package series; /* This Program is taken from the following site (without permission) solely for the experimentation of cost analysis of practial java programs http://www.physics.unlv.edu/~pang/cp2_j.html */ /////////////////////////////////////////////////////////////////////////// // // // Program file name: Inverse.java // // // // Tao Pang 2006 // // // // Last modified: January 18, 2006 // // // // (1) This Java program is part of the book, "An Introduction to // // Computational Physics, 2nd Edition," written by Tao Pang and // // published by Cambridge University Press on January 19, 2006. // // // // (2) No warranties, express or implied, are made for this program. // // // /////////////////////////////////////////////////////////////////////////// // An example of performing matrix inversion through the // partial-pivoting Gaussian elimination. import java.lang.*; public class Inverse { public static void main(String argv[]) { double a[][]= {{ 100, 100, 100}, {-100, 300, -100}, {-100, -100, 300}}; int n = a.length; double d[][] = invert(a); for (int i=0; i<n; ++i) for (int j=0; j<n; ++j) System.out.println(d[i][j]); } public static double[][] invert(double a[][]) { int n = a.length; double x[][] = new double[n][n]; double b[][] = new double[n][n]; int index[] = new int[n]; for (int i=0; i<n; ++i) b[i][i] = 1; // Transform the matrix into an upper triangle gaussian(a, index); // Update the matrix b[i][j] with the ratios stored for (int i=0; i<n-1; ++i) for (int j=i+1; j<n; ++j) for (int k=0; k<n; ++k) b[index[j]][k] -= a[index[j]][i]*b[index[i]][k]; // Perform backward substitutions for (int i=0; i<n; ++i) { x[n-1][i] = b[index[n-1]][i]/a[index[n-1]][n-1]; for (int j=n-2; j>=0; --j) { x[j][i] = b[index[j]][i]; for (int k=j+1; k<n; ++k) { x[j][i] -= a[index[j]][k]*x[k][i]; } x[j][i] /= a[index[j]][j]; } } return x; } // Method to carry out the partial-pivoting Gaussian // elimination. Here index[] stores pivoting order. public static void gaussian(double a[][], int index[]) { int n = index.length; double c[] = new double[n]; // Initialize the index for (int i=0; i<n; ++i) index[i] = i; // Find the rescaling factors, one from each row for (int i=0; i<n; ++i) { double c1 = 0; for (int j=0; j<n; ++j) { double c0 = Math.abs(a[i][j]); if (c0 > c1) c1 = c0; } c[i] = c1; } // Search the pivoting element from each column int k = 0; for (int j=0; j<n-1; ++j) { double pi1 = 0; for (int i=j; i<n; ++i) { double pi0 = Math.abs(a[index[i]][j]); pi0 /= c[index[i]]; if (pi0 > pi1) { pi1 = pi0; k = i; } } // Interchange rows according to the pivoting order int itmp = index[j]; index[j] = index[k]; index[k] = itmp; for (int i=j+1; i<n; ++i) { double pj = a[index[i]][j]/a[index[j]][j]; // Record pivoting ratios below the diagonal a[index[i]][j] = pj; // Modify other elements accordingly for (int l=j+1; l<n; ++l) a[index[i]][l] -= pj*a[index[j]][l]; } } } }