# Compressed storage of symmetric and sparse matrices of C++ data structures

• 2020-05-27 06:45:10
• OfStack

Compression storage of symmetric and sparse matrices

1. Sparse matrix

For those matrices where the number of zero elements is much more than the number of non-zero elements, and the distribution of non-zero elements is irregular, it is called sparse matrix (sparse).

People can not give the exact definition of sparse matrix, 1 is generally only based on personal intuition to understand the concept, that is, the number of non-zero elements in the matrix is much smaller than the total number of elements in the matrix, and there is no distribution law of non-zero elements.

Implementation code:

``````
// Sparse matrix and its compressed storage
#pragma once

#include <vector>
#include <iostream>
using namespace std;

template<class T>
struct Triple
{
size_t _r;
size_t _c;
T _value;

Triple(size_t row = 0, size_t col = 0, const T& value = T())
:_r(row)
,_c(col)
,_value(value)
{}
};

template <class T>
class SparseMatrix
{
public:
SparseMatrix()
:_row(0)
,_col(0)
,_illegal(T())
{}

SparseMatrix(T* arr, size_t row, size_t col, const T& illegal)
:_row(row)
,_col(col)
,_illegal(illegal)
{
for(size_t i = 0; i<row; ++i)
{
for(size_t j = 0; j<col; ++j)
{
if(arr[i*col+j] != illegal)
{
Triple<T> t(i,j,arr[i*col+j]);
_matrix.push_back(t);
}
}
}
}

void Display()
{

vector<Triple<T> >::iterator iter;
iter = _matrix.begin();
for(size_t i = 0; i<_row; ++i)
{
for(size_t j = 0; j<_col; ++j)
{
if(iter!=_matrix.end()
&&iter->_r == i
&&iter->_c == j)
{
cout << iter->_value <<" ";
++iter;
}
else
{
cout << _illegal <<" ";
}
}
cout << endl;
}
cout << endl;
}
// Ordinary transpose ( Row first storage )
// The column changes to the row from 0 The column starts and columns the data 1 a 1 Let's put 1, 2 into the transpose
SparseMatrix<T> Transpose()
{
SparseMatrix<T> tm;
tm._row = _col;
tm._col = _row;
tm._illegal = _illegal;
tm._matrix.reserve(_matrix.size());

for(size_t i = 0; i<_col; ++i)
{
size_t index = 0;
while(index < _matrix.size())
{
if(_matrix[index]._c == i)
{
Triple<T> t(_matrix[index]._c, _matrix[index]._r, _matrix[index]._value);
tm._matrix.push_back(t);
}
++index;
}
}
return tm;
}

SparseMatrix<T> FastTranspose()
{
SparseMatrix<T> tm;
tm._row = _col;
tm._col = _row;
tm._illegal = _illegal;
tm._matrix.resize(_matrix.size());

int* count = new int[_col];// Records the number of elements per row
memset(count, 0, sizeof(int)*_col);
int* start = new int[_col];// The position of the elements in the transpose
start[0] = 0;

size_t index = 0;
while(index < _matrix.size())
{
count[_matrix[index]._c]++;
++index;
}

for(size_t i=1; i<_col; ++i)
{
start[i] = start[i-1] + count[i-1];
}

index = 0;
while(index < _matrix.size())
{
Triple<T> t(_matrix[index]._c, _matrix[index]._r, _matrix[index]._value);
tm._matrix[start[_matrix[index]._c]++] = t; // The core code
++index;
}

delete[] count;
delete[] start;
return tm;
}
protected:
vector<Triple<T> > _matrix;
size_t _row;
size_t _col;
T _illegal;
};

``````

2. Symmetric matrix

Implementation code:

``````
// Symmetric matrices and their compressed storage

#pragma once
#include <iostream>
using namespace std;

template <class T>
class SymmetricMatrix
{
public:
SymmetricMatrix(T* arr, size_t n)
:_n(n)
,_matrix(new T[n*(n+1)/2])
{
size_t index = 0;
for(size_t i = 0; i<n; ++i)
{
for(size_t j=0; j<n;++j)
{
if(i >= j)
{
_matrix[index] = arr[i*n+j];
++index;
}
else
{
continue;
}
}
}
}
void Display()
{
for(size_t i =0; i < _n; ++i)
{
for(size_t j = 0; j < _n; ++j)
{
/* if(i<j)
{
swap(i,j);
cout<<_matrix[i*(i+1)/2+j]<<" ";
swap(i,j);
}
else
cout<<_matrix[i*(i+1)/2+j]<<" ";
*/
cout << Access(i,j) << " ";
}
cout << endl;
}
cout << endl;
}

T& Access(size_t row, size_t col)
{
if(row<col)
{
swap(row, col);
}
return _matrix[row*(row+1)/2+col];
}
~SymmetricMatrix()
{
if(_matrix != NULL)
{
delete[] _matrix;
_matrix = NULL;
}
}
protected:
T* _matrix;
size_t _n; // The size of the columns and columns of a symmetric matrix
};

``````

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