blas/PackedTriangularSolverVector.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
//
// 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_PACKED_TRIANGULAR_SOLVER_VECTOR_H
#define EIGEN_PACKED_TRIANGULAR_SOLVER_VECTOR_H

namespace internal {

template <typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
struct packed_triangular_solve_vector;

// forward and backward substitution, row-major, rhs is a vector
template <typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>
struct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, RowMajor> {
  enum { IsLower = (Mode & Lower) == Lower };
  static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs) {
    internal::conj_if<Conjugate> cj;
    typedef Map<const Matrix<LhsScalar, Dynamic, 1> > LhsMap;
    typedef typename conj_expr_if<Conjugate, LhsMap>::type ConjLhsType;

    lhs += IsLower ? 0 : (size * (size + 1) >> 1) - 1;
    for (Index pi = 0; pi < size; ++pi) {
      Index i = IsLower ? pi : size - pi - 1;
      Index s = IsLower ? 0 : 1;
      if (pi > 0)
        rhs[i] -= (ConjLhsType(LhsMap(lhs + s, pi))
                       .cwiseProduct(Map<const Matrix<RhsScalar, Dynamic, 1> >(rhs + (IsLower ? 0 : i + 1), pi)))
                      .sum();
      if (!(Mode & UnitDiag)) rhs[i] /= cj(lhs[IsLower ? i : 0]);
      IsLower ? lhs += pi + 1 : lhs -= pi + 2;
    }
  }
};

// forward and backward substitution, column-major, rhs is a vector
template <typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>
struct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, ColMajor> {
  enum { IsLower = (Mode & Lower) == Lower };
  static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs) {
    internal::conj_if<Conjugate> cj;
    typedef Map<const Matrix<LhsScalar, Dynamic, 1> > LhsMap;
    typedef typename conj_expr_if<Conjugate, LhsMap>::type ConjLhsType;

    lhs += IsLower ? 0 : size * (size - 1) >> 1;
    for (Index pi = 0; pi < size; ++pi) {
      Index i = IsLower ? pi : size - pi - 1;
      Index r = size - pi - 1;
      if (!(Mode & UnitDiag)) rhs[i] /= cj(lhs[IsLower ? 0 : i]);
      if (r > 0)
        Map<Matrix<RhsScalar, Dynamic, 1> >(rhs + (IsLower ? i + 1 : 0), r) -=
            rhs[i] * ConjLhsType(LhsMap(lhs + (IsLower ? 1 : 0), r));
      IsLower ? lhs += size - pi : lhs -= r;
    }
  }
};

template <typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate, int StorageOrder>
struct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheRight, Mode, Conjugate, StorageOrder> {
  static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs) {
    packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft,
                                   ((Mode & Upper) == Upper ? Lower : Upper) | (Mode & UnitDiag), Conjugate,
                                   StorageOrder == RowMajor ? ColMajor : RowMajor>::run(size, lhs, rhs);
  }
};

}  // end namespace internal

#endif  // EIGEN_PACKED_TRIANGULAR_SOLVER_VECTOR_H