I need help with writing a generic implementation of Gaussian Elimination in Jav
ID: 3828839 • Letter: I
Question
I need help with writing a generic implementation of Gaussian Elimination in Java. I have the implementation done normally, but I do not know how to make it to where it is uses Java Generics and not is not type-specific (not using ints or doubles but instead uses a generic class). Please help. Below is the normal implementation:
public class GaussianElimination {
private static final double EPSILON = 1e-10;
// Gaussian elimination with partial pivoting
public static double[] lsolve(double[][] A, double[] b) {
int n = b.length;
for (int p = 0; p < n; p++) {
// find pivot row and swap
int max = p;
for (int i = p + 1; i < n; i++) {
if (Math.abs(A[i][p]) > Math.abs(A[max][p])) {
max = i;
}
}
double[] temp = A[p]; A[p] = A[max]; A[max] = temp;
double t = b[p]; b[p] = b[max]; b[max] = t;
// singular or nearly singular
if (Math.abs(A[p][p]) <= EPSILON) {
throw new ArithmeticException("Matrix is singular or nearly singular");
}
// pivot within A and b
for (int i = p + 1; i < n; i++) {
double alpha = A[i][p] / A[p][p];
b[i] -= alpha * b[p];
for (int j = p; j < n; j++) {
A[i][j] -= alpha * A[p][j];
}
}
}
// back substitution
double[] x = new double[n];
for (int i = n - 1; i >= 0; i--) {
double sum = 0.0;
for (int j = i + 1; j < n; j++) {
sum += A[i][j] * x[j];
}
x[i] = (b[i] - sum) / A[i][i];
}
return x;
}
// sample client
public static void main(String[] args) {
int n = 3;
double[][] A = {
{ 0, 1, 1 },
{ 2, 4, -2 },
{ 0, 3, 15 }
};
double[] b = { 4, 2, 36 };
double[] x = lsolve(A, b);
// print results
for (int i = 0; i < n; i++) {
StdOut.println(x[i]);
}
}
}
Explanation / Answer
public class GaussianElimination {
private static final double EPSILON = 1e-10;
// Gaussian elimination with partial pivoting
public static double[] lsolve(double[][] A, double[] b) {
int n = b.length;
for (int p = 0; p < n; p++) {
// find pivot row and swap
int max = p;
for (int i = p + 1; i < n; i++) {
if (Math.abs(A[i][p]) > Math.abs(A[max][p])) {
max = i;
}
}
double[] temp = A[p]; A[p] = A[max]; A[max] = temp;
double t = b[p]; b[p] = b[max]; b[max] = t;
// singular or nearly singular
if (Math.abs(A[p][p]) <= EPSILON) {
throw new ArithmeticException("Matrix is singular or nearly singular");
}
// pivot within A and b
for (int i = p + 1; i < n; i++) {
double alpha = A[i][p] / A[p][p];
b[i] -= alpha * b[p];
for (int j = p; j < n; j++) {
A[i][j] -= alpha * A[p][j];
}
}
}
// back substitution
double[] x = new double[n];
for (int i = n - 1; i >= 0; i--) {
double sum = 0.0;
for (int j = i + 1; j < n; j++) {
sum += A[i][j] * x[j];
}
x[i] = (b[i] - sum) / A[i][i];
}
return x;
}
// sample client
public static void main(String[] args) {
int n = 3;
double[][] A = {
{ 0, 1, 1 },
{ 2, 4, -2 },
{ 0, 3, 15 }
};
double[] b = { 4, 2, 36 };
double[] x = lsolve(A, b);
// print results
for (int i = 0; i < n; i++) {
StdOut.println(x[i]);
}
}
}