LinearAlgebra[Modular]
LUApply
apply PLU Decomposition to a mod m Matrix or Vector
Calling Sequence
Parameters
Description
Examples
LUApply(m, A, pvec, B)
m
-
modulus
A
mod m Matrix (from LUDecomposition)
pvec
permutation vector (from LUDecomposition)
B
mod m Matrix or Vector representing right-hand side of problem
The LUApply function applies the permutation pvec and the forward and backward substitutions encoded in A directly to the right-hand side mod m Matrix or Vector B, where pvec and A are the output of the LUDecomposition function.
B must have the same number of rows as columns in A.
The function works directly on B, returning the solution in B on successful completion. If the function fails, B can be altered.
LUApply is simply the application of Permute, ForwardSubstitute, and then BackwardSubstitute.
This command is part of the LinearAlgebra[Modular] package, so it can be used in the form LUApply(..) only after executing the command with(LinearAlgebra[Modular]). However, it can always be used in the form LinearAlgebra[Modular][LUApply](..).
Compute LU decomposition of a random 5 x 5 Matrix, and use LUApply to obtain a solution.
Check the solution.
Use float[8] with a nontrivial permutation.
Now apply to a random vector and check it.
See Also
LinearAlgebra/Details
LinearAlgebra[Modular][BackwardSubstitute]
LinearAlgebra[Modular][Copy]
LinearAlgebra[Modular][ForwardSubstitute]
LinearAlgebra[Modular][LUDecomposition]
LinearAlgebra[Modular][Mod]
LinearAlgebra[Modular][Multiply]
LinearAlgebra[Modular][Permute]
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