Learning Log---matrix representation and special matrix compression

Matrix class: Two-dimensional array implementation!!

Each row is considered a one-dimensional array, which can be put into several sets;

Random numbers can be produced, and the maximum value in parentheses is used.

Matrix class: public class mymatrix {   int[][] matrix ;//Matrix array Random random  =new random ()  ;//random Number object//default construction method, generate 3*3 matrix Public mymatrix () {         //default is the 3*3 matrix matrix = new int[3][3];//initial matrix for (int i=0;i<matrix.length;i+ +) {for (int j=0;j<matrix[i].length;j++) {matrix[i][j]=random.nextint (100);}}} Construction method for generating square matrices Public mymatrix (int n) {    matrix = new int[n][n];     //initial matrix for (int i=0;i<matrix.length;i++) {for (int j=0;j<matrix[i].length; J + +) {matrix[i][j]=random.nextint (100);}}} Generates a m*n matrix. Public mymatrix (int m,int n) {matrix = new int[m][n];//initial matrix for (int i=0;i< matrix.length;i++) {for (int j=0;j<matrix[i].length;j++) {matrix[i][j]=random.nextint (100);}}} Generates a matrix Public mymatrix (Int[][] matrix) {This.matrix = matrix, according to a known two-dimensional array;} Returns a matrix array public Int[][] getmatrix () {Return this.matrix;} Print Matrix Public void print () {for (int i=0;i<matrix.length;i++) {for (Int j=0;j<matrix[i]. length;j++) {System.out.print (matrix[i][j]+ " ");} System.out.println ();}  }//transpose Matrix Public mymatrix transport () {    //row variable column int m = matrix[ 0].length;//Column Change Line int n = matrix.length; Mymatrix transmatrix = new mymatrix (m,n);//Initialize//The new matrix is traversed here, and the original matrix symmetry points are placed in for (int i=0;i< transmatrix.matrix.length;i++) {for (int j=0;j<transmatrix.matrix[i].length;j++) {transMatrix.matrix[i][j ] = matrix[j][i];}} return transmatrix; }//The judgment matrix is the upper triangular matrix Public boolean isuptriangle () {   for (int  i=1;i<matrix.length;i++)    {   for (int j=0;j<i;j++)     {   if (matrix[i][j]!=0)    {   return false;    }   }    }   return true;} Judging if it is the lower triangular matrix     public boolean isdowntriangle ()     {     for (int i=0;i<matrix.length;i++)     {    for (int j=matrix[i].length-1;j>i;j--)     {        if (matrix[i][j]!=0)      {     return false;      }    }    }    return true;     }        //Judging whether it is a symmetric matrix      Public boolean issynmetry ()     {       for ( int i=1;i<matrix.length;i++)      {             //here can be j<i, because only half view can, this will repeat &NBSP;&NBSP;   for (int j=0;j<matrix[i].length;j++)     {    if ( Matrix[i][j]!=matrix[j][i])     {    return false;     }    }     }     return  true;    }        //Matrix summation      public void add (mymatrix b)     {        int m = b.matrix.length;       int n =  B.matrix[0].length;       if (m!=matrix.length| | N!=matrix[0].length)        {        System.out.println ("The matrix type is not the same, cannot add!") ");       }       else        {       for (int i=0;i<matrix.length;i++)        {    for (int j=0;j<matrix[i].length;j++)     {    matrix[i][j]+=b.matrix[i][j];    }           }         }    }}

A compression algorithm for symmetric matrices:

The lower triangle or the upper triangle exists in a one-dimensional array;

The two-dimensional array of data in a triangular line of the existence of a one-dimensional array, when taken out, corresponding to the n*n loop, find the location of a one-dimensional array of data in a two-dimensional array, that is, a two-dimensional array.

Symmetric matrix class Compression public class synmematrix {           A is used to store a copy of the Matrix double [] a;//the order of the matrix elements int n; //matrices; int m; //the number of one-dimensional arrays public  Synmematrix (int n) {//The number of elements that need to be persisted is m=n* (n+1)/2 ;//here to note the size of M m = n* (n+1)/2 ;a =  New double[m];this.n = n;} Initializes a two-dimensional array of public void evaluate (double[][] b) {  int k=0;  for (int  i=0;i<n;i++)   {  for (int j=0;j<n;j++)   {      if (I&GT;=J)      {        // System.out.println ("a[" +k+ "]=" +b[i][j]);                                //Save the data in B to a copy of the                               //because it's a symmetric array, A triangular line of a row of the inside, so as to save space for the role of     a[k++]=b[i][j]; //only the lower triangular elements      }   }  }}//is initialized by a one-dimensional array, this one-dimensional array is a copy of the symmetric matrix element         / /b is a copy, passed in, so with a equal public void evaluate (double[] b) {for (int k=0;k<m;k++) {a[k]= b[k];}} Symmetric matrix addition Public synmematrix add (SYNMEMATRIX&NBSP;B) {   synmematrix t =  New synmematrix (n);    int k;   for (int i=1;i<=n;i++)     {   for (int j=1;j<=n;j++)    {                             //k refers to the position in the copy, according to I and J to find the value of the position should be the same, two synmematrix the same, so with the same rules    if (I&GT;=J)    {   k= i* (i-1)/2+j-1;   }   else   {    k= j* (j-1)/2+i-1;   }   t.a[k] = a[k]+b.a[k];    }   }   return t;} Print symmetric matrix Public void print () {   int k;                    //is a copy, a one-dimensional array, Therefore, we can find the data of the corresponding position in one array from the position coordinates of the two-dimensional data, that is, the data    for (int i=1;i<=n;i++) in the two-dimensional array    {    for (int j=1;j<=n;j++)    {   if (i>=j)     {   k= i* (i-1)/2+j-1;   }   else   {    k= j* (j-1)/2+i-1;   }   system.out.print (" " +a[k]);    }   system.out.println ();    }}}

Sparse matrix compression algorithm:

Only the location and elements of the data are stored in ternary group;

The storage structure of ternary group can be used in one-dimensional array or linked list structure;

This uses the previous Myvector collection to store non-0 data information;

The following is a matrix of coefficients established by the structure of arrays;

Ternary class, non-0 element information, rows, columns, data//Each node is a data point public class three {public int row;public int  col;public double value;public three (int r,int c,double v) {this.row =  r;this.col = c;this.value = v;} Public three () {this (0,0,0.0);}} Sparse matrix class//required rows and columns, and non-0 element number and position can be public class spamatrix {   int rows; // Number of rows int cols; //number of columns int dnum;//non 0 elements//v is a collection of non-0 elements, the order in V is not important, because they are independent of each other      Myvector v;        spamatrix (Int max)      {    rows = cols = dNum=0;    v =  New myvector (max);     }        //array of triples based on user To initialize the matrix     public void evaluate (int r,int c,int d,three[]  Item) throws exception   &nbsp {    this.rows = r;    this.cols = c;     this.dnum = d;    for (int i=0;i<d;i++)      {    v.add (I, item[i]);    }    }         //Sparse Matrix Transpose     public SpaMatrix  Transport () throws exception    {        // The sparse matrix requires no more than 0 elements of location and data, so the size of the incoming V is constructed;     spamatrix a = new spamatrix (v.size ());    a.rows = this.cols;    a.cols = this.rows;     a.dnum = this.dnum;        for (int  i=0;i<dnum;i++)     {    Three t =  (three) V.get (i);    &Nbsp;    a.v.add (I, new three (T.col,t.row,t.value));     }     return a;    }         //method for printing sparse matrices     public void print ()  throws Exception   &NBSP;&NBSP;{&NBSP;&NBSP;&NBSP;&NBSP;SYSTEM.OUT.PRINTLN (number of rows in the matrix: +this.rows);     System.out.println ("Number of columns of the matrix:" +this.cols),     system.out.println ("Number of elements not 0:" +this.dnum);         system.out.println ("Matrix ternary is:");     for (int i =0;i<dnum;i++)     {       system.out.println ("a<" + ((three) v.get (i)). row+ "," + ((three) v.get (i)). col+ ">=" + ((three) v.get (i)). value);     }     }}

It can also be implemented using the linked list structure:

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Arrays are combined with chained structures:

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The picture is not clear, the text description: This method is better than the place is very clear, the array record row, the following list records the column information in the row, connected in turn.

Learning Log---matrix representation and special matrix compression