eigen_assert(degree <= maxPadeDegree); 377 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 378 result.setZero(T.rows(), T.rows()); 379 for (int k = 0; k < degree; ++k) 380 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 381 .template triangularView<Upper>().solve(TminusI); 382 } 383 384 template <typename MatrixType> 385 void MatrixLogarithmAtomic<MatrixType>::computePade11(MatrixType& result, const MatrixType& T) 386 { 387 const int degree = 11; 388 const RealScalar nodes[] = { 0.0108856709269715035980309994385713L, 0.0564687001159523504624211153480364L, 389 0.1349239972129753379532918739844233L, 0.2404519353965940920371371652706952L, 390 0.3652284220238275138342340072995692L, 0.5000000000000000000000000000000000L, 391 0.6347715779761724861657659927004308L, 0.7595480646034059079628628347293048L, 392 0.8650760027870246620467081260155767L, 0.9435312998840476495375788846519636L, 393 0.9891143290730284964019690005614287L }; 394 const RealScalar weights[] = { 0.0278342835580868332413768602212743L, 0.0627901847324523123173471496119701L, 395 0.0931451054638671257130488207158280L, 0.1165968822959952399592618524215876L, 396 0.1314022722551233310903444349452546L, 0.1364625433889503153572417641681711L, 397 0.1314022722551233310903444349452546L, 0.1165968822959952399592618524215876L, 398 0.0931451054638671257130488207158280L, 0.0627901847324523123173471496119701L, 399 0.0278342835580868332413768602212743L }; 400 eigen_assert(degree <= maxPadeDegree); 401 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 402 result.setZero(T.rows(), T.rows()); 403 for (int k = 0; k < degree; ++k) 404 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 405 .template triangularView<Upper>().solve(TminusI); 406 } 407 408 /** \ingroup MatrixFunctions_Module 409 * 410 * \brief Proxy for the matrix logarithm of some matrix (expression). 411 * 412 * \tparam Derived Type of the argument to the matrix function. 413 * 414 * This class holds the argument to the matrix function until it is 415 * assigned or evaluated for some other reason (so the argument 416 * should not be changed in the meantime). It is the return type of 417 * MatrixBase::log() and most of the time this is the only way it 418 * is used. 419 */ 420 template<typename Derived> class MatrixLogarithmReturnValue 421 : public ReturnByValue<MatrixLogarithmReturnValue<Derived> > 422 { 423 public: 424 425 typedef typename Derived::Scalar Scalar; 426 typedef typename Derived::Index Index; 427 428 /** \brief Constructor. 429 * 430 * \param[in] A %Matrix (expression) forming the argument of the matrix logarithm. 431 */ 432 MatrixLogarithmReturnValue(const Derived& A) : m_A(A) { } 433 434 /** \brief Compute the matrix logarithm. 435 * 436 * \param[out] result Logarithm of \p A, where \A is as specified in the constructor. 437 */ 438 template <typename ResultType> 439 inline void evalTo(ResultType& result) const 440 { 441 typedef typename Derived::PlainObject PlainObject; 442 typedef internal::traits<PlainObject> Traits; 443 static const int RowsAtCompileTime = Traits::RowsAtCompileTime; 444 static const int ColsAtCompileTime = Traits::ColsAtCompileTime; 445 static const int Options = PlainObject::Options; 446 typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar; 447 typedef Matrix<ComplexScalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType; 448 typedef MatrixLogarithmAtomic<DynMatrixType> AtomicType; 449 AtomicType atomic; 450 451 const PlainObject Aevaluated = m_A.eval(); 452 MatrixFunction<PlainObject, AtomicType> mf(Aevaluated, atomic); 453 mf.compute(result); 454 } 455 456 Index rows() const { return m_A.rows(); } 457 Index cols() const { return m_A.cols(); } 458 459 private: 460 typename internal::nested<Derived>::type m_A; 461 462 MatrixLogarithmReturnValue& operator=(const MatrixLogarithmReturnValue&); 463 }; 464 465 namespace internal { 466 template<typename Derived> 467 struct traits<MatrixLogarithmReturnValue<Derived> > 468 { 469 typedef typename Derived::PlainObject ReturnType; 470 }; 471 } 472 473 474 /********** MatrixBase method **********/ 475 476 477 template <typename Derived> 478 const MatrixLogarithmReturnValue<Derived> MatrixBase<Derived>::log() const 479 { 480 eigen_assert(rows() == cols()); 481 return MatrixLogarithmReturnValue<Derived>(derived()); 482 } 483 484 } // end namespace Eigen 485 486 #endif // EIGEN_MATRIX_LOGARITHM 487
