MFEM  v3.4
Finite element discretization library
Public Member Functions | Friends | List of all members
mfem::DenseMatrix Class Reference

Data type dense matrix using column-major storage. More...

#include <densemat.hpp>

Inheritance diagram for mfem::DenseMatrix:
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Collaboration diagram for mfem::DenseMatrix:
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Public Member Functions

 DenseMatrix ()
 
 DenseMatrix (const DenseMatrix &)
 Copy constructor. More...
 
 DenseMatrix (int s)
 Creates square matrix of size s. More...
 
 DenseMatrix (int m, int n)
 Creates rectangular matrix of size m x n. More...
 
 DenseMatrix (const DenseMatrix &mat, char ch)
 Creates rectangular matrix equal to the transpose of mat. More...
 
 DenseMatrix (double *d, int h, int w)
 
void UseExternalData (double *d, int h, int w)
 Change the data array and the size of the DenseMatrix. More...
 
void Reset (double *d, int h, int w)
 Change the data array and the size of the DenseMatrix. More...
 
void ClearExternalData ()
 
void Clear ()
 Delete the matrix data array (if owned) and reset the matrix state. More...
 
int Size () const
 For backward compatibility define Size to be synonym of Width() More...
 
void SetSize (int s)
 Change the size of the DenseMatrix to s x s. More...
 
void SetSize (int h, int w)
 Change the size of the DenseMatrix to h x w. More...
 
double * Data () const
 Returns the matrix data array. More...
 
double * GetData () const
 Returns the matrix data array. More...
 
bool OwnsData () const
 
double & operator() (int i, int j)
 Returns reference to a_{ij}. More...
 
const double & operator() (int i, int j) const
 Returns constant reference to a_{ij}. More...
 
double operator* (const DenseMatrix &m) const
 Matrix inner product: tr(A^t B) More...
 
double Trace () const
 Trace of a square matrix. More...
 
virtual double & Elem (int i, int j)
 Returns reference to a_{ij}. More...
 
virtual const double & Elem (int i, int j) const
 Returns constant reference to a_{ij}. More...
 
void Mult (const double *x, double *y) const
 Matrix vector multiplication. More...
 
virtual void Mult (const Vector &x, Vector &y) const
 Matrix vector multiplication. More...
 
void MultTranspose (const double *x, double *y) const
 Multiply a vector with the transpose matrix. More...
 
virtual void MultTranspose (const Vector &x, Vector &y) const
 Multiply a vector with the transpose matrix. More...
 
void AddMult (const Vector &x, Vector &y) const
 y += A.x More...
 
void AddMultTranspose (const Vector &x, Vector &y) const
 y += A^t x More...
 
void AddMult_a (double a, const Vector &x, Vector &y) const
 y += a * A.x More...
 
void AddMultTranspose_a (double a, const Vector &x, Vector &y) const
 y += a * A^t x More...
 
double InnerProduct (const double *x, const double *y) const
 Compute y^t A x. More...
 
void LeftScaling (const Vector &s)
 LeftScaling this = diag(s) * this. More...
 
void InvLeftScaling (const Vector &s)
 InvLeftScaling this = diag(1./s) * this. More...
 
void RightScaling (const Vector &s)
 RightScaling: this = this * diag(s);. More...
 
void InvRightScaling (const Vector &s)
 InvRightScaling: this = this * diag(1./s);. More...
 
void SymmetricScaling (const Vector &s)
 SymmetricScaling this = diag(sqrt(s)) * this * diag(sqrt(s)) More...
 
void InvSymmetricScaling (const Vector &s)
 InvSymmetricScaling this = diag(sqrt(1./s)) * this * diag(sqrt(1./s)) More...
 
double InnerProduct (const Vector &x, const Vector &y) const
 Compute y^t A x. More...
 
virtual MatrixInverseInverse () const
 Returns a pointer to the inverse matrix. More...
 
void Invert ()
 Replaces the current matrix with its inverse. More...
 
void SquareRootInverse ()
 Replaces the current matrix with its square root inverse. More...
 
double Det () const
 
double Weight () const
 
void Set (double alpha, const double *A)
 Set the matrix to alpha * A, assuming that A has the same dimensions as the matrix and uses column-major layout. More...
 
void Set (double alpha, const DenseMatrix &A)
 Set the matrix to alpha * A. More...
 
void Add (const double c, const DenseMatrix &A)
 Adds the matrix A multiplied by the number c to the matrix. More...
 
DenseMatrixoperator= (double c)
 Sets the matrix elements equal to constant c. More...
 
DenseMatrixoperator= (const double *d)
 Copy the matrix entries from the given array. More...
 
DenseMatrixoperator= (const DenseMatrix &m)
 Sets the matrix size and elements equal to those of m. More...
 
DenseMatrixoperator+= (const double *m)
 
DenseMatrixoperator+= (const DenseMatrix &m)
 
DenseMatrixoperator-= (const DenseMatrix &m)
 
DenseMatrixoperator*= (double c)
 
void Neg ()
 (*this) = -(*this) More...
 
void Norm2 (double *v) const
 Take the 2-norm of the columns of A and store in v. More...
 
double MaxMaxNorm () const
 Compute the norm ||A|| = max_{ij} |A_{ij}|. More...
 
double FNorm () const
 Compute the Frobenius norm of the matrix. More...
 
double FNorm2 () const
 Compute the square of the Frobenius norm of the matrix. More...
 
void Eigenvalues (Vector &ev)
 
void Eigenvalues (Vector &ev, DenseMatrix &evect)
 
void Eigensystem (Vector &ev, DenseMatrix &evect)
 
void SingularValues (Vector &sv) const
 
int Rank (double tol) const
 
double CalcSingularvalue (const int i) const
 Return the i-th singular value (decreasing order) of NxN matrix, N=1,2,3. More...
 
void CalcEigenvalues (double *lambda, double *vec) const
 
void GetRow (int r, Vector &row) const
 
void GetColumn (int c, Vector &col) const
 
double * GetColumn (int col)
 
const double * GetColumn (int col) const
 
void GetColumnReference (int c, Vector &col)
 
void SetRow (int r, const Vector &row)
 
void SetCol (int c, const Vector &col)
 
void SetRow (int row, double value)
 Set all entries of a row to the specified value. More...
 
void SetCol (int col, double value)
 Set all entries of a column to the specified value. More...
 
void GetDiag (Vector &d) const
 Returns the diagonal of the matrix. More...
 
void Getl1Diag (Vector &l) const
 Returns the l1 norm of the rows of the matrix v_i = sum_j |a_ij|. More...
 
void GetRowSums (Vector &l) const
 Compute the row sums of the DenseMatrix. More...
 
void Diag (double c, int n)
 Creates n x n diagonal matrix with diagonal elements c. More...
 
void Diag (double *diag, int n)
 Creates n x n diagonal matrix with diagonal given by diag. More...
 
void Transpose ()
 (*this) = (*this)^t More...
 
void Transpose (const DenseMatrix &A)
 (*this) = A^t More...
 
void Symmetrize ()
 (*this) = 1/2 ((*this) + (*this)^t) More...
 
void Lump ()
 
void GradToCurl (DenseMatrix &curl)
 
void GradToDiv (Vector &div)
 
void CopyRows (const DenseMatrix &A, int row1, int row2)
 Copy rows row1 through row2 from A to *this. More...
 
void CopyCols (const DenseMatrix &A, int col1, int col2)
 Copy columns col1 through col2 from A to *this. More...
 
void CopyMN (const DenseMatrix &A, int m, int n, int Aro, int Aco)
 Copy the m x n submatrix of A at row/col offsets Aro/Aco to *this. More...
 
void CopyMN (const DenseMatrix &A, int row_offset, int col_offset)
 Copy matrix A to the location in *this at row_offset, col_offset. More...
 
void CopyMNt (const DenseMatrix &A, int row_offset, int col_offset)
 Copy matrix A^t to the location in *this at row_offset, col_offset. More...
 
void CopyMN (const DenseMatrix &A, int m, int n, int Aro, int Aco, int row_offset, int col_offset)
 
void CopyMNDiag (double c, int n, int row_offset, int col_offset)
 Copy c on the diagonal of size n to *this at row_offset, col_offset. More...
 
void CopyMNDiag (double *diag, int n, int row_offset, int col_offset)
 Copy diag on the diagonal of size n to *this at row_offset, col_offset. More...
 
void CopyExceptMN (const DenseMatrix &A, int m, int n)
 Copy All rows and columns except m and n from A. More...
 
void AddMatrix (DenseMatrix &A, int ro, int co)
 Perform (ro+i,co+j)+=A(i,j) for 0<=i<A.Height, 0<=j<A.Width. More...
 
void AddMatrix (double a, DenseMatrix &A, int ro, int co)
 Perform (ro+i,co+j)+=a*A(i,j) for 0<=i<A.Height, 0<=j<A.Width. More...
 
void AddToVector (int offset, Vector &v) const
 Add the matrix 'data' to the Vector 'v' at the given 'offset'. More...
 
void GetFromVector (int offset, const Vector &v)
 Get the matrix 'data' from the Vector 'v' at the given 'offset'. More...
 
void AdjustDofDirection (Array< int > &dofs)
 
void Threshold (double eps)
 Replace small entries, abs(a_ij) <= eps, with zero. More...
 
int CheckFinite () const
 
virtual void Print (std::ostream &out=mfem::out, int width_=4) const
 Prints matrix to stream out. More...
 
virtual void PrintMatlab (std::ostream &out=mfem::out) const
 
virtual void PrintT (std::ostream &out=mfem::out, int width_=4) const
 Prints the transpose matrix to stream out. More...
 
void TestInversion ()
 Invert and print the numerical conditioning of the inversion. More...
 
long MemoryUsage () const
 
virtual ~DenseMatrix ()
 Destroys dense matrix. More...
 
- Public Member Functions inherited from mfem::Matrix
 Matrix (int s)
 Creates a square matrix of size s. More...
 
 Matrix (int h, int w)
 Creates a matrix of the given height and width. More...
 
virtual void Finalize (int)
 Finalizes the matrix initialization. More...
 
virtual ~Matrix ()
 Destroys matrix. More...
 
- Public Member Functions inherited from mfem::Operator
 Operator (int s=0)
 Construct a square Operator with given size s (default 0). More...
 
 Operator (int h, int w)
 Construct an Operator with the given height (output size) and width (input size). More...
 
int Height () const
 Get the height (size of output) of the Operator. Synonym with NumRows(). More...
 
int NumRows () const
 Get the number of rows (size of output) of the Operator. Synonym with Height(). More...
 
int Width () const
 Get the width (size of input) of the Operator. Synonym with NumCols(). More...
 
int NumCols () const
 Get the number of columns (size of input) of the Operator. Synonym with Width(). More...
 
virtual OperatorGetGradient (const Vector &x) const
 Evaluate the gradient operator at the point x. The default behavior in class Operator is to generate an error. More...
 
virtual const OperatorGetProlongation () const
 Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity. More...
 
virtual const OperatorGetRestriction () const
 Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL means identity. More...
 
void FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B, int copy_interior=0)
 Form a constrained linear system using a matrix-free approach. More...
 
virtual void RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x)
 Reconstruct a solution vector x (e.g. a GridFunction) from the solution X of a constrained linear system obtained from Operator::FormLinearSystem(). More...
 
void PrintMatlab (std::ostream &out, int n=0, int m=0) const
 Prints operator with input size n and output size m in Matlab format. More...
 
virtual ~Operator ()
 Virtual destructor. More...
 
Type GetType () const
 Return the type ID of the Operator class. More...
 

Friends

class DenseTensor
 
class DenseMatrixInverse
 

Additional Inherited Members

- Public Types inherited from mfem::Matrix
enum  DiagonalPolicy { DIAG_ZERO, DIAG_ONE, DIAG_KEEP }
 
- Public Types inherited from mfem::Operator
enum  Type {
  ANY_TYPE, MFEM_SPARSEMAT, Hypre_ParCSR, PETSC_MATAIJ,
  PETSC_MATIS, PETSC_MATSHELL, PETSC_MATNEST, PETSC_MATHYPRE,
  PETSC_MATGENERIC
}
 Enumeration defining IDs for some classes derived from Operator. More...
 
- Protected Attributes inherited from mfem::Operator
int height
 Dimension of the output / number of rows in the matrix. More...
 
int width
 Dimension of the input / number of columns in the matrix. More...
 

Detailed Description

Data type dense matrix using column-major storage.

Definition at line 23 of file densemat.hpp.

Constructor & Destructor Documentation

◆ DenseMatrix() [1/6]

mfem::DenseMatrix::DenseMatrix ( )

Default constructor for DenseMatrix. Sets data = NULL and height = width = 0.

Definition at line 64 of file densemat.cpp.

◆ DenseMatrix() [2/6]

mfem::DenseMatrix::DenseMatrix ( const DenseMatrix m)

Copy constructor.

Definition at line 70 of file densemat.cpp.

◆ DenseMatrix() [3/6]

mfem::DenseMatrix::DenseMatrix ( int  s)
explicit

Creates square matrix of size s.

Definition at line 87 of file densemat.cpp.

◆ DenseMatrix() [4/6]

mfem::DenseMatrix::DenseMatrix ( int  m,
int  n 
)

Creates rectangular matrix of size m x n.

Definition at line 101 of file densemat.cpp.

◆ DenseMatrix() [5/6]

mfem::DenseMatrix::DenseMatrix ( const DenseMatrix mat,
char  ch 
)

Creates rectangular matrix equal to the transpose of mat.

Definition at line 116 of file densemat.cpp.

◆ DenseMatrix() [6/6]

mfem::DenseMatrix::DenseMatrix ( double *  d,
int  h,
int  w 
)
inline

Construct a DenseMatrix using existing data array. The DenseMatrix does not assume ownership of the data array, i.e. it will not delete the array.

Definition at line 57 of file densemat.hpp.

◆ ~DenseMatrix()

mfem::DenseMatrix::~DenseMatrix ( )
virtual

Destroys dense matrix.

Definition at line 2932 of file densemat.cpp.

Member Function Documentation

◆ Add()

void mfem::DenseMatrix::Add ( const double  c,
const DenseMatrix A 
)

Adds the matrix A multiplied by the number c to the matrix.

Definition at line 553 of file densemat.cpp.

◆ AddMatrix() [1/2]

void mfem::DenseMatrix::AddMatrix ( DenseMatrix A,
int  ro,
int  co 
)

Perform (ro+i,co+j)+=A(i,j) for 0<=i<A.Height, 0<=j<A.Width.

Definition at line 2692 of file densemat.cpp.

◆ AddMatrix() [2/2]

void mfem::DenseMatrix::AddMatrix ( double  a,
DenseMatrix A,
int  ro,
int  co 
)

Perform (ro+i,co+j)+=a*A(i,j) for 0<=i<A.Height, 0<=j<A.Width.

Definition at line 2722 of file densemat.cpp.

◆ AddMult()

void mfem::DenseMatrix::AddMult ( const Vector x,
Vector y 
) const

y += A.x

Definition at line 242 of file densemat.cpp.

◆ AddMult_a()

void mfem::DenseMatrix::AddMult_a ( double  a,
const Vector x,
Vector y 
) const

y += a * A.x

Definition at line 278 of file densemat.cpp.

◆ AddMultTranspose()

void mfem::DenseMatrix::AddMultTranspose ( const Vector x,
Vector y 
) const

y += A^t x

Definition at line 260 of file densemat.cpp.

◆ AddMultTranspose_a()

void mfem::DenseMatrix::AddMultTranspose_a ( double  a,
const Vector x,
Vector y 
) const

y += a * A^t x

Definition at line 296 of file densemat.cpp.

◆ AddToVector()

void mfem::DenseMatrix::AddToVector ( int  offset,
Vector v 
) const

Add the matrix 'data' to the Vector 'v' at the given 'offset'.

Definition at line 2752 of file densemat.cpp.

◆ AdjustDofDirection()

void mfem::DenseMatrix::AdjustDofDirection ( Array< int > &  dofs)

If (dofs[i] < 0 and dofs[j] >= 0) or (dofs[i] >= 0 and dofs[j] < 0) then (*this)(i,j) = -(*this)(i,j).

Definition at line 2774 of file densemat.cpp.

◆ CalcEigenvalues()

void mfem::DenseMatrix::CalcEigenvalues ( double *  lambda,
double *  vec 
) const

Return the eigenvalues (in increasing order) and eigenvectors of a 2x2 or 3x3 symmetric matrix.

Definition at line 2056 of file densemat.cpp.

◆ CalcSingularvalue()

double mfem::DenseMatrix::CalcSingularvalue ( const int  i) const

Return the i-th singular value (decreasing order) of NxN matrix, N=1,2,3.

Definition at line 1758 of file densemat.cpp.

◆ CheckFinite()

int mfem::DenseMatrix::CheckFinite ( ) const
inline

Count the number of entries in the matrix for which isfinite is false, i.e. the entry is a NaN or +/-Inf.

Definition at line 325 of file densemat.hpp.

◆ Clear()

void mfem::DenseMatrix::Clear ( )
inline

Delete the matrix data array (if owned) and reset the matrix state.

Definition at line 79 of file densemat.hpp.

◆ ClearExternalData()

void mfem::DenseMatrix::ClearExternalData ( )
inline

Clear the data array and the dimensions of the DenseMatrix. This method should not be used with DenseMatrix that owns its current data array.

Definition at line 76 of file densemat.hpp.

◆ CopyCols()

void mfem::DenseMatrix::CopyCols ( const DenseMatrix A,
int  col1,
int  col2 
)

Copy columns col1 through col2 from A to *this.

Definition at line 2556 of file densemat.cpp.

◆ CopyExceptMN()

void mfem::DenseMatrix::CopyExceptMN ( const DenseMatrix A,
int  m,
int  n 
)

Copy All rows and columns except m and n from A.

Definition at line 2666 of file densemat.cpp.

◆ CopyMN() [1/3]

void mfem::DenseMatrix::CopyMN ( const DenseMatrix A,
int  m,
int  n,
int  Aro,
int  Aco 
)

Copy the m x n submatrix of A at row/col offsets Aro/Aco to *this.

Definition at line 2567 of file densemat.cpp.

◆ CopyMN() [2/3]

void mfem::DenseMatrix::CopyMN ( const DenseMatrix A,
int  row_offset,
int  col_offset 
)

Copy matrix A to the location in *this at row_offset, col_offset.

Definition at line 2580 of file densemat.cpp.

◆ CopyMN() [3/3]

void mfem::DenseMatrix::CopyMN ( const DenseMatrix A,
int  m,
int  n,
int  Aro,
int  Aco,
int  row_offset,
int  col_offset 
)

Copy the m x n submatrix of A at row/col offsets Aro/Aco to *this at row_offset, col_offset

Definition at line 2604 of file densemat.cpp.

◆ CopyMNDiag() [1/2]

void mfem::DenseMatrix::CopyMNDiag ( double  c,
int  n,
int  row_offset,
int  col_offset 
)

Copy c on the diagonal of size n to *this at row_offset, col_offset.

Definition at line 2635 of file densemat.cpp.

◆ CopyMNDiag() [2/2]

void mfem::DenseMatrix::CopyMNDiag ( double *  diag,
int  n,
int  row_offset,
int  col_offset 
)

Copy diag on the diagonal of size n to *this at row_offset, col_offset.

Definition at line 2650 of file densemat.cpp.

◆ CopyMNt()

void mfem::DenseMatrix::CopyMNt ( const DenseMatrix A,
int  row_offset,
int  col_offset 
)

Copy matrix A^t to the location in *this at row_offset, col_offset.

Definition at line 2592 of file densemat.cpp.

◆ CopyRows()

void mfem::DenseMatrix::CopyRows ( const DenseMatrix A,
int  row1,
int  row2 
)

Copy rows row1 through row2 from A to *this.

Definition at line 2545 of file densemat.cpp.

◆ Data()

double* mfem::DenseMatrix::Data ( ) const
inline

Returns the matrix data array.

Definition at line 92 of file densemat.hpp.

◆ Det()

double mfem::DenseMatrix::Det ( ) const

Calculates the determinant of the matrix (optimized for 2x2, 3x3, and 4x4 matrices)

Definition at line 460 of file densemat.cpp.

◆ Diag() [1/2]

void mfem::DenseMatrix::Diag ( double  c,
int  n 
)

Creates n x n diagonal matrix with diagonal elements c.

Definition at line 2371 of file densemat.cpp.

◆ Diag() [2/2]

void mfem::DenseMatrix::Diag ( double *  diag,
int  n 
)

Creates n x n diagonal matrix with diagonal given by diag.

Definition at line 2386 of file densemat.cpp.

◆ Eigensystem()

void mfem::DenseMatrix::Eigensystem ( Vector ev,
DenseMatrix evect 
)
inline

Definition at line 225 of file densemat.hpp.

◆ Eigenvalues() [1/2]

void mfem::DenseMatrix::Eigenvalues ( Vector ev)
inline

Definition at line 219 of file densemat.hpp.

◆ Eigenvalues() [2/2]

void mfem::DenseMatrix::Eigenvalues ( Vector ev,
DenseMatrix evect 
)
inline

Definition at line 222 of file densemat.hpp.

◆ Elem() [1/2]

double & mfem::DenseMatrix::Elem ( int  i,
int  j 
)
virtual

Returns reference to a_{ij}.

Implements mfem::Matrix.

Definition at line 158 of file densemat.cpp.

◆ Elem() [2/2]

const double & mfem::DenseMatrix::Elem ( int  i,
int  j 
) const
virtual

Returns constant reference to a_{ij}.

Implements mfem::Matrix.

Definition at line 163 of file densemat.cpp.

◆ FNorm()

double mfem::DenseMatrix::FNorm ( ) const
inline

Compute the Frobenius norm of the matrix.

Definition at line 214 of file densemat.hpp.

◆ FNorm2()

double mfem::DenseMatrix::FNorm2 ( ) const
inline

Compute the square of the Frobenius norm of the matrix.

Definition at line 217 of file densemat.hpp.

◆ GetColumn() [1/3]

void mfem::DenseMatrix::GetColumn ( int  c,
Vector col 
) const

Definition at line 2312 of file densemat.cpp.

◆ GetColumn() [2/3]

double* mfem::DenseMatrix::GetColumn ( int  col)
inline

Definition at line 240 of file densemat.hpp.

◆ GetColumn() [3/3]

const double* mfem::DenseMatrix::GetColumn ( int  col) const
inline

Definition at line 241 of file densemat.hpp.

◆ GetColumnReference()

void mfem::DenseMatrix::GetColumnReference ( int  c,
Vector col 
)
inline

Definition at line 243 of file densemat.hpp.

◆ GetData()

double* mfem::DenseMatrix::GetData ( ) const
inline

Returns the matrix data array.

Definition at line 94 of file densemat.hpp.

◆ GetDiag()

void mfem::DenseMatrix::GetDiag ( Vector d) const

Returns the diagonal of the matrix.

Definition at line 2326 of file densemat.cpp.

◆ GetFromVector()

void mfem::DenseMatrix::GetFromVector ( int  offset,
const Vector v 
)

Get the matrix 'data' from the Vector 'v' at the given 'offset'.

Definition at line 2763 of file densemat.cpp.

◆ Getl1Diag()

void mfem::DenseMatrix::Getl1Diag ( Vector l) const

Returns the l1 norm of the rows of the matrix v_i = sum_j |a_ij|.

Definition at line 2340 of file densemat.cpp.

◆ GetRow()

void mfem::DenseMatrix::GetRow ( int  r,
Vector row 
) const

Definition at line 2296 of file densemat.cpp.

◆ GetRowSums()

void mfem::DenseMatrix::GetRowSums ( Vector l) const

Compute the row sums of the DenseMatrix.

Definition at line 2357 of file densemat.cpp.

◆ GradToCurl()

void mfem::DenseMatrix::GradToCurl ( DenseMatrix curl)

Given a DShape matrix (from a scalar FE), stored in this, returns the CurlShape matrix. If *this is a N by D matrix, then curl is a D*N by D(D-1)/2 matrix. The size of curl must be set outside. The dimension D can be either 2 or 3.

Definition at line 2465 of file densemat.cpp.

◆ GradToDiv()

void mfem::DenseMatrix::GradToDiv ( Vector div)

Given a DShape matrix (from a scalar FE), stored in *this, returns the DivShape vector. If *this is a N by dim matrix, then div is a dim*N vector. The size of div must be set outside.

Definition at line 2524 of file densemat.cpp.

◆ InnerProduct() [1/2]

double mfem::DenseMatrix::InnerProduct ( const double *  x,
const double *  y 
) const

Compute y^t A x.

Definition at line 315 of file densemat.cpp.

◆ InnerProduct() [2/2]

double mfem::DenseMatrix::InnerProduct ( const Vector x,
const Vector y 
) const
inline

Compute y^t A x.

Definition at line 157 of file densemat.hpp.

◆ Inverse()

MatrixInverse * mfem::DenseMatrix::Inverse ( ) const
virtual

Returns a pointer to the inverse matrix.

Implements mfem::Matrix.

Definition at line 455 of file densemat.cpp.

◆ Invert()

void mfem::DenseMatrix::Invert ( )

Replaces the current matrix with its inverse.

Definition at line 642 of file densemat.cpp.

◆ InvLeftScaling()

void mfem::DenseMatrix::InvLeftScaling ( const Vector s)

InvLeftScaling this = diag(1./s) * this.

Definition at line 344 of file densemat.cpp.

◆ InvRightScaling()

void mfem::DenseMatrix::InvRightScaling ( const Vector s)

InvRightScaling: this = this * diag(1./s);.

Definition at line 370 of file densemat.cpp.

◆ InvSymmetricScaling()

void mfem::DenseMatrix::InvSymmetricScaling ( const Vector s)

InvSymmetricScaling this = diag(sqrt(1./s)) * this * diag(sqrt(1./s))

Definition at line 411 of file densemat.cpp.

◆ LeftScaling()

void mfem::DenseMatrix::LeftScaling ( const Vector s)

LeftScaling this = diag(s) * this.

Definition at line 333 of file densemat.cpp.

◆ Lump()

void mfem::DenseMatrix::Lump ( )

Definition at line 2451 of file densemat.cpp.

◆ MaxMaxNorm()

double mfem::DenseMatrix::MaxMaxNorm ( ) const

Compute the norm ||A|| = max_{ij} |A_{ij}|.

Definition at line 810 of file densemat.cpp.

◆ MemoryUsage()

long mfem::DenseMatrix::MemoryUsage ( ) const
inline

Definition at line 336 of file densemat.hpp.

◆ Mult() [1/2]

void mfem::DenseMatrix::Mult ( const double *  x,
double *  y 
) const

Matrix vector multiplication.

Definition at line 168 of file densemat.cpp.

◆ Mult() [2/2]

void mfem::DenseMatrix::Mult ( const Vector x,
Vector y 
) const
virtual

Matrix vector multiplication.

Implements mfem::Operator.

Definition at line 196 of file densemat.cpp.

◆ MultTranspose() [1/2]

void mfem::DenseMatrix::MultTranspose ( const double *  x,
double *  y 
) const

Multiply a vector with the transpose matrix.

Definition at line 219 of file densemat.cpp.

◆ MultTranspose() [2/2]

void mfem::DenseMatrix::MultTranspose ( const Vector x,
Vector y 
) const
virtual

Multiply a vector with the transpose matrix.

Reimplemented from mfem::Operator.

Definition at line 234 of file densemat.cpp.

◆ Neg()

void mfem::DenseMatrix::Neg ( )

(*this) = -(*this)

Definition at line 633 of file densemat.cpp.

◆ Norm2()

void mfem::DenseMatrix::Norm2 ( double *  v) const

Take the 2-norm of the columns of A and store in v.

Definition at line 797 of file densemat.cpp.

◆ operator()() [1/2]

double & mfem::DenseMatrix::operator() ( int  i,
int  j 
)
inline

Returns reference to a_{ij}.

Definition at line 734 of file densemat.hpp.

◆ operator()() [2/2]

const double & mfem::DenseMatrix::operator() ( int  i,
int  j 
) const
inline

Returns constant reference to a_{ij}.

Definition at line 740 of file densemat.hpp.

◆ operator*()

double mfem::DenseMatrix::operator* ( const DenseMatrix m) const

Matrix inner product: tr(A^t B)

Definition at line 204 of file densemat.cpp.

◆ operator*=()

DenseMatrix & mfem::DenseMatrix::operator*= ( double  c)

Definition at line 623 of file densemat.cpp.

◆ operator+=() [1/2]

DenseMatrix & mfem::DenseMatrix::operator+= ( const double *  m)

Definition at line 595 of file densemat.cpp.

◆ operator+=() [2/2]

DenseMatrix & mfem::DenseMatrix::operator+= ( const DenseMatrix m)

Definition at line 605 of file densemat.cpp.

◆ operator-=()

DenseMatrix & mfem::DenseMatrix::operator-= ( const DenseMatrix m)

Definition at line 612 of file densemat.cpp.

◆ operator=() [1/3]

DenseMatrix & mfem::DenseMatrix::operator= ( double  c)

Sets the matrix elements equal to constant c.

Definition at line 562 of file densemat.cpp.

◆ operator=() [2/3]

DenseMatrix & mfem::DenseMatrix::operator= ( const double *  d)

Copy the matrix entries from the given array.

Definition at line 572 of file densemat.cpp.

◆ operator=() [3/3]

DenseMatrix & mfem::DenseMatrix::operator= ( const DenseMatrix m)

Sets the matrix size and elements equal to those of m.

Definition at line 582 of file densemat.cpp.

◆ OwnsData()

bool mfem::DenseMatrix::OwnsData ( ) const
inline

Definition at line 96 of file densemat.hpp.

◆ Print()

void mfem::DenseMatrix::Print ( std::ostream &  out = mfem::out,
int  width_ = 4 
) const
virtual

Prints matrix to stream out.

Reimplemented from mfem::Matrix.

Definition at line 2847 of file densemat.cpp.

◆ PrintMatlab()

void mfem::DenseMatrix::PrintMatlab ( std::ostream &  out = mfem::out) const
virtual

Definition at line 2873 of file densemat.cpp.

◆ PrintT()

void mfem::DenseMatrix::PrintT ( std::ostream &  out = mfem::out,
int  width_ = 4 
) const
virtual

Prints the transpose matrix to stream out.

Definition at line 2892 of file densemat.cpp.

◆ Rank()

int mfem::DenseMatrix::Rank ( double  tol) const

Definition at line 1131 of file densemat.cpp.

◆ Reset()

void mfem::DenseMatrix::Reset ( double *  d,
int  h,
int  w 
)
inline

Change the data array and the size of the DenseMatrix.

The DenseMatrix does not assume ownership of the data array, i.e. it will not delete the new array d. This method will delete the current data array, if owned.

Definition at line 71 of file densemat.hpp.

◆ RightScaling()

void mfem::DenseMatrix::RightScaling ( const Vector s)

RightScaling: this = this * diag(s);.

Definition at line 355 of file densemat.cpp.

◆ Set() [1/2]

void mfem::DenseMatrix::Set ( double  alpha,
const double *  A 
)

Set the matrix to alpha * A, assuming that A has the same dimensions as the matrix and uses column-major layout.

Definition at line 544 of file densemat.cpp.

◆ Set() [2/2]

void mfem::DenseMatrix::Set ( double  alpha,
const DenseMatrix A 
)
inline

Set the matrix to alpha * A.

Definition at line 179 of file densemat.hpp.

◆ SetCol() [1/2]

void mfem::DenseMatrix::SetCol ( int  c,
const Vector col 
)

Definition at line 2825 of file densemat.cpp.

◆ SetCol() [2/2]

void mfem::DenseMatrix::SetCol ( int  col,
double  value 
)

Set all entries of a column to the specified value.

Definition at line 2809 of file densemat.cpp.

◆ SetRow() [1/2]

void mfem::DenseMatrix::SetRow ( int  r,
const Vector row 
)

Definition at line 2817 of file densemat.cpp.

◆ SetRow() [2/2]

void mfem::DenseMatrix::SetRow ( int  row,
double  value 
)

Set all entries of a row to the specified value.

Definition at line 2801 of file densemat.cpp.

◆ SetSize() [1/2]

void mfem::DenseMatrix::SetSize ( int  s)
inline

Change the size of the DenseMatrix to s x s.

Definition at line 86 of file densemat.hpp.

◆ SetSize() [2/2]

void mfem::DenseMatrix::SetSize ( int  h,
int  w 
)

Change the size of the DenseMatrix to h x w.

Definition at line 136 of file densemat.cpp.

◆ SingularValues()

void mfem::DenseMatrix::SingularValues ( Vector sv) const

Definition at line 1092 of file densemat.cpp.

◆ Size()

int mfem::DenseMatrix::Size ( ) const
inline

For backward compatibility define Size to be synonym of Width()

Definition at line 83 of file densemat.hpp.

◆ SquareRootInverse()

void mfem::DenseMatrix::SquareRootInverse ( )

Replaces the current matrix with its square root inverse.

Definition at line 752 of file densemat.cpp.

◆ SymmetricScaling()

void mfem::DenseMatrix::SymmetricScaling ( const Vector s)

SymmetricScaling this = diag(sqrt(s)) * this * diag(sqrt(s))

Definition at line 385 of file densemat.cpp.

◆ Symmetrize()

void mfem::DenseMatrix::Symmetrize ( )

(*this) = 1/2 ((*this) + (*this)^t)

Definition at line 2434 of file densemat.cpp.

◆ TestInversion()

void mfem::DenseMatrix::TestInversion ( )

Invert and print the numerical conditioning of the inversion.

Definition at line 2918 of file densemat.cpp.

◆ Threshold()

void mfem::DenseMatrix::Threshold ( double  eps)

Replace small entries, abs(a_ij) <= eps, with zero.

Definition at line 2833 of file densemat.cpp.

◆ Trace()

double mfem::DenseMatrix::Trace ( ) const

Trace of a square matrix.

Definition at line 436 of file densemat.cpp.

◆ Transpose() [1/2]

void mfem::DenseMatrix::Transpose ( )

(*this) = (*this)^t

Definition at line 2401 of file densemat.cpp.

◆ Transpose() [2/2]

void mfem::DenseMatrix::Transpose ( const DenseMatrix A)

(*this) = A^t

Definition at line 2423 of file densemat.cpp.

◆ UseExternalData()

void mfem::DenseMatrix::UseExternalData ( double *  d,
int  h,
int  w 
)
inline

Change the data array and the size of the DenseMatrix.

The DenseMatrix does not assume ownership of the data array, i.e. it will not delete the data array d. This method should not be used with DenseMatrix that owns its current data array.

Definition at line 64 of file densemat.hpp.

◆ Weight()

double mfem::DenseMatrix::Weight ( ) const

Definition at line 517 of file densemat.cpp.

Friends And Related Function Documentation

◆ DenseMatrixInverse

friend class DenseMatrixInverse
friend

Definition at line 26 of file densemat.hpp.

◆ DenseTensor

friend class DenseTensor
friend

Definition at line 25 of file densemat.hpp.


The documentation for this class was generated from the following files: