An n x n matrix (i.e., a vector of length n*n), stored row-wise: that is, A(i,j) = A[ij], where ij = i*n + j. More...

#include </home/werner/origo/vish/ocean/eagle/QuadraticMatrix.hpp>

Public Types

typedef Matrix< N, N, Value > Base_t
typedef FixedArray< int, N > PermutationVector_t
Type of the permutation vector that is required for the functions GaussDecompose() and GaussSolve().
typedef Value value_type

Public Member Functions

bool GaussDecompose (FixedArray< int, N > &perm, double EPSWEIGHT=1E-3)
Perform gauss decomposition of the matrix, which can and should be used instead of computing the inverse of a matrix.
void GaussSolve (const PermutationVector_t &perm, const Column< N, value > &b, Column< N, value > &x) const
Instead of inverting a matrix, solve a linear system of equations by forward and backward elimination.
value maxoffd () const
Return maximum off-diagonal element of n by n square matrix A.
template<class OutputValue > Quadratic< N, OutputValue > operator() (const Quadratic< N, OutputValue > &A) const
template<class OutputValue > LowerTriangular< N, OutputValue > operator() (const LowerTriangular< N, OutputValue > &A) const
Quadratic & operator= (const LowerTriangular< N, value > &)
Quadratic ()
Default constructor.
Quadratic (const Matrix< N, N, value > &A)
Construct quadratic matrix from base class.
template<int C, class ValueA , class ValueB > Quadratic (const Matrix< N, C, ValueA > &A, const Matrix< C, N, ValueB > &B)
Construct quadratic matrix from multiplication for two fitting non-quadratic matrices.
Quadratic (Quadratic &, const TransposeOperation &)
Quadratic (const LowerTriangular< N, value > &)
Construct a quadratic matrix from a lower triangular matrix.

Detailed Description

An n x n matrix (i.e., a vector of length n*n), stored row-wise: that is, A(i,j) = A[ij], where ij = i*n + j.

See also:: Matrix

Examples:: Matrix.cpp.

Member Function Documentation

bool Eagle::Quadratic::GaussDecompose	(	FixedArray< int, N > &	perm,
		double	EPSWEIGHT = `1E-3`
	)		`[inline]`

Perform gauss decomposition of the matrix, which can and should be used instead of computing the inverse of a matrix.

The permutation operations during the composition is stored in the perm parameter, which then needs to be provided to the GaussSolve() routine.

Author:: Marcus Weber, ZIB, based on "Formelsammlung zur Numerischen Mathematik mit C-Programmen" von G.Engeln-Maellges und F.Reutter"

Note:: The original matrix is destroyed during this operation.

Parameters:

EPSWEIGHT square root of the absolut precision of the computation

void Eagle::Quadratic::GaussSolve	(	const PermutationVector_t &	perm,
		const Column< N, value > &	b,
		Column< N, value > &	x
	)		const `[inline]`

Instead of inverting a matrix, solve a linear system of equations $ Ax = b $ by forward and backward elimination.

Parameters:

perm	A permutation vector as computed by GaussDecompose()
b	The right-hand side of the equation
x	On return, will contain the solution.

        Eagle::Quadratic<3, double> A;
        Eagle::Column<3, double> b;
        Eagle::Column<3, double> x;
        Eagle::FixedArray<int, 3> perm;

        A = 2.5,  3.0, 1.1,
            0.2,  0.1, 2.1,
            0.12, 1.0, 0.3;

        b = 39.0, 1.0, 34.33;

        A.GaussDecompose(perm);
        A.GaussSolve(perm, b, x);

The result in x then is < 16.809817, -24.730900, 16.013638 >.

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

ocean/eagle/QuadraticMatrix.hpp