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Symmetric matrix. More...
#include <MatrixSymmetric.h>
Public Types | |
typedef VectorGeneral< Treal, typename Tmatrix::VectorType > | VectorType |
typedef Treal | real |
Public Member Functions | |
MatrixSymmetric () | |
Default constructor. | |
MatrixSymmetric (const MatrixSymmetric< Treal, Tmatrix > &symm) | |
Copy constructor. | |
MatrixSymmetric (const XY< Treal, MatrixSymmetric< Treal, Tmatrix > > &sm) | |
MatrixSymmetric (const MatrixGeneral< Treal, Tmatrix > &matr) | |
'Copy from normal matrix' - constructor | |
void | assignFromFull (std::vector< Treal > const &fullMat) |
void | assignFromFull (std::vector< Treal > const &fullMat, std::vector< int > const &rowPermutation, std::vector< int > const &colPermutation) |
void | fullMatrix (std::vector< Treal > &fullMat) const |
Save matrix as full matrix. | |
void | fullMatrix (std::vector< Treal > &fullMat, std::vector< int > const &rowInversePermutation, std::vector< int > const &colInversePermutation) const |
Save matrix as full matrix. | |
void | assign_from_sparse (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values) |
Assign from sparse matrix given by three vectors. | |
void | assign_from_sparse (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values, SizesAndBlocks const &newRows, SizesAndBlocks const &newCols) |
Assign from sparse matrix given by three vectors. | |
void | assign_from_sparse (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values, std::vector< int > const &rowPermutation, std::vector< int > const &colPermutation) |
Same as above, except taking two additional arguments specifying the permutation of rows and columns. | |
void | assign_from_sparse (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values, SizesAndBlocks const &newRows, SizesAndBlocks const &newCols, std::vector< int > const &rowPermutation, std::vector< int > const &colPermutation) |
Same as above, except taking sizes and blocks arguments. | |
void | add_values (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values) |
Add given set of values to the matrix. | |
void | add_values (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values, std::vector< int > const &rowPermutation, std::vector< int > const &colPermutation) |
Same as above, except taking two additional arguments specifying the permutation of rows and columns. | |
void | get_values (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > &values) const |
Get values given by row and column index lists. | |
void | get_values (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > &values, std::vector< int > const &rowPermutation, std::vector< int > const &colPermutation) const |
Same as above, except taking two additional arguments specifying the permutation of rows and columns. | |
void | get_all_values (std::vector< int > &rowind, std::vector< int > &colind, std::vector< Treal > &values) const |
Get all values and corresponding row and column index lists, in matrix. | |
void | get_all_values (std::vector< int > &rowind, std::vector< int > &colind, std::vector< Treal > &values, std::vector< int > const &rowInversePermutation, std::vector< int > const &colInversePermutation) const |
Same as above, except taking two additional arguments specifying the permutation of rows and columns. | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const MatrixSymmetric< Treal, Tmatrix > &symm) |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const MatrixGeneral< Treal, Tmatrix > &matr) |
MatrixSymmetric< Treal, Tmatrix > & | operator= (int const k) |
Treal | frob () const |
Treal | mixed_norm (Treal const requestedAccuracy, int maxIter=-1) const |
Treal | eucl (Treal const requestedAccuracy, int maxIter=-1) const |
void | quickEuclBounds (Treal &euclLowerBound, Treal &euclUpperBound) const |
Treal | thresh (Treal const threshold, normType const norm) |
Does thresholding so that the error in the chosen norm is below the given threshold. | |
Treal | frob_thresh (Treal const threshold) |
Does thresholding so that the error in the Frobenius norm is below the given threshold. | |
Treal | eucl_thresh (Treal const threshold, MatrixTriangular< Treal, Tmatrix > const *const Zptr=NULL) |
Treal | eucl_element_level_thresh (Treal const threshold) |
void | getSizesAndBlocksForFrobNormMat (SizesAndBlocks &rows_new, SizesAndBlocks &cols_new) const |
Treal | mixed_norm_thresh (Treal const threshold) |
void | simple_blockwise_frob_thresh (Treal const threshold) |
void | gershgorin (Treal &lmin, Treal &lmax) const |
size_t | nnz () const |
size_t | nvalues () const |
void | write_to_buffer (void *buffer, const int n_bytes) const |
void | read_from_buffer (void *buffer, const int n_bytes) |
MatrixSymmetric< Treal, Tmatrix > & | operator= (XY< Treal, MatrixSymmetric< Treal, Tmatrix > > const &sm) |
B = alpha * A : A and B are symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const XYZpUV< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix >, Treal, MatrixSymmetric< Treal, Tmatrix > > &sm2psm) |
C = alpha * A * A + beta * C : A and C are symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const XYZ< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > &sm2) |
C = alpha * A * A : A and C are symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator+= (const XYZ< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > &sm2) |
C += alpha * A * A : A and C are symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const XYZpUV< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix >, Treal, MatrixSymmetric< Treal, Tmatrix > > &smmpsm) |
C = alpha * A * transpose(A) + beta * C : C is symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const XYZ< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix > > &smm) |
C = alpha * A * transpose(A) : C is symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator+= (const XYZ< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix > > &smm) |
C += alpha * A * transpose(A) : C is symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const XYZ< MatrixTriangular< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix >, MatrixTriangular< Treal, Tmatrix > > &zaz) |
A = Z * A * transpose(Z) : Z is upper triangular and A is symmetric; A = transpose(Z) * A * Z : Z is upper triangular and A is symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (XpY< MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > const &mpm) |
C = A + B : A, B, and C are symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (XmY< MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > const &mm) |
C = A - B : A, B, and C are symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator+= (MatrixSymmetric< Treal, Tmatrix > const &A) |
B += A : A and B are symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator-= (MatrixSymmetric< Treal, Tmatrix > const &A) |
B -= A : A and B are symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator+= (XY< Treal, MatrixSymmetric< Treal, Tmatrix > > const &sm) |
B += alpha * A : A and B are symmetric. | |
MatrixSymmetric< Treal, Tmatrix > & | operator-= (XY< Treal, MatrixSymmetric< Treal, Tmatrix > > const &sm) |
B -= alpha * A : A and B are symmetric. | |
template<typename Top> | |
Treal | accumulateWith (Top &op) |
void | random () |
void | randomZeroStructure (Treal probabilityBeingZero) |
template<typename TRule> | |
void | setElementsByRule (TRule &rule) |
Uses rule depending on the row and column indexes to set matrix elements The Trule class should have the function "Treal = set(int row,int col)" which is used to set the elements. | |
void | transfer (MatrixSymmetric< Treal, Tmatrix > &dest) |
Transfer this matrix to dest, clearing previous content of dest if any. | |
template<typename Tvector> | |
void | matVecProd (Tvector &y, Tvector const &x) const |
std::string | obj_type_id () const |
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void | resetSizesAndBlocks (SizesAndBlocks const &newRows, SizesAndBlocks const &newCols) |
void | getRows (SizesAndBlocks &rowsCopy) const |
void | getCols (SizesAndBlocks &colsCopy) const |
bool | is_empty () const |
Check if matrix is empty. | |
Treal | trace () const |
void | add_identity (Treal alpha) |
MatrixBase< Treal, Tmatrix > & | operator*= (Treal const alpha) |
bool | operator== (int k) const |
void | clear () |
Release memory for the information written to file. | |
size_t | memory_usage () const |
void | write_to_buffer_count (int &n_bytes) const |
int | get_nrows () const |
int | get_ncols () const |
Tmatrix const & | getMatrix () const |
Tmatrix & | getMatrix () |
Treal | maxAbsValue () const |
Get largest absolute value of matrix element in the matrix. | |
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void | writeToFile () |
Write object to file if filewrite is active. | |
void | readFromFile () |
Read object from file if filewrite is active. | |
void | copyToFile (const char *destFileName) |
void | copyFromFile (const char *sourceFileName) |
bool | isOnFile () |
Check if object is on file. | |
long int | fileSize () |
Return file size. | |
Static Public Member Functions | |
static Interval< Treal > | diff (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, normType const norm, Treal const requestedAccuracy) |
Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 ) | |
static Interval< Treal > | diffIfSmall (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, normType const norm, Treal const requestedAccuracy, Treal const maxAbsVal) |
Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 ) based on the chosen norm. | |
static Treal | frob_diff (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B) |
Returns the Frobenius norm of A - B ( || A - B ||_F ) | |
static Treal | eucl_diff (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, Treal const requestedAccuracy, int maxIter=-1) |
Returns the Euclidean norm of A - B ( || A - B ||_2 ) | |
static Treal | mixed_diff (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, Treal const requestedAccuracy) |
Returns the 'mixed' norm of A - B ( || A - B ||_mixed ) | |
static Interval< Treal > | euclDiffIfSmall (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, Treal const requestedAccuracy, Treal const maxAbsVal, VectorType *const eVecPtr=0) |
Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 ). | |
static Treal | trace_ab (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B) |
static void | ssmmUpperTriangleOnly (const Treal alpha, const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, const Treal beta, MatrixSymmetric< Treal, Tmatrix > &C) |
C = alpha * A * B + beta * C where A and B are symmetric and only the upper triangle of C is computed, C is enforced to be symmetric! | |
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static void | setPath (char const *const newPath) |
Set the path to which the objects will be written. | |
static void | activate () |
Activate the filewriting. | |
static std::string | getStatsFileSizes () |
static std::string | writeAndReadAll () |
static void | resetStats () |
static std::string | getStatsTimeWrite () |
static std::string | getStatsTimeRead () |
static std::string | getStatsTimeCopyAndAssign () |
static std::string | getStatsCountWrite () |
static std::string | getStatsCountRead () |
static std::string | getStatsCountCopyAndAssign () |
Protected Member Functions | |
void | writeToFileProt (std::ofstream &file) const |
Write object to file. | |
void | readFromFileProt (std::ifstream &file) |
Read object from file. | |
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MatrixBase () | |
MatrixBase (const MatrixBase< Treal, Tmatrix > &other) | |
MatrixBase< Treal, Tmatrix > & | operator= (const MatrixBase< Treal, Tmatrix > &other) |
MatrixBase< Treal, Tmatrix > & | operator= (const Xtrans< MatrixGeneral< Treal, Tmatrix > > &mt) |
void | write_to_buffer_base (void *buffer, const int n_bytes, const matrix_type mattype) const |
void | read_from_buffer_base (void *buffer, const int n_bytes, const matrix_type mattype) |
void | writeToFileBase (std::ofstream &file, matrix_type const mattype) const |
void | readFromFileBase (std::ifstream &file, matrix_type const mattype) |
void | inMemorySet (bool inMem) |
Make object invalid (false) via this function when object is written to file and valid (true) when object is read from file. | |
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FileWritable () | |
Gives each object a unique ID-number and filename. | |
virtual | ~FileWritable () |
Removes file, if any. | |
FileWritable (FileWritable const &) | |
FileWritable & | operator= (FileWritable const &) |
Static Protected Member Functions | |
static void | getPermutedAndSymmetrized (std::vector< int > const &rowind, std::vector< int > const &rowPermutation, std::vector< int > &newRowind, std::vector< int > const &colind, std::vector< int > const &colPermutation, std::vector< int > &newColind) |
This function permutes row and column indices according to the specified permutation and gives the indices as upper triangle in the new permutation. | |
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static void | getPermutedIndexes (std::vector< int > const &index, std::vector< int > const &permutation, std::vector< int > &newIndex) |
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static std::string | getStatsTime (TypeTimeMap &theMap) |
static std::string | getStatsCount (TypeCountMap &theMap) |
static std::string | getStatsFileSizes (ObjPtrSet const &set) |
Additional Inherited Members | |
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typedef std::map< std::string, double > | TypeTimeMap |
typedef std::map< std::string, int > | TypeCountMap |
typedef std::set< FileWritable * > | ObjPtrSet |
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ValidPtr< Tmatrix > | matrixPtr |
Symmetric matrix.
This class belongs to the matrix API
The matrix is stored in the upper triangle.
Treal: Type for real numbers
Tmatrix: The matrix class
typedef Treal mat::MatrixSymmetric< Treal, Tmatrix >::real |
typedef VectorGeneral<Treal, typename Tmatrix::VectorType> mat::MatrixSymmetric< Treal, Tmatrix >::VectorType |
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Default constructor.
Referenced by diff(), diffIfSmall(), eucl(), eucl_diff(), euclDiffIfSmall(), mixed_diff(), mixed_norm(), mixed_norm_thresh(), operator+=(), operator+=(), operator+=(), operator+=(), operator-=(), operator-=(), operator=(), operator=(), operator=(), operator=(), operator=(), operator=(), operator=(), operator=(), and ssmmUpperTriangleOnly().
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Copy constructor.
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'Copy from normal matrix' - constructor
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Add given set of values to the matrix.
The values should be given in upper triangular storage.
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Same as above, except taking two additional arguments specifying the permutation of rows and columns.
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Assign from sparse matrix given by three vectors.
The vectors contain row indices, column indices and values. The indices start at zero. The elements to be added must be given in upper triangluar storage. Information about sizes and blocks for rows as well as columns must also be given. Assumes that sizes and blocks are already set.
Referenced by mat::MatrixSymmetric< real, matri >::assign_from_sparse(), mat::MatrixSymmetric< real, matri >::assignFromFull(), main(), mainFun(), test1(), test2(), test3(), and test4().
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Assign from sparse matrix given by three vectors.
The vectors contain row indices, column indices and values. The indices start at zero. The elements to be added must be given in upper triangluar storage. Information about sizes and blocks for rows as well as columns must also be given.
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Same as above, except taking sizes and blocks arguments.
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Same as above, except taking two additional arguments specifying the permutation of rows and columns.
Also, assuming that sizes and blocks are already set.
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Referenced by mainFun().
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Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 )
References A, B, diff(), eucl_diff(), mat::euclNorm, frob_diff(), mat::frobNorm, MatrixSymmetric(), and template_blas_sqrt().
Referenced by diff(), and diffIfSmall().
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Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 ) based on the chosen norm.
BUT, in the case of Euclidean norm, the norm is only computed with the requested accuracy if it is smaller than 'maxAbsVal'.
References A, B, diff(), euclDiffIfSmall(), mat::euclNorm, frob_diff(), mat::frobNorm, MatrixSymmetric(), and template_blas_sqrt().
Treal mat::MatrixSymmetric< Treal, Tmatrix >::eucl | ( | Treal const | requestedAccuracy, |
int | maxIter = -1 ) const |
References cols, frob(), frob_thresh(), mat::MatrixBase< Treal, Tmatrix >::get_nrows(), mat::MatrixBase< Treal, Tmatrix >::getCols(), mat::arn::LanczosLargestMagnitudeEig< Treal, Tmatrix, Tvector >::getLargestMagnitudeEig(), MatrixSymmetric(), mat::VectorGeneral< Treal, Tvector >::rand(), mat::VectorGeneral< Treal, Tvector >::resetSizesAndBlocks(), and template_blas_fabs().
Referenced by mainFun(), mixed_diff(), mixed_norm(), and MatAccInvestigator< Treal, Tworker >::Scan().
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Returns the Euclidean norm of A - B ( || A - B ||_2 )
References A, B, mat::euclIfSmall(), frob_diff(), mat::getMachineEpsilon(), MatrixSymmetric(), mat::Interval< Treal >::midPoint(), and template_blas_sqrt().
Referenced by diff().
Treal mat::MatrixSymmetric< Treal, Tmatrix >::eucl_element_level_thresh | ( | Treal const | threshold | ) |
Treal mat::MatrixSymmetric< Treal, Tmatrix >::eucl_thresh | ( | Treal const | threshold, |
MatrixTriangular< Treal, Tmatrix > const *const | Zptr = NULL ) |
References mat::EuclTruncationBase< Tmatrix, Treal >::run().
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Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 ).
BUT, the norm is only computed with the requested accuracy if it is smaller than 'maxAbsVal'. Otherwise, the Frobenius norm is used to get the bounds.
References A, B, mat::euclIfSmall(), mat::getMachineEpsilon(), mat::Interval< Treal >::length(), MatrixSymmetric(), mat::Interval< Treal >::midPoint(), and template_blas_sqrt().
Referenced by diffIfSmall().
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Returns the Frobenius norm of A - B ( || A - B ||_F )
Referenced by diff(), diffIfSmall(), and eucl_diff().
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Save matrix as full matrix.
Whole matrix is written in columnwise order. Both lower and upper triangle. NOTE that no permutation is used in this operation.
Referenced by mainFun().
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Save matrix as full matrix.
Whole matrix is written in columnwise order. Both lower and upper triangle. Permutation is used.
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Referenced by mainFun().
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Get all values and corresponding row and column index lists, in matrix.
Only upper triangle values are returned.
Referenced by mat::MatrixSymmetric< real, matri >::fullMatrix(), and mainFun().
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Same as above, except taking two additional arguments specifying the permutation of rows and columns.
Note, however, that this permutation is the inverse permutation compared to the permutations provided in the functions "assign_from_sparse", "add_values", and "get_values"
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Get values given by row and column index lists.
Input arrays contain row and column indices. The wanted elements must be given in upper triangluar storage. The output array contains values for the given indices.
Referenced by mainFun().
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Same as above, except taking two additional arguments specifying the permutation of rows and columns.
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This function permutes row and column indices according to the specified permutation and gives the indices as upper triangle in the new permutation.
Referenced by mat::MatrixSymmetric< real, matri >::add_values(), mat::MatrixSymmetric< real, matri >::assign_from_sparse(), mat::MatrixSymmetric< real, matri >::get_all_values(), and mat::MatrixSymmetric< real, matri >::get_values().
void mat::MatrixSymmetric< Treal, Tmatrix >::getSizesAndBlocksForFrobNormMat | ( | SizesAndBlocks & | rows_new, |
SizesAndBlocks & | cols_new ) const |
References cols, mat::MatrixBase< Treal, Tmatrix >::getCols(), mat::MatrixBase< Treal, Tmatrix >::getRows(), and rows.
Referenced by mixed_norm(), and mixed_norm_thresh().
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Returns the 'mixed' norm of A - B ( || A - B ||_mixed )
References A, B, eucl(), mat::MatrixBase< Treal, Tmatrix >::getMatrix(), MatrixSymmetric(), and mat::MatrixBase< Treal, Tmatrix >::resetSizesAndBlocks().
Treal mat::MatrixSymmetric< Treal, Tmatrix >::mixed_norm | ( | Treal const | requestedAccuracy, |
int | maxIter = -1 ) const |
Treal mat::MatrixSymmetric< Treal, Tmatrix >::mixed_norm_thresh | ( | Treal const | threshold | ) |
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Referenced by mat::MatrixSymmetric< real, matri >::get_all_values(), and main().
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Reimplemented from mat::MatrixBase< Treal, Tmatrix >.
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator+= | ( | const XYZ< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix > > & | smm | ) |
C += alpha * A * transpose(A) : C is symmetric.
References MatrixSymmetric().
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator+= | ( | const XYZ< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > & | sm2 | ) |
C += alpha * A * A : A and C are symmetric.
References MatrixSymmetric().
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B += A : A and B are symmetric.
References A, and MatrixSymmetric().
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B += alpha * A : A and B are symmetric.
References MatrixSymmetric().
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B -= A : A and B are symmetric.
References A, and MatrixSymmetric().
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B -= alpha * A : A and B are symmetric.
References MatrixSymmetric().
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MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator= | ( | const XYZ< MatrixTriangular< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix >, MatrixTriangular< Treal, Tmatrix > > & | zaz | ) |
A = Z * A * transpose(Z) : Z is upper triangular and A is symmetric; A = transpose(Z) * A * Z : Z is upper triangular and A is symmetric.
References MatrixSymmetric().
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator= | ( | const XYZ< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix > > & | smm | ) |
C = alpha * A * transpose(A) : C is symmetric.
References MatrixSymmetric().
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator= | ( | const XYZ< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > & | sm2 | ) |
C = alpha * A * A : A and C are symmetric.
References mat::MatrixBase< Treal, Tmatrix >::matrixPtr, and MatrixSymmetric().
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator= | ( | const XYZpUV< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix >, Treal, MatrixSymmetric< Treal, Tmatrix > > & | smmpsm | ) |
C = alpha * A * transpose(A) + beta * C : C is symmetric.
References MatrixSymmetric().
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator= | ( | const XYZpUV< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix >, Treal, MatrixSymmetric< Treal, Tmatrix > > & | sm2psm | ) |
C = alpha * A * A + beta * C : A and C are symmetric.
References MatrixSymmetric().
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C = A - B : A, B, and C are symmetric.
References MatrixSymmetric().
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C = A + B : A, B, and C are symmetric.
References MatrixSymmetric().
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B = alpha * A : A and B are symmetric.
References mat::MatrixBase< Treal, Tmatrix >::matrixPtr, and MatrixSymmetric().
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Referenced by mainFun().
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Uses rule depending on the row and column indexes to set matrix elements The Trule class should have the function "Treal = set(int row,int col)" which is used to set the elements.
Referenced by mainFun().
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C = alpha * A * B + beta * C where A and B are symmetric and only the upper triangle of C is computed, C is enforced to be symmetric!
References A, B, mat::MatrixBase< Treal, Tmatrix >::matrixPtr, and MatrixSymmetric().
Treal mat::MatrixSymmetric< Treal, Tmatrix >::thresh | ( | Treal const | threshold, |
normType const | norm ) |
Does thresholding so that the error in the chosen norm is below the given threshold.
Returns the actual introduced error. In case of the Frobenius norm the return value may be an upper bound. In case of the Euclidean norm the return value is sometimes an upper bound as well but it can only happen if the whole matrix is removed.
References eucl_thresh(), mat::euclNorm, frob_thresh(), mat::frobNorm, mixed_norm_thresh(), and mat::mixedNorm.
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Transfer this matrix to dest, clearing previous content of dest if any.
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