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Raghav Purankar
finding the eigenvalues and eigenvector of n*n matrix in java
1 Answer(s)      2 years and 11 months ago
Posted in : Java Beginners


Here is my code:

/** * Jacobi eigenvalue algorithm  */
public class Jacobi {
    public static void main(String[] args) {
double[][] A = new double[][] {{4,3,1,2},{1,1,1,1},{1,2,1,1},{1,1,1,1}    };
double t, c, s; 
int p, q, icount, state, size = 4; 
double tol = 1.e-5; // the tolerance level of convergence 
int icmax = 10; // the maximum iterations number
int[] colRowOfElMax = new int[size], rowOfElMax = new int[1];
double[][] temp = new double[size][size], D = new double[size][size];
double[][] V, diagD;
double[] maxElColRow = new double[size], maxElRow = new double[1];
double[][] dMinusDiagD = new double[size][size], absDminusDiagD = new double[size][size];
double[][] rot = new double[2][2], rotT = new double[2][2];    // makes V into a unit matrix
V = new double[size][size];
for (int i = 0; i < size; i++) {
    for (int j = 0; j < size; j++) {
        V[i][j] = 0;
        }
        V[i][i] = 1.0;
        }
        D = A; // copies A to D
        diagD = diag(D, size);// outputs DiagD=diagonal of D
        dMinusDiagD = minus(D, diagD, size); // does D-DiagD
        abs(dMinusDiagD, absDminusDiagD, size);// does abs(D-DiagD)
        maxMatrix(absDminusDiagD, size, colRowOfElMax, maxElColRow);
        maxVector(maxElColRow, size, rowOfElMax, maxElRow);
        q = rowOfElMax[0];
        p = colRowOfElMax[q];
        icount = 0;
        state = 1;    // Iterations
        while (state == 1 && icount < icmax) {
            icount = icount + 1;
                if (D[q][q] == D[p][p]) { // check to prevent t from diverging
                    D[q][q] = D[p][p] + 1.e-10;
                    }
                    t = D[p][q] / (D[q][q] - D[p][p]);
                    c = 1 / Math.sqrt(t * t + 1);
                    s = c * t; 
                    rot[0][0] = c;
                    rot[0][1] = s; 
                    rot[1][0] = -s; 
                    rot[1][1] = c;
                    transpose(rot, rotT, 2);// rotT=transpose(Rot)
                    for (int i = 0; i < size; i++) { 
                        temp[p][i] = rotT[0][0] * D[p][i] + rotT[0][1] * D[q][i];
                        temp[q][i] = rotT[1][0] * D[p][i] + rotT[1][1] * D[q][i]; 
                        D[p][i] = temp[p][i];
                        D[q][i] = temp[q][i];
                        }
                        for (int i = 0; i < size; i++) {
                            temp[i][p] = D[i][p] * rot[0][0] + D[i][q] * rot[1][0];
                            temp[i][q] = D[i][p] * rot[0][1] + D[i][q] * rot[1][1];
                            D[i][p] = temp[i][p];
                            D[i][q] = temp[i][q]; 
                            } 
                            for (int i = 0; i < size; i++) {
                                temp[i][p] = V[i][p] * rot[0][0] + V[i][q] * rot[1][0];
                                temp[i][q] = V[i][p] * rot[0][1] + V[i][q] * rot[1][1];
                                V[i][p] = temp[i][p];
                                V[i][q] = temp[i][q];
                                }      // find the new q, p element array values that need to be changed
                                diagD = diag(D, size); // outputs diagD=diagonal of D
                                dMinusDiagD = minus(D, diagD, size); // does D-DiagD
                                abs(dMinusDiagD, absDminusDiagD, size); // does abs(D-DiagD) 
                                maxMatrix(absDminusDiagD, size, colRowOfElMax, maxElColRow);
                                maxVector(maxElColRow, size, rowOfElMax, maxElRow);
                                q = rowOfElMax[0];
                                p = colRowOfElMax[q];
                                if (Math.abs(D[p][q]) < tol * Math.sqrt(sumDiagElSq(diagD, size)) / size) {
                                    state = 0;
                                    }
                                    }    // V is the eigen vectors
                                    System.out.println("Jacobi Eigenvalues");
                                    for (int i = 0; i < size; i++) {
                                        for (int j = 0; j < size; j++) {
                                            System.out.print(diagD[i][j] + "\t"); 
                                            }
                                            System.out.println(" ");
                                            }
                                            }  

// finds the diagonal elements of A and puts them into B   *    * @param A   * @param n   * @return   
    public static double[][] diag(double A[][], int n) { 
        double[][] B = new double[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                B[i][j] = 0;
                }
                B[i][i] = A[i][i];
                }
                return B;
                }  /**   * C = A - B   *    * @param A   * @param B   * @param n   * @return C   */
                public static double[][] minus(double A[][], double B[][], int n) {
                    double[][] C = new double[n][n];
                    for (int i = 0; i < n; i++) {
                        for (int j = 0; j < n; j++) {
                            C[i][j] = A[i][j] - B[i][j];

                            }
                            } 
                            return C;
                            } 
/**   * Finds the absolute value of a matrix   *    * @param A   * @param B   * @param n   */ 
public static void abs(double A[][], double B[][], int n) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            B[i][j] = Math.abs(A[i][j]);

            }
            }
            }
/**   * finds the maximum elements of each column; returns the maximums in Max and   * their array positions in Row   *    * @param A   * @param n   * @param Row   * @param Max   */
public static void maxMatrix(double A[][], int n, int Row[], double Max[]) {
    for (int i = 0; i < n; i++) {
        int k = 0;
        Max[i] = A[k][i];
        Row[i] = k; 
        for (int j = 0; j < n; j++) {
            if (A[j][i] > Max[i]) { 
                Max[i] = A[j][i];
                Row[i] = j;  
                } 
                } 
                k = k + 1;
                } 
                }  /**   * finds the maximum elements of a column of A; returns the maximum of a   * column as Max and its array position as Row   *    * @param A   * @param n   * @param Row   * @param Max   */
                public static void maxVector(double A[], int n, int Row[], double Max[]) {
                    Max[0] = A[0];
                    Row[0] = 0;
                    for (int i = 0; i < n; i++) {
                        if (A[i] > Max[0]) {
                            Max[0] = A[i];
                            Row[0] = i; 
                            } 
                            } 
                            }
        /**   * finds the transpose of A and puts it into B   *    * @param A   * @param B   * @param n   */
        public static void transpose(double A[][], double B[][], int n) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    B[i][j] = A[j][i];
                    }
                    }
                    }
/**   * finds the sums of the squared of the diagonal elements of A   *    * @param A   * @param n   * @return   */
public static double sumDiagElSq(double A[][], int n) {
    double sum = 0;    for (int i = 0; i < n; i++) {
        sum = A[i][i] * A[i][i] + sum;
        //System.out.print(sum);
        } 
        return sum;
        }
        }

this program gives correct output for 22matrix only and afterward it gives wrong output for 33,44,55.....and so on. please help me to resolve the problem.if you are having something new code pls mentioned it for reference. thanks in adv.


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July 22, 2012 at 5:56 AM


This code is terrible. It is C converted to Java and has a number of potentially fatal flaws. Don't use it.



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