LUApply - Maple Help
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LinearAlgebra[Modular]

  

LUApply

  

apply PLU Decomposition to a mod m Matrix or Vector

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

LUApply(m, A, pvec, B)

Parameters

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

Description

• 

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](..).

Examples

Compute LU decomposition of a random 5 x 5 Matrix, and use LUApply to obtain a solution.

(1)

(2)

(3)

(4)

(5)

Check the solution.

(6)

Use float[8] with a nontrivial permutation.

(7)

(8)

Now apply to a random vector and check it.

(9)

(10)

(11)

See Also

LinearAlgebra/Details

LinearAlgebra[Modular]

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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