dfullsymmatrix_functions.h

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#ifndef DFULLSYMMATRIX_FUNCTIONS
#define DFULLSYMMATRIX_FUNCTIONS

#include "lapack_functions.h"

 void DoubleFullSymmetricMatrixVectorProduct(const tLVectorIndex& nX,
                                             const tLVectorIncrement& incX,
                                             const double* x,
                                             const tLVectorIndex& nRows,//number of viewed rows of symmetric A
                                             const tLVectorIndex& ldA,//memory distance between A[i][j] and A[i][j+1] 
                                             const double* A,
                                             const lapack_real& alpha,
                                             const lapack_real& beta,
                                             const tLVectorIndex& nY,
                                             const tLVectorIncrement& incY,
                                             double* y);

void DoubleFullSymmetricMatrixMatrixProduct(const tBoolean& isLeftSide,
                                            const tLVectorIndex& nRowsA,
                                            const tLVectorIndex& ldA,
                                            const double* A,
                                            const tLVectorIndex& nRowsB,
                                            const tLVectorIndex& nColsB,
                                            const tLVectorIndex& ldB,
                                            const tBoolean& isBSymmetric,
                                            const double* B,
                                            const lapack_real& alpha,
                                            const lapack_real& beta,
                                            const tLVectorIndex& nRowsC,
                                            const tLVectorIndex& nColsC,
                                            const tLVectorIndex& ldC,
                                            double *C);




void DoubleFullSymmetricMatrixRankSymmetricProduct(const tLVectorIncrement& incX,
                                                   const double *X,
                                                   const double& alpha,
                                                   const tLVectorIndex& nS,
                                                   const tLVectorIndex& ldS,
                                                   double *S);

void DoubleFullSymmetricMatrixKRankSymmetricProduct(const tLVectorIndex& nRowAs,
                                                    const tLVectorIndex& nColsA,
                                                    const tLVectorIncrement& incA,
                                                    const tLVectorIndex& ldA,
                                                    const tBoolean& isTransA,
                                                    const double *A,
                                                    const double& alpha,
                                                    const double& beta,
                                                    const tLVectorIndex& nD,
                                                    const tLVectorIncrement& incD,
                                                    const double* D,
                                                    const tLVectorIndex& nS,
                                                    const tLVectorIncrement& incS,
                                                    const tLVectorIndex& ldS,
                                                    double *S);


//eigen decomposition
//=====================
tBoolean DoubleFullSymmetricMatrixEigenValues(const tLVectorIndex& nRowsA,
                                             const tLVectorIndex& nColsA,
                                             const tLVectorIndex& ldA,
                                             double* A,
                                             const tLVectorIndex& nU,
                                             double* U,
                                             const tBoolean& areEigenVectorComputed);



tBoolean DoubleFullSymmetricMatrixBoundedEigenValues(const tLVectorIndex& nRowsA,
                                                    const tLVectorIndex& nColsA,
                                                    const tLVectorIndex& ldA,
                                                    double* A,
                                                    const tLVectorIndex& nU,//of size M=N  or M=iu-il+1
                                                    double* U,
                                                    const tBoolean& areEigenVectorComputed,
                                                    const tLVectorIndex& minIndex,
                                                    const tLVectorIndex& maxIndex,
                                                    const double& minBound,
                                                    const double& maxBound,
                                                    const tLVectorIndex& ldZ,//Z of size nRows  x M
                                                    double *Z);

/* \brief  build the cholesky factorization A:= tU U
 * A is an Upper matrix U
 */
tBoolean DoubleFullSymmetricMatrixCholeskyFactorization(const tLVectorIndex& nRowsA,
                                                       const tLVectorIndex& ldA,
                                                       double* A);

/* \brief  build the cholesky factorization A:= U . D . tU
 * A is an Upper matrix U
 */
tBoolean DoubleFullSymmetricMatrixBunchKaufmanFactorization(const tLVectorIndex& nRows,
                                                            const tLVectorIndex& ldA,
                                                            double *A,
                                                            lapack_int *ipiv);


/* \brief compute the inverse of the full symmetric matrix 
 * A is an Upper matrix U
 */
tBoolean DoubleFullSymmetricMatrixInverse(const tLVectorIndex& nRows,
                                          const tLVectorIndex& ldA,
                                          double *A,
                                          const lapack_int *ipiv);
    
#endif