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Diffstat (limited to 'extern/Eigen3/Eigen/src/Core/products/TriangularSolverMatrix.h')
| -rw-r--r-- | extern/Eigen3/Eigen/src/Core/products/TriangularSolverMatrix.h | 319 |
1 files changed, 319 insertions, 0 deletions
diff --git a/extern/Eigen3/Eigen/src/Core/products/TriangularSolverMatrix.h b/extern/Eigen3/Eigen/src/Core/products/TriangularSolverMatrix.h new file mode 100644 index 00000000000..4dced6b0eb9 --- /dev/null +++ b/extern/Eigen3/Eigen/src/Core/products/TriangularSolverMatrix.h @@ -0,0 +1,319 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// Eigen is free software; you can redistribute it and/or +// modify it under the terms of the GNU Lesser General Public +// License as published by the Free Software Foundation; either +// version 3 of the License, or (at your option) any later version. +// +// Alternatively, you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of +// the License, or (at your option) any later version. +// +// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY +// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU Lesser General Public +// License and a copy of the GNU General Public License along with +// Eigen. If not, see <http://www.gnu.org/licenses/>. + +#ifndef EIGEN_TRIANGULAR_SOLVER_MATRIX_H +#define EIGEN_TRIANGULAR_SOLVER_MATRIX_H + +namespace internal { + +// if the rhs is row major, let's transpose the product +template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder> +struct triangular_solve_matrix<Scalar,Index,Side,Mode,Conjugate,TriStorageOrder,RowMajor> +{ + static EIGEN_DONT_INLINE void run( + Index size, Index cols, + const Scalar* tri, Index triStride, + Scalar* _other, Index otherStride) + { + triangular_solve_matrix< + Scalar, Index, Side==OnTheLeft?OnTheRight:OnTheLeft, + (Mode&UnitDiag) | ((Mode&Upper) ? Lower : Upper), + NumTraits<Scalar>::IsComplex && Conjugate, + TriStorageOrder==RowMajor ? ColMajor : RowMajor, ColMajor> + ::run(size, cols, tri, triStride, _other, otherStride); + } +}; + +/* Optimized triangular solver with multiple right hand side and the triangular matrix on the left + */ +template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder> +struct triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor> +{ + static EIGEN_DONT_INLINE void run( + Index size, Index otherSize, + const Scalar* _tri, Index triStride, + Scalar* _other, Index otherStride) + { + Index cols = otherSize; + const_blas_data_mapper<Scalar, Index, TriStorageOrder> tri(_tri,triStride); + blas_data_mapper<Scalar, Index, ColMajor> other(_other,otherStride); + + typedef gebp_traits<Scalar,Scalar> Traits; + enum { + SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr), + IsLower = (Mode&Lower) == Lower + }; + + Index kc = size; // cache block size along the K direction + Index mc = size; // cache block size along the M direction + Index nc = cols; // cache block size along the N direction + computeProductBlockingSizes<Scalar,Scalar,4>(kc, mc, nc); + + std::size_t sizeW = kc*Traits::WorkSpaceFactor; + std::size_t sizeB = sizeW + kc*cols; + ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0); + ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0); + Scalar* blockB = allocatedBlockB + sizeW; + + conj_if<Conjugate> conj; + gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, Conjugate, false> gebp_kernel; + gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, TriStorageOrder> pack_lhs; + gemm_pack_rhs<Scalar, Index, Traits::nr, ColMajor, false, true> pack_rhs; + + for(Index k2=IsLower ? 0 : size; + IsLower ? k2<size : k2>0; + IsLower ? k2+=kc : k2-=kc) + { + const Index actual_kc = (std::min)(IsLower ? size-k2 : k2, kc); + + // We have selected and packed a big horizontal panel R1 of rhs. Let B be the packed copy of this panel, + // and R2 the remaining part of rhs. The corresponding vertical panel of lhs is split into + // A11 (the triangular part) and A21 the remaining rectangular part. + // Then the high level algorithm is: + // - B = R1 => general block copy (done during the next step) + // - R1 = L1^-1 B => tricky part + // - update B from the new R1 => actually this has to be performed continuously during the above step + // - R2 = L2 * B => GEPP + + // The tricky part: compute R1 = L1^-1 B while updating B from R1 + // The idea is to split L1 into multiple small vertical panels. + // Each panel can be split into a small triangular part A1 which is processed without optimization, + // and the remaining small part A2 which is processed using gebp with appropriate block strides + { + // for each small vertical panels of lhs + for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth) + { + Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth); + // tr solve + for (Index k=0; k<actualPanelWidth; ++k) + { + // TODO write a small kernel handling this (can be shared with trsv) + Index i = IsLower ? k2+k1+k : k2-k1-k-1; + Index s = IsLower ? k2+k1 : i+1; + Index rs = actualPanelWidth - k - 1; // remaining size + + Scalar a = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(tri(i,i)); + for (Index j=0; j<cols; ++j) + { + if (TriStorageOrder==RowMajor) + { + Scalar b = 0; + const Scalar* l = &tri(i,s); + Scalar* r = &other(s,j); + for (Index i3=0; i3<k; ++i3) + b += conj(l[i3]) * r[i3]; + + other(i,j) = (other(i,j) - b)*a; + } + else + { + Index s = IsLower ? i+1 : i-rs; + Scalar b = (other(i,j) *= a); + Scalar* r = &other(s,j); + const Scalar* l = &tri(s,i); + for (Index i3=0;i3<rs;++i3) + r[i3] -= b * conj(l[i3]); + } + } + } + + Index lengthTarget = actual_kc-k1-actualPanelWidth; + Index startBlock = IsLower ? k2+k1 : k2-k1-actualPanelWidth; + Index blockBOffset = IsLower ? k1 : lengthTarget; + + // update the respective rows of B from other + pack_rhs(blockB, _other+startBlock, otherStride, actualPanelWidth, cols, actual_kc, blockBOffset); + + // GEBP + if (lengthTarget>0) + { + Index startTarget = IsLower ? k2+k1+actualPanelWidth : k2-actual_kc; + + pack_lhs(blockA, &tri(startTarget,startBlock), triStride, actualPanelWidth, lengthTarget); + + gebp_kernel(_other+startTarget, otherStride, blockA, blockB, lengthTarget, actualPanelWidth, cols, Scalar(-1), + actualPanelWidth, actual_kc, 0, blockBOffset); + } + } + } + + // R2 = A2 * B => GEPP + { + Index start = IsLower ? k2+kc : 0; + Index end = IsLower ? size : k2-kc; + for(Index i2=start; i2<end; i2+=mc) + { + const Index actual_mc = (std::min)(mc,end-i2); + if (actual_mc>0) + { + pack_lhs(blockA, &tri(i2, IsLower ? k2 : k2-kc), triStride, actual_kc, actual_mc); + + gebp_kernel(_other+i2, otherStride, blockA, blockB, actual_mc, actual_kc, cols, Scalar(-1)); + } + } + } + } + } +}; + +/* Optimized triangular solver with multiple left hand sides and the trinagular matrix on the right + */ +template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder> +struct triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor> +{ + static EIGEN_DONT_INLINE void run( + Index size, Index otherSize, + const Scalar* _tri, Index triStride, + Scalar* _other, Index otherStride) + { + Index rows = otherSize; + const_blas_data_mapper<Scalar, Index, TriStorageOrder> rhs(_tri,triStride); + blas_data_mapper<Scalar, Index, ColMajor> lhs(_other,otherStride); + + typedef gebp_traits<Scalar,Scalar> Traits; + enum { + RhsStorageOrder = TriStorageOrder, + SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr), + IsLower = (Mode&Lower) == Lower + }; + +// Index kc = std::min<Index>(Traits::Max_kc/4,size); // cache block size along the K direction +// Index mc = std::min<Index>(Traits::Max_mc,size); // cache block size along the M direction + // check that !!!! + Index kc = size; // cache block size along the K direction + Index mc = size; // cache block size along the M direction + Index nc = rows; // cache block size along the N direction + computeProductBlockingSizes<Scalar,Scalar,4>(kc, mc, nc); + + std::size_t sizeW = kc*Traits::WorkSpaceFactor; + std::size_t sizeB = sizeW + kc*size; + ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0); + ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0); + Scalar* blockB = allocatedBlockB + sizeW; + + conj_if<Conjugate> conj; + gebp_kernel<Scalar,Scalar, Index, Traits::mr, Traits::nr, false, Conjugate> gebp_kernel; + gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs; + gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel; + gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, ColMajor, false, true> pack_lhs_panel; + + for(Index k2=IsLower ? size : 0; + IsLower ? k2>0 : k2<size; + IsLower ? k2-=kc : k2+=kc) + { + const Index actual_kc = (std::min)(IsLower ? k2 : size-k2, kc); + Index actual_k2 = IsLower ? k2-actual_kc : k2 ; + + Index startPanel = IsLower ? 0 : k2+actual_kc; + Index rs = IsLower ? actual_k2 : size - actual_k2 - actual_kc; + Scalar* geb = blockB+actual_kc*actual_kc; + + if (rs>0) pack_rhs(geb, &rhs(actual_k2,startPanel), triStride, actual_kc, rs); + + // triangular packing (we only pack the panels off the diagonal, + // neglecting the blocks overlapping the diagonal + { + for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth) + { + Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth); + Index actual_j2 = actual_k2 + j2; + Index panelOffset = IsLower ? j2+actualPanelWidth : 0; + Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2; + + if (panelLength>0) + pack_rhs_panel(blockB+j2*actual_kc, + &rhs(actual_k2+panelOffset, actual_j2), triStride, + panelLength, actualPanelWidth, + actual_kc, panelOffset); + } + } + + for(Index i2=0; i2<rows; i2+=mc) + { + const Index actual_mc = (std::min)(mc,rows-i2); + + // triangular solver kernel + { + // for each small block of the diagonal (=> vertical panels of rhs) + for (Index j2 = IsLower + ? (actual_kc - ((actual_kc%SmallPanelWidth) ? Index(actual_kc%SmallPanelWidth) + : Index(SmallPanelWidth))) + : 0; + IsLower ? j2>=0 : j2<actual_kc; + IsLower ? j2-=SmallPanelWidth : j2+=SmallPanelWidth) + { + Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth); + Index absolute_j2 = actual_k2 + j2; + Index panelOffset = IsLower ? j2+actualPanelWidth : 0; + Index panelLength = IsLower ? actual_kc - j2 - actualPanelWidth : j2; + + // GEBP + if(panelLength>0) + { + gebp_kernel(&lhs(i2,absolute_j2), otherStride, + blockA, blockB+j2*actual_kc, + actual_mc, panelLength, actualPanelWidth, + Scalar(-1), + actual_kc, actual_kc, // strides + panelOffset, panelOffset, // offsets + allocatedBlockB); // workspace + } + + // unblocked triangular solve + for (Index k=0; k<actualPanelWidth; ++k) + { + Index j = IsLower ? absolute_j2+actualPanelWidth-k-1 : absolute_j2+k; + + Scalar* r = &lhs(i2,j); + for (Index k3=0; k3<k; ++k3) + { + Scalar b = conj(rhs(IsLower ? j+1+k3 : absolute_j2+k3,j)); + Scalar* a = &lhs(i2,IsLower ? j+1+k3 : absolute_j2+k3); + for (Index i=0; i<actual_mc; ++i) + r[i] -= a[i] * b; + } + Scalar b = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(rhs(j,j)); + for (Index i=0; i<actual_mc; ++i) + r[i] *= b; + } + + // pack the just computed part of lhs to A + pack_lhs_panel(blockA, _other+absolute_j2*otherStride+i2, otherStride, + actualPanelWidth, actual_mc, + actual_kc, j2); + } + } + + if (rs>0) + gebp_kernel(_other+i2+startPanel*otherStride, otherStride, blockA, geb, + actual_mc, actual_kc, rs, Scalar(-1), + -1, -1, 0, 0, allocatedBlockB); + } + } + } +}; + +} // end namespace internal + +#endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_H |