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