NCAllPermutationLDU[aMatrix]

Aliases: None.

Description: $NCAllPermutationLDU[aMatrix]$ returns the LDU decomposition of a matrix for all possible permutations. The code cycles through all possible permutations and calls NCLDUDecomposition for each one.

Arguments: $aMatrix$ is a square matrix. The default options for NCAllPermutationLDU are: PermutationSelection $\rightarrow$ False, CheckDecomposition $\rightarrow$ False, NCSimplifyPivots $\rightarrow$ False, StopAutoPermutation $\rightarrow$ False, ReturnPermutation $\rightarrow$ False, Stop2by2Pivoting $\rightarrow$ False. All of these options have the same effect as in NCLDUDecomposition, except for PermutationSelection. PermutationSelection should be a list of numbers between 1 and the number of possible permutations. NCAllPermutationLDU will use this list to choose the permutations from its canonical list to decompose the matrix using NCLDUDecomposition. For example, PermutationSelection can be $\{1,\ldots,n\}$.

Comments / Limitations: The output is a list of all successful outputs from NCLDUDecomposition. Note that some permutations may lead to a zero pivot in the process of doing the LDU decomposition. In that case, the LDU decomposition is not well defined, actually in Mathematica one gets a lot of $\infty$ signs, but this output will not be included in the list of successful outputs.