在块矩阵中找到一个值 [英] find a value in a block matrix
本文介绍了在块矩阵中找到一个值的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！
问题描述
我写了一个基于Block压缩存储的稀疏矩阵类，几乎写了所有方法，但是我不知道如何编写给出原始矩阵2个索引的方法findValue(i,j)！存储由四个向量组成:
I wrote a sparse matrix class, based on Block compressed storage, I wrote almost all the method, but I have not idea to how to write the method findValue(i,j) that give 2 indexes of the original matrix ! the storage consists in four vectors :
-
`ba_':以自上而下的左右顺序存储矩阵的非零块(几乎一个元素与零不同的矩形块)
`ba_': stored the non zero block (rectangular block in which almost one element is different from zero) of the matrix in top-down left-right order
an_是索引向量，指向向量ba
an_ is the vector of index that points to the first element of the block in the vector ba
ai_将每行的第一块存储在块矩阵中.
ai_ stored the first block of each row in the blocked matrix.
图片澄清了任何内容:
the picture clarify anything :
在下面的类中，我使用两种方法来获得结果，即findBlockIndex和findValue(i,j,Brows,Bcols)，但是我需要使用findValue(i,j)获取原始i，j索引的值，其中i,j是稀疏完整矩阵中的索引
here the following class in which I use two methods to achieve the result, findBlockIndex and findValue(i,j,Brows,Bcols) but I need to get the value of the original i,j index using findValue(i,j) in which i,j are the index in the sparse complete matrix
# include <iosfwd>
# include <vector>
# include <string>
# include <initializer_list>
# include "MatrixException.H"
# include <sstream>
# include <fstream>
# include <algorithm>
# include <iomanip>
// forward declarations
template <typename T, std::size_t R, std::size_t C>
class BCRSmatrix ;
template <typename T, std::size_t R, std::size_t C>
std::ostream& operator<<(std::ostream& os , const BCRSmatrix<T,R,C>& m );
template <typename T, std::size_t Br, std::size_t Bc >
std::vector<T> operator*(const BCRSmatrix<T,Br,Bc>& m, const std::vector<T>& x );
template <typename data_type, std::size_t BR , std::size_t BC>
class BCRSmatrix {
template <typename T, std::size_t R, std::size_t C>
friend std::ostream& operator<<(std::ostream& os , const BCRSmatrix<T,R,C>& m );
template <typename T, std::size_t Br,std::size_t Bc>
friend std::vector<T> operator*(const BCRSmatrix<T,Br,Bc>& m, const std::vector<T>& x );
public:
constexpr BCRSmatrix(std::initializer_list<std::vector<data_type>> dense );
constexpr BCRSmatrix(const std::string& );
virtual ~BCRSmatrix() = default ;
auto constexpr print_block(const std::vector<std::vector<data_type>>& dense,
std::size_t i, std::size_t j) const noexcept ;
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 ;
auto constexpr printBlockMatrix() const noexcept ;
auto constexpr size1() const noexcept { return denseRows ;}
auto constexpr size2() const noexcept { return denseCols ;}
auto constexpr printBlock(std::size_t i) const noexcept ;
auto constexpr print() const noexcept ;
private:
std::size_t bn ;
std::size_t bBR ;
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 recomposeMatrix() 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 ;
};
//--------------------------- IMPLEMENTATION
template <typename T, std::size_t BR, std::size_t BC>
constexpr BCRSmatrix<T,BR,BC>::BCRSmatrix(std::initializer_list<std::vector<T>> dense_ )
{
this->denseRows = dense_.size();
auto it = *(dense_.begin());
this->denseCols = it.size();
if( (denseRows*denseCols) % BR != 0 )
{
throw InvalidSizeException("Error block size is not multiple of dense matrix size");
}
std::vector<std::vector<T>> dense(dense_);
bBR = BR*BC ;
bn = denseRows*denseCols/(BR*BC) ;
ai_.resize(denseRows/BR +1);
ai_[0] = 1;
for(std::size_t i = 0; i < dense.size() / BR ; i++)
{
auto rowCount =0;
for(std::size_t j = 0; j < dense[i].size() / BC ; 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 BR, std::size_t BC>
constexpr BCRSmatrix<T,BR,BC>::BCRSmatrix(const std::string& fname)
{
std::ifstream f(fname , std::ios::in);
if(!f)
{
throw OpeningFileException("error opening file in constructor !");
}
else
{
std::vector<std::vector<T>> dense;
std::string line, tmp;
T elem = 0 ;
std::vector<T> row;
std::size_t i=0, j=0 ;
while(getline(f, line))
{
row.clear();
std::istringstream ss(line);
if(i==0)
{
while(ss >> elem)
{
row.push_back(elem);
j++;
}
}
else
{
while(ss >> elem)
row.push_back(elem);
}
dense.push_back(row);
i++;
}
this->denseRows = i;
this->denseCols = j;
bBR = BR*BR ;
bn = denseRows*denseCols/(BR*BC) ;
ai_.resize(denseRows/BR +1);
ai_[0] = 1;
for(std::size_t i = 0; i < dense.size() / BR ; i++)
{
auto rowCount =0;
for(std::size_t j = 0; j < dense[i].size() / BC ; 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 BR, std::size_t BC>
inline auto constexpr BCRSmatrix<T,BR,BC>::printBlockMatrix() const noexcept
{
for(auto i=0 ; i < denseRows / BR ; i++)
{
for(auto j=1 ; j <= denseCols / BC ; j++)
{
std::cout << findBlockIndex(i,j) << ' ' ;
}
std::cout << std::endl;
}
}
template <typename T,std::size_t BR,std::size_t BC>
inline auto constexpr BCRSmatrix<T,BR,BC>::printBlock(std::size_t i) const noexcept
{
auto w = i-1 ;
auto k = 0;
for(std::size_t i = 0 ; i < BR ; ++i)
{
for(std::size_t j=0 ; j < BC ; ++j )
{
std::cout << std::setw(8) << ba_.at(an_.at(w)-1+k) << ' ';
k++;
}
}
}
template <typename T,std::size_t BR, std::size_t BC>
inline auto constexpr BCRSmatrix<T,BR,BC>::print_block(const std::vector<std::vector<T>>& dense,
std::size_t i, std::size_t j) const noexcept
{
for(std::size_t m = i * BR ; m < BR * (i + 1); ++m)
{
for(std::size_t n = j * BC ; n < BC * (j + 1); ++n)
std::cout << dense[m][n] << ' ';
std::cout << '\n';
}
}
template <typename T,std::size_t BR, std::size_t BC>
inline auto constexpr BCRSmatrix<T,BR,BC>::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 * BR ; m < BR * (i + 1); ++m)
{
for(std::size_t n = j * BC ; n < BC * (j + 1); ++n)
{
if(dense[m][n] != 0) nonzero = true;
}
}
return nonzero ;
}
template <typename T,std::size_t BR, std::size_t BC>
inline auto constexpr BCRSmatrix<T,BR,BC>::insert_block(const std::vector<std::vector<T>>& dense,
std::size_t i, std::size_t j) noexcept
{
bool firstElem = true ;
for(std::size_t m = i * BR ; m < BR * (i + 1); ++m)
{
for(std::size_t n = j * BC ; n < BC * (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 BR,std::size_t BC>
auto constexpr BCRSmatrix<T,BR,BC>::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 BR, std::size_t BC>
auto constexpr BCRSmatrix<T,BR,BC>::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 BR, std::size_t BC>
auto constexpr BCRSmatrix<T,BR,BC>::print() const noexcept
{
//for each BCRS row
for(auto i=0 ; i < denseRows / BR ; i++){
//for each Block sub row.
for(auto rBlock = 0; rBlock < BR; rBlock++){
//for each BCSR col.
for(auto j = 1; j <= denseCols / BC; j++){
//for each Block sub col.
for(auto cBlock = 0; cBlock < BC; cBlock++){
std::cout<< findValue(i, j, rBlock, cBlock) <<'\t';
}
}
std::cout << std::endl;
}
}
}
template <typename T, std::size_t BR,std::size_t BC>
auto constexpr BCRSmatrix<T,BR,BC>::recomposeMatrix() const noexcept
{
std::vector<std::vector<T>> sparseMat(denseRows, std::vector<T>(denseCols, 0));
auto BA_i = 0, AJ_i = 0;
//for each BCSR row
for(auto r = 0; r < denseRows/BR; r++){
//for each Block in row
for(auto nBlock = 0; nBlock < ai_.at(r+1)-ai_.at(r); nBlock++){
//for each subMatrix (Block)
for(auto rBlock = 0; rBlock < BR; rBlock++){
for(auto cBlock = 0; cBlock < BC; cBlock++){
//insert value
sparseMat.at(rBlock + r*BR).at(cBlock + (aj_.at(AJ_i)-1)*BC) = ba_.at(BA_i);
++BA_i;
}
}
++AJ_i;
}
}
return sparseMat;
}
template <typename T, std::size_t BR,std::size_t BC>
auto constexpr BCRSmatrix<T,BR,BC>::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*BC);
else
return T(0);
}
template <typename T, std::size_t BR,std::size_t BC>
std::ostream& operator<<(std::ostream& os , const BCRSmatrix<T,BR,BC>& m )
{
for(auto i=0 ; i < m.denseRows / BR ; i++)
{
//for each Block sub row.
for(auto rBlock = 0; rBlock < BR; rBlock++)
{
//for each BCSR col.
for(auto j = 1; j <= m.denseCols / BC; j++)
{
//for each Block sub col.
for(auto cBlock = 0; cBlock < BC; cBlock++)
{
os << m.findValue(i, j, rBlock, cBlock) <<'\t';
}
}
os << std::endl;
}
}
return os;
}
template <typename T, std::size_t BR, std::size_t BC>
std::vector<T> operator*(const BCRSmatrix<T,BR,BC>& 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 InvalidSizeException(mess.c_str());
}
else
{
auto brows = m.denseRows/BR ;
auto bnze = m.an_.size() ;
auto z=0;
for(auto b=0 ; b < brows ; b++)
{
for(auto j= m.ai_.at(b) ; j <= m.ai_.at(b+1)-1; j++ )
{
for(auto k=0 ; k < BR ; k++ )
{
for(auto t=0 ; t < BC ; t++)
{
y.at(BC*b+k) += m.ba_.at(z) * x.at(BC*(m.aj_.at(j-1)-1)+t) ;
z++ ;
}
}
}
}
}
return y;
}
这是主要的
# include "BCSmatrix.H"
using namespace std;
int main(){
BCRSmatrix<int,2,2> bbcsr1 = {{11,12,13,14,0,0},{0,22,23,0,0,0},{0,0,33,34,35,36},{0,0,0,44,45,0},
{0,0,0,0,0,56},{0,0,0,0,0,66}};
BCRSmatrix<int,2,2> 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}};
BCRSmatrix<int,2,4> bbcsr3 = {{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}};
bbcsr3.printBlockMatrix();
bbcsr3.print();
BCRSmatrix<int,2,2> bbcsr4("input17.dat");
bbcsr4.printBlockMatrix();
BCRSmatrix<int,2,4> bbcsr5("input18.dat");
bbcsr5.printBlockMatrix();
cout << bbcsr5 ;
BCRSmatrix<int,4,4> bbcsr6("input18.dat");
bbcsr6.printBlockMatrix();
bbcsr6.print();
cout << bbcsr4 ; //.print();
BCRSmatrix<int,2,4> bbcsr7("input20.dat");
cout << bbcsr7;
bbcsr7.printBlockMatrix();
std::vector<int> v1 = {3,4,0,1,6,8,1,19};
std::vector<int> v01 = {3,4,0,1,6,8,1,19,15,2};
std::vector<int> v2 = bbcsr4 *v1 ;
for(auto& x : v2)
cout << x << ' ' ;
cout << endl;
BCRSmatrix<double,2,2> bbcsr8("input21.dat");
bbcsr8.print() ;
bbcsr8.printBlockMatrix();
return 0;
}
推荐答案
如何编写给出原始矩阵的2个索引的方法
findValue(i,j)
它与以前的 findValue 方法相似:
template <typename T, std::size_t BR,std::size_t BC>
auto constexpr BCRSmatrix<T,BR,BC>::myNewfindValue(const std::size_t i, const std::size_t j) const noexcept{
auto index = findBlockIndex(i/BR, j/BC);
if(index != 0)
return ba_.at(an_.at(index-1)-1 + j%BC + (i%BR)*BC);
else
return T(0);
}
要调用此函数:您必须对findBlockIndex进行一些更改:只需更改if( aj_.at(j-1) == c )白色if( aj_.at(j-1) == c+1 )，而不是必须在其他函数for(auto j = 0; j < ...
To recall this function: you have to do a little change to your findBlockIndex: just change if( aj_.at(j-1) == c ) whit if( aj_.at(j-1) == c+1 ), than you have to modify your for statements in the others functions for(auto j = 1; j <= .. whit for(auto j = 0; j < ...
让我知道是否有问题，或者这不是您要寻找的答案. 希望对您有所帮助，
Let me know if there are problems or this is not the answer you were looking for. I hope to be of help to you,
问候马可.
这篇关于在块矩阵中找到一个值的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！
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