Lu factorisation or Lu decomposit of Armadillo)

In the armadillo library, the Lu decomposition (LU factorisation or Lu decomposition) of the matrix uses the Lu function. The Lu function has two versions.

1 Lu (L, U, P, X)

X is the matrix to be decomposed to generate L, U, and P.

1) P is a permutation matrix, so the inverse of P is equal to its transpose (transpose)

2) L is a unit of lower Triangle Matrix (unit lower triangular matrix)

3) U is a strict upper triangular matrix)

4) Px = LU, that is, ptlu = x

Example:

mat m = "2,4,2;1,5,2;4,-1,9;";mat l, u, p;lu(l, u, p, m);cout << "L:" << endl;l.print();cout << "U:" << endl;u.print();cout << "P:" << endl;p.print();

Running result:

2 Lu (L, U, X)

X is the matrix to be decomposed to generate L, and u meets

1) U is a strict upper triangular matrix)

2) x = Lu

Due to the algorithm, the L generated by decomposition using this function is generally not of the lower triangle.

Example:

mat m = "2,4,2;1,5,2;4,-1,9;";mat l, u;lu(l, u, m);cout << "L:" << endl;l.print();cout << "U:" << endl;u.print();

Running result:

NOTE: If matrix X cannot be decomposed, the Lu function returns false and clears the L, U, and P matrices. Returns true if the decomposition is successful.