1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 42b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang// Copyright (C) 2011, 2013 Jitse Niesen <jitse@maths.leeds.ac.uk> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2011 Chen-Pang He <jdh8@ms63.hinet.net> 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#ifndef EIGEN_MATRIX_LOGARITHM 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#define EIGEN_MATRIX_LOGARITHM 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathnamespace Eigen { 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 162b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangnamespace internal { 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 182b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangtemplate <typename Scalar> 192b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangstruct matrix_log_min_pade_degree 202b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang{ 212b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang static const int value = 3; 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 242b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangtemplate <typename Scalar> 252b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangstruct matrix_log_max_pade_degree 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 272b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef typename NumTraits<Scalar>::Real RealScalar; 282b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang static const int value = std::numeric_limits<RealScalar>::digits<= 24? 5: // single precision 292b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang std::numeric_limits<RealScalar>::digits<= 53? 7: // double precision 302b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang std::numeric_limits<RealScalar>::digits<= 64? 8: // extended precision 312b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang std::numeric_limits<RealScalar>::digits<=106? 10: // double-double 322b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 11; // quadruple precision 332b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang}; 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \brief Compute logarithm of 2x2 triangular matrix. */ 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename MatrixType> 372b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangvoid matrix_log_compute_2x2(const MatrixType& A, MatrixType& result) 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 392b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef typename MatrixType::Scalar Scalar; 402b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef typename MatrixType::RealScalar RealScalar; 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath using std::abs; 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath using std::ceil; 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath using std::imag; 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath using std::log; 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar logA00 = log(A(0,0)); 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar logA11 = log(A(1,1)); 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath result(0,0) = logA00; 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath result(1,0) = Scalar(0); 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath result(1,1) = logA11; 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 532b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang Scalar y = A(1,1) - A(0,0); 542b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang if (y==Scalar(0)) 552b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath result(0,1) = A(0,1) / A(0,0); 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 582b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang else if ((abs(A(0,0)) < RealScalar(0.5)*abs(A(1,1))) || (abs(A(0,0)) > 2*abs(A(1,1)))) 592b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 602b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang result(0,1) = A(0,1) * (logA11 - logA00) / y; 612b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang } 622b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang else 632b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 642b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang // computation in previous branch is inaccurate if A(1,1) \approx A(0,0) 652b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang int unwindingNumber = static_cast<int>(ceil((imag(logA11 - logA00) - RealScalar(EIGEN_PI)) / RealScalar(2*EIGEN_PI))); 662b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang result(0,1) = A(0,1) * (numext::log1p(y/A(0,0)) + Scalar(0,2*EIGEN_PI*unwindingNumber)) / y; 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = float) */ 712b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wanginline int matrix_log_get_pade_degree(float normTminusI) 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const float maxNormForPade[] = { 2.5111573934555054e-1 /* degree = 3 */ , 4.0535837411880493e-1, 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 5.3149729967117310e-1 }; 752b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const int minPadeDegree = matrix_log_min_pade_degree<float>::value; 762b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const int maxPadeDegree = matrix_log_max_pade_degree<float>::value; 772b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang int degree = minPadeDegree; 787faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for (; degree <= maxPadeDegree; ++degree) 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (normTminusI <= maxNormForPade[degree - minPadeDegree]) 807faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez break; 817faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez return degree; 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = double) */ 852b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wanginline int matrix_log_get_pade_degree(double normTminusI) 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const double maxNormForPade[] = { 1.6206284795015624e-2 /* degree = 3 */ , 5.3873532631381171e-2, 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 }; 892b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const int minPadeDegree = matrix_log_min_pade_degree<double>::value; 902b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const int maxPadeDegree = matrix_log_max_pade_degree<double>::value; 912b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang int degree = minPadeDegree; 927faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for (; degree <= maxPadeDegree; ++degree) 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (normTminusI <= maxNormForPade[degree - minPadeDegree]) 947faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez break; 957faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez return degree; 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = long double) */ 992b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wanginline int matrix_log_get_pade_degree(long double normTminusI) 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#if LDBL_MANT_DIG == 53 // double precision 1027faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez const long double maxNormForPade[] = { 1.6206284795015624e-2L /* degree = 3 */ , 5.3873532631381171e-2L, 1037faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 1.1352802267628681e-1L, 1.8662860613541288e-1L, 2.642960831111435e-1L }; 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#elif LDBL_MANT_DIG <= 64 // extended precision 1057faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez const long double maxNormForPade[] = { 5.48256690357782863103e-3L /* degree = 3 */, 2.34559162387971167321e-2L, 1067faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 5.84603923897347449857e-2L, 1.08486423756725170223e-1L, 1.68385767881294446649e-1L, 1077faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 2.32777776523703892094e-1L }; 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#elif LDBL_MANT_DIG <= 106 // double-double 1097faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez const long double maxNormForPade[] = { 8.58970550342939562202529664318890e-5L /* degree = 3 */, 1107faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 9.34074328446359654039446552677759e-4L, 4.26117194647672175773064114582860e-3L, 1117faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 1.21546224740281848743149666560464e-2L, 2.61100544998339436713088248557444e-2L, 1127faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 4.66170074627052749243018566390567e-2L, 7.32585144444135027565872014932387e-2L, 1137faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 1.05026503471351080481093652651105e-1L }; 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#else // quadruple precision 1157faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez const long double maxNormForPade[] = { 4.7419931187193005048501568167858103e-5L /* degree = 3 */, 1167faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 5.8853168473544560470387769480192666e-4L, 2.9216120366601315391789493628113520e-3L, 1177faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 8.8415758124319434347116734705174308e-3L, 1.9850836029449446668518049562565291e-2L, 1187faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 3.6688019729653446926585242192447447e-2L, 5.9290962294020186998954055264528393e-2L, 1197faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez 8.6998436081634343903250580992127677e-2L, 1.1880960220216759245467951592883642e-1L }; 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#endif 1212b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const int minPadeDegree = matrix_log_min_pade_degree<long double>::value; 1222b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const int maxPadeDegree = matrix_log_max_pade_degree<long double>::value; 1232b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang int degree = minPadeDegree; 1247faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez for (; degree <= maxPadeDegree; ++degree) 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (normTminusI <= maxNormForPade[degree - minPadeDegree]) 1267faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez break; 1277faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez return degree; 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/* \brief Compute Pade approximation to matrix logarithm */ 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename MatrixType> 1322b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangvoid matrix_log_compute_pade(MatrixType& result, const MatrixType& T, int degree) 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 1342b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; 1352b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const int minPadeDegree = 3; 1362b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const int maxPadeDegree = 11; 1372b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang assert(degree >= minPadeDegree && degree <= maxPadeDegree); 1382b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 1392b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const RealScalar nodes[][maxPadeDegree] = { 1402b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.1127016653792583114820734600217600L, 0.5000000000000000000000000000000000L, // degree 3 1412b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.8872983346207416885179265399782400L }, 1422b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0694318442029737123880267555535953L, 0.3300094782075718675986671204483777L, // degree 4 1432b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.6699905217924281324013328795516223L, 0.9305681557970262876119732444464048L }, 1442b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0469100770306680036011865608503035L, 0.2307653449471584544818427896498956L, // degree 5 1452b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.5000000000000000000000000000000000L, 0.7692346550528415455181572103501044L, 1462b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.9530899229693319963988134391496965L }, 1472b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0337652428984239860938492227530027L, 0.1693953067668677431693002024900473L, // degree 6 1482b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.3806904069584015456847491391596440L, 0.6193095930415984543152508608403560L, 1492b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.8306046932331322568306997975099527L, 0.9662347571015760139061507772469973L }, 1502b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0254460438286207377369051579760744L, 0.1292344072003027800680676133596058L, // degree 7 1512b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.2970774243113014165466967939615193L, 0.5000000000000000000000000000000000L, 1522b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.7029225756886985834533032060384807L, 0.8707655927996972199319323866403942L, 1532b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.9745539561713792622630948420239256L }, 1542b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0198550717512318841582195657152635L, 0.1016667612931866302042230317620848L, // degree 8 1552b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.2372337950418355070911304754053768L, 0.4082826787521750975302619288199080L, 1562b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.5917173212478249024697380711800920L, 0.7627662049581644929088695245946232L, 1572b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.8983332387068133697957769682379152L, 0.9801449282487681158417804342847365L }, 1582b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0159198802461869550822118985481636L, 0.0819844463366821028502851059651326L, // degree 9 1592b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1933142836497048013456489803292629L, 0.3378732882980955354807309926783317L, 1602b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.5000000000000000000000000000000000L, 0.6621267117019044645192690073216683L, 1612b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.8066857163502951986543510196707371L, 0.9180155536633178971497148940348674L, 1622b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.9840801197538130449177881014518364L }, 1632b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0130467357414141399610179939577740L, 0.0674683166555077446339516557882535L, // degree 10 1642b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1602952158504877968828363174425632L, 0.2833023029353764046003670284171079L, 1652b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.4255628305091843945575869994351400L, 0.5744371694908156054424130005648600L, 1662b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.7166976970646235953996329715828921L, 0.8397047841495122031171636825574368L, 1672b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.9325316833444922553660483442117465L, 0.9869532642585858600389820060422260L }, 1682b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0108856709269715035980309994385713L, 0.0564687001159523504624211153480364L, // degree 11 1692b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1349239972129753379532918739844233L, 0.2404519353965940920371371652706952L, 1702b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.3652284220238275138342340072995692L, 0.5000000000000000000000000000000000L, 1712b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.6347715779761724861657659927004308L, 0.7595480646034059079628628347293048L, 1722b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.8650760027870246620467081260155767L, 0.9435312998840476495375788846519636L, 1732b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.9891143290730284964019690005614287L } }; 1742b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 1752b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const RealScalar weights[][maxPadeDegree] = { 1762b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.2777777777777777777777777777777778L, 0.4444444444444444444444444444444444L, // degree 3 1772b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.2777777777777777777777777777777778L }, 1782b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.1739274225687269286865319746109997L, 0.3260725774312730713134680253890003L, // degree 4 1792b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.3260725774312730713134680253890003L, 0.1739274225687269286865319746109997L }, 1802b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.1184634425280945437571320203599587L, 0.2393143352496832340206457574178191L, // degree 5 1812b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.2844444444444444444444444444444444L, 0.2393143352496832340206457574178191L, 1822b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1184634425280945437571320203599587L }, 1832b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0856622461895851725201480710863665L, 0.1803807865240693037849167569188581L, // degree 6 1842b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.2339569672863455236949351719947755L, 0.2339569672863455236949351719947755L, 1852b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1803807865240693037849167569188581L, 0.0856622461895851725201480710863665L }, 1862b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0647424830844348466353057163395410L, 0.1398526957446383339507338857118898L, // degree 7 1872b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1909150252525594724751848877444876L, 0.2089795918367346938775510204081633L, 1882b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1909150252525594724751848877444876L, 0.1398526957446383339507338857118898L, 1892b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.0647424830844348466353057163395410L }, 1902b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0506142681451881295762656771549811L, 0.1111905172266872352721779972131204L, // degree 8 1912b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1568533229389436436689811009933007L, 0.1813418916891809914825752246385978L, 1922b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1813418916891809914825752246385978L, 0.1568533229389436436689811009933007L, 1932b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1111905172266872352721779972131204L, 0.0506142681451881295762656771549811L }, 1942b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0406371941807872059859460790552618L, 0.0903240803474287020292360156214564L, // degree 9 1952b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1303053482014677311593714347093164L, 0.1561735385200014200343152032922218L, 1962b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1651196775006298815822625346434870L, 0.1561735385200014200343152032922218L, 1972b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1303053482014677311593714347093164L, 0.0903240803474287020292360156214564L, 1982b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.0406371941807872059859460790552618L }, 1992b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0333356721543440687967844049466659L, 0.0747256745752902965728881698288487L, // degree 10 2002b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1095431812579910219977674671140816L, 0.1346333596549981775456134607847347L, 2012b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1477621123573764350869464973256692L, 0.1477621123573764350869464973256692L, 2022b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1346333596549981775456134607847347L, 0.1095431812579910219977674671140816L, 2032b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.0747256745752902965728881698288487L, 0.0333356721543440687967844049466659L }, 2042b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang { 0.0278342835580868332413768602212743L, 0.0627901847324523123173471496119701L, // degree 11 2052b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.0931451054638671257130488207158280L, 0.1165968822959952399592618524215876L, 2062b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1314022722551233310903444349452546L, 0.1364625433889503153572417641681711L, 2072b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.1314022722551233310903444349452546L, 0.1165968822959952399592618524215876L, 2082b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.0931451054638671257130488207158280L, 0.0627901847324523123173471496119701L, 2092b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 0.0278342835580868332413768602212743L } }; 210c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 211c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows()); 212c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath result.setZero(T.rows(), T.rows()); 2132b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang for (int k = 0; k < degree; ++k) { 2142b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang RealScalar weight = weights[degree-minPadeDegree][k]; 2152b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang RealScalar node = nodes[degree-minPadeDegree][k]; 2162b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang result += weight * (MatrixType::Identity(T.rows(), T.rows()) + node * TminusI) 2172b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang .template triangularView<Upper>().solve(TminusI); 2182b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang } 2192b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang} 220c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 2212b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang/** \brief Compute logarithm of triangular matrices with size > 2. 2222b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang * \details This uses a inverse scale-and-square algorithm. */ 223c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename MatrixType> 2242b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangvoid matrix_log_compute_big(const MatrixType& A, MatrixType& result) 225c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 2262b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef typename MatrixType::Scalar Scalar; 2272b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef typename NumTraits<Scalar>::Real RealScalar; 2282b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang using std::pow; 229c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 2302b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang int numberOfSquareRoots = 0; 2312b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang int numberOfExtraSquareRoots = 0; 2322b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang int degree; 2332b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang MatrixType T = A, sqrtT; 234c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 2352b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang int maxPadeDegree = matrix_log_max_pade_degree<Scalar>::value; 2362b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const RealScalar maxNormForPade = maxPadeDegree<= 5? 5.3149729967117310e-1L: // single precision 2372b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang maxPadeDegree<= 7? 2.6429608311114350e-1L: // double precision 2382b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang maxPadeDegree<= 8? 2.32777776523703892094e-1L: // extended precision 2392b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang maxPadeDegree<=10? 1.05026503471351080481093652651105e-1L: // double-double 2402b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 1.1880960220216759245467951592883642e-1L; // quadruple precision 241c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 2422b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang while (true) { 2432b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang RealScalar normTminusI = (T - MatrixType::Identity(T.rows(), T.rows())).cwiseAbs().colwise().sum().maxCoeff(); 2442b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang if (normTminusI < maxNormForPade) { 2452b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang degree = matrix_log_get_pade_degree(normTminusI); 2462b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang int degree2 = matrix_log_get_pade_degree(normTminusI / RealScalar(2)); 2472b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang if ((degree - degree2 <= 1) || (numberOfExtraSquareRoots == 1)) 2482b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang break; 2492b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang ++numberOfExtraSquareRoots; 2502b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang } 2512b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang matrix_sqrt_triangular(T, sqrtT); 2522b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang T = sqrtT.template triangularView<Upper>(); 2532b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang ++numberOfSquareRoots; 2542b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang } 255c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 2562b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang matrix_log_compute_pade(result, T, degree); 2572b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang result *= pow(RealScalar(2), numberOfSquareRoots); 258c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 259c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 2602b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang/** \ingroup MatrixFunctions_Module 2612b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang * \class MatrixLogarithmAtomic 2622b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang * \brief Helper class for computing matrix logarithm of atomic matrices. 2632b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang * 2642b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang * Here, an atomic matrix is a triangular matrix whose diagonal entries are close to each other. 2652b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang * 2662b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang * \sa class MatrixFunctionAtomic, MatrixBase::log() 2672b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang */ 268c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename MatrixType> 2692b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangclass MatrixLogarithmAtomic 270c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 2712b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangpublic: 2722b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang /** \brief Compute matrix logarithm of atomic matrix 2732b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang * \param[in] A argument of matrix logarithm, should be upper triangular and atomic 2742b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang * \returns The logarithm of \p A. 2752b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang */ 2762b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang MatrixType compute(const MatrixType& A); 2772b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang}; 278c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 279c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename MatrixType> 2802b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao WangMatrixType MatrixLogarithmAtomic<MatrixType>::compute(const MatrixType& A) 281c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 2822b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang using std::log; 2832b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang MatrixType result(A.rows(), A.rows()); 2842b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang if (A.rows() == 1) 2852b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang result(0,0) = log(A(0,0)); 2862b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang else if (A.rows() == 2) 2872b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang matrix_log_compute_2x2(A, result); 2882b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang else 2892b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang matrix_log_compute_big(A, result); 2902b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang return result; 291c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 292c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 2932b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang} // end of namespace internal 294c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 295c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/** \ingroup MatrixFunctions_Module 296c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 297c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \brief Proxy for the matrix logarithm of some matrix (expression). 298c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 299c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \tparam Derived Type of the argument to the matrix function. 300c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 301c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * This class holds the argument to the matrix function until it is 302c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * assigned or evaluated for some other reason (so the argument 303c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * should not be changed in the meantime). It is the return type of 3047faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * MatrixBase::log() and most of the time this is the only way it 3057faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez * is used. 306c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 307c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Derived> class MatrixLogarithmReturnValue 308c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath: public ReturnByValue<MatrixLogarithmReturnValue<Derived> > 309c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 310c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathpublic: 311c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename Derived::Scalar Scalar; 312c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename Derived::Index Index; 313c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 3142b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangprotected: 3152b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef typename internal::ref_selector<Derived>::type DerivedNested; 3162b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 3172b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wangpublic: 3182b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang 319c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Constructor. 320c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 321c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param[in] A %Matrix (expression) forming the argument of the matrix logarithm. 322c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 3232b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang explicit MatrixLogarithmReturnValue(const Derived& A) : m_A(A) { } 324c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 325c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /** \brief Compute the matrix logarithm. 326c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * 327c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * \param[out] result Logarithm of \p A, where \A is as specified in the constructor. 328c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 329c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template <typename ResultType> 330c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath inline void evalTo(ResultType& result) const 331c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 3322b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef typename internal::nested_eval<Derived, 10>::type DerivedEvalType; 3332b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef typename internal::remove_all<DerivedEvalType>::type DerivedEvalTypeClean; 3342b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef internal::traits<DerivedEvalTypeClean> Traits; 335c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static const int RowsAtCompileTime = Traits::RowsAtCompileTime; 336c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath static const int ColsAtCompileTime = Traits::ColsAtCompileTime; 337c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar; 3382b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType; 3392b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang typedef internal::MatrixLogarithmAtomic<DynMatrixType> AtomicType; 340c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AtomicType atomic; 341c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 342eda03298de395cf6217486971e6529f92da8da79Miao Wang internal::matrix_function_compute<typename DerivedEvalTypeClean::PlainObject>::run(m_A, atomic, result); 343c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 344c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 345c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index rows() const { return m_A.rows(); } 346c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index cols() const { return m_A.cols(); } 347c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 348c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathprivate: 3492b8756b6f1de65d3f8bffab45be6c44ceb7411fcMiao Wang const DerivedNested m_A; 350c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath}; 351c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 352c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathnamespace internal { 353c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath template<typename Derived> 354c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath struct traits<MatrixLogarithmReturnValue<Derived> > 355c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 356c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename Derived::PlainObject ReturnType; 357c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath }; 358c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 359c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 360c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 361c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath/********** MatrixBase method **********/ 362c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 363c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 364c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate <typename Derived> 365c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathconst MatrixLogarithmReturnValue<Derived> MatrixBase<Derived>::log() const 366c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 367c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen_assert(rows() == cols()); 368c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath return MatrixLogarithmReturnValue<Derived>(derived()); 369c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 370c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 371c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} // end namespace Eigen 372c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 373c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#endif // EIGEN_MATRIX_LOGARITHM 374