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) 2009-2010 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_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
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11 | #define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
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16 | struct selfadjoint_rank1_update;
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17 |
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18 | namespace internal {
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19 |
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20 | /**********************************************************************
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21 | * This file implements a general A * B product while
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22 | * evaluating only one triangular part of the product.
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23 | * This is more general version of self adjoint product (C += A A^T)
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24 | * as the level 3 SYRK Blas routine.
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25 | **********************************************************************/
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26 |
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27 | // forward declarations (defined at the end of this file)
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28 | template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
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29 | struct tribb_kernel;
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30 |
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31 | /* Optimized matrix-matrix product evaluating only one triangular half */
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32 | template <typename Index,
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33 | typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
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34 | typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
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35 | int ResStorageOrder, int UpLo, int Version = Specialized>
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36 | struct general_matrix_matrix_triangular_product;
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37 |
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38 | // as usual if the result is row major => we transpose the product
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39 | template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
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40 | typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
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41 | struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version>
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42 | {
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43 | typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
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44 | static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride,
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45 | const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha)
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46 | {
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47 | general_matrix_matrix_triangular_product<Index,
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48 | RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
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49 | LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
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50 | ColMajor, UpLo==Lower?Upper:Lower>
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51 | ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha);
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52 | }
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53 | };
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54 |
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55 | template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
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56 | typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
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57 | struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version>
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58 | {
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59 | typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
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60 | static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride,
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61 | const RhsScalar* _rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha)
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62 | {
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63 | const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
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64 | const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
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65 |
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66 | typedef gebp_traits<LhsScalar,RhsScalar> Traits;
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67 |
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68 | Index kc = depth; // cache block size along the K direction
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69 | Index mc = size; // cache block size along the M direction
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70 | Index nc = size; // cache block size along the N direction
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71 | computeProductBlockingSizes<LhsScalar,RhsScalar>(kc, mc, nc);
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72 | // !!! mc must be a multiple of nr:
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73 | if(mc > Traits::nr)
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74 | mc = (mc/Traits::nr)*Traits::nr;
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75 |
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76 | std::size_t sizeW = kc*Traits::WorkSpaceFactor;
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77 | std::size_t sizeB = sizeW + kc*size;
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78 | ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, kc*mc, 0);
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79 | ei_declare_aligned_stack_constructed_variable(RhsScalar, allocatedBlockB, sizeB, 0);
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80 | RhsScalar* blockB = allocatedBlockB + sizeW;
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81 |
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82 | gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
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83 | gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs;
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84 | gebp_kernel <LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
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85 | tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb;
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86 |
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87 | for(Index k2=0; k2<depth; k2+=kc)
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88 | {
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89 | const Index actual_kc = (std::min)(k2+kc,depth)-k2;
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90 |
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91 | // note that the actual rhs is the transpose/adjoint of mat
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92 | pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, size);
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93 |
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94 | for(Index i2=0; i2<size; i2+=mc)
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95 | {
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96 | const Index actual_mc = (std::min)(i2+mc,size)-i2;
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97 |
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98 | pack_lhs(blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
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99 |
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100 | // the selected actual_mc * size panel of res is split into three different part:
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101 | // 1 - before the diagonal => processed with gebp or skipped
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102 | // 2 - the actual_mc x actual_mc symmetric block => processed with a special kernel
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103 | // 3 - after the diagonal => processed with gebp or skipped
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104 | if (UpLo==Lower)
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105 | gebp(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, (std::min)(size,i2), alpha,
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106 | -1, -1, 0, 0, allocatedBlockB);
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107 |
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108 | sybb(res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha, allocatedBlockB);
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109 |
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110 | if (UpLo==Upper)
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111 | {
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112 | Index j2 = i2+actual_mc;
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113 | gebp(res+resStride*j2+i2, resStride, blockA, blockB+actual_kc*j2, actual_mc, actual_kc, (std::max)(Index(0), size-j2), alpha,
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114 | -1, -1, 0, 0, allocatedBlockB);
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115 | }
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116 | }
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117 | }
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118 | }
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119 | };
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120 |
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121 | // Optimized packed Block * packed Block product kernel evaluating only one given triangular part
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122 | // This kernel is built on top of the gebp kernel:
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123 | // - the current destination block is processed per panel of actual_mc x BlockSize
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124 | // where BlockSize is set to the minimal value allowing gebp to be as fast as possible
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125 | // - then, as usual, each panel is split into three parts along the diagonal,
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126 | // the sub blocks above and below the diagonal are processed as usual,
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127 | // while the triangular block overlapping the diagonal is evaluated into a
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128 | // small temporary buffer which is then accumulated into the result using a
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129 | // triangular traversal.
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130 | template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
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131 | struct tribb_kernel
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132 | {
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133 | typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits;
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134 | typedef typename Traits::ResScalar ResScalar;
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135 |
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136 | enum {
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137 | BlockSize = EIGEN_PLAIN_ENUM_MAX(mr,nr)
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138 | };
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139 | void operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha, RhsScalar* workspace)
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140 | {
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141 | gebp_kernel<LhsScalar, RhsScalar, Index, mr, nr, ConjLhs, ConjRhs> gebp_kernel;
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142 | Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer;
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143 |
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144 | // let's process the block per panel of actual_mc x BlockSize,
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145 | // again, each is split into three parts, etc.
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146 | for (Index j=0; j<size; j+=BlockSize)
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147 | {
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148 | Index actualBlockSize = std::min<Index>(BlockSize,size - j);
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149 | const RhsScalar* actual_b = blockB+j*depth;
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150 |
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151 | if(UpLo==Upper)
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152 | gebp_kernel(res+j*resStride, resStride, blockA, actual_b, j, depth, actualBlockSize, alpha,
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153 | -1, -1, 0, 0, workspace);
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154 |
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155 | // selfadjoint micro block
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156 | {
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157 | Index i = j;
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158 | buffer.setZero();
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159 | // 1 - apply the kernel on the temporary buffer
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160 | gebp_kernel(buffer.data(), BlockSize, blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha,
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161 | -1, -1, 0, 0, workspace);
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162 | // 2 - triangular accumulation
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163 | for(Index j1=0; j1<actualBlockSize; ++j1)
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164 | {
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165 | ResScalar* r = res + (j+j1)*resStride + i;
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166 | for(Index i1=UpLo==Lower ? j1 : 0;
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167 | UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1)
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168 | r[i1] += buffer(i1,j1);
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169 | }
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170 | }
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171 |
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172 | if(UpLo==Lower)
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173 | {
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174 | Index i = j+actualBlockSize;
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175 | gebp_kernel(res+j*resStride+i, resStride, blockA+depth*i, actual_b, size-i, depth, actualBlockSize, alpha,
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176 | -1, -1, 0, 0, workspace);
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177 | }
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178 | }
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179 | }
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180 | };
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181 |
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182 | } // end namespace internal
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183 |
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184 | // high level API
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185 |
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186 | template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct>
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187 | struct general_product_to_triangular_selector;
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188 |
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189 |
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190 | template<typename MatrixType, typename ProductType, int UpLo>
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191 | struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true>
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192 | {
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193 | static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha)
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194 | {
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195 | typedef typename MatrixType::Scalar Scalar;
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196 | typedef typename MatrixType::Index Index;
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197 |
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198 | typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
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199 | typedef internal::blas_traits<Lhs> LhsBlasTraits;
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200 | typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
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201 | typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
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202 | typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
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203 |
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204 | typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
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205 | typedef internal::blas_traits<Rhs> RhsBlasTraits;
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206 | typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
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207 | typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
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208 | typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
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209 |
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210 | Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
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211 |
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212 | enum {
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213 | StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,
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214 | UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1,
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215 | UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1
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216 | };
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217 |
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218 | internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs;
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219 | ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(),
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220 | (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data()));
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221 | if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs;
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222 |
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223 | internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs;
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224 | ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(),
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225 | (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data()));
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226 | if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
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227 |
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228 |
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229 | selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,
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230 | LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
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231 | RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex>
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232 | ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha);
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233 | }
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234 | };
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235 |
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236 | template<typename MatrixType, typename ProductType, int UpLo>
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237 | struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false>
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238 | {
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239 | static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha)
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240 | {
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241 | typedef typename MatrixType::Index Index;
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242 |
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243 | typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
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244 | typedef internal::blas_traits<Lhs> LhsBlasTraits;
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245 | typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
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246 | typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
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247 | typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
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248 |
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249 | typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
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250 | typedef internal::blas_traits<Rhs> RhsBlasTraits;
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251 | typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
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252 | typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
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253 | typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
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254 |
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255 | typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
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256 |
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257 | internal::general_matrix_matrix_triangular_product<Index,
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258 | typename Lhs::Scalar, _ActualLhs::Flags&RowMajorBit ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
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259 | typename Rhs::Scalar, _ActualRhs::Flags&RowMajorBit ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
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260 | MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo>
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261 | ::run(mat.cols(), actualLhs.cols(),
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262 | &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &actualRhs.coeffRef(0,0), actualRhs.outerStride(),
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263 | mat.data(), mat.outerStride(), actualAlpha);
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264 | }
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265 | };
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266 |
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267 | template<typename MatrixType, unsigned int UpLo>
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268 | template<typename ProductDerived, typename _Lhs, typename _Rhs>
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269 | TriangularView<MatrixType,UpLo>& TriangularView<MatrixType,UpLo>::assignProduct(const ProductBase<ProductDerived, _Lhs,_Rhs>& prod, const Scalar& alpha)
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270 | {
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271 | general_product_to_triangular_selector<MatrixType, ProductDerived, UpLo, (_Lhs::ColsAtCompileTime==1) || (_Rhs::RowsAtCompileTime==1)>::run(m_matrix.const_cast_derived(), prod.derived(), alpha);
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272 |
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273 | return *this;
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274 | }
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275 |
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276 | } // end namespace Eigen
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277 |
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278 | #endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
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