/usr/include/libwildmagic/Wm5BandedMatrix.h is in libwildmagic-dev 5.13-1+b2.
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// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.0 (2010/01/01)
#ifndef WM5BANDEDMATRIX_H
#define WM5BANDEDMATRIX_H
#include "Wm5MathematicsLIB.h"
#include "Wm5Math.h"
#include "Wm5Memory.h"
namespace Wm5
{
template <typename Real>
class BandedMatrix
{
public:
// Construction and destruction.
BandedMatrix (int size, int numLBands, int numUBands);
BandedMatrix (const BandedMatrix& mat);
~BandedMatrix ();
// Assignment.
BandedMatrix& operator= (const BandedMatrix& mat);
// Member access.
int GetSize () const;
int GetNumLBands () const;
int GetNumUBands () const;
Real* GetDBand ();
const Real* GetDBand () const;
int GetLBandMax (int i) const; // LBand(i): 0 <= index < LBandMax
Real* GetLBand (int i);
const Real* GetLBand (int i) const;
int GetUBandMax (int i) const; // UBand(i): 0 <= index < UBandMax
Real* GetUBand (int i);
const Real* GetUBand (int i) const;
Real& operator() (int row, int column);
Real operator() (int row, int column) const;
// Convenience functions for initializing matrices.
void SetZero ();
void SetIdentity ();
// Factor the square banded matrix A into A = L*L^T, where L is a
// lower-triangular matrix (L^T is an upper-triangular matrix).
// This is an LU decomposition that allows for stable inversion
// of A to solve A*X = B. The return value is 'true' iff the
// factorizing is successful (L is invertible). If successful, A
// contains the Cholesky factorization (L in the lower-triangular part
// of A and/ L^T in the upper-triangular part of A).
bool CholeskyFactor ();
// Solve the linear system A*X = B, where A is an NxN banded matrix and
// B is an Nx1 vector. The unknown X is also Nx1. The input to this
// function is B. The output X is computed and stored in B. The return
// value is 'true' iff the system has a solution. The matrix A and the
// vector B are both modified by this function. If successful, A contains
// the Cholesky factorization (L in the lower-triangular part of A and
// L^T in the upper-triangular part of A).
bool SolveSystem (Real* bVector);
// Solve the linear system A*X = B, where A is an NxN banded matrix and
// B is an NxM matrix. The unknown X is also NxM. The input to this
// function is B. The output X is computed and stored in B. The return
// value is 'true' iff the system has a solution. The matrix A and the
// vector B are both modified by this function. If successful, A contains
// the Cholesky factorization (L in the lower-triangular part of A and
// L^T in the upper-triangular part of A).
bool SolveSystem (Real** bMatrix, int numBColumns);
private:
// The linear system is L*U*X = B, where A = L*U and U = L^T, Reduce this
// to U*X = L^{-1}*B. The return value is 'true' iff the operation is
// successful.
bool SolveLower (Real* dataVector) const;
// The linear system is U*X = L^{-1}*B. Reduce this to
// X = U^{-1}*L^{-1}*B. The return value is 'true' iff the operation is
// successful.
bool SolveUpper (Real* dataVector) const;
// The linear system is L*U*X = B, where A = L*U and U = L^T, Reduce this
// to U*X = L^{-1}*B. The return value is 'true' iff the operation is
// successful.
bool SolveLower (Real** dataMatrix, int numColumns) const;
// The linear system is U*X = L^{-1}*B. Reduce this to
// X = U^{-1}*L^{-1}*B. The return value is 'true' iff the operation is
// successful.
bool SolveUpper (Real** dataMatrix, int numColumns) const;
void Allocate ();
void Deallocate ();
int mSize, mNumLBands, mNumUBands;
Real* mDBand;
Real** mLBand;
Real** mUBand;
};
#include "Wm5BandedMatrix.inl"
typedef BandedMatrix<float> BandedMatrixf;
typedef BandedMatrix<double> BandedMatrixd;
}
#endif
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