# LUDecomposition D¶

LUDecomposition contains procedures to solve linear systems of equations or to compute inverses using a LU decomposition.

LUDecomp: Matrix D -> Record(LU: Matrix D, Perm: Vector Integer, Pivots: List D)
LUDecomp(A) computes a LU decomposition of A using the algorithm of Crout. LU contains both triangular matrices; Perm is the permutation used for partial pivoting and Pivots yields the used pivots.
LUInverse: Matrix D -> Record(Inv: Matrix D, Pivots: List D)
LUInverse(A) computes the inverse of A using a LU decomposition.
LUSolve: (Matrix D, Vector Integer, Vector D) -> Vector D
LUSolve(LU, Perm, B) uses a previously computed LU decomposition to solve a linear system with right hand side B. LU and Perm are as given by LUDecomp.