1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud (at) inria.fr> 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 #ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_H 11 #define EIGEN_SELFADJOINT_MATRIX_VECTOR_H 12 13 namespace Eigen { 14 15 namespace internal { 16 17 /* Optimized selfadjoint matrix * vector product: 18 * This algorithm processes 2 columns at onces that allows to both reduce 19 * the number of load/stores of the result by a factor 2 and to reduce 20 * the instruction dependency. 21 */ 22 23 template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version=Specialized> 24 struct selfadjoint_matrix_vector_product; 25 26 template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version> 27 struct selfadjoint_matrix_vector_product 28 29 { 30 static EIGEN_DONT_INLINE void run( 31 Index size, 32 const Scalar* lhs, Index lhsStride, 33 const Scalar* _rhs, Index rhsIncr, 34 Scalar* res, 35 Scalar alpha); 36 }; 37 38 template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version> 39 EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,Version>::run( 40 Index size, 41 const Scalar* lhs, Index lhsStride, 42 const Scalar* _rhs, Index rhsIncr, 43 Scalar* res, 44 Scalar alpha) 45 { 46 typedef typename packet_traits<Scalar>::type Packet; 47 const Index PacketSize = sizeof(Packet)/sizeof(Scalar); 48 49 enum { 50 IsRowMajor = StorageOrder==RowMajor ? 1 : 0, 51 IsLower = UpLo == Lower ? 1 : 0, 52 FirstTriangular = IsRowMajor == IsLower 53 }; 54 55 conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, IsRowMajor), ConjugateRhs> cj0; 56 conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> cj1; 57 conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex, ConjugateRhs> cjd; 58 59 conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, IsRowMajor), ConjugateRhs> pcj0; 60 conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> pcj1; 61 62 Scalar cjAlpha = ConjugateRhs ? numext::conj(alpha) : alpha; 63 64 // FIXME this copy is now handled outside product_selfadjoint_vector, so it could probably be removed. 65 // if the rhs is not sequentially stored in memory we copy it to a temporary buffer, 66 // this is because we need to extract packets 67 ei_declare_aligned_stack_constructed_variable(Scalar,rhs,size,rhsIncr==1 ? const_cast<Scalar*>(_rhs) : 0); 68 if (rhsIncr!=1) 69 { 70 const Scalar* it = _rhs; 71 for (Index i=0; i<size; ++i, it+=rhsIncr) 72 rhs[i] = *it; 73 } 74 75 Index bound = (std::max)(Index(0),size-8) & 0xfffffffe; 76 if (FirstTriangular) 77 bound = size - bound; 78 79 for (Index j=FirstTriangular ? bound : 0; 80 j<(FirstTriangular ? size : bound);j+=2) 81 { 82 const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride; 83 const Scalar* EIGEN_RESTRICT A1 = lhs + (j+1)*lhsStride; 84 85 Scalar t0 = cjAlpha * rhs[j]; 86 Packet ptmp0 = pset1<Packet>(t0); 87 Scalar t1 = cjAlpha * rhs[j+1]; 88 Packet ptmp1 = pset1<Packet>(t1); 89 90 Scalar t2(0); 91 Packet ptmp2 = pset1<Packet>(t2); 92 Scalar t3(0); 93 Packet ptmp3 = pset1<Packet>(t3); 94 95 size_t starti = FirstTriangular ? 0 : j+2; 96 size_t endi = FirstTriangular ? j : size; 97 size_t alignedStart = (starti) + internal::first_aligned(&res[starti], endi-starti); 98 size_t alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize); 99 100 // TODO make sure this product is a real * complex and that the rhs is properly conjugated if needed 101 res[j] += cjd.pmul(numext::real(A0[j]), t0); 102 res[j+1] += cjd.pmul(numext::real(A1[j+1]), t1); 103 if(FirstTriangular) 104 { 105 res[j] += cj0.pmul(A1[j], t1); 106 t3 += cj1.pmul(A1[j], rhs[j]); 107 } 108 else 109 { 110 res[j+1] += cj0.pmul(A0[j+1],t0); 111 t2 += cj1.pmul(A0[j+1], rhs[j+1]); 112 } 113 114 for (size_t i=starti; i<alignedStart; ++i) 115 { 116 res[i] += t0 * A0[i] + t1 * A1[i]; 117 t2 += numext::conj(A0[i]) * rhs[i]; 118 t3 += numext::conj(A1[i]) * rhs[i]; 119 } 120 // Yes this an optimization for gcc 4.3 and 4.4 (=> huge speed up) 121 // gcc 4.2 does this optimization automatically. 122 const Scalar* EIGEN_RESTRICT a0It = A0 + alignedStart; 123 const Scalar* EIGEN_RESTRICT a1It = A1 + alignedStart; 124 const Scalar* EIGEN_RESTRICT rhsIt = rhs + alignedStart; 125 Scalar* EIGEN_RESTRICT resIt = res + alignedStart; 126 for (size_t i=alignedStart; i<alignedEnd; i+=PacketSize) 127 { 128 Packet A0i = ploadu<Packet>(a0It); a0It += PacketSize; 129 Packet A1i = ploadu<Packet>(a1It); a1It += PacketSize; 130 Packet Bi = ploadu<Packet>(rhsIt); rhsIt += PacketSize; // FIXME should be aligned in most cases 131 Packet Xi = pload <Packet>(resIt); 132 133 Xi = pcj0.pmadd(A0i,ptmp0, pcj0.pmadd(A1i,ptmp1,Xi)); 134 ptmp2 = pcj1.pmadd(A0i, Bi, ptmp2); 135 ptmp3 = pcj1.pmadd(A1i, Bi, ptmp3); 136 pstore(resIt,Xi); resIt += PacketSize; 137 } 138 for (size_t i=alignedEnd; i<endi; i++) 139 { 140 res[i] += cj0.pmul(A0[i], t0) + cj0.pmul(A1[i],t1); 141 t2 += cj1.pmul(A0[i], rhs[i]); 142 t3 += cj1.pmul(A1[i], rhs[i]); 143 } 144 145 res[j] += alpha * (t2 + predux(ptmp2)); 146 res[j+1] += alpha * (t3 + predux(ptmp3)); 147 } 148 for (Index j=FirstTriangular ? 0 : bound;j<(FirstTriangular ? bound : size);j++) 149 { 150 const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride; 151 152 Scalar t1 = cjAlpha * rhs[j]; 153 Scalar t2(0); 154 // TODO make sure this product is a real * complex and that the rhs is properly conjugated if needed 155 res[j] += cjd.pmul(numext::real(A0[j]), t1); 156 for (Index i=FirstTriangular ? 0 : j+1; i<(FirstTriangular ? j : size); i++) 157 { 158 res[i] += cj0.pmul(A0[i], t1); 159 t2 += cj1.pmul(A0[i], rhs[i]); 160 } 161 res[j] += alpha * t2; 162 } 163 } 164 165 } // end namespace internal 166 167 /*************************************************************************** 168 * Wrapper to product_selfadjoint_vector 169 ***************************************************************************/ 170 171 namespace internal { 172 template<typename Lhs, int LhsMode, typename Rhs> 173 struct traits<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true> > 174 : traits<ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true>, Lhs, Rhs> > 175 {}; 176 } 177 178 template<typename Lhs, int LhsMode, typename Rhs> 179 struct SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true> 180 : public ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true>, Lhs, Rhs > 181 { 182 EIGEN_PRODUCT_PUBLIC_INTERFACE(SelfadjointProductMatrix) 183 184 enum { 185 LhsUpLo = LhsMode&(Upper|Lower) 186 }; 187 188 SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {} 189 190 template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const 191 { 192 typedef typename Dest::Scalar ResScalar; 193 typedef typename Base::RhsScalar RhsScalar; 194 typedef Map<Matrix<ResScalar,Dynamic,1>, Aligned> MappedDest; 195 196 eigen_assert(dest.rows()==m_lhs.rows() && dest.cols()==m_rhs.cols()); 197 198 typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs); 199 typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs); 200 201 Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs) 202 * RhsBlasTraits::extractScalarFactor(m_rhs); 203 204 enum { 205 EvalToDest = (Dest::InnerStrideAtCompileTime==1), 206 UseRhs = (_ActualRhsType::InnerStrideAtCompileTime==1) 207 }; 208 209 internal::gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,!EvalToDest> static_dest; 210 internal::gemv_static_vector_if<RhsScalar,_ActualRhsType::SizeAtCompileTime,_ActualRhsType::MaxSizeAtCompileTime,!UseRhs> static_rhs; 211 212 ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(), 213 EvalToDest ? dest.data() : static_dest.data()); 214 215 ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,rhs.size(), 216 UseRhs ? const_cast<RhsScalar*>(rhs.data()) : static_rhs.data()); 217 218 if(!EvalToDest) 219 { 220 #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN 221 int size = dest.size(); 222 EIGEN_DENSE_STORAGE_CTOR_PLUGIN 223 #endif 224 MappedDest(actualDestPtr, dest.size()) = dest; 225 } 226 227 if(!UseRhs) 228 { 229 #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN 230 int size = rhs.size(); 231 EIGEN_DENSE_STORAGE_CTOR_PLUGIN 232 #endif 233 Map<typename _ActualRhsType::PlainObject>(actualRhsPtr, rhs.size()) = rhs; 234 } 235 236 237 internal::selfadjoint_matrix_vector_product<Scalar, Index, (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, int(LhsUpLo), bool(LhsBlasTraits::NeedToConjugate), bool(RhsBlasTraits::NeedToConjugate)>::run 238 ( 239 lhs.rows(), // size 240 &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info 241 actualRhsPtr, 1, // rhs info 242 actualDestPtr, // result info 243 actualAlpha // scale factor 244 ); 245 246 if(!EvalToDest) 247 dest = MappedDest(actualDestPtr, dest.size()); 248 } 249 }; 250 251 namespace internal { 252 template<typename Lhs, typename Rhs, int RhsMode> 253 struct traits<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false> > 254 : traits<ProductBase<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false>, Lhs, Rhs> > 255 {}; 256 } 257 258 template<typename Lhs, typename Rhs, int RhsMode> 259 struct SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false> 260 : public ProductBase<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false>, Lhs, Rhs > 261 { 262 EIGEN_PRODUCT_PUBLIC_INTERFACE(SelfadjointProductMatrix) 263 264 enum { 265 RhsUpLo = RhsMode&(Upper|Lower) 266 }; 267 268 SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {} 269 270 template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const 271 { 272 // let's simply transpose the product 273 Transpose<Dest> destT(dest); 274 SelfadjointProductMatrix<Transpose<const Rhs>, int(RhsUpLo)==Upper ? Lower : Upper, false, 275 Transpose<const Lhs>, 0, true>(m_rhs.transpose(), m_lhs.transpose()).scaleAndAddTo(destT, alpha); 276 } 277 }; 278 279 } // end namespace Eigen 280 281 #endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_H 282
