To handle dense matrices. More...
Public Member Functions  
DMatrix ()  
Default constructor. More...  
DMatrix (size_t nr)  
Constructor for a matrix with nr rows and nr columns. More...  
DMatrix (size_t nr, size_t nc)  
Constructor for a matrix with nr rows and nc columns. More...  
DMatrix (Vect< T_ > &v)  
Constructor that uses a Vect instance. The class uses the memory space occupied by this vector. More...  
DMatrix (const DMatrix< T_ > &m)  
Copy Constructor. More...  
~DMatrix ()  
Destructor.  
void  setDiag () 
Store diagonal entries in a separate internal vector.  
void  setDiag (const T_ &a) 
Set matrix as diagonal and assign its diagonal entries as a constant. More...  
void  setDiag (const vector< T_ > &d) 
Set matrix as diagonal and assign its diagonal entries. More...  
void  setSize (size_t size) 
Set size (number of rows) of matrix. More...  
void  setSize (size_t nr, size_t nc) 
Set size (number of rows and columns) of matrix. More...  
void  getColumn (size_t j, Vect< T_ > &v) const 
Get j th column vector. More...  
Vect< T_ >  getColumn (size_t j) const 
Get j th column vector. More...  
void  getRow (size_t i, Vect< T_ > &v) const 
Get i th row vector. More...  
Vect< T_ >  getRow (size_t i) const 
Get i th row vector. More...  
void  set (size_t i, size_t j, const T_ &val) 
Assign a constant value to an entry of the matrix. More...  
void  setRow (size_t i, const Vect< T_ > &v) 
Copy a given vector to a prescribed row in the matrix. More...  
void  setColumn (size_t i, const Vect< T_ > &v) 
Copy a given vector to a prescribed column in the matrix. More...  
void  MultAdd (T_ a, const Vect< T_ > &x, Vect< T_ > &y) const 
Multiply matrix by vector a*x and add result to y . More...  
void  MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const 
Multiply matrix by vector x and add result to y . More...  
void  Mult (const Vect< T_ > &x, Vect< T_ > &y) const 
Multiply matrix by vector x and save result in y . More...  
void  TMult (const Vect< T_ > &x, Vect< T_ > &y) const 
Multiply transpose of matrix by vector x and add result in y . More...  
void  add (size_t i, size_t j, const T_ &val) 
Add constant val to entry (i,j) of the matrix. More...  
void  Axpy (T_ a, const DMatrix< 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...  
int  setQR () 
Construct a QR factorization of the matrix. More...  
int  setTransQR () 
Construct a QR factorization of the transpose of the matrix. More...  
int  solveQR (const Vect< T_ > &b, Vect< T_ > &x) 
Solve a linear system by QR decomposition. More...  
int  solveTransQR (const Vect< T_ > &b, Vect< T_ > &x) 
Solve a transpose linear system by QR decomposition. More...  
T_  operator() (size_t i, size_t j) const 
Operator () (Constant version). Return a(i,j) More...  
T_ &  operator() (size_t i, size_t j) 
Operator () (Non constant version). Return a(i,j) More...  
int  setLU () 
Factorize the matrix (LU factorization) More...  
int  setTransLU () 
Factorize the transpose of the matrix (LU factorization) More...  
int  solve (Vect< T_ > &b) 
Solve linear system. More...  
int  solveTrans (Vect< T_ > &b) 
Solve the transpose linear system. More...  
int  solve (const Vect< T_ > &b, Vect< T_ > &x) 
Solve linear system. More...  
int  solveTrans (const Vect< T_ > &b, Vect< T_ > &x) 
Solve the transpose linear system. More...  
DMatrix &  operator= (DMatrix< T_ > &m) 
Operator = More...  
DMatrix &  operator+= (const DMatrix< T_ > &m) 
Operator +=. More...  
DMatrix &  operator= (const DMatrix< T_ > &m) 
Operator =. More...  
DMatrix &  operator= (const T_ &x) 
Operator = More...  
DMatrix &  operator*= (const T_ &x) 
Operator *= More...  
DMatrix &  operator+= (const T_ &x) 
Operator += More...  
DMatrix &  operator= (const T_ &x) 
Operator = More...  
T_ *  getArray () const 
Return matrix as CArray. More...  
T_  get (size_t i, size_t j) const 
Return entry (i,j) of matrix.  
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 (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 Element &el, T_ *a) 
Assembly of element matrix into global matrix. More...  
void  Assembly (const Element &el, const DMatrix< T_ > &a) 
Assembly of element matrix into global matrix. More...  
void  Assembly (const Side &sd, T_ *a) 
Assembly of side matrix into global matrix. More...  
void  Assembly (const Side &sd, const DMatrix< T_ > &a) 
Assembly of side matrix into global matrix. 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 (int dof, int code, 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, int flag=0) 
Impose by a penalty method a homegeneous (=0) essential boundary condition. 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 () 
Impose by a penalty method an essential boundary condition when DOFs are supported by sides. More...  
virtual int  Factor ()=0 
Factorize matrix. Available only if the storage class enables it.  
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...  
size_t  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 Matrix< T_ > &m) 
Operator =. More...  
Detailed Description
template<class T_>
class OFELI::DMatrix< T_ >
To handle dense matrices.
This class enables storing and manipulating general dense matrices. Matrices can be square or rectangle ones.
 Template Parameters

T_ Data type (double, float, complex<double>, ...)
Constructor & Destructor Documentation
DMatrix  (  ) 
Default constructor.
Initializes a zerodimension matrix.
DMatrix  (  size_t  nr  ) 
Constructor for a matrix with nr
rows and nr
columns.
Matrix entries are set to 0
.
DMatrix  (  size_t  nr, 
size_t  nc  
) 
Constructor for a matrix with nr
rows and nc
columns.
Matrix entries are set to 0.
Constructor that uses a Vect instance. The class uses the memory space occupied by this vector.
 Parameters

[in] v Vector to copy
Member Function Documentation
void setDiag  (  const T_ &  a  ) 
Set matrix as diagonal and assign its diagonal entries as a constant.
 Parameters

[in] a Value to assign to all diagonal entries
void setDiag  (  const vector< T_ > &  d  ) 
Set matrix as diagonal and assign its diagonal entries.
 Parameters

[in] d Vector entries to assign to matrix diagonal entries
void setSize  (  size_t  size  ) 
Set size (number of rows) of matrix.
 Parameters

[in] size Number of rows and columns.
void setSize  (  size_t  nr, 
size_t  nc  
) 
Set size (number of rows and columns) of matrix.
 Parameters

[in] nr Number of rows. [in] nc Number of columns.
void getColumn  (  size_t  j, 
Vect< T_ > &  v  
)  const 
Get j
th column vector.
 Parameters

[in] j Index of column to extract [out] v Reference to Vect instance where the column is stored
 Remarks
 Vector v does not need to be sized before. It is resized in the function
Vect<T_> getColumn  (  size_t  j  )  const 
Get j
th column vector.
 Parameters

[in] j Index of column to extract
 Returns
 Vect instance where the column is stored
 Remarks
 Vector v does not need to be sized before. It is resized in the function
void getRow  (  size_t  i, 
Vect< T_ > &  v  
)  const 
Get i
th row vector.
 Parameters

[in] i Index of row to extract [out] v Reference to Vect instance where the row is stored
 Remarks
 Vector v does not need to be sized before. It is resized in the function
Vect<T_> getRow  (  size_t  i  )  const 
Get i
th row vector.
 Parameters

[in] i Index of row to extract
 Returns
 Vect instance where the row is stored
 Remarks
 Vector v does not need to be sized before. It is resized in the function

virtual 
Assign a constant value to an entry of the matrix.
 Parameters

[in] i row index of matrix [in] j column index of matrix [in] val Value to assign to a(i,j)
.
Implements Matrix< T_ >.
void setRow  (  size_t  i, 
const Vect< T_ > &  v  
) 
Copy a given vector to a prescribed row in the matrix.
 Parameters

[in] i row index to be assigned [in] v Vect instance to copy
void setColumn  (  size_t  i, 
const Vect< T_ > &  v  
) 
Copy a given vector to a prescribed column in the matrix.
 Parameters

[in] i column index to be assigned [in] v Vect instance to copy
Multiply matrix by vector a*x
and add result to y
.
 Parameters

[in] a constant to multiply by [in] x Vector to multiply by a
[in,out] y on input, vector to add to. On output, result.
Implements Matrix< T_ >.
Multiply matrix by vector x
and add result to y
.
 Parameters

[in] x Vector to add to y
[in,out] y on input, vector to add to. On output, result.
Implements Matrix< T_ >.
Multiply matrix by vector x
and save result in y
.
 Parameters

[in] x Vector to add to y
[out] y Result.
Implements Matrix< T_ >.
Multiply transpose of matrix by vector x
and add result in y
.
 Parameters

[in] x Vector to add to y
[in,out] y on input, vector to add to. On output, result.
Implements Matrix< T_ >.

virtual 
Add constant val
to entry (i,j)
of the matrix.
 Parameters

[in] i row index [in] j column index [in] val Constant to add
Implements Matrix< T_ >.
void Axpy  (  T_  a, 
const DMatrix< 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 Matrix by which a
is multiplied. The result is added to current instance
Implements Matrix< T_ >.
int setQR  (  ) 
Construct a QR factorization of the matrix.
This function constructs the QR decomposition using the Householder method. The upper triangular matrix R is returned in the upper triangle of the current matrix, except for the diagonal elements of R which are stored in an internal vector. The orthogonal matrix Q is represented as a product of n1 Householder matrices Q1 . . . Qn1, where Qj = 1  uj.uj /cj . The ith component of uj is zero for i = 1, ..., j1 while the nonzero components are returned in a[i][j] for i = j, ..., n.
 Returns
0
if the decomposition was successful,k
is thekth
row is singular
 Remarks
 The matrix can be square or rectangle
int setTransQR  (  ) 
Construct a QR factorization of the transpose of the matrix.
This function constructs the QR decomposition using the Householder method. The upper triangular matrix R is returned in the upper triangle of the current matrix, except for the diagonal elements of R which are stored in an internal vector. The orthogonal matrix Q is represented as a product of n1 Householder matrices Q1 . . . Qn1, where Qj = 1  uj.uj /cj . The ith component of uj is zero for i = 1, ..., j1 while the nonzero components are returned in a[i][j] for i = j, ..., n.
 Returns
0
if the decomposition was successful,k
is thekth
row is singular
 Remarks
 The matrix can be square or rectangle
Solve a linear system by QR decomposition.
This function constructs the QR decomposition, if this was not already done by using the member function QR and solves the linear system
 Parameters

[in] b Righthand side vector [out] x Solution vector. Must have been sized before using this function.
 Returns
 The same value as returned by the function QR
Solve a transpose linear system by QR decomposition.
This function constructs the QR decomposition, if this was not already done by using the member function QR and solves the linear system
 Parameters

[in] b Righthand side vector [out] x Solution vector. Must have been sized before using this function.
 Returns
 The same value as returned by the function QR

virtual 
Operator () (Constant version). Return a(i,j)
 Parameters

[in] i row index [in] j column index
Implements Matrix< T_ >.

virtual 
Operator () (Non constant version). Return a(i,j)
 Parameters

[in] i row index [in] j column index
Implements Matrix< T_ >.
int setLU  (  ) 
Factorize the matrix (LU factorization)
LU factorization of the matrix is realized. Note that since this is an in place factorization, the contents of the matrix are modified.
 Returns

0
if factorization was normally performed, 
n
if then
th pivot is null.

 Remarks
 A flag in this class indicates after factorization that this one has been realized, so that, if the member function solve is called after this no further factorization is done.
int setTransLU  (  ) 
Factorize the transpose of the matrix (LU factorization)
LU factorization of the transpose of the matrix is realized. Note that since this is an in place factorization, the contents of the matrix are modified.
 Returns

0
if factorization was normally performed, 
n
if then
th pivot is null.

 Remarks
 A flag in this class indicates after factorization that this one has been realized, so that, if the member function solve is called after this no further factorization is done.

virtual 
Solve linear system.
The linear system having the current instance as a matrix is solved by using the LU decomposition. Solution is thus realized after a factorization step and a forward/backward substitution step. The factorization step is realized only if this was not already done.
Note that this function modifies the matrix contents is a factorization is performed. Naturally, if the the matrix has been modified after using this function, the user has to refactorize it using the function setLU. This is because the class has no nonexpensive way to detect if the matrix has been modified. The function setLU realizes the factorization step only.
 Parameters

[in,out] b Vect instance that contains righthand side on input and solution on output.
 Returns

0
if solution was normally performed, 
n
if then
th pivot is null.

Implements Matrix< T_ >.
int solveTrans  (  Vect< T_ > &  b  ) 
Solve the transpose linear system.
The linear system having the current instance as a transpose matrix is solved by using the LU decomposition. Solution is thus realized after a factorization step and a forward/backward substitution step. The factorization step is realized only if this was not already done.
Note that this function modifies the matrix contents is a factorization is performed. Naturally, if the the matrix has been modified after using this function, the user has to refactorize it using the function setLU. This is because the class has no nonexpensive way to detect if the matrix has been modified. The function setLU realizes the factorization step only.
 Parameters

[in,out] b Vect instance that contains righthand side on input and solution on output.
 Returns

0
if solution was normally performed, 
n
if then
th pivot is null.

Solve linear system.
The linear system having the current instance as a matrix is solved by using the LU decomposition. Solution is thus realized after a factorization step and a forward/backward substitution step. The factorization step is realized only if this was not already done.
Note that this function modifies the matrix contents is a factorization is performed. Naturally, if the the matrix has been modified after using this function, the user has to refactorize it using the function setLU. This is because the class has no nonexpensive way to detect if the matrix has been modified. The function setLU realizes the factorization step only.
 Parameters

[in] b Vect instance that contains righthand side. [out] x Vect instance that contains solution
 Returns

0
if solution was normally performed, 
n
if then
th pivot is null.

Solve the transpose linear system.
The linear system having the current instance as a transpose matrix is solved by using the LU decomposition. Solution is thus realized after a factorization step and a forward/backward substitution step. The factorization step is realized only if this was not already done.
Note that this function modifies the matrix contents is a factorization is performed. Naturally, if the the matrix has been modified after using this function, the user has to refactorize it using the function setLU. This is because the class has no nonexpensive way to detect if the matrix has been modified. The function setLU realizes the factorization step only.
 Parameters

[in] b Vect instance that contains righthand side. [out] x Vect instance that contains solution
 Returns

0
if solution was normally performed, 
n
if then
th pivot is null.

Operator +=.
Add matrix m
to current matrix instance.
Operator =.
Subtract matrix m
from current matrix instance.
DMatrix& operator=  (  const T_ &  x  ) 
Operator =
Assign matrix to identity times x
DMatrix& operator*=  (  const T_ &  x  ) 
Operator *=
Premultiply matrix entries by constant value x
.
DMatrix& operator+=  (  const T_ &  x  ) 
Operator +=
Add constant value x
to matrix entries
DMatrix& operator=  (  const T_ &  x  ) 
Operator =
Subtract constant value x
from matrix entries.
T_* getArray  (  )  const 
Return matrix as CArray.
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 Carray.
 Parameters

[in] el Pointer to element instance [in] a Element matrix as a Carray

inherited 
Assembly of side matrix into global matrix.
Case where side matrix is given by a Carray.
 Parameters

[in] sd Pointer to side instance [in] a Side matrix as a Carray instance
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 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,out] b Vect instance that contains righthand 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 righthand side is to be modified
(dof>0
) or both matrix and righthand side (dof=0
, default value).

inherited 
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(..).
 Parameters

[in,out] b Vect instance that contains righthand side. [in] flag Parameter to determine whether only the righthand side is to be modified ( dof>0
)
or both matrix and righthand side (dof=0
, default value).
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,out] b Vect instance that contains righthand 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 righthand side is to be modified ( dof>0
)
or both matrix and righthand side (dof=0
, default value).

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 cass enables it.
 Parameters

[in,out] b Vect instance that contains righthand 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.