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 static Scalar atanh(Scalar x); 55 int getPadeDegree(float normTminusI); 56 int getPadeDegree(double normTminusI); 57 int getPadeDegree(long double normTminusI); 58 void computePade(MatrixType& result, const MatrixType& T, int degree); 59 void computePade3(MatrixType& result, const MatrixType& T); 60 void computePade4(MatrixType& result, const MatrixType& T); 61 void computePade5(MatrixType& result, const MatrixType& T); 62 void computePade6(MatrixType& result, const MatrixType& T); 63 void computePade7(MatrixType& result, const MatrixType& T); 64 void computePade8(MatrixType& result, const MatrixType& T); 65 void computePade9(MatrixType& result, const MatrixType& T); 66 void computePade10(MatrixType& result, const MatrixType& T); 67 void computePade11(MatrixType& result, const MatrixType& T); 68 69 static const int minPadeDegree = 3; 70 static const int maxPadeDegree = std::numeric_limits<RealScalar>::digits<= 24? 5: // single precision 71 std::numeric_limits<RealScalar>::digits<= 53? 7: // double precision 72 std::numeric_limits<RealScalar>::digits<= 64? 8: // extended precision 73 std::numeric_limits<RealScalar>::digits<=106? 10: 11; // double-double or 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 atanh (inverse hyperbolic tangent). */ 96 template <typename MatrixType> 97 typename MatrixType::Scalar MatrixLogarithmAtomic<MatrixType>::atanh(typename MatrixType::Scalar x) 98 { 99 using std::abs; 100 using std::sqrt; 101 if (abs(x) > sqrt(NumTraits<Scalar>::epsilon())) 102 return Scalar(0.5) * log((Scalar(1) + x) / (Scalar(1) - x)); 103 else 104 return x + x*x*x / Scalar(3); 105 } 106 107 /** \brief Compute logarithm of 2x2 triangular matrix. */ 108 template <typename MatrixType> 109 void MatrixLogarithmAtomic<MatrixType>::compute2x2(const MatrixType& A, MatrixType& result) 110 { 111 using std::abs; 112 using std::ceil; 113 using std::imag; 114 using std::log; 115 116 Scalar logA00 = log(A(0,0)); 117 Scalar logA11 = log(A(1,1)); 118 119 result(0,0) = logA00; 120 result(1,0) = Scalar(0); 121 result(1,1) = logA11; 122 123 if (A(0,0) == A(1,1)) { 124 result(0,1) = A(0,1) / A(0,0); 125 } else if ((abs(A(0,0)) < 0.5*abs(A(1,1))) || (abs(A(0,0)) > 2*abs(A(1,1)))) { 126 result(0,1) = A(0,1) * (logA11 - logA00) / (A(1,1) - A(0,0)); 127 } else { 128 // computation in previous branch is inaccurate if A(1,1) \approx A(0,0) 129 int unwindingNumber = static_cast<int>(ceil((imag(logA11 - logA00) - M_PI) / (2*M_PI))); 130 Scalar z = (A(1,1) - A(0,0)) / (A(1,1) + A(0,0)); 131 result(0,1) = A(0,1) * (Scalar(2) * atanh(z) + Scalar(0,2*M_PI*unwindingNumber)) / (A(1,1) - A(0,0)); 132 } 133 } 134 135 /** \brief Compute logarithm of triangular matrices with size > 2. 136 * \details This uses a inverse scale-and-square algorithm. */ 137 template <typename MatrixType> 138 void MatrixLogarithmAtomic<MatrixType>::computeBig(const MatrixType& A, MatrixType& result) 139 { 140 int numberOfSquareRoots = 0; 141 int numberOfExtraSquareRoots = 0; 142 int degree; 143 MatrixType T = A; 144 const RealScalar maxNormForPade = maxPadeDegree<= 5? 5.3149729967117310e-1: // single precision 145 maxPadeDegree<= 7? 2.6429608311114350e-1: // double precision 146 maxPadeDegree<= 8? 2.32777776523703892094e-1L: // extended precision 147 maxPadeDegree<=10? 1.05026503471351080481093652651105e-1L: // double-double 148 1.1880960220216759245467951592883642e-1L; // quadruple precision 149 150 while (true) { 151 RealScalar normTminusI = (T - MatrixType::Identity(T.rows(), T.rows())).cwiseAbs().colwise().sum().maxCoeff(); 152 if (normTminusI < maxNormForPade) { 153 degree = getPadeDegree(normTminusI); 154 int degree2 = getPadeDegree(normTminusI / RealScalar(2)); 155 if ((degree - degree2 <= 1) || (numberOfExtraSquareRoots == 1)) 156 break; 157 ++numberOfExtraSquareRoots; 158 } 159 MatrixType sqrtT; 160 MatrixSquareRootTriangular<MatrixType>(T).compute(sqrtT); 161 T = sqrtT; 162 ++numberOfSquareRoots; 163 } 164 165 computePade(result, T, degree); 166 result *= pow(RealScalar(2), numberOfSquareRoots); 167 } 168 169 /* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = float) */ 170 template <typename MatrixType> 171 int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(float normTminusI) 172 { 173 const float maxNormForPade[] = { 2.5111573934555054e-1 /* degree = 3 */ , 4.0535837411880493e-1, 174 5.3149729967117310e-1 }; 175 for (int degree = 3; degree <= maxPadeDegree; ++degree) 176 if (normTminusI <= maxNormForPade[degree - minPadeDegree]) 177 return degree; 178 assert(false); // this line should never be reached 179 } 180 181 /* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = double) */ 182 template <typename MatrixType> 183 int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(double normTminusI) 184 { 185 const double maxNormForPade[] = { 1.6206284795015624e-2 /* degree = 3 */ , 5.3873532631381171e-2, 186 1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 }; 187 for (int degree = 3; degree <= maxPadeDegree; ++degree) 188 if (normTminusI <= maxNormForPade[degree - minPadeDegree]) 189 return degree; 190 assert(false); // this line should never be reached 191 } 192 193 /* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = long double) */ 194 template <typename MatrixType> 195 int MatrixLogarithmAtomic<MatrixType>::getPadeDegree(long double normTminusI) 196 { 197 #if LDBL_MANT_DIG == 53 // double precision 198 const double maxNormForPade[] = { 1.6206284795015624e-2 /* degree = 3 */ , 5.3873532631381171e-2, 199 1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 }; 200 #elif LDBL_MANT_DIG <= 64 // extended precision 201 const double maxNormForPade[] = { 5.48256690357782863103e-3 /* degree = 3 */, 2.34559162387971167321e-2, 202 5.84603923897347449857e-2, 1.08486423756725170223e-1, 1.68385767881294446649e-1, 203 2.32777776523703892094e-1 }; 204 #elif LDBL_MANT_DIG <= 106 // double-double 205 const double maxNormForPade[] = { 8.58970550342939562202529664318890e-5 /* degree = 3 */, 206 9.34074328446359654039446552677759e-4, 4.26117194647672175773064114582860e-3, 207 1.21546224740281848743149666560464e-2, 2.61100544998339436713088248557444e-2, 208 4.66170074627052749243018566390567e-2, 7.32585144444135027565872014932387e-2, 209 1.05026503471351080481093652651105e-1 }; 210 #else // quadruple precision 211 const double maxNormForPade[] = { 4.7419931187193005048501568167858103e-5 /* degree = 3 */, 212 5.8853168473544560470387769480192666e-4, 2.9216120366601315391789493628113520e-3, 213 8.8415758124319434347116734705174308e-3, 1.9850836029449446668518049562565291e-2, 214 3.6688019729653446926585242192447447e-2, 5.9290962294020186998954055264528393e-2, 215 8.6998436081634343903250580992127677e-2, 1.1880960220216759245467951592883642e-1 }; 216 #endif 217 for (int degree = 3; degree <= maxPadeDegree; ++degree) 218 if (normTminusI <= maxNormForPade[degree - minPadeDegree]) 219 return degree; 220 assert(false); // this line should never be reached 221 } 222 223 /* \brief Compute Pade approximation to matrix logarithm */ 224 template <typename MatrixType> 225 void MatrixLogarithmAtomic<MatrixType>::computePade(MatrixType& result, const MatrixType& T, int degree) 226 { 227 switch (degree) { 228 case 3: computePade3(result, T); break; 229 case 4: computePade4(result, T); break; 230 case 5: computePade5(result, T); break; 231 case 6: computePade6(result, T); break; 232 case 7: computePade7(result, T); break; 233 case 8: computePade8(result, T); break; 234 case 9: computePade9(result, T); break; 235 case 10: computePade10(result, T); break; 236 case 11: computePade11(result, T); break; 237 default: assert(false); // should never happen 238 } 239 } 240 241 template <typename MatrixType> 242 void MatrixLogarithmAtomic<MatrixType>::computePade3(MatrixType& result, const MatrixType& T) 243 { 244 const int degree = 3; 245 const RealScalar nodes[] = { 0.1127016653792583114820734600217600L, 0.5000000000000000000000000000000000L, 246 0.8872983346207416885179265399782400L }; 247 const RealScalar weights[] = { 0.2777777777777777777777777777777778L, 0.4444444444444444444444444444444444L, 248 0.2777777777777777777777777777777778L }; 249 assert(degree <= maxPadeDegree); 250 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 251 result.setZero(T.rows(), T.rows()); 252 for (int k = 0; k < degree; ++k) 253 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 254 .template triangularView<Upper>().solve(TminusI); 255 } 256 257 template <typename MatrixType> 258 void MatrixLogarithmAtomic<MatrixType>::computePade4(MatrixType& result, const MatrixType& T) 259 { 260 const int degree = 4; 261 const RealScalar nodes[] = { 0.0694318442029737123880267555535953L, 0.3300094782075718675986671204483777L, 262 0.6699905217924281324013328795516223L, 0.9305681557970262876119732444464048L }; 263 const RealScalar weights[] = { 0.1739274225687269286865319746109997L, 0.3260725774312730713134680253890003L, 264 0.3260725774312730713134680253890003L, 0.1739274225687269286865319746109997L }; 265 assert(degree <= maxPadeDegree); 266 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 267 result.setZero(T.rows(), T.rows()); 268 for (int k = 0; k < degree; ++k) 269 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 270 .template triangularView<Upper>().solve(TminusI); 271 } 272 273 template <typename MatrixType> 274 void MatrixLogarithmAtomic<MatrixType>::computePade5(MatrixType& result, const MatrixType& T) 275 { 276 const int degree = 5; 277 const RealScalar nodes[] = { 0.0469100770306680036011865608503035L, 0.2307653449471584544818427896498956L, 278 0.5000000000000000000000000000000000L, 0.7692346550528415455181572103501044L, 279 0.9530899229693319963988134391496965L }; 280 const RealScalar weights[] = { 0.1184634425280945437571320203599587L, 0.2393143352496832340206457574178191L, 281 0.2844444444444444444444444444444444L, 0.2393143352496832340206457574178191L, 282 0.1184634425280945437571320203599587L }; 283 assert(degree <= maxPadeDegree); 284 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 285 result.setZero(T.rows(), T.rows()); 286 for (int k = 0; k < degree; ++k) 287 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 288 .template triangularView<Upper>().solve(TminusI); 289 } 290 291 template <typename MatrixType> 292 void MatrixLogarithmAtomic<MatrixType>::computePade6(MatrixType& result, const MatrixType& T) 293 { 294 const int degree = 6; 295 const RealScalar nodes[] = { 0.0337652428984239860938492227530027L, 0.1693953067668677431693002024900473L, 296 0.3806904069584015456847491391596440L, 0.6193095930415984543152508608403560L, 297 0.8306046932331322568306997975099527L, 0.9662347571015760139061507772469973L }; 298 const RealScalar weights[] = { 0.0856622461895851725201480710863665L, 0.1803807865240693037849167569188581L, 299 0.2339569672863455236949351719947755L, 0.2339569672863455236949351719947755L, 300 0.1803807865240693037849167569188581L, 0.0856622461895851725201480710863665L }; 301 assert(degree <= maxPadeDegree); 302 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 303 result.setZero(T.rows(), T.rows()); 304 for (int k = 0; k < degree; ++k) 305 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 306 .template triangularView<Upper>().solve(TminusI); 307 } 308 309 template <typename MatrixType> 310 void MatrixLogarithmAtomic<MatrixType>::computePade7(MatrixType& result, const MatrixType& T) 311 { 312 const int degree = 7; 313 const RealScalar nodes[] = { 0.0254460438286207377369051579760744L, 0.1292344072003027800680676133596058L, 314 0.2970774243113014165466967939615193L, 0.5000000000000000000000000000000000L, 315 0.7029225756886985834533032060384807L, 0.8707655927996972199319323866403942L, 316 0.9745539561713792622630948420239256L }; 317 const RealScalar weights[] = { 0.0647424830844348466353057163395410L, 0.1398526957446383339507338857118898L, 318 0.1909150252525594724751848877444876L, 0.2089795918367346938775510204081633L, 319 0.1909150252525594724751848877444876L, 0.1398526957446383339507338857118898L, 320 0.0647424830844348466353057163395410L }; 321 assert(degree <= maxPadeDegree); 322 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 323 result.setZero(T.rows(), T.rows()); 324 for (int k = 0; k < degree; ++k) 325 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 326 .template triangularView<Upper>().solve(TminusI); 327 } 328 329 template <typename MatrixType> 330 void MatrixLogarithmAtomic<MatrixType>::computePade8(MatrixType& result, const MatrixType& T) 331 { 332 const int degree = 8; 333 const RealScalar nodes[] = { 0.0198550717512318841582195657152635L, 0.1016667612931866302042230317620848L, 334 0.2372337950418355070911304754053768L, 0.4082826787521750975302619288199080L, 335 0.5917173212478249024697380711800920L, 0.7627662049581644929088695245946232L, 336 0.8983332387068133697957769682379152L, 0.9801449282487681158417804342847365L }; 337 const RealScalar weights[] = { 0.0506142681451881295762656771549811L, 0.1111905172266872352721779972131204L, 338 0.1568533229389436436689811009933007L, 0.1813418916891809914825752246385978L, 339 0.1813418916891809914825752246385978L, 0.1568533229389436436689811009933007L, 340 0.1111905172266872352721779972131204L, 0.0506142681451881295762656771549811L }; 341 assert(degree <= maxPadeDegree); 342 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 343 result.setZero(T.rows(), T.rows()); 344 for (int k = 0; k < degree; ++k) 345 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 346 .template triangularView<Upper>().solve(TminusI); 347 } 348 349 template <typename MatrixType> 350 void MatrixLogarithmAtomic<MatrixType>::computePade9(MatrixType& result, const MatrixType& T) 351 { 352 const int degree = 9; 353 const RealScalar nodes[] = { 0.0159198802461869550822118985481636L, 0.0819844463366821028502851059651326L, 354 0.1933142836497048013456489803292629L, 0.3378732882980955354807309926783317L, 355 0.5000000000000000000000000000000000L, 0.6621267117019044645192690073216683L, 356 0.8066857163502951986543510196707371L, 0.9180155536633178971497148940348674L, 357 0.9840801197538130449177881014518364L }; 358 const RealScalar weights[] = { 0.0406371941807872059859460790552618L, 0.0903240803474287020292360156214564L, 359 0.1303053482014677311593714347093164L, 0.1561735385200014200343152032922218L, 360 0.1651196775006298815822625346434870L, 0.1561735385200014200343152032922218L, 361 0.1303053482014677311593714347093164L, 0.0903240803474287020292360156214564L, 362 0.0406371941807872059859460790552618L }; 363 assert(degree <= maxPadeDegree); 364 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 365 result.setZero(T.rows(), T.rows()); 366 for (int k = 0; k < degree; ++k) 367 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 368 .template triangularView<Upper>().solve(TminusI); 369 } 370 371 template <typename MatrixType> 372 void MatrixLogarithmAtomic<MatrixType>::computePade10(MatrixType& result, const MatrixType& T) 373 { 374 const int degree = 10; 375 const RealScalar nodes[] = { 0.0130467357414141399610179939577740L, 0.0674683166555077446339516557882535L, 376 0.1602952158504877968828363174425632L, 0.2833023029353764046003670284171079L, 377 0.4255628305091843945575869994351400L, 0.5744371694908156054424130005648600L, 378 0.7166976970646235953996329715828921L, 0.8397047841495122031171636825574368L, 379 0.9325316833444922553660483442117465L, 0.9869532642585858600389820060422260L }; 380 const RealScalar weights[] = { 0.0333356721543440687967844049466659L, 0.0747256745752902965728881698288487L, 381 0.1095431812579910219977674671140816L, 0.1346333596549981775456134607847347L, 382 0.1477621123573764350869464973256692L, 0.1477621123573764350869464973256692L, 383 0.1346333596549981775456134607847347L, 0.1095431812579910219977674671140816L, 384 0.0747256745752902965728881698288487L, 0.0333356721543440687967844049466659L }; 385 assert(degree <= maxPadeDegree); 386 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 387 result.setZero(T.rows(), T.rows()); 388 for (int k = 0; k < degree; ++k) 389 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 390 .template triangularView<Upper>().solve(TminusI); 391 } 392 393 template <typename MatrixType> 394 void MatrixLogarithmAtomic<MatrixType>::computePade11(MatrixType& result, const MatrixType& T) 395 { 396 const int degree = 11; 397 const RealScalar nodes[] = { 0.0108856709269715035980309994385713L, 0.0564687001159523504624211153480364L, 398 0.1349239972129753379532918739844233L, 0.2404519353965940920371371652706952L, 399 0.3652284220238275138342340072995692L, 0.5000000000000000000000000000000000L, 400 0.6347715779761724861657659927004308L, 0.7595480646034059079628628347293048L, 401 0.8650760027870246620467081260155767L, 0.9435312998840476495375788846519636L, 402 0.9891143290730284964019690005614287L }; 403 const RealScalar weights[] = { 0.0278342835580868332413768602212743L, 0.0627901847324523123173471496119701L, 404 0.0931451054638671257130488207158280L, 0.1165968822959952399592618524215876L, 405 0.1314022722551233310903444349452546L, 0.1364625433889503153572417641681711L, 406 0.1314022722551233310903444349452546L, 0.1165968822959952399592618524215876L, 407 0.0931451054638671257130488207158280L, 0.0627901847324523123173471496119701L, 408 0.0278342835580868332413768602212743L }; 409 assert(degree <= maxPadeDegree); 410 MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 411 result.setZero(T.rows(), T.rows()); 412 for (int k = 0; k < degree; ++k) 413 result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI) 414 .template triangularView<Upper>().solve(TminusI); 415 } 416 417 /** \ingroup MatrixFunctions_Module 418 * 419 * \brief Proxy for the matrix logarithm of some matrix (expression). 420 * 421 * \tparam Derived Type of the argument to the matrix function. 422 * 423 * This class holds the argument to the matrix function until it is 424 * assigned or evaluated for some other reason (so the argument 425 * should not be changed in the meantime). It is the return type of 426 * matrixBase::matrixLogarithm() and most of the time this is the 427 * only way it is used. 428 */ 429 template<typename Derived> class MatrixLogarithmReturnValue 430 : public ReturnByValue<MatrixLogarithmReturnValue<Derived> > 431 { 432 public: 433 434 typedef typename Derived::Scalar Scalar; 435 typedef typename Derived::Index Index; 436 437 /** \brief Constructor. 438 * 439 * \param[in] A %Matrix (expression) forming the argument of the matrix logarithm. 440 */ 441 MatrixLogarithmReturnValue(const Derived& A) : m_A(A) { } 442 443 /** \brief Compute the matrix logarithm. 444 * 445 * \param[out] result Logarithm of \p A, where \A is as specified in the constructor. 446 */ 447 template <typename ResultType> 448 inline void evalTo(ResultType& result) const 449 { 450 typedef typename Derived::PlainObject PlainObject; 451 typedef internal::traits<PlainObject> Traits; 452 static const int RowsAtCompileTime = Traits::RowsAtCompileTime; 453 static const int ColsAtCompileTime = Traits::ColsAtCompileTime; 454 static const int Options = PlainObject::Options; 455 typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar; 456 typedef Matrix<ComplexScalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType; 457 typedef MatrixLogarithmAtomic<DynMatrixType> AtomicType; 458 AtomicType atomic; 459 460 const PlainObject Aevaluated = m_A.eval(); 461 MatrixFunction<PlainObject, AtomicType> mf(Aevaluated, atomic); 462 mf.compute(result); 463 } 464 465 Index rows() const { return m_A.rows(); } 466 Index cols() const { return m_A.cols(); } 467 468 private: 469 typename internal::nested<Derived>::type m_A; 470 471 MatrixLogarithmReturnValue& operator=(const MatrixLogarithmReturnValue&); 472 }; 473 474 namespace internal { 475 template<typename Derived> 476 struct traits<MatrixLogarithmReturnValue<Derived> > 477 { 478 typedef typename Derived::PlainObject ReturnType; 479 }; 480 } 481 482 483 /********** MatrixBase method **********/ 484 485 486 template <typename Derived> 487 const MatrixLogarithmReturnValue<Derived> MatrixBase<Derived>::log() const 488 { 489 eigen_assert(rows() == cols()); 490 return MatrixLogarithmReturnValue<Derived>(derived()); 491 } 492 493 } // end namespace Eigen 494 495 #endif // EIGEN_MATRIX_LOGARITHM 496
