高斯消元法

高斯消元法

原理（CMU - PSP）：

1. I = 1

2. LET P=A[K] , I = max { |A[J, I]| , I <= J <= N}

3. IF P = 0 THEN EXIT

4. IF K > I THEN FOR J = I TO N + 1, SWAP A[I, J] AND A[K, J]

5. 5.a FOR J = I + 1 TO N + 1 LET A[I, J] = A[I, J] / A[I, I]

    5.b SET A[I, I]  = 1

6. FOR L = I + 1 to N, multiply row I by -A[L, I]   and add to row L

7. I = I + 1. IF I < N THEN GO TO 2

8. EXIT to back-substitution

/*cb*/public class GaussElimination {private double[][] matrix;/*mb*/public double[] gaussElimination(double[][] m) {this.matrix = m;final int N = matrix.length;final double[] ret = new double[N];int i = 0;int j = 0;int k;while(i < N - 1) {k = findMax(matrix, i);if(k > i) {for(j = i; j < N + 1; j ++) {swap(i, j, k);}}for(j = i + 1; j < N + 1; j ++) {matrix[i][j] /= matrix[i][i];}matrix[i][i] = 1.0;for(int l = i + 1; l < N; l ++) {double factor = -matrix[l][i];for(int c = 0; c < matrix[0].length; c ++) {matrix[l][c] += matrix[i][c] * factor;}}i ++;} for(int s = N - 1; s >= 0; s --) {if(s == N - 1) {ret[s] = matrix[s][matrix[s].length - 1] / matrix[s][matrix[s].length - 2];} else {ret[s] = matrix[s][matrix[s].length - 1];int t = matrix[s].length - 2;for(; t > s; t --) {ret[s] -= ret[t] * matrix[s][t];}ret[s] /= matrix[s][t];}}return ret;}/*me*//*mb*/private int findMax(double[][] matrix, int position) {int index = 0;double max = 0.0;for(int i = position; i < matrix.length; i ++) {if(Math.abs(matrix[i][position]) > max) {max = matrix[i][position];index = i;}}return index;}/*me*//*mb*/private void swap(int i, int j, int k) {double temp = matrix[i][j];matrix[i][j] = matrix[k][j];matrix[k][j] = temp;}/*me*/}/*ce*/