[136] | 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 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_MATRIX_H
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| 11 | #define EIGEN_SELFADJOINT_MATRIX_MATRIX_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 | // pack a selfadjoint block diagonal for use with the gebp_kernel
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| 18 | template<typename Scalar, typename Index, int Pack1, int Pack2, int StorageOrder>
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| 19 | struct symm_pack_lhs
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| 20 | {
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| 21 | template<int BlockRows> inline
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| 22 | void pack(Scalar* blockA, const const_blas_data_mapper<Scalar,Index,StorageOrder>& lhs, Index cols, Index i, Index& count)
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| 23 | {
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| 24 | // normal copy
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| 25 | for(Index k=0; k<i; k++)
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| 26 | for(Index w=0; w<BlockRows; w++)
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| 27 | blockA[count++] = lhs(i+w,k); // normal
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| 28 | // symmetric copy
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| 29 | Index h = 0;
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| 30 | for(Index k=i; k<i+BlockRows; k++)
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| 31 | {
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| 32 | for(Index w=0; w<h; w++)
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| 33 | blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
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| 34 |
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| 35 | blockA[count++] = numext::real(lhs(k,k)); // real (diagonal)
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| 36 |
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| 37 | for(Index w=h+1; w<BlockRows; w++)
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| 38 | blockA[count++] = lhs(i+w, k); // normal
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| 39 | ++h;
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| 40 | }
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| 41 | // transposed copy
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| 42 | for(Index k=i+BlockRows; k<cols; k++)
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| 43 | for(Index w=0; w<BlockRows; w++)
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| 44 | blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
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| 45 | }
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| 46 | void operator()(Scalar* blockA, const Scalar* _lhs, Index lhsStride, Index cols, Index rows)
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| 47 | {
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| 48 | const_blas_data_mapper<Scalar,Index,StorageOrder> lhs(_lhs,lhsStride);
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| 49 | Index count = 0;
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| 50 | Index peeled_mc = (rows/Pack1)*Pack1;
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| 51 | for(Index i=0; i<peeled_mc; i+=Pack1)
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| 52 | {
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| 53 | pack<Pack1>(blockA, lhs, cols, i, count);
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| 54 | }
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| 55 |
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| 56 | if(rows-peeled_mc>=Pack2)
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| 57 | {
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| 58 | pack<Pack2>(blockA, lhs, cols, peeled_mc, count);
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| 59 | peeled_mc += Pack2;
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| 60 | }
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| 61 |
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| 62 | // do the same with mr==1
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| 63 | for(Index i=peeled_mc; i<rows; i++)
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| 64 | {
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| 65 | for(Index k=0; k<i; k++)
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| 66 | blockA[count++] = lhs(i, k); // normal
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| 67 |
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| 68 | blockA[count++] = numext::real(lhs(i, i)); // real (diagonal)
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| 69 |
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| 70 | for(Index k=i+1; k<cols; k++)
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| 71 | blockA[count++] = numext::conj(lhs(k, i)); // transposed
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| 72 | }
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| 73 | }
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| 74 | };
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| 75 |
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| 76 | template<typename Scalar, typename Index, int nr, int StorageOrder>
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| 77 | struct symm_pack_rhs
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| 78 | {
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| 79 | enum { PacketSize = packet_traits<Scalar>::size };
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| 80 | void operator()(Scalar* blockB, const Scalar* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
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| 81 | {
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| 82 | Index end_k = k2 + rows;
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| 83 | Index count = 0;
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| 84 | const_blas_data_mapper<Scalar,Index,StorageOrder> rhs(_rhs,rhsStride);
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| 85 | Index packet_cols = (cols/nr)*nr;
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| 86 |
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| 87 | // first part: normal case
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| 88 | for(Index j2=0; j2<k2; j2+=nr)
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| 89 | {
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| 90 | for(Index k=k2; k<end_k; k++)
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| 91 | {
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| 92 | blockB[count+0] = rhs(k,j2+0);
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| 93 | blockB[count+1] = rhs(k,j2+1);
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| 94 | if (nr==4)
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| 95 | {
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| 96 | blockB[count+2] = rhs(k,j2+2);
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| 97 | blockB[count+3] = rhs(k,j2+3);
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| 98 | }
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| 99 | count += nr;
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| 100 | }
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| 101 | }
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| 102 |
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| 103 | // second part: diagonal block
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| 104 | for(Index j2=k2; j2<(std::min)(k2+rows,packet_cols); j2+=nr)
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| 105 | {
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| 106 | // again we can split vertically in three different parts (transpose, symmetric, normal)
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| 107 | // transpose
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| 108 | for(Index k=k2; k<j2; k++)
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| 109 | {
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| 110 | blockB[count+0] = numext::conj(rhs(j2+0,k));
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| 111 | blockB[count+1] = numext::conj(rhs(j2+1,k));
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| 112 | if (nr==4)
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| 113 | {
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| 114 | blockB[count+2] = numext::conj(rhs(j2+2,k));
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| 115 | blockB[count+3] = numext::conj(rhs(j2+3,k));
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| 116 | }
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| 117 | count += nr;
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| 118 | }
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| 119 | // symmetric
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| 120 | Index h = 0;
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| 121 | for(Index k=j2; k<j2+nr; k++)
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| 122 | {
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| 123 | // normal
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| 124 | for (Index w=0 ; w<h; ++w)
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| 125 | blockB[count+w] = rhs(k,j2+w);
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| 126 |
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| 127 | blockB[count+h] = numext::real(rhs(k,k));
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| 128 |
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| 129 | // transpose
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| 130 | for (Index w=h+1 ; w<nr; ++w)
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| 131 | blockB[count+w] = numext::conj(rhs(j2+w,k));
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| 132 | count += nr;
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| 133 | ++h;
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| 134 | }
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| 135 | // normal
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| 136 | for(Index k=j2+nr; k<end_k; k++)
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| 137 | {
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| 138 | blockB[count+0] = rhs(k,j2+0);
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| 139 | blockB[count+1] = rhs(k,j2+1);
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| 140 | if (nr==4)
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| 141 | {
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| 142 | blockB[count+2] = rhs(k,j2+2);
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| 143 | blockB[count+3] = rhs(k,j2+3);
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| 144 | }
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| 145 | count += nr;
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| 146 | }
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| 147 | }
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| 148 |
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| 149 | // third part: transposed
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| 150 | for(Index j2=k2+rows; j2<packet_cols; j2+=nr)
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| 151 | {
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| 152 | for(Index k=k2; k<end_k; k++)
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| 153 | {
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| 154 | blockB[count+0] = numext::conj(rhs(j2+0,k));
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| 155 | blockB[count+1] = numext::conj(rhs(j2+1,k));
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| 156 | if (nr==4)
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| 157 | {
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| 158 | blockB[count+2] = numext::conj(rhs(j2+2,k));
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| 159 | blockB[count+3] = numext::conj(rhs(j2+3,k));
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| 160 | }
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| 161 | count += nr;
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| 162 | }
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| 163 | }
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| 164 |
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| 165 | // copy the remaining columns one at a time (=> the same with nr==1)
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| 166 | for(Index j2=packet_cols; j2<cols; ++j2)
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| 167 | {
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| 168 | // transpose
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| 169 | Index half = (std::min)(end_k,j2);
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| 170 | for(Index k=k2; k<half; k++)
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| 171 | {
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| 172 | blockB[count] = numext::conj(rhs(j2,k));
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| 173 | count += 1;
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| 174 | }
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| 175 |
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| 176 | if(half==j2 && half<k2+rows)
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| 177 | {
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| 178 | blockB[count] = numext::real(rhs(j2,j2));
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| 179 | count += 1;
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| 180 | }
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| 181 | else
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| 182 | half--;
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| 183 |
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| 184 | // normal
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| 185 | for(Index k=half+1; k<k2+rows; k++)
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| 186 | {
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| 187 | blockB[count] = rhs(k,j2);
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| 188 | count += 1;
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| 189 | }
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| 190 | }
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| 191 | }
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| 192 | };
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| 193 |
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| 194 | /* Optimized selfadjoint matrix * matrix (_SYMM) product built on top of
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| 195 | * the general matrix matrix product.
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| 196 | */
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| 197 | template <typename Scalar, typename Index,
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| 198 | int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
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| 199 | int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs,
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| 200 | int ResStorageOrder>
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| 201 | struct product_selfadjoint_matrix;
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| 202 |
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| 203 | template <typename Scalar, typename Index,
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| 204 | int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
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| 205 | int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs>
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| 206 | struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,LhsSelfAdjoint,ConjugateLhs, RhsStorageOrder,RhsSelfAdjoint,ConjugateRhs,RowMajor>
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| 207 | {
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| 208 |
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| 209 | static EIGEN_STRONG_INLINE void run(
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| 210 | Index rows, Index cols,
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| 211 | const Scalar* lhs, Index lhsStride,
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| 212 | const Scalar* rhs, Index rhsStride,
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| 213 | Scalar* res, Index resStride,
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| 214 | const Scalar& alpha)
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| 215 | {
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| 216 | product_selfadjoint_matrix<Scalar, Index,
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| 217 | EIGEN_LOGICAL_XOR(RhsSelfAdjoint,RhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
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| 218 | RhsSelfAdjoint, NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(RhsSelfAdjoint,ConjugateRhs),
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| 219 | EIGEN_LOGICAL_XOR(LhsSelfAdjoint,LhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
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| 220 | LhsSelfAdjoint, NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsSelfAdjoint,ConjugateLhs),
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| 221 | ColMajor>
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| 222 | ::run(cols, rows, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha);
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| 223 | }
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| 224 | };
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| 225 |
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| 226 | template <typename Scalar, typename Index,
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| 227 | int LhsStorageOrder, bool ConjugateLhs,
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| 228 | int RhsStorageOrder, bool ConjugateRhs>
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| 229 | struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor>
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| 230 | {
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| 231 |
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| 232 | static EIGEN_DONT_INLINE void run(
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| 233 | Index rows, Index cols,
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| 234 | const Scalar* _lhs, Index lhsStride,
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| 235 | const Scalar* _rhs, Index rhsStride,
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| 236 | Scalar* res, Index resStride,
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| 237 | const Scalar& alpha);
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| 238 | };
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| 239 |
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| 240 | template <typename Scalar, typename Index,
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| 241 | int LhsStorageOrder, bool ConjugateLhs,
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| 242 | int RhsStorageOrder, bool ConjugateRhs>
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| 243 | EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor>::run(
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| 244 | Index rows, Index cols,
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| 245 | const Scalar* _lhs, Index lhsStride,
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| 246 | const Scalar* _rhs, Index rhsStride,
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| 247 | Scalar* res, Index resStride,
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| 248 | const Scalar& alpha)
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| 249 | {
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| 250 | Index size = rows;
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| 251 |
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| 252 | const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
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| 253 | const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
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| 254 |
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| 255 | typedef gebp_traits<Scalar,Scalar> Traits;
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| 256 |
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| 257 | Index kc = size; // cache block size along the K direction
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| 258 | Index mc = rows; // cache block size along the M direction
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| 259 | Index nc = cols; // cache block size along the N direction
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| 260 | computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc);
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| 261 | // kc must smaller than mc
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| 262 | kc = (std::min)(kc,mc);
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| 263 |
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| 264 | std::size_t sizeW = kc*Traits::WorkSpaceFactor;
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| 265 | std::size_t sizeB = sizeW + kc*cols;
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| 266 | ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
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| 267 | ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
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| 268 | Scalar* blockB = allocatedBlockB + sizeW;
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| 269 |
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| 270 | gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
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| 271 | symm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
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| 272 | gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
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| 273 | gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder==RowMajor?ColMajor:RowMajor, true> pack_lhs_transposed;
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| 274 |
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| 275 | for(Index k2=0; k2<size; k2+=kc)
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| 276 | {
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| 277 | const Index actual_kc = (std::min)(k2+kc,size)-k2;
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| 278 |
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| 279 | // we have selected one row panel of rhs and one column panel of lhs
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| 280 | // pack rhs's panel into a sequential chunk of memory
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| 281 | // and expand each coeff to a constant packet for further reuse
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| 282 | pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, cols);
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| 283 |
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| 284 | // the select lhs's panel has to be split in three different parts:
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| 285 | // 1 - the transposed panel above the diagonal block => transposed packed copy
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| 286 | // 2 - the diagonal block => special packed copy
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| 287 | // 3 - the panel below the diagonal block => generic packed copy
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| 288 | for(Index i2=0; i2<k2; i2+=mc)
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| 289 | {
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| 290 | const Index actual_mc = (std::min)(i2+mc,k2)-i2;
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| 291 | // transposed packed copy
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| 292 | pack_lhs_transposed(blockA, &lhs(k2, i2), lhsStride, actual_kc, actual_mc);
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| 293 |
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| 294 | gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
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| 295 | }
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| 296 | // the block diagonal
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| 297 | {
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| 298 | const Index actual_mc = (std::min)(k2+kc,size)-k2;
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| 299 | // symmetric packed copy
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| 300 | pack_lhs(blockA, &lhs(k2,k2), lhsStride, actual_kc, actual_mc);
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| 301 |
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| 302 | gebp_kernel(res+k2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
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| 303 | }
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| 304 |
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| 305 | for(Index i2=k2+kc; i2<size; i2+=mc)
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| 306 | {
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| 307 | const Index actual_mc = (std::min)(i2+mc,size)-i2;
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| 308 | gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder,false>()
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| 309 | (blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
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| 310 |
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| 311 | gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
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| 312 | }
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| 313 | }
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| 314 | }
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| 315 |
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| 316 | // matrix * selfadjoint product
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| 317 | template <typename Scalar, typename Index,
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| 318 | int LhsStorageOrder, bool ConjugateLhs,
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| 319 | int RhsStorageOrder, bool ConjugateRhs>
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| 320 | struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor>
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| 321 | {
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| 322 |
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| 323 | static EIGEN_DONT_INLINE void run(
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| 324 | Index rows, Index cols,
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| 325 | const Scalar* _lhs, Index lhsStride,
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| 326 | const Scalar* _rhs, Index rhsStride,
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| 327 | Scalar* res, Index resStride,
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| 328 | const Scalar& alpha);
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| 329 | };
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| 330 |
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| 331 | template <typename Scalar, typename Index,
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| 332 | int LhsStorageOrder, bool ConjugateLhs,
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| 333 | int RhsStorageOrder, bool ConjugateRhs>
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| 334 | EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor>::run(
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| 335 | Index rows, Index cols,
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| 336 | const Scalar* _lhs, Index lhsStride,
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| 337 | const Scalar* _rhs, Index rhsStride,
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| 338 | Scalar* res, Index resStride,
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| 339 | const Scalar& alpha)
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| 340 | {
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| 341 | Index size = cols;
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| 342 |
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| 343 | const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
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| 344 |
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| 345 | typedef gebp_traits<Scalar,Scalar> Traits;
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| 346 |
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| 347 | Index kc = size; // cache block size along the K direction
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| 348 | Index mc = rows; // cache block size along the M direction
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| 349 | Index nc = cols; // cache block size along the N direction
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| 350 | computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc);
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| 351 | std::size_t sizeW = kc*Traits::WorkSpaceFactor;
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| 352 | std::size_t sizeB = sizeW + kc*cols;
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| 353 | ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
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| 354 | ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
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| 355 | Scalar* blockB = allocatedBlockB + sizeW;
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| 356 |
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| 357 | gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
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| 358 | gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
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| 359 | symm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
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| 360 |
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| 361 | for(Index k2=0; k2<size; k2+=kc)
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| 362 | {
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| 363 | const Index actual_kc = (std::min)(k2+kc,size)-k2;
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| 364 |
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| 365 | pack_rhs(blockB, _rhs, rhsStride, actual_kc, cols, k2);
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| 366 |
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| 367 | // => GEPP
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| 368 | for(Index i2=0; i2<rows; i2+=mc)
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| 369 | {
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| 370 | const Index actual_mc = (std::min)(i2+mc,rows)-i2;
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| 371 | pack_lhs(blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
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| 372 |
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| 373 | gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
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| 374 | }
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| 375 | }
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| 376 | }
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| 377 |
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| 378 | } // end namespace internal
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| 379 |
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| 380 | /***************************************************************************
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| 381 | * Wrapper to product_selfadjoint_matrix
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| 382 | ***************************************************************************/
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| 383 |
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| 384 | namespace internal {
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| 385 | template<typename Lhs, int LhsMode, typename Rhs, int RhsMode>
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| 386 | struct traits<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false> >
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| 387 | : traits<ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false>, Lhs, Rhs> >
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| 388 | {};
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| 389 | }
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| 390 |
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| 391 | template<typename Lhs, int LhsMode, typename Rhs, int RhsMode>
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| 392 | struct SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false>
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| 393 | : public ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false>, Lhs, Rhs >
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| 394 | {
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| 395 | EIGEN_PRODUCT_PUBLIC_INTERFACE(SelfadjointProductMatrix)
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| 396 |
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| 397 | SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
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| 398 |
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| 399 | enum {
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| 400 | LhsIsUpper = (LhsMode&(Upper|Lower))==Upper,
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| 401 | LhsIsSelfAdjoint = (LhsMode&SelfAdjoint)==SelfAdjoint,
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| 402 | RhsIsUpper = (RhsMode&(Upper|Lower))==Upper,
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| 403 | RhsIsSelfAdjoint = (RhsMode&SelfAdjoint)==SelfAdjoint
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| 404 | };
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| 405 |
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| 406 | template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
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| 407 | {
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| 408 | eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols());
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| 409 |
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| 410 | typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
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| 411 | typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
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| 412 |
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| 413 | Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
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| 414 | * RhsBlasTraits::extractScalarFactor(m_rhs);
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| 415 |
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| 416 | internal::product_selfadjoint_matrix<Scalar, Index,
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| 417 | EIGEN_LOGICAL_XOR(LhsIsUpper,
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| 418 | internal::traits<Lhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, LhsIsSelfAdjoint,
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| 419 | NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsIsUpper,bool(LhsBlasTraits::NeedToConjugate)),
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| 420 | EIGEN_LOGICAL_XOR(RhsIsUpper,
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| 421 | internal::traits<Rhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, RhsIsSelfAdjoint,
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| 422 | NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(RhsIsUpper,bool(RhsBlasTraits::NeedToConjugate)),
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| 423 | internal::traits<Dest>::Flags&RowMajorBit ? RowMajor : ColMajor>
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| 424 | ::run(
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| 425 | lhs.rows(), rhs.cols(), // sizes
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| 426 | &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
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| 427 | &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info
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| 428 | &dst.coeffRef(0,0), dst.outerStride(), // result info
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| 429 | actualAlpha // alpha
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| 430 | );
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| 431 | }
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| 432 | };
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| 433 |
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| 434 | } // end namespace Eigen
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| 435 |
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| 436 | #endif // EIGEN_SELFADJOINT_MATRIX_MATRIX_H
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