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LuDecomposition Class

LU decomposition of a rectangular matrix.
Inheritance Hierarchy

Namespace:  Accord.Math.Decompositions
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.6.0
public sealed class LuDecomposition : ICloneable, 
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The LuDecomposition type exposes the following members.

Public propertyDeterminant
Returns the determinant of the matrix.
Public propertyLogDeterminant
Returns the log-determinant of the matrix.
Public propertyLowerTriangularFactor
Returns the lower triangular factor L with A=LU.
Public propertyNonsingular
Returns if the matrix is non-singular (i.e. invertible). Please see remarks for important information regarding numerical stability when using this method.
Public propertyPivotPermutationVector
Returns the pivot permutation vector.
Public propertyUpperTriangularFactor
Returns the lower triangular factor L with A=LU.
Public methodClone
Creates a new object that is a copy of the current instance.
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetInformationMatrix
Computes (Xt * X)^1 (the inverse of the covariance matrix). This matrix can be used to determine standard errors for the coefficients when solving a linear set of equations through any of the Solve(Double) methods.
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodInverse
Solves a set of equation systems of type A * X = I.
Public methodReverse
Reverses the decomposition, reconstructing the original matrix X.
Public methodSolve(Double)
Solves a set of equation systems of type A * X = B.
Public methodSolve(Double)
Solves a set of equation systems of type A * X = B.
Public methodSolveTranspose
Solves a set of equation systems of type X * A = B.
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
Extension Methods
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodToT
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)

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 decomposition 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 Nonsingular returns .

See Also