LinearAlgebra.h

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#ifndef _LINEAR_ALGEBRA_H_
#define _LINEAR_ALGEBRA_H_

// ****************************************************************************
// Forward declarations
// ****************************************************************************

class CFloatMatrix;
class CFloatVector;
class CDoubleMatrix;
class CDoubleVector;
struct Mat3d;
struct Vec2d;



// ****************************************************************************
// LinearAlgebra
// ****************************************************************************

namespace LinearAlgebra
{
        // operating on CFloatMatrix and CFloatVector
        void Zero(CFloatMatrix *pMatrix);
        void Zero(CFloatVector *pVector);
        
        void SelfProduct(const CFloatMatrix *pMatrix, CFloatMatrix *pResultMatrix, bool AAT = false);
        void MulMatMat(const CFloatMatrix *A, const CFloatMatrix *B, CFloatMatrix *pResultMatrix, bool bTransposeB = false);
        void Transpose(const CFloatMatrix *pMatrix, CFloatMatrix *pResultMatrix);

        void MulMatVec(const CFloatMatrix *pMatrix, const CFloatVector *pVector, CFloatVector *pResultVector);
        void MulMatVec(const CFloatMatrix *pMatrix, const CFloatVector *pVector1, const CFloatVector *pVector2, CFloatVector *pResultVector);

        void AddMatMat(const CFloatMatrix *pMatrix1, const CFloatMatrix *pMatrix2, CFloatMatrix *pResultMatrix);
        void SubtractMatMat(const CFloatMatrix *pMatrix1, const CFloatMatrix *pMatrix2, CFloatMatrix *pResultMatrix);
        void AddVecVec(const CFloatVector *pVector1, const CFloatVector *pVector2, CFloatVector *pResultVector);
        void SubtractVecVec(const CFloatVector *pVector1, const CFloatVector *pVector2, CFloatVector *pResultVector);
        
        void AddToMat(CFloatMatrix *pMatrix, const CFloatMatrix *pMatrixToAdd);
        void SubtractFromMat(CFloatMatrix *pMatrix, const CFloatMatrix *pMatrixToSubtract);
        void AddToVec(CFloatVector *pVector, const CFloatVector *pVectorToAdd);
        void SubtractFromVec(CFloatVector *pVector, const CFloatVector *pVectorToSubtract);
        
        void SubtractMeanFromColumns(const CFloatMatrix *pMatrix, CFloatMatrix *pResultMatrix);
        void SubtractMeanFromRows(const CFloatMatrix *pMatrix, CFloatMatrix *pResultMatrix);

        extern void SVD(const CFloatMatrix *A, CFloatMatrix *W, CFloatMatrix *U = 0, CFloatMatrix *V = 0,
                bool bAllowModifyA = false, bool bReturnUTransposed = false, bool bReturnVTransposed = false);

        // linear least squares
        bool SolveLinearLeastSquaresSimple(const CFloatMatrix *A, const CFloatVector *b, CFloatVector *x);
        void SolveLinearLeastSquaresSVD(const CFloatMatrix *A, const CFloatVector *b, CFloatVector *x);
        void SolveLinearLeastSquaresHomogeneousSVD(const CFloatMatrix *A, CFloatVector *x);
                
        // calculation of pseudoinverse
        void CalculatePseudoInverseSVD(const CFloatMatrix *pInputMatrix, CFloatMatrix *pOutputMatrix);
        bool CalculatePseudoInverseSimple(const CFloatMatrix *pInputMatrix, CFloatMatrix *pResultMatrix);

        // calculation of inverse
        bool Invert(const CFloatMatrix *pInputMatrix, CFloatMatrix *pResultMatrix);

        // PCA
        void PCA(const CFloatMatrix *pData, CFloatMatrix *pTransformationMatrix, CFloatMatrix *pTransformedData, int nTargetDimension);
        void PCA(const CFloatMatrix *pData, CFloatMatrix *pTransformationMatrix, CFloatMatrix *pEigenValues);


        // operating on CDoubleMatrix and CDoubleVector
        void Zero(CDoubleMatrix *pMatrix);
        void Zero(CDoubleVector *pVector);
        
        void SelfProduct(const CDoubleMatrix *pMatrix, CDoubleMatrix *pResultMatrix, bool AAT = false);
        void MulMatMat(const CDoubleMatrix *pMatrix1, const CDoubleMatrix *pMatrix2, CDoubleMatrix *pResultMatrix, bool bTransposeB = false);
        void Transpose(const CDoubleMatrix *pMatrix, CDoubleMatrix *pResultMatrix);

        void MulMatVec(const CDoubleMatrix *pMatrix, const CDoubleVector *pVector, CDoubleVector *pResultVector);
        void MulMatVec(const CDoubleMatrix *pMatrix, const CDoubleVector *pVector1, const CDoubleVector *pVector2, CDoubleVector *pResultVector);

        void AddMatMat(const CDoubleMatrix *pMatrix1, const CDoubleMatrix *pMatrix2, CDoubleMatrix *pResultMatrix);
        void SubtractMatMat(const CDoubleMatrix *pMatrix1, const CDoubleMatrix *pMatrix2, CDoubleMatrix *pResultMatrix);
        void AddVecVec(const CDoubleVector *pVector1, const CDoubleVector *pVector2, CDoubleVector *pResultVector);
        void SubtractVecVec(const CDoubleVector *pVector1, const CDoubleVector *pVector2, CDoubleVector *pResultVector);
        
        void AddToMat(CDoubleMatrix *pMatrix, const CDoubleMatrix *pMatrixToAdd);
        void SubtractFromMat(CDoubleMatrix *pMatrix, const CDoubleMatrix *pMatrixToSubtract);
        void AddToVec(CDoubleVector *pVector, const CDoubleVector *pVectorToAdd);
        void SubtractFromVec(CDoubleVector *pVector, const CDoubleVector *pVectorToSubtract);
        
        void SubtractMeanFromColumns(const CDoubleMatrix *pMatrix, CDoubleMatrix *pResultMatrix);
        void SubtractMeanFromRows(const CDoubleMatrix *pMatrix, CDoubleMatrix *pResultMatrix);

        extern void SVD(const CDoubleMatrix *A, CDoubleMatrix *W, CDoubleMatrix *U = 0, CDoubleMatrix *V = 0,
                bool bAllowModifyA = false, bool bReturnUTransposed = false, bool bReturnVTransposed = false);

        // linear least squares
        bool SolveLinearLeastSquaresSimple(const CDoubleMatrix *A, const CDoubleVector *b, CDoubleVector *x);
        void SolveLinearLeastSquaresSVD(const CDoubleMatrix *A, const CDoubleVector *b, CDoubleVector *x);
        void SolveLinearLeastSquaresHomogeneousSVD(const CDoubleMatrix *A, CDoubleVector *x);
                
        // calculation of pseudoinverse
        void CalculatePseudoInverseSVD(const CDoubleMatrix *pInputMatrix, CDoubleMatrix *pOutputMatrix);
        bool CalculatePseudoInverseSimple(const CDoubleMatrix *pInputMatrix, CDoubleMatrix *pResultMatrix);

        // calculation of inverse
        bool Invert(const CDoubleMatrix *pInputMatrix, CDoubleMatrix *pResultMatrix);



        // 2d homographies

        bool DetermineAffineTransformation(const Vec2d *pSourcePoints, const Vec2d *pTargetPoints, int nPoints, Mat3d &A, bool bUseSVD = false);

        bool DetermineHomography(const Vec2d *pSourcePoints, const Vec2d *pTargetPoints, int nPoints, Mat3d &A, bool bUseSVD = false);
}



#endif /* _LINEAR_ALGEBRA_H_ */