TNT::Linear_Algebra::LU< Real > Class Template Reference

#include <tnt_linalg.h>

Public Member Functions
	LU (const Matrix< Real > &A)
int	isNonsingular ()
Matrix< Real >	getL ()
Matrix< Real >	getU ()
Vector< int >	getPivot ()
Real	det ()
Matrix< Real >	solve (const Matrix< Real > &B)
Vector< Real >	solve (const Vector< Real > &b)

---

Detailed Description

template<class Real>
class TNT::Linear_Algebra::LU< Real >

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.

---

Constructor & Destructor Documentation

template<class Real >

TNT::Linear_Algebra::LU< Real >::LU

(

const Matrix< Real > &

A

)

[inline]

LU Decomposition

Parameters:

A

Rectangular matrix

Returns:

LU Decomposition object to access L, U and piv.

---

Member Function Documentation

template<class Real >

Real TNT::Linear_Algebra::LU< Real >::det

(

)

[inline]

Compute determinant using LU factors.

Returns:

determinant of A, or 0 if A is not square.

template<class Real >

Matrix<Real> TNT::Linear_Algebra::LU< Real >::getL

(

)

[inline]

Return lower triangular factor

Returns:

L

template<class Real >

Vector<int> TNT::Linear_Algebra::LU< Real >::getPivot

(

)

[inline]

Return pivot permutation vector

Returns:

piv

template<class Real >

Matrix<Real> TNT::Linear_Algebra::LU< Real >::getU

(

)

[inline]

Return upper triangular factor

Returns:

U portion of LU factorization.

template<class Real >

int TNT::Linear_Algebra::LU< Real >::isNonsingular

(

)

[inline]

Is the matrix nonsingular?

Returns:

1 (true) if upper triangular factor U (and hence A) is nonsingular, 0 otherwise.

template<class Real >

Vector<Real> TNT::Linear_Algebra::LU< Real >::solve

(

const Vector< Real > &

b

)

[inline]

Solve A*x = b, where x and b are vectors of length equal to the number of rows in A.

Parameters:

b

a vector (Vector> of length equal to the first dimension of A.

Returns:

x a vector (Vector> so that L*U*x = b(piv), if B is nonconformant, returns Real(0.0) (null) array.

template<class Real >

Matrix<Real> TNT::Linear_Algebra::LU< Real >::solve

(

const Matrix< Real > &

B

)

[inline]

Solve A*X = B

Parameters:

B

A Matrix with as many rows as A and any number of columns.

Returns:

X so that L*U*X = B(piv,:), if B is nonconformant, returns Real(0.0) (null) array.

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The documentation for this class was generated from the following file:

• tnt/tnt_linalg.h