cholesky decomposition time complexity code example

Example 1: cholesky decomposition

for (j = 0; j < dimensionSize; j++) {
    float sum = 0;
    for (k = 0; k < j; k++) {
        sum += L[j][k] * L[j][k];
    }
    L[j][j] = sqrt(A[j][j] - sum);

    for (i = j + 1; i < dimensionSize; i++) {
        sum = 0;
        for (k = 0; k < j; k++) {
            sum += L[i][k] * L[j][k];
        }
        L[i][j] = (1.0 / L[j][j] * (A[i][j] - sum));
    }
}

Example 2: cholesky decomposition

for (i = 0; i < dimensionSize; i++) {
    for (j = 0; j < (i + 1); j++) {
        float sum = 0;
        for (k = 0; k < j; k++)
            sum += L[i][k] * L[j][k];

        if (i == j)
            L[i][j] = sqrt(A[i][i] - sum);
        else
            L[i][j] = (1.0 / L[j][j] * (A[i][j] - sum));
    }
}