Compressed storage and transpose of sparse matrices

Sparse matrices: matrices in which most elements are 0 (this is the main sequence of lines)

Ternary representation method for sparse matrices:

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Type structure:

Template <typename t>struct triple{int _row;int _col; T _value;}; Template <typename T>class Sparsematrix{public:sparsematrix<t>::sparsematrix (); Sparsematrix (const t* Array, size_t row, size_t col, const t& Invalid); ~sparsematrix (); void Display () const; Sparsematrix<t> Transport () const; Sparsematrix<t> fasttransport () const;protected:vector<triple<t>> _array;size_t _rowCount;size_t _colcount; T _invalid;};

Code to implement compressed storage:

Sparse Matrix Template <typename t>sparsematrix<t>::sparsematrix () {}template <typename  t>sparsematrix<t>::sparsematrix (const t* array, size_t row, size_t  col, const t& invalid): _rowcount (Row),  _colcount (col),  _invalid (invalid) { ASSERT (Array);for  (size_t i = 0; i < row; ++i) {for  (size_t &NBSP;J&NBSP;=&NBSP;0;&NBSP;J&NBSP;&LT;&NBSP;COL;&NBSP;++J) {if  (array[i*col + j] !=  Invalid) {this->_array.push_back ({ i, j, array[i*col + j] });}}} Template <typename t>sparsematrix<t>::~sparsematrix () {}template <typename t >void sparsematrix<t&gt::D isplay () const{size_t size = this->_array.size (); size_t  iCount = 0;for  (size_t i = 0; i < this->_rowcount;  ++i) {for  (size_t j  = 0; j < this->_colcount; ++j) {if  (icount < size & & i == this->_array[icount]._row && j == this->_array[ Icount]._col) {cout << this->_array[icount]._value <<  " "; ++iCount;} else{cout << this->_invalid <<  " ";}} Cout << endl;}}

Transpose of sparse matrices:

1) Sequence increment transpose method: Find all elements of line I: Scan the ternary table A from start to finish, find out the ternary group of all _col==i, transpose and put into the ternary Group table B. The code is implemented as follows:

Template <typename t>sparsematrix<t> sparsematrix<t>::transport () const{sparsematrix<t> ret ; ret._rowcount = This->_colcount;ret._colcount = This->_rowcount;ret._invalid = this->_invalid;size_t size = This->_array.size (); for (size_t col = 0, col < this->_colcount; ++col) {for (size_t iCount = 0; iCount < size; ++icount) {if (This->_array[icount]._col = = col) {ret._array.push_back ({this->_array[icount]._col, this->_ Array[icount]._row, This->_array[icount]._value});}} return ret;}

2) One position quick Transpose method

In Method 1, in order to make the ternary table B of the transpose matrix continue to be stored sequentially, the ternary table A of the matrix being transpose must be scanned multiple times. In order to be able to position the elements of the ternary table A at once to the correct position of the triples B, the following data needs to be calculated beforehand:

i) to transpose matrix ternary table a the total number of non-0 elements in each column, that is, the total number of 0 elements of each row of the matrix ternary element B after the transpose

II) The first non-0 element in each column of the matrix to be placed in the correct position in the ternary table B, that is, the correct position of the first non-0 element in the triples B in each row of the transpose matrix

For this purpose, you need to set two arrays for num[] and pos[], where Num[col] is used to hold the total number of elements in the tuple table a col 0 element, Pos[col] is used to store the first non-0 element in the Col column of the previous Ternary group table A in the tuple table B storage location.

Num[col] Calculation method: The ternary table A is scanned once, for the element in which the column number is col, the corresponding num array is labeled COL element plus 1.

Pos[col] Method of calculation:

i) pos[0] = 0, which represents the subscript value of the first non-0 element of the ternary table A with a column value of 0 in the Triples table B.

II) Pos[col] = Pos[col-1] + num[col-1], wherein 1<=col<a.size ();

eg

0 1 9 0 0 0 0

0 0 0 0 0 0 0

3 0 0 0 0 4 0

0 0 2 0 0 0 0

0 8 0 0 0 0 0

5 0 0 7 0 0 0

col	0	1	2	3	4		6
num[col]	2	2	2	1	0		0
Pos[col]	0	2	4	6	7	7	8

Code implementation:

Template <typename t>sparsematrix<t> sparsematrix<t>::transport () const{ sparsematrix<t> ret;ret._rowcount = this->_colcount;ret._colcount = this- >_rowcount;ret._invalid = this->_invalid;size_t size = this->_array.size (); for  (Size_t col = 0; col < this->_colcount; ++col) {for  ( Size_t icount = 0; icount < size; ++icount) {if  (this->_array[ Icount]._col == col) {ret._array.push_back ({ this->_array[icount]._col, this->_array[ icount]._row, this->_array[icount]._value });}} Return ret;} Template <typename t>sparsematrix<t> sparsematrix<t>::fasttransport () const{ sparsematrix<t> ret;ret._rowcount = this->_colcount;ret._colcount = this- >_rowcount;ret._invalid = this->_invalid;size_t size = this->_array.size (); ret._array.resize (size); Vector<int> num (this->_ ColCount); Vector<int> pos (this->_colcount);  //pos[i] = pos[i-1]+num[i-1] i >0for  (size_t i = 0; i < size; ++i) {++num[this->_array[i]._ Col];} for  (Size_t col = 1; col < this->_colcount; ++col) {Pos[col] &NBSP;=&NBSP;POS[COL&NBSP;-&NBSP;1]&NBSP;+&NBSP;NUM[COL&NBSP;-&NBSP;1];} for  (size_t i = 0; i < size; ++i) {Ret._array[pos[this->_array[i] . _col]++] = { this->_array[i]._col, this->_array[i]._row, this->_array[i]._ value };} Return ret;}

Operation Result:

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Compressed storage and transpose of sparse matrices