Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.
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.
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...
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.