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Concept# Crout matrix decomposition

Summary

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:
:A = LDU
being L a unit lower triangular matrix, D a diagonal matrix and U a unit upper triangular matrix, then Doolittle's method produces
:A = L(DU)
and Crout's method produces
:A = (LD)U.
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;
```

Official source

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