Crout matrix decomposition

In linear algebra, the Crout matrix decomposition is an LU decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and, although not always needed, a permutation matrix (P). It was developed by Prescott Durand Crout. 
The Crout matrix decomposition algorithm differs slightly from the Doolittle method. Doolittle's method returns a unit lower triangular matrix and an upper triangular matrix, while the Crout method returns a lower triangular matrix and a unit upper triangular matrix.
So, if a matrix decomposition of a matrix A is such that:
being L a unit lower triangular matrix, D a diagonal matrix and U a unit upper triangular matrix, then Doolittle's method produces
and Crout's method produces
Implementations.
C implementation:
void crout(double const **A, double **L, double **U, int n) {
 int i, j, k;
 double sum = 0;
 for (i = 0; i < n; i++) {
 U[i][i] = 1;
 for (j = 0; j < n; j++) {
 for (i = j; i < n; i++) {
 sum = 0;
 for (k = 0; k < j; k++) {
 sum = sum + L[i][k] * U[k][j]; 
 L[i][j] = A[i][j] - sum;
 for (i = j; i < n; i++) {
 sum = 0;
 for(k = 0; k < j; k++) {
 sum = sum + L[j][k] * U[k][i];
 if (L[j][j] == 0) {
 printf("det(L) close to 0!\n Can't divide by 0...\n");
 exit(EXIT_FAILURE);
 U[j][i] = (A[j][i] - sum) / L[j][j];
Octave/Matlab implementation:
 function [L, U] = LUdecompCrout(A)
 [R, C] = size(A);
 for i = 1:R
 L(i, 1) = A(i, 1);
 U(i, i) = 1;
 end
 for j = 2:R
 U(1, j) = A(1, j) / L(1, 1);
 end
 for i = 2:R
 for j = 2:i
 L(i, j) = A(i, j) - L(i, 1:j - 1) * U(1:j - 1, j);
 end
 for j = i + 1:R
 U(i, j) = (A(i, j) - L(i, 1:i - 1) * U(1:i - 1, j)) / L(i, i);
 end
 end
 end