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