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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
#define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
namespace Eigen {
template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
struct selfadjoint_rank1_update;
namespace internal {
/**********************************************************************
* This file implements a general A * B product while
* evaluating only one triangular part of the product.
* This is a more general version of self adjoint product (C += A A^T)
* as the level 3 SYRK Blas routine.
**********************************************************************/
// forward declarations (defined at the end of this file)
template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
struct tribb_kernel;
/* Optimized matrix-matrix product evaluating only one triangular half */
template <typename Index,
typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
int ResStorageOrder, int UpLo, int Version = Specialized>
struct general_matrix_matrix_triangular_product;
// as usual if the result is row major => we transpose the product
template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version>
{
typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride,
const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride,
const ResScalar& alpha, level3_blocking<RhsScalar,LhsScalar>& blocking)
{
general_matrix_matrix_triangular_product<Index,
RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
ColMajor, UpLo==Lower?Upper:Lower>
::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking);
}
};
template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version>
{
typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride,
const RhsScalar* _rhs, Index rhsStride, ResScalar* _res, Index resStride,
const ResScalar& alpha, level3_blocking<LhsScalar,RhsScalar>& blocking)
{
typedef gebp_traits<LhsScalar,RhsScalar> Traits;
typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper;
typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper;
typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;
LhsMapper lhs(_lhs,lhsStride);
RhsMapper rhs(_rhs,rhsStride);
ResMapper res(_res, resStride);
Index kc = blocking.kc();
Index mc = (std::min)(size,blocking.mc());
// !!! mc must be a multiple of nr:
if(mc > Traits::nr)
mc = (mc/Traits::nr)*Traits::nr;
std::size_t sizeA = kc*mc;
std::size_t sizeB = kc*size;
ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());
ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());
gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;
gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb;
for(Index k2=0; k2<depth; k2+=kc)
{
const Index actual_kc = (std::min)(k2+kc,depth)-k2;
// note that the actual rhs is the transpose/adjoint of mat
pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, size);
for(Index i2=0; i2<size; i2+=mc)
{
const Index actual_mc = (std::min)(i2+mc,size)-i2;
pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);
// the selected actual_mc * size panel of res is split into three different part:
// 1 - before the diagonal => processed with gebp or skipped
// 2 - the actual_mc x actual_mc symmetric block => processed with a special kernel
// 3 - after the diagonal => processed with gebp or skipped
if (UpLo==Lower)
gebp(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc,
(std::min)(size,i2), alpha, -1, -1, 0, 0);
sybb(_res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha);
if (UpLo==Upper)
{
Index j2 = i2+actual_mc;
gebp(res.getSubMapper(i2, j2), blockA, blockB+actual_kc*j2, actual_mc,
actual_kc, (std::max)(Index(0), size-j2), alpha, -1, -1, 0, 0);
}
}
}
}
};
// Optimized packed Block * packed Block product kernel evaluating only one given triangular part
// This kernel is built on top of the gebp kernel:
// - the current destination block is processed per panel of actual_mc x BlockSize
// where BlockSize is set to the minimal value allowing gebp to be as fast as possible
// - then, as usual, each panel is split into three parts along the diagonal,
// the sub blocks above and below the diagonal are processed as usual,
// while the triangular block overlapping the diagonal is evaluated into a
// small temporary buffer which is then accumulated into the result using a
// triangular traversal.
template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
struct tribb_kernel
{
typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits;
typedef typename Traits::ResScalar ResScalar;
enum {
BlockSize = meta_least_common_multiple<EIGEN_PLAIN_ENUM_MAX(mr,nr),EIGEN_PLAIN_ENUM_MIN(mr,nr)>::ret
};
void operator()(ResScalar* _res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha)
{
typedef blas_data_mapper<ResScalar, Index, ColMajor> ResMapper;
ResMapper res(_res, resStride);
gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel;
Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer((internal::constructor_without_unaligned_array_assert()));
// let's process the block per panel of actual_mc x BlockSize,
// again, each is split into three parts, etc.
for (Index j=0; j<size; j+=BlockSize)
{
Index actualBlockSize = std::min<Index>(BlockSize,size - j);
const RhsScalar* actual_b = blockB+j*depth;
if(UpLo==Upper)
gebp_kernel(res.getSubMapper(0, j), blockA, actual_b, j, depth, actualBlockSize, alpha,
-1, -1, 0, 0);
// selfadjoint micro block
{
Index i = j;
buffer.setZero();
// 1 - apply the kernel on the temporary buffer
gebp_kernel(ResMapper(buffer.data(), BlockSize), blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha,
-1, -1, 0, 0);
// 2 - triangular accumulation
for(Index j1=0; j1<actualBlockSize; ++j1)
{
ResScalar* r = &res(i, j + j1);
for(Index i1=UpLo==Lower ? j1 : 0;
UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1)
r[i1] += buffer(i1,j1);
}
}
if(UpLo==Lower)
{
Index i = j+actualBlockSize;
gebp_kernel(res.getSubMapper(i, j), blockA+depth*i, actual_b, size-i,
depth, actualBlockSize, alpha, -1, -1, 0, 0);
}
}
}
};
} // end namespace internal
// high level API
template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct>
struct general_product_to_triangular_selector;
template<typename MatrixType, typename ProductType, int UpLo>
struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true>
{
static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta)
{
typedef typename MatrixType::Scalar Scalar;
typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
typedef internal::blas_traits<Lhs> LhsBlasTraits;
typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
typedef internal::blas_traits<Rhs> RhsBlasTraits;
typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
if(!beta)
mat.template triangularView<UpLo>().setZero();
enum {
StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,
UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1,
UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1
};
internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs;
ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(),
(UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data()));
if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs;
internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs;
ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(),
(UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data()));
if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,
LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex>
::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha);
}
};
template<typename MatrixType, typename ProductType, int UpLo>
struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false>
{
static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta)
{
typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
typedef internal::blas_traits<Lhs> LhsBlasTraits;
typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
typedef internal::blas_traits<Rhs> RhsBlasTraits;
typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
if(!beta)
mat.template triangularView<UpLo>().setZero();
enum {
IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0,
LhsIsRowMajor = _ActualLhs::Flags&RowMajorBit ? 1 : 0,
RhsIsRowMajor = _ActualRhs::Flags&RowMajorBit ? 1 : 0,
SkipDiag = (UpLo&(UnitDiag|ZeroDiag))!=0
};
Index size = mat.cols();
if(SkipDiag)
size--;
Index depth = actualLhs.cols();
typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,typename Lhs::Scalar,typename Rhs::Scalar,
MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, _ActualRhs::MaxColsAtCompileTime> BlockingType;
BlockingType blocking(size, size, depth, 1, false);
internal::general_matrix_matrix_triangular_product<Index,
typename Lhs::Scalar, LhsIsRowMajor ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
typename Rhs::Scalar, RhsIsRowMajor ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
IsRowMajor ? RowMajor : ColMajor, UpLo&(Lower|Upper)>
::run(size, depth,
&actualLhs.coeffRef(SkipDiag&&(UpLo&Lower)==Lower ? 1 : 0,0), actualLhs.outerStride(),
&actualRhs.coeffRef(0,SkipDiag&&(UpLo&Upper)==Upper ? 1 : 0), actualRhs.outerStride(),
mat.data() + (SkipDiag ? (bool(IsRowMajor) != ((UpLo&Lower)==Lower) ? 1 : mat.outerStride() ) : 0), mat.outerStride(), actualAlpha, blocking);
}
};
template<typename MatrixType, unsigned int UpLo>
template<typename ProductType>
TriangularView<MatrixType,UpLo>& TriangularViewImpl<MatrixType,UpLo,Dense>::_assignProduct(const ProductType& prod, const Scalar& alpha, bool beta)
{
EIGEN_STATIC_ASSERT((UpLo&UnitDiag)==0, WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED);
eigen_assert(derived().nestedExpression().rows() == prod.rows() && derived().cols() == prod.cols());
general_product_to_triangular_selector<MatrixType, ProductType, UpLo, internal::traits<ProductType>::InnerSize==1>::run(derived().nestedExpression().const_cast_derived(), prod, alpha, beta);
return derived();
}
} // end namespace Eigen
#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H