To handle symmetric matrices in skyline storage format. More...


Public Member Functions | |
SkSMatrix () | |
Default constructor. More... | |
SkSMatrix (size_t size, int is_diagonal=false) | |
Constructor that initializes a dense symmetric matrix. More... | |
SkSMatrix (class Mesh &mesh, size_t dof=0, int is_diagonal=false) | |
Constructor using mesh to initialize skyline structure of matrix. More... | |
SkSMatrix (const Vect< size_t > &ColHt) | |
Constructor that initializes skyline structure of matrix using vector of column height. More... | |
SkSMatrix (const Vect< size_t > &I, const Vect< size_t > &J, int opt=1) | |
Constructor for a square matrix using non zero row and column indices. More... | |
SkSMatrix (const Vect< size_t > &I, const Vect< size_t > &J, const Vect< T_ > &a, int opt=1) | |
Constructor for a square matrix using non zero row and column indices. More... | |
SkSMatrix (const SkSMatrix< T_ > &m) | |
Copy Constructor. | |
~SkSMatrix () | |
Destructor. | |
void | setMesh (class Mesh &mesh, size_t dof=0) |
Determine mesh graph and initialize matrix. More... | |
void | setSkyline (class Mesh &mesh) |
Determine matrix structure. More... | |
void | setDiag () |
Store diagonal entries in a separate internal vector. | |
void | set (size_t i, size_t j, const T_ &val) |
Assign a value to an entry ofthe matrix. More... | |
void | Axpy (T_ a, const SkSMatrix< T_ > &m) |
Add to matrix the product of a matrix by a scalar. More... | |
void | Axpy (T_ a, const Matrix< T_ > *m) |
Add to matrix the product of a matrix by a scalar. More... | |
void | MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const |
Multiply matrix by vector x and add to y . More... | |
void | MultAdd (T_ a, const Vect< T_ > &x, Vect< T_ > &y) const |
Multiply matrix by vector a*x and add to y . More... | |
void | Mult (const Vect< T_ > &x, Vect< T_ > &y) const |
Multiply matrix by vector x and save in y More... | |
void | TMult (const Vect< T_ > &x, Vect< T_ > &y) const |
Multiply transpose of matrix by vector x and save in y. More... | |
void | add (size_t i, size_t j, const T_ &val) |
Add a constant to an entry of the matrix. More... | |
size_t | getColHeight (size_t i) const |
Return column height. More... | |
Vect< T_ > | getColumn (size_t j) const |
Get j -th column vector. | |
Vect< T_ > | getRow (size_t i) const |
Get i -th row vector. | |
T_ & | operator() (size_t i, size_t j) |
Operator () (Non constant version). More... | |
T_ | operator() (size_t i, size_t j) const |
Operator () (Constant version). More... | |
SkSMatrix< T_ > & | operator= (const SkSMatrix< T_ > &m) |
Operator =. More... | |
SkSMatrix< T_ > & | operator= (const T_ &x) |
Operator =. More... | |
SkSMatrix< T_ > & | operator+= (const SkSMatrix< T_ > &m) |
Operator +=. More... | |
SkSMatrix< T_ > & | operator*= (const T_ &x) |
Operator *=. More... | |
int | Factor () |
Factorize matrix (LDLt factorization). More... | |
int | Solve (Vect< T_ > &b) |
Solve system with factorized matrix (forward and back substitution). More... | |
int | Solve (const Vect< T_ > &b, Vect< T_ > &x) |
Solve system with factorized matrix (forward and back substitution). More... | |
T_ * | get () const |
Return C-Array. More... | |
void | set (size_t i, T_ x) |
Assign a value to the i-th entry of C-array containing matrix. | |
T_ | get (size_t i, size_t j) const |
Return entry (i,j) of matrix if this one is stored, 0 else. | |
size_t | getNbRows () const |
Return number of rows. | |
size_t | getNbColumns () const |
Return number of columns. | |
void | setPenal (real_t p) |
Set Penalty Parameter (For boundary condition prescription). | |
void | setDiagonal () |
Set the matrix as diagonal. | |
void | setDiagonal (const class Mesh &mesh) |
Initialize matrix storage in the case where only diagonal terms are stored. More... | |
T_ | getDiag (size_t k) const |
Return k -th diagonal entry of matrix. More... | |
size_t | size () const |
Return matrix dimension (Number of rows and columns). | |
void | Assembly (const class Element *el, T_ *a) |
Assembly of element matrix into global matrix. More... | |
void | Assembly (const class Element *el, const DMatrix< T_ > &a) |
Assembly of element matrix into global matrix. More... | |
void | Assembly (const class Side *sd, T_ *a) |
Assembly of side matrix into global matrix. More... | |
void | Assembly (const class Side *sd, const DMatrix< T_ > &a) |
Assembly of side matrix into global matrix. More... | |
void | Prescribe (const class Mesh &mesh, Vect< T_ > &b, const Vect< T_ > &u, int flag=0) |
Impose by a penalty method an essential boundary condition. More... | |
void | Prescribe (int dof, int code, const class Mesh &mesh, Vect< T_ > &b, const Vect< T_ > &u, int flag=0) |
Impose by a penalty method an essential boundary condition to a given degree of freedom for a given code. More... | |
void | Prescribe (Vect< T_ > &b, const Vect< T_ > &u, int flag=0) |
Impose by a penalty method an essential boundary condition, using the Mesh instance provided by the constructor. More... | |
void | Prescribe (const class Mesh &mesh, Vect< T_ > &b, int flag=0) |
Impose by a penalty method a homegeneous (=0) essential boundary condition. More... | |
void | Prescribe (Vect< T_ > &b, int flag=0) |
Impose by a penalty method a homegeneous (=0 ) essential boundary condition, using the Mesh instance provided by the constructor. More... | |
void | Prescribe (size_t dof, const class Mesh &mesh, Vect< T_ > &b, const Vect< T_ > &u, int flag=0) |
Impose by a penalty method an essential boundary condition when only one DOF is treated. More... | |
void | Prescribe (size_t dof, Vect< T_ > &b, const Vect< T_ > &u, int flag=0) |
Impose by a penalty method an essential boundary condition when only one DOF is treated. More... | |
void | PrescribeSide (const class Mesh &mesh) |
Impose by a penalty method an essential boundary condition when DOFs are supported by sides. More... | |
void | PrescribeSide () |
Impose by a penalty method an essential boundary condition when DOFs are supported by sides. More... | |
int | FactorAndSolve (Vect< T_ > &b) |
Factorize matrix and solve the linear system. More... | |
int | FactorAndSolve (const Vect< T_ > &b, Vect< T_ > &x) |
Factorize matrix and solve the linear system. More... | |
unsigned long | getLength () const |
Return number of stored terms in matrix. | |
int | isDiagonal () const |
Say if matrix is diagonal or not. | |
int | isFactorized () const |
Say if matrix is factorized or not. More... | |
virtual size_t | getColInd (size_t i) const |
Return Column index for column i (See the description for class SpMatrix). | |
virtual size_t | getRowPtr (size_t i) const |
Return Row pointer for row i (See the description for class SpMatrix). | |
T_ | operator() (size_t i) const |
Operator () with one argument (Constant version). More... | |
T_ & | operator() (size_t i) |
Operator () with one argument (Non Constant version). More... | |
T_ & | operator[] (size_t k) |
Operator [] (Non constant version). More... | |
T_ | operator[] (size_t k) const |
Operator [] (Constant version). More... | |
Matrix & | operator+= (const Matrix< T_ > &m) |
Operator +=. More... | |
Matrix & | operator+= (const T_ &x) |
Operator +=. More... | |
Matrix & | operator-= (const Matrix< T_ > &m) |
Operator -=. More... | |
Matrix & | operator-= (const T_ &x) |
Operator -=. More... | |
void | setPrintView (size_t rmin, size_t rmax, size_t cmin, size_t cmax) |
Set a window for matrix printing. More... | |
void | getPrintView (size_t &rmin, size_t &rmax, size_t &cmin, size_t &cmax) const |
Return window data for matrix printing. More... | |
Detailed Description
template<class T_>
class OFELI::SkSMatrix< T_ >
To handle symmetric matrices in skyline storage format.
This template class allows storing and manipulating a symmetric matrix in skyline storage format.
The matrix entries are stored column by column as in the following example:
/ \ | a0 a1 0 0 a7 | | a2 a3 0 a8 | | ... a4 a5 a9 | | a6 a10 | | a11 | \ /
- Template Parameters
-
<T_> Data type (double, float, complex<double>, ...)
Constructor & Destructor Documentation
SkSMatrix | ( | ) |
Default constructor.
Initializes a zero-dimension matrix
SkSMatrix | ( | size_t | size, |
int | is_diagonal = false |
||
) |
Constructor that initializes a dense symmetric matrix.
Normally, for a dense matrix this is not the right class.
- Parameters
-
[in] size Number of matrix rows (and columns). [in] is_diagonal Boolean to select if the matrix is diagonal or not [Default: false]
Constructor using mesh to initialize skyline structure of matrix.
- Parameters
-
[in] mesh Mesh instance for which matrix graph is determined. [in] dof Option parameter, with default value 0
.
dof=1
means that only one degree of freedom for each node (or element or side) is taken to determine matrix structure. The valuedof=0
means that matrix structure is determined using all DOFs.[in] is_diagonal Boolean argument to say is the matrix is actually a diagonal matrix or not.
Constructor that initializes skyline structure of matrix using vector of column height.
- Parameters
-
[in] ColHt Vect instance that contains rows lengths of matrix.
Constructor for a square matrix using non zero row and column indices.
- Parameters
-
[in] I Vector containing row indices [in] J Vector containing column indices [in] opt Flag indicating if vectors I and J are cleaned and ordered (opt=1) or not (opt=0).
In the latter case, these vectors can contain the same contents more than once and are not necessarily ordered.
Constructor for a square matrix using non zero row and column indices.
- Parameters
-
[in] I Vector containing row indices [in] J Vector containing column indices [in] a Vector containing matrix entries in the same order than the one given by I
andJ
[in] opt Flag indicating if vectors I
andJ
are cleaned and ordered (opt=1
) or not (opt=0
).
In the latter case, these vectors can contain the same contents more than once and are not necessarily ordered
Member Function Documentation
void setMesh | ( | class Mesh & | mesh, |
size_t | dof = 0 |
||
) |
Determine mesh graph and initialize matrix.
This member function is called by constructor with the same arguments
- Parameters
-
[in] mesh Mesh instance for which matrix graph is determined. [in] dof Option parameter, with default value 0
.
dof=1
means that only one degree of freedom for each node (or element or side) is taken to determine matrix structure. The valuedof=0
means that matrix structure is determined using all DOFs.
void setSkyline | ( | class Mesh & | mesh | ) |
Determine matrix structure.
This member function calculates matrix structure using Mesh instance mesh
.
|
virtual |
Assign a value to an entry ofthe matrix.
- Parameters
-
[in] i Row index [in] j Column index [in] val Value to assign to a(i,j)
Implements Matrix< T_ >.
void Axpy | ( | T_ | a, |
const SkSMatrix< T_ > & | m | ||
) |
Add to matrix the product of a matrix by a scalar.
- Parameters
-
[in] a Scalar to premultiply [in] m Matrix by which a
is multiplied. The result is added to current instance
|
virtual |
Add to matrix the product of a matrix by a scalar.
- Parameters
-
[in] a Scalar to premultiply [in] m Pointer to Matrix by which a
is multiplied. The result is added to current instance
Implements Matrix< T_ >.
Multiply matrix by vector x
and add to y
.
- Parameters
-
[in] x Vector to multiply by matrix [in,out] y Vector to add to the result. y
contains on output the result.
Implements Matrix< T_ >.
Multiply matrix by vector a*x
and add to y
.
- Parameters
-
[in] a Constant to multiply by matrix [in] x Vector to multiply by matrix [in,out] y Vector to add to the result. y
contains on output the result.
Implements Matrix< T_ >.
Multiply matrix by vector x
and save in y
- Parameters
-
[in] x Vector to multiply by matrix [out] y Vector that contains on output the result.
Implements Matrix< T_ >.
Multiply transpose of matrix by vector x and save in y.
- Parameters
-
[in] x Vector to multiply by matrix [out] y Vector that contains on output the result.
Implements Matrix< T_ >.
|
virtual |
Add a constant to an entry of the matrix.
- Parameters
-
[in] i Row index [in] j Column index [in] val Constant value to add to a(i,j)
Implements Matrix< T_ >.
size_t getColHeight | ( | size_t | i | ) | const |
Return column height.
Column height at entry i
is returned.
|
virtual |
Operator () (Non constant version).
- Parameters
-
[in] i Row index [in] j Column index
Implements Matrix< T_ >.
|
virtual |
Operator () (Constant version).
- Parameters
-
[in] i Row index [in] j Column index
Implements Matrix< T_ >.
Operator =.
Copy matrix m
to current matrix instance.
SkSMatrix< T_ > & operator= | ( | const T_ & | x | ) |
Operator =.
Assign constant value x
to all matrix entries.
Operator +=.
Add matrix m
to current matrix instance.
SkSMatrix< T_ > & operator*= | ( | const T_ & | x | ) |
Operator *=.
Premultiply matrix entries by constant value x
.
|
virtual |
Factorize matrix (LDLt factorization).
- Returns
0
if factorization was normally performed,
n
if then
-th pivot is null.
Implements Matrix< T_ >.
|
virtual |
Solve system with factorized matrix (forward and back substitution).
- Parameters
-
[in,out] b Vect instance that contains right-hand side on input and solution on output.
- Returns
0
, if solution was normally performed,n
if then
-th pivot is null. Solution is performed only is factorization has previouly been invoked.
Implements Matrix< T_ >.
Solve system with factorized matrix (forward and back substitution).
- Parameters
-
[in] b Vect instance that contains right-hand side [out] x Vect instance that contains solution
- Returns
0
if solution was normally performed,n
if then
-th pivot is null. Solution is performed only is factorization has previouly been invoked.
T_* get | ( | ) | const |
Return C-Array.
Skyline of matrix is stored row by row.
|
inherited |
Initialize matrix storage in the case where only diagonal terms are stored.
This member function is to be used for explicit time integration schemes
|
inherited |
Return k
-th diagonal entry of matrix.
First entry is given by getDiag(1).
|
inherited |
Assembly of element matrix into global matrix.
Case where element matrix is given by a C-array.
- Parameters
-
[in] el Pointer to element instance [in] a Element matrix as a C-array
|
inherited |
Assembly of side matrix into global matrix.
Case where side matrix is given by a C-array.
- Parameters
-
[in] sd Pointer to side instance [in] a Side matrix as a C-array instance
|
inherited |
Impose by a penalty method an essential boundary condition.
This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).
- Parameters
-
[in] mesh Mesh instance from which information is extracted. [in,out] b Vect instance that contains right-hand side. [in] u Vect instance that contains imposed valued at DOFs where they are to be imposed. [in] flag Parameter to determine whether only the right-hand side is to be modified
(dof>0
) or both matrix and right-hand side (dof=0
, default value).
|
inherited |
Impose by a penalty method an essential boundary condition to a given degree of freedom for a given code.
This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).
- Parameters
-
[in] dof Degree of freedom for which a boundary condition is to be enforced [in] code Code for which a boundary condition is to be enforced [in] mesh Mesh instance from which information is extracted. [in,out] b Vect instance that contains right-hand side. [in] u Vect instance that contains imposed valued at DOFs where they are to be imposed. [in] flag Parameter to determine whether only the right-hand side is to be modified
(dof>0
) or both matrix and right-hand side (dof=0
, default value).
Impose by a penalty method an essential boundary condition, using the Mesh instance provided by the constructor.
This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).
Impose by a penalty method a homegeneous (=0) essential boundary condition.
This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).
|
inherited |
Impose by a penalty method a homegeneous (=0
) essential boundary condition, using the Mesh instance provided by the constructor.
This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).
- Parameters
-
[in,out] b Vect instance that contains right-hand side. [in] flag Parameter to determine whether only the right-hand side is to be modified ( dof>0
)
or both matrix and right-hand side (dof=0
, default value).
|
inherited |
Impose by a penalty method an essential boundary condition when only one DOF is treated.
This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. This gunction is to be used if only one DOF per node is treated in the linear system. The penalty parameter is by default equal to 1.e20. It can be modified by member function setPenal.
- Parameters
-
[in] dof Label of the concerned degree of freedom (DOF). [in] mesh Mesh instance from which information is extracted. [in,out] b Vect instance that contains right-hand side. [in] u Vect instance that conatins imposed valued at DOFs where they are to be imposed. [in] flag Parameter to determine whether only the right-hand side is to be modified ( dof>0
)
or both matrix and right-hand side (dof=0
, default value).
Impose by a penalty method an essential boundary condition when only one DOF is treated.
This member function uses the Mesh instance provided by the constructor.
It modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. This gunction is to be used if only one DOF per node is treated in the linear system. The penalty parameter is by default equal to 1.e20. It can be modified by member function setPenal.
- Parameters
-
[in] dof Label of the concerned degree of freedom (DOF). [in,out] b Vect instance that contains right-hand side. [in] u Vect instance that conatins imposed valued at DOFs where they are to be imposed. [in] flag Parameter to determine whether only the right-hand side is to be modified ( dof>0
)
or both matrix and right-hand side (dof=0
, default value).
|
inherited |
Impose by a penalty method an essential boundary condition when DOFs are supported by sides.
This member function uses the Mesh instance provided by the constructor
It modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).
|
inherited |
Impose by a penalty method an essential boundary condition when DOFs are supported by sides.
This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).
|
inherited |
Factorize matrix and solve the linear system.
This is available only if the storage class enables it.
- Parameters
-
[in,out] b Vect instance that contains right-hand side on input and solution on output
|
inherited |
Say if matrix is factorized or not.
If the matrix was not factorized, the class does not allow solving by a direct solver.
|
inherited |
Operator () with one argument (Constant version).
Returns i
-th position in the array storing matrix entries. The first entry is at location 1. Entries are stored row by row.
- Parameters
-
[in] i entry index
|
inherited |
Operator () with one argument (Non Constant version).
Returns i
-th position in the array storing matrix entries. The first entry is at location 1. Entries are stored row by row.
- Parameters
-
[in] i entry index
|
inherited |
Operator [] (Non constant version).
Returns k
-th stored element in matrix Index k
starts at 0
.
|
inherited |
Operator [] (Constant version).
Returns k
-th stored element in matrix Index k
starts at 0
.
Operator +=.
Add matrix m
to current matrix instance.
|
inherited |
Operator +=.
Add constant value x
to all matrix entries.
Operator -=.
Subtract matrix m
from current matrix instance.
|
inherited |
Operator -=.
Subtract constant value x
from all matrix entries.
|
inherited |
Set a window for matrix printing.
- Parameters
-
[in] rmin first row index to view [in] rmax last row index to view [in] cmin first column index to view [in] cmax last column index to view
|
inherited |
Return window data for matrix printing.
- Parameters
-
[out] rmin first row index to view [out] rmax last row index to view [out] cmin first column index to view [out] cmax last column index to view