[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_TRIANGULAR_SOLVER_MATRIX_H
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| 11 | #define EIGEN_TRIANGULAR_SOLVER_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 | // if the rhs is row major, let's transpose the product
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| 18 | template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder>
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| 19 | struct triangular_solve_matrix<Scalar,Index,Side,Mode,Conjugate,TriStorageOrder,RowMajor>
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| 20 | {
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| 21 | static void run(
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| 22 | Index size, Index cols,
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| 23 | const Scalar* tri, Index triStride,
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| 24 | Scalar* _other, Index otherStride,
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| 25 | level3_blocking<Scalar,Scalar>& blocking)
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| 26 | {
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| 27 | triangular_solve_matrix<
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| 28 | Scalar, Index, Side==OnTheLeft?OnTheRight:OnTheLeft,
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| 29 | (Mode&UnitDiag) | ((Mode&Upper) ? Lower : Upper),
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| 30 | NumTraits<Scalar>::IsComplex && Conjugate,
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| 31 | TriStorageOrder==RowMajor ? ColMajor : RowMajor, ColMajor>
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| 32 | ::run(size, cols, tri, triStride, _other, otherStride, blocking);
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| 33 | }
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| 34 | };
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| 35 |
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| 36 | /* Optimized triangular solver with multiple right hand side and the triangular matrix on the left
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| 37 | */
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| 38 | template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
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| 39 | struct triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor>
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| 40 | {
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| 41 | static EIGEN_DONT_INLINE void run(
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| 42 | Index size, Index otherSize,
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| 43 | const Scalar* _tri, Index triStride,
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| 44 | Scalar* _other, Index otherStride,
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| 45 | level3_blocking<Scalar,Scalar>& blocking);
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| 46 | };
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| 47 | template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
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| 48 | EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor>::run(
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| 49 | Index size, Index otherSize,
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| 50 | const Scalar* _tri, Index triStride,
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| 51 | Scalar* _other, Index otherStride,
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| 52 | level3_blocking<Scalar,Scalar>& blocking)
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| 53 | {
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| 54 | Index cols = otherSize;
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| 55 | const_blas_data_mapper<Scalar, Index, TriStorageOrder> tri(_tri,triStride);
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| 56 | blas_data_mapper<Scalar, Index, ColMajor> other(_other,otherStride);
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| 57 |
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| 58 | typedef gebp_traits<Scalar,Scalar> Traits;
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| 59 | enum {
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| 60 | SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
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| 61 | IsLower = (Mode&Lower) == Lower
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| 62 | };
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| 63 |
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| 64 | Index kc = blocking.kc(); // cache block size along the K direction
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| 65 | Index mc = (std::min)(size,blocking.mc()); // cache block size along the M direction
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| 66 |
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| 67 | std::size_t sizeA = kc*mc;
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| 68 | std::size_t sizeB = kc*cols;
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| 69 | std::size_t sizeW = kc*Traits::WorkSpaceFactor;
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| 70 |
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| 71 | ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
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| 72 | ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
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| 73 | ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
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| 74 |
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| 75 | conj_if<Conjugate> conj;
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| 76 | gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, Conjugate, false> gebp_kernel;
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| 77 | gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, TriStorageOrder> pack_lhs;
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| 78 | gemm_pack_rhs<Scalar, Index, Traits::nr, ColMajor, false, true> pack_rhs;
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| 79 |
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| 80 | // the goal here is to subdivise the Rhs panels such that we keep some cache
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| 81 | // coherence when accessing the rhs elements
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| 82 | std::ptrdiff_t l1, l2;
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| 83 | manage_caching_sizes(GetAction, &l1, &l2);
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| 84 | Index subcols = cols>0 ? l2/(4 * sizeof(Scalar) * std::max<Index>(otherStride,size)) : 0;
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| 85 | subcols = std::max<Index>((subcols/Traits::nr)*Traits::nr, Traits::nr);
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| 86 |
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| 87 | for(Index k2=IsLower ? 0 : size;
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| 88 | IsLower ? k2<size : k2>0;
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| 89 | IsLower ? k2+=kc : k2-=kc)
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| 90 | {
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| 91 | const Index actual_kc = (std::min)(IsLower ? size-k2 : k2, kc);
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| 92 |
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| 93 | // We have selected and packed a big horizontal panel R1 of rhs. Let B be the packed copy of this panel,
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| 94 | // and R2 the remaining part of rhs. The corresponding vertical panel of lhs is split into
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| 95 | // A11 (the triangular part) and A21 the remaining rectangular part.
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| 96 | // Then the high level algorithm is:
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| 97 | // - B = R1 => general block copy (done during the next step)
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| 98 | // - R1 = A11^-1 B => tricky part
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| 99 | // - update B from the new R1 => actually this has to be performed continuously during the above step
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| 100 | // - R2 -= A21 * B => GEPP
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| 101 |
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| 102 | // The tricky part: compute R1 = A11^-1 B while updating B from R1
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| 103 | // The idea is to split A11 into multiple small vertical panels.
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| 104 | // Each panel can be split into a small triangular part T1k which is processed without optimization,
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| 105 | // and the remaining small part T2k which is processed using gebp with appropriate block strides
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| 106 | for(Index j2=0; j2<cols; j2+=subcols)
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| 107 | {
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| 108 | Index actual_cols = (std::min)(cols-j2,subcols);
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| 109 | // for each small vertical panels [T1k^T, T2k^T]^T of lhs
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| 110 | for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
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| 111 | {
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| 112 | Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
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| 113 | // tr solve
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| 114 | for (Index k=0; k<actualPanelWidth; ++k)
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| 115 | {
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| 116 | // TODO write a small kernel handling this (can be shared with trsv)
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| 117 | Index i = IsLower ? k2+k1+k : k2-k1-k-1;
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| 118 | Index rs = actualPanelWidth - k - 1; // remaining size
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| 119 | Index s = TriStorageOrder==RowMajor ? (IsLower ? k2+k1 : i+1)
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| 120 | : IsLower ? i+1 : i-rs;
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| 121 |
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| 122 | Scalar a = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(tri(i,i));
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| 123 | for (Index j=j2; j<j2+actual_cols; ++j)
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| 124 | {
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| 125 | if (TriStorageOrder==RowMajor)
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| 126 | {
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| 127 | Scalar b(0);
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| 128 | const Scalar* l = &tri(i,s);
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| 129 | Scalar* r = &other(s,j);
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| 130 | for (Index i3=0; i3<k; ++i3)
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| 131 | b += conj(l[i3]) * r[i3];
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| 132 |
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| 133 | other(i,j) = (other(i,j) - b)*a;
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| 134 | }
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| 135 | else
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| 136 | {
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| 137 | Scalar b = (other(i,j) *= a);
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| 138 | Scalar* r = &other(s,j);
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| 139 | const Scalar* l = &tri(s,i);
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| 140 | for (Index i3=0;i3<rs;++i3)
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| 141 | r[i3] -= b * conj(l[i3]);
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| 142 | }
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| 143 | }
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| 144 | }
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| 145 |
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| 146 | Index lengthTarget = actual_kc-k1-actualPanelWidth;
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| 147 | Index startBlock = IsLower ? k2+k1 : k2-k1-actualPanelWidth;
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| 148 | Index blockBOffset = IsLower ? k1 : lengthTarget;
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| 149 |
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| 150 | // update the respective rows of B from other
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| 151 | pack_rhs(blockB+actual_kc*j2, &other(startBlock,j2), otherStride, actualPanelWidth, actual_cols, actual_kc, blockBOffset);
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| 152 |
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| 153 | // GEBP
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| 154 | if (lengthTarget>0)
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| 155 | {
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| 156 | Index startTarget = IsLower ? k2+k1+actualPanelWidth : k2-actual_kc;
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| 157 |
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| 158 | pack_lhs(blockA, &tri(startTarget,startBlock), triStride, actualPanelWidth, lengthTarget);
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| 159 |
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| 160 | gebp_kernel(&other(startTarget,j2), otherStride, blockA, blockB+actual_kc*j2, lengthTarget, actualPanelWidth, actual_cols, Scalar(-1),
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| 161 | actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
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| 162 | }
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| 163 | }
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| 164 | }
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| 165 |
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| 166 | // R2 -= A21 * B => GEPP
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| 167 | {
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| 168 | Index start = IsLower ? k2+kc : 0;
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| 169 | Index end = IsLower ? size : k2-kc;
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| 170 | for(Index i2=start; i2<end; i2+=mc)
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| 171 | {
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| 172 | const Index actual_mc = (std::min)(mc,end-i2);
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| 173 | if (actual_mc>0)
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| 174 | {
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| 175 | pack_lhs(blockA, &tri(i2, IsLower ? k2 : k2-kc), triStride, actual_kc, actual_mc);
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| 176 |
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| 177 | gebp_kernel(_other+i2, otherStride, blockA, blockB, actual_mc, actual_kc, cols, Scalar(-1), -1, -1, 0, 0, blockW);
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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 | }
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| 183 |
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| 184 | /* Optimized triangular solver with multiple left hand sides and the trinagular matrix on the right
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| 185 | */
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| 186 | template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
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| 187 | struct triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor>
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| 188 | {
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| 189 | static EIGEN_DONT_INLINE void run(
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| 190 | Index size, Index otherSize,
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| 191 | const Scalar* _tri, Index triStride,
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| 192 | Scalar* _other, Index otherStride,
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| 193 | level3_blocking<Scalar,Scalar>& blocking);
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| 194 | };
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| 195 | template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
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| 196 | EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor>::run(
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| 197 | Index size, Index otherSize,
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| 198 | const Scalar* _tri, Index triStride,
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| 199 | Scalar* _other, Index otherStride,
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| 200 | level3_blocking<Scalar,Scalar>& blocking)
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| 201 | {
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| 202 | Index rows = otherSize;
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| 203 | const_blas_data_mapper<Scalar, Index, TriStorageOrder> rhs(_tri,triStride);
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| 204 | blas_data_mapper<Scalar, Index, ColMajor> lhs(_other,otherStride);
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| 205 |
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| 206 | typedef gebp_traits<Scalar,Scalar> Traits;
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| 207 | enum {
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| 208 | RhsStorageOrder = TriStorageOrder,
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| 209 | SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
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| 210 | IsLower = (Mode&Lower) == Lower
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| 211 | };
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| 212 |
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| 213 | Index kc = blocking.kc(); // cache block size along the K direction
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| 214 | Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
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| 215 |
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| 216 | std::size_t sizeA = kc*mc;
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| 217 | std::size_t sizeB = kc*size;
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| 218 | std::size_t sizeW = kc*Traits::WorkSpaceFactor;
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| 219 |
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| 220 | ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
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| 221 | ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
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| 222 | ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
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| 223 |
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| 224 | conj_if<Conjugate> conj;
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| 225 | gebp_kernel<Scalar,Scalar, Index, Traits::mr, Traits::nr, false, Conjugate> gebp_kernel;
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| 226 | gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
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| 227 | gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
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| 228 | gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, ColMajor, false, true> pack_lhs_panel;
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| 229 |
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| 230 | for(Index k2=IsLower ? size : 0;
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| 231 | IsLower ? k2>0 : k2<size;
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| 232 | IsLower ? k2-=kc : k2+=kc)
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| 233 | {
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| 234 | const Index actual_kc = (std::min)(IsLower ? k2 : size-k2, kc);
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| 235 | Index actual_k2 = IsLower ? k2-actual_kc : k2 ;
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| 236 |
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| 237 | Index startPanel = IsLower ? 0 : k2+actual_kc;
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| 238 | Index rs = IsLower ? actual_k2 : size - actual_k2 - actual_kc;
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| 239 | Scalar* geb = blockB+actual_kc*actual_kc;
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| 240 |
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| 241 | if (rs>0) pack_rhs(geb, &rhs(actual_k2,startPanel), triStride, actual_kc, rs);
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| 242 |
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| 243 | // triangular packing (we only pack the panels off the diagonal,
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| 244 | // neglecting the blocks overlapping the diagonal
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| 245 | {
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| 246 | for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
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| 247 | {
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| 248 | Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
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| 249 | Index actual_j2 = actual_k2 + j2;
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| 250 | Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
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| 251 | Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
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| 252 |
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| 253 | if (panelLength>0)
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| 254 | pack_rhs_panel(blockB+j2*actual_kc,
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| 255 | &rhs(actual_k2+panelOffset, actual_j2), triStride,
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| 256 | panelLength, actualPanelWidth,
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| 257 | actual_kc, panelOffset);
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| 258 | }
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| 259 | }
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| 260 |
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| 261 | for(Index i2=0; i2<rows; i2+=mc)
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| 262 | {
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| 263 | const Index actual_mc = (std::min)(mc,rows-i2);
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| 264 |
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| 265 | // triangular solver kernel
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| 266 | {
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| 267 | // for each small block of the diagonal (=> vertical panels of rhs)
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| 268 | for (Index j2 = IsLower
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| 269 | ? (actual_kc - ((actual_kc%SmallPanelWidth) ? Index(actual_kc%SmallPanelWidth)
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| 270 | : Index(SmallPanelWidth)))
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| 271 | : 0;
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| 272 | IsLower ? j2>=0 : j2<actual_kc;
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| 273 | IsLower ? j2-=SmallPanelWidth : j2+=SmallPanelWidth)
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| 274 | {
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| 275 | Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
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| 276 | Index absolute_j2 = actual_k2 + j2;
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| 277 | Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
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| 278 | Index panelLength = IsLower ? actual_kc - j2 - actualPanelWidth : j2;
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| 279 |
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| 280 | // GEBP
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| 281 | if(panelLength>0)
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| 282 | {
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| 283 | gebp_kernel(&lhs(i2,absolute_j2), otherStride,
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| 284 | blockA, blockB+j2*actual_kc,
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| 285 | actual_mc, panelLength, actualPanelWidth,
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| 286 | Scalar(-1),
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| 287 | actual_kc, actual_kc, // strides
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| 288 | panelOffset, panelOffset, // offsets
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| 289 | blockW); // workspace
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| 290 | }
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| 291 |
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| 292 | // unblocked triangular solve
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| 293 | for (Index k=0; k<actualPanelWidth; ++k)
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| 294 | {
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| 295 | Index j = IsLower ? absolute_j2+actualPanelWidth-k-1 : absolute_j2+k;
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| 296 |
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| 297 | Scalar* r = &lhs(i2,j);
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| 298 | for (Index k3=0; k3<k; ++k3)
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| 299 | {
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| 300 | Scalar b = conj(rhs(IsLower ? j+1+k3 : absolute_j2+k3,j));
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| 301 | Scalar* a = &lhs(i2,IsLower ? j+1+k3 : absolute_j2+k3);
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| 302 | for (Index i=0; i<actual_mc; ++i)
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| 303 | r[i] -= a[i] * b;
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| 304 | }
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| 305 | if((Mode & UnitDiag)==0)
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| 306 | {
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| 307 | Scalar b = conj(rhs(j,j));
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| 308 | for (Index i=0; i<actual_mc; ++i)
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| 309 | r[i] /= b;
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| 310 | }
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| 311 | }
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| 312 |
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| 313 | // pack the just computed part of lhs to A
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| 314 | pack_lhs_panel(blockA, _other+absolute_j2*otherStride+i2, otherStride,
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| 315 | actualPanelWidth, actual_mc,
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| 316 | actual_kc, j2);
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| 317 | }
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| 318 | }
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| 319 |
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| 320 | if (rs>0)
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| 321 | gebp_kernel(_other+i2+startPanel*otherStride, otherStride, blockA, geb,
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| 322 | actual_mc, actual_kc, rs, Scalar(-1),
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| 323 | -1, -1, 0, 0, blockW);
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| 324 | }
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| 325 | }
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| 326 | }
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| 327 |
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| 328 | } // end namespace internal
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| 329 |
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| 330 | } // end namespace Eigen
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| 331 |
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| 332 | #endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_H
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