java实现cholesky分解求逆

以下是Java实现Cholesky分解求逆的代码：

public class CholeskyInverse {

    public static void main(String[] args) {
        double[][] A = {{4, 2, 2}, {2, 5, 4}, {2, 4, 11}}; //待求逆矩阵
        double[][] AInv = choleskyInverse(A); //调用choleskyInverse方法求逆矩阵
        printMatrix(AInv); //输出逆矩阵
    }

    public static double[][] choleskyInverse(double[][] A) {
        int n = A.length;
        double[][] L = choleskyDecomposition(A);
        double[][] LInv = inverseLowerTriangle(L);
        double[][] AInv = multiply(transpose(LInv), LInv);
        return AInv;
    }

    public static double[][] choleskyDecomposition(double[][] A) {
        int n = A.length;
        double[][] L = new double[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < (i + 1); j++) {
                double s = 0;
                for (int k = 0; k < j; k++) {
                    s += L[i][k] * L[j][k];
                }
                if (i == j) {
                    L[i][j] = Math.sqrt(A[i][i] - s);
                } else {
                    L[i][j] = (1.0 / L[j][j] * (A[i][j] - s));
                }
            }
        }
        return L;
    }

    public static double[][] inverseLowerTriangle(double[][] L) {
        int n = L.length;
        double[][] LInv = new double[n][n];
        for (int i = 0; i < n; i++) {
            LInv[i][i] = 1.0 / L[i][i];
            for (int j = 0; j < i; j++) {
                double s = 0;
                for (int k = j; k < i; k++) {
                    s += L[i][k] * LInv[k][j];
                }
                LInv[i][j] = -1.0 / L[i][i] * s;
            }
        }
        return LInv;
    }

    public static double[][] multiply(double[][] A, double[][] B) {
        int m = A.length;
        int n = B[0].length;
        double[][] C = new double[m][n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                for (int k = 0; k < B.length; k++) {
                    C[i][j] += A[i][k] * B[k][j];
                }
            }
        }
        return C;
    }

    public static double[][] transpose(double[][] A) {
        int m = A.length;
        int n = A[0].length;
        double[][] B = new double[n][m];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                B[j][i] = A[i][j];
            }
        }
        return B;
    }

    public static void printMatrix(double[][] A) {
        int m = A.length;
        int n = A[0].length;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                System.out.print(A[i][j] + "\t");
            }
            System.out.println();
        }
    }
}

在这个代码中，我们首先定义了一个待求逆矩阵A，然后调用choleskyInverse方法求解逆矩阵。在choleskyInverse方法中，我们先调用choleskyDecomposition方法求解A的Cholesky分解，然后调用inverseLowerTriangle方法求解下三角矩阵L的逆矩阵，最后调用multiply方法计算L的转置与L的乘积，得到A的逆矩阵。最后，我们输出A的逆矩阵，以验证结果是否正确。