c++ - 为什么找不到这个算法？

Question

我正在实现 BCRSmatrix 类( block 压缩行存储)，我在这里找到了 the algorithm对于计算矩阵 vector 积，所以我定义了 operator*(std::vector<type>,BCRSmatrix<type,size>)完全遵循这个算法，但发生了一些奇怪的事情:让我们定义这个矩阵:

   11 12  0  0  0  0  0   0
   0  22  0  0  0  0  0   0
   31 32 33  0  0  0  0   0
   41 42 43 44  0  0  0   0 
   0   0  0  0  55 56 0   0 
   0   0  0  0  0  66 67  0
   0   0  0  0  0  0  77 78
   0   0  0  0  0  0  87 88

和这个 vector :

3,4,0,1,6,8,1,19

矩阵的乘积( block 大小为 2x2)给我:

81 0 0 0 778 595 1559 1759 

矩阵的乘积( block 大小为 4x4)给我:

81 0 221 335 778 595 1559 1759 

octave 给我正确的结果:

81 88 221 335 778 595 1559 1759

我不明白为什么!我尝试使用调试器，但没有发现任何异常!

这里是最小的可编译代码:编辑 我已经修复了这个错误!抱歉，谢谢@Marco

  # include <iosfwd>
    # include <vector>
    # include <string>
    # include <initializer_list>
    # include <sstream>
    # include <fstream>
    # include <algorithm>
    # include <iomanip>

template <typename data_type, std::size_t BS>
class BCRSmatrix {


      template <typename T, std::size_t S>
      friend std::ostream& operator<<(std::ostream& os , const BCRSmatrix<T,S>& m ) noexcept ;

      template <typename T, std::size_t S>
      friend std::vector<T> operator*(const BCRSmatrix<T,S>& m, const std::vector<T>& x );

 public:

     constexpr BCRSmatrix(std::initializer_list<std::vector<data_type>> dense );  
      auto constexpr validate_block(const std::vector<std::vector<data_type>>& dense,
                                  std::size_t i, std::size_t j) const noexcept ; 

     auto constexpr insert_block(const std::vector<std::vector<data_type>>& dense,
                                                       std::size_t i, std::size_t j) noexcept ;

auto constexpr printBCRS() const noexcept ; 

  private:

    std::size_t bn  ;
    std::size_t bBS ;
    std::size_t nnz ;
    std::size_t denseRows ;
    std::size_t denseCols ;

    std::vector<data_type>    ba_ ; 
    std::vector<std::size_t>  an_ ;
    std::vector<std::size_t>  ai_ ;
    std::vector<std::size_t>  aj_ ;


    std::size_t index =0 ;

    auto constexpr findBlockIndex(const std::size_t r, const std::size_t c) const noexcept ;  



    auto constexpr findValue(
                              const std::size_t i, const std::size_t j, 
                              const std::size_t rBlock, const std::size_t cBlock
                            ) const noexcept ;

};

emplate <typename T, std::size_t BS>
constexpr BCRSmatrix<T,BS>::BCRSmatrix(std::initializer_list<std::vector<T>> dense_ )
{
      this->denseRows = dense_.size();   
      auto it         = *(dense_.begin());
      this->denseCols = it.size();

      if( (denseRows*denseCols) % BS != 0 )
      {
            throw std::runtime_error("Error block size is not multiple of dense matrix size");
      }

     std::vector<std::vector<T>> dense(dense_);
     bBS = BS*BS ;  
     bn  = denseRows*denseCols/(BS*BS) ;
    ai_.resize(denseRows/BS +1);
    ai_[0] = 1;

    for(std::size_t i = 0; i < dense.size() / BS ; i++)
    {    
        auto rowCount =0;
        for(std::size_t j = 0; j < dense[i].size() / BS ; j++)
        {
            if(validate_block(dense,i,j))
            {     
                  aj_.push_back(j+1);
                  insert_block(dense, i, j);
                  rowCount ++ ;
            }      

        }
        ai_[i+1] = ai_[i] + rowCount ;
     }
 printBCRS();
}

template <typename T,std::size_t BS>
inline auto constexpr BCRSmatrix<T,BS>::validate_block(const std::vector<std::vector<T>>& dense,
                                                       std::size_t i, std::size_t j) const noexcept
{   
   bool nonzero = false ;
   for(std::size_t m = i * BS ; m < BS * (i + 1); ++m)
   {
      for(std::size_t n = j * BS ; n < BS * (j + 1); ++n)
      {
            if(dense[m][n] != 0) nonzero = true;
      }
   }
   return nonzero ;
}
template <typename T,std::size_t BS>
inline auto constexpr BCRSmatrix<T,BS>::insert_block(const std::vector<std::vector<T>>& dense,
                                                       std::size_t i, std::size_t j) noexcept
{   
   //std::size_t value = index;   
   bool firstElem = true ;
   for(std::size_t m = i * BS ; m < BS * (i + 1); ++m)
   {
      for(std::size_t n = j * BS ; n < BS * (j + 1); ++n)
      {    
            if(firstElem)
            {
                  an_.push_back(index+1);
                  firstElem = false ;
            }
            ba_.push_back(dense[m][n]);
            index ++ ;
      }
   }
}   
template <typename T, std::size_t BS> 
auto constexpr BCRSmatrix<T,BS>::findBlockIndex(const std::size_t r, const std::size_t c) const noexcept 
{
      for(auto j= ai_.at(r) ; j < ai_.at(r+1) ; j++ )
      {   
         if( aj_.at(j-1) == c  )
         {
            return j ;
         }
      }
}
template <typename T, std::size_t BS>
auto constexpr BCRSmatrix<T,BS>::printBCRS() const noexcept 
{ 

  std::cout << "ba_ :   " ;
  for(auto &x : ba_ ) 
      std::cout << x << ' ' ;
    std::cout << std::endl; 

  std::cout << "an_ :   " ;
  for(auto &x : an_ ) 
      std::cout <<  x << ' ' ;
    std::cout << std::endl; 

  std::cout << "aj_ :   " ;
  for(auto &x : aj_ ) 
      std::cout <<  x << ' ' ;
    std::cout << std::endl; 

   std::cout << "ai_ :   " ; 
   for(auto &x : ai_ ) 
      std::cout << x << ' ' ;
    std::cout << std::endl; 

}

template <typename T, std::size_t BS> 
auto constexpr BCRSmatrix<T,BS>::findValue(
                                           const std::size_t i, const std::size_t j, 
                                           const std::size_t rBlock, const std::size_t cBlock
                                          ) const noexcept 
{
    auto index = findBlockIndex(i,j);
    if(index != 0)
        return ba_.at(an_.at(index-1)-1 + cBlock + rBlock*BS);
}

template <typename T, std::size_t BS>
std::ostream& operator<<(std::ostream& os , const BCRSmatrix<T,BS>& m ) noexcept 
{
    for(auto i=0 ; i < m.denseRows / BS ; i++)
    {
        //for each Block sub row.
        for(auto rBlock = 0; rBlock < BS; rBlock++)
        {
            //for each BCSR col.
            for(auto j = 1; j <= m.denseCols / BS; j++)
            {
                //for each Block sub col.
                for(auto cBlock = 0; cBlock < BS; cBlock++)
                {
                    os << m.findValue(i, j, rBlock, cBlock) <<'\t';
                }
            }
            os << std::endl;
        }
    }
    return os;  
}


template <typename T, std::size_t BS>
std::vector<T> operator*(const BCRSmatrix<T,BS>& m, const std::vector<T>& x )
{
      std::vector<T> y(x.size());
      if(m.size1() != x.size())
      {
       std::string to = "x" ;
       std::string mess = "Error occured in operator* attempt to perfor productor between op1: "
                        + std::to_string(m.size1()) + to + std::to_string(m.size2()) +
                                 " and op2: " + std::to_string(x.size());
            throw std::runtime_error(mess.c_str());
      }
      else
      {
            auto brows = m.denseRows/BS ;  
            auto bnze  = m.an_.size()   ;

            auto z=0;

            for(auto b=0 ; b < brows ; b++)
            {     
              // y.at(b) = 0; <-- bug
               for(auto j= m.ai_.at(b) ; j <= m.ai_.at(b+1)-1; j++ )
               {      
                  for(auto k=0 ; k < BS ; k++ )
                  {
                     for(auto t=0 ; t < BS ; t++)
                     {
                         y.at(BS*b+k) += m.ba_.at(z) * x.at(BS*(m.aj_.at(j-1)-1)+t) ;          
                         z++ ;
                     }     
                  }
               }   
            }

      }
      return y;      

}

这里是主要功能:

using namespace std;



int main(){
    BCRSmatrix<int,2> bbcsr2 = {{11,12,0,0,0,0,0,0} ,{0,22,0,0,0,0,0,0} ,{31,32,33,0,0,0,0,0},
                              {41,42,43,44,0,0,0,0}, {0,0,0,0,55,56,0,0},{0,0,0,0,0,66,67,0},{0,0,0,0,0,0,77,78},{0,0,0,0,0,0,87,88}};

std::vector<int> v1 = {3,4,0,1,6,8,1,19};

std::vector<int> v2 = bbcsr2 *v1 ;
for(auto& x : v2)
     cout << x << ' ' ;
  cout << endl;  

return 0;
}

Answer 1

您必须删除第一个 for 中的 y.at(b) = 0; !