LUDecomposition {Microsoft.VisualBasic.Math.LinearAlgebra.Matrix}

.NET clr documentation

LUDecomposition

Description

LU Decomposition. For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. ' If m < n, then L is m-by-m and U is m-by-n. ' The LU decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if IsNonSingular() returns false.

Declare

            
# namespace Microsoft.VisualBasic.Math.LinearAlgebra.Matrix
export class LUDecomposition extends Decomposition {
   # Return pivot permutation vector as a one-dimensional double array
   DoublePivot: double;
   # Is the matrix nonsingular?
   IsNonSingular: boolean;
   # Return lower triangular factor
   L: GeneralMatrix;
   # Return pivot permutation vector
   Pivot: integer;
   # Return upper triangular factor
   U: GeneralMatrix;
}

        

.NET clr type reference tree

1. this class extends from Decomposition class: Decomposition
2. use by property member L: GeneralMatrix
3. use by property member U: GeneralMatrix

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