A matrix class that constructs a BANDED matrix. More...

#include <BandedMatrix.h>

Inheritance diagram for CppNoddy::BandedMatrix< _Type >:

Public Types
typedef DenseVector< _Type >::elt_iter	elt_iter

Public Member Functions
	BandedMatrix ()
	Empty constructor .. should we stop this? More...

void	blank ()

	BandedMatrix (const std::size_t &rows, const std::size_t &offdiag, const _Type &fill)
	Noddy Banded Matrix constructor. More...

	BandedMatrix (const BandedMatrix &source)
	Copy constructor. More...

BandedMatrix &	operator= (const BandedMatrix &source)
	Assignment operator. More...

const _Type &	operator() (const std::size_t &row, const std::size_t &col) const
	Access operator. More...

_Type &	operator() (const std::size_t &row, const std::size_t &col)
	Access operator. More...

const _Type &	get (const std::size_t &row, const std::size_t &col) const
	Access operator. More...

_Type &	set (const std::size_t &row, const std::size_t &col)
	Access operator. More...

std::size_t	nrows () const
	Get the number of rows. More...

std::size_t	ncols () const
	Get the number of columns. More...

std::size_t	nelts () const
	Get the number of elements. More...

void	scale (const _Type &mult)
	Scale all entries in the matrix by a scalar. More...

void	transpose ()
	Transpose the matrix. More...

double	one_norm () const

double	two_norm () const

double	inf_norm () const

double	frob_norm () const

DenseVector< _Type >	multiply (const DenseVector< _Type > &X) const
	Right multiply the matrix by a DENSE vector. More...

void	dump () const
	Output the matrix contents to std::cout. More...

void	assign (_Type elt)
	Assign a value the matrix so that it has the same geometry, but zero entries in all locations including those reserved for pivotting. More...

std::size_t	noffdiag () const
	Get the number of off-diagonal elements where the total INPUT band width is 2*noffdiag+1 since the band structure is symmetric. More...

void	row_swap (const std::size_t &row1, const std::size_t &row2)
	Exchange rows in the matrix. More...

double *	base ()
	Allow direct access to the vector m_storage. More...

elt_iter	get_elt_iter (std::size_t row, std::size_t col)

double *	base ()

double *	base ()

Public Member Functions inherited from CppNoddy::Sequential_Matrix_base< _Type >
	Sequential_Matrix_base ()
	An empty constructor. More...

virtual	~Sequential_Matrix_base ()

virtual const _Type &	operator() (const std::size_t &row, const std::size_t &col) const =0

virtual _Type &	operator() (const std::size_t &row, const std::size_t &col)=0

virtual const _Type &	get (const std::size_t &row, const std::size_t &col) const =0

virtual _Type &	set (const std::size_t &row, const std::size_t &col)=0

virtual std::size_t	nrows () const =0

virtual std::size_t	ncols () const =0

virtual std::size_t	nelts () const =0

virtual void	scale (const _Type &mult)=0

virtual void	dump () const =0

Public Attributes
DenseVector< _Type >	m_storage
	A contiguous vector. More...

std::size_t	m_N
	The number of rows/cols in the matrix. More...

std::size_t	m_L
	Max number of (INPUT) bands above OR below the main diagonal. More...

Detailed Description

template<typename _Type>
class CppNoddy::BandedMatrix< _Type >

A matrix class that constructs a BANDED matrix.

Definition at line 16 of file BandedMatrix.h.

Member Typedef Documentation

◆ elt_iter

template<typename _Type >

typedef DenseVector<_Type>::elt_iter CppNoddy::BandedMatrix< _Type >::elt_iter

Definition at line 20 of file BandedMatrix.h.

Constructor & Destructor Documentation

◆ BandedMatrix() [1/3]

template<typename _Type >

CppNoddy::BandedMatrix< _Type >::BandedMatrix ( )

inline

Empty constructor .. should we stop this?

Definition at line 23 of file BandedMatrix.h.

24 {}

◆ BandedMatrix() [2/3]

template<typename _Type >

CppNoddy::BandedMatrix< _Type >::BandedMatrix	(	const std::size_t &	rows,
		const std::size_t &	offdiag,
		const _Type &	fill
	)

Noddy Banded Matrix constructor.

Parameters

rows	The number of rows in the matrix.
offdiag	The maximum number of bands above OR below the diagonal. The total number stored will be 3 * offdiag + 1; i.e. assumes the number of offdiagonal elts is the same both above and below, and we must an extra 'offdiag' because of fill-in during pivotting.
fill	The initial value to be placed in each element of the banded matrix.

Definition at line 16 of file BandedMatrix.cpp.

                                                       :
    Sequential_Matrix_base<_Type>(),
    m_N(rows),
    m_L(upper_offdiag_bands) {
    // we'll assume that the upper & lower offdiags are of equal size.
    // logical m_storage is the main diagonal + upper offdiagonal + lower offdiagonal
    // = 2 * m_L + 1.
    // However, allowing for row interchanging during pivotting leads to additional
    // padding of m_L, to make a total of 3*m_L+1.
    m_storage = DenseVector<_Type>(m_N * (3 * m_L + 1), 0.0);
  }

References CppNoddy::BandedMatrix< _Type >::m_L, CppNoddy::BandedMatrix< _Type >::m_N, and CppNoddy::BandedMatrix< _Type >::m_storage.

◆ BandedMatrix() [3/3]

template<typename _Type >

CppNoddy::BandedMatrix< _Type >::BandedMatrix ( const BandedMatrix< _Type > & source )

Copy constructor.

Parameters

source The source object to be copied

Definition at line 31 of file BandedMatrix.cpp.

                                                                     :
    Sequential_Matrix_base<_Type>() {
    *this = source;
  }

Member Function Documentation

◆ assign()

template<typename _Type >

void CppNoddy::BandedMatrix< _Type >::assign ( _Type elt )

inline

Assign a value the matrix so that it has the same geometry, but zero entries in all locations including those reserved for pivotting.

Parameters

elt	The value to be assigned to all entries

Definition at line 106 of file BandedMatrix.h.

                           {
      m_storage.assign(m_storage.size(), elt);
    }

References CppNoddy::BandedMatrix< _Type >::m_storage.

Referenced by CppNoddy::PDE_IBVP< _Type >::assemble_matrix_problem().

◆ base() [1/3]

template<typename _Type >

double * CppNoddy::BandedMatrix< _Type >::base ( )

Allow direct access to the vector m_storage.

Dangerous, but used for passing to LAPACK.

◆ base() [2/3]

double * CppNoddy::BandedMatrix< double >::base ( )

Definition at line 160 of file BandedMatrix.cpp.

                                     {
    return &(m_storage[0]);
  }

◆ base() [3/3]

double * CppNoddy::BandedMatrix< std::complex< double > >::base ( )

Definition at line 165 of file BandedMatrix.cpp.

                                                  {
    //return &( m_storage[0].real() );
    return &reinterpret_cast<double(&)[2]>(m_storage[0])[0];
  }

◆ blank()

template<typename _Type >

void CppNoddy::BandedMatrix< _Type >::blank ( )

inline

Definition at line 26 of file BandedMatrix.h.

                 {
      m_storage = DenseVector<_Type>(m_N * (3 * m_L + 1), 0.0);
    }

References CppNoddy::BandedMatrix< _Type >::m_L, CppNoddy::BandedMatrix< _Type >::m_N, and CppNoddy::BandedMatrix< _Type >::m_storage.

◆ dump()

template<typename _Type >

void CppNoddy::BandedMatrix< _Type >::dump

virtual

Output the matrix contents to std::cout.

Implements CppNoddy::Sequential_Matrix_base< _Type >.

Definition at line 137 of file BandedMatrix.cpp.

                                       {
    std::cout << "BANDED mtx size = " << nrows() << " x " << ncols()
              << " with INPUT no. of bands = " << 2 * m_L + 1
              << " and total bands STORED (for pivotting) = " << 3 * m_L + 1 << "\n";
    std::cout.precision(4);
    std::cout << "- start matrix \n";
    for(std::size_t i = 0; i < nrows(); ++i) {
      std::cout << " row " << i << " =  ";
      for(std::size_t j = 0; j < nrows(); ++j) {
        if(i == j)
          std::cout << "*";
        if(((int) j < (int) i - (int) m_L) || ((int) j > (int) i + (int)(2*m_L))) {
          std::cout << 0 << ", ";
        } else {
          std::cout << operator()(i, j) << ", ";
        }
      }
      std::cout << "\n";
    }
    std::cout << "- end matrix \n";
  }

◆ frob_norm()

template<typename _Type >

double CppNoddy::BandedMatrix< _Type >::frob_norm

Returns: The sum of the two_norm of all rows

Definition at line 126 of file BandedMatrix.cpp.

                                              {
    double sum(0.0);
    for(unsigned row = 0; row < m_N; ++row) {
      // copy the row into a temp vector
      DenseVector<_Type> temp(3 * m_L + 1, &m_storage[ row * (3 * m_L + 1) ]);
      sum += temp.two_norm();
    }
    return sum;
  }

References CppNoddy::DenseVector< _Type >::two_norm().

◆ get()

template<typename _Type >

const _Type & CppNoddy::BandedMatrix< _Type >::get	(	const std::size_t &	row,
		const std::size_t &	col
	)		const

inlinevirtual

Access operator.

Implements CppNoddy::Sequential_Matrix_base< _Type >.

Definition at line 205 of file BandedMatrix.h.

                                                     {
    return operator()(row, col);
  }

◆ get_elt_iter()

template<typename _Type >

elt_iter CppNoddy::BandedMatrix< _Type >::get_elt_iter	(	std::size_t	row,
		std::size_t	col
	)

inline

Definition at line 127 of file BandedMatrix.h.

                                                        {
      return m_storage.begin() + m_L * (3 * col + 2) + row;
    }

References CppNoddy::BandedMatrix< _Type >::m_L, and CppNoddy::BandedMatrix< _Type >::m_storage.

Referenced by CppNoddy::PDE_IBVP< _Type >::assemble_matrix_problem().

◆ inf_norm()

template<typename _Type >

double CppNoddy::BandedMatrix< _Type >::inf_norm

Returns: The maximum inf_norm of all rows

Definition at line 114 of file BandedMatrix.cpp.

                                             {
    double max(0.0);
    for(unsigned row = 0; row < m_N; ++row) {
      // copy the row into a temp vector
      DenseVector<_Type> temp(3 * m_L + 1, &m_storage[ row * (3 * m_L + 1) ]);
      max = std::max(max, temp.inf_norm());
    }
    return max;
  }

References CppNoddy::DenseVector< _Type >::inf_norm().

◆ multiply()

template<typename _Type >

DenseVector< _Type > CppNoddy::BandedMatrix< _Type >::multiply ( const DenseVector< _Type > & X ) const

Right multiply the matrix by a DENSE vector.

Parameters

X	The DENSE vector to multiply by

Returns: A DENSE vector of length ncols() produced from the multiplication

Definition at line 58 of file BandedMatrix.cpp.

                                                                                    {
    std::string problem;
    problem = " The multiply method of the BandedMatrix class has \n";
    problem += " not been implemented. \n";
    throw ExceptionRuntime(problem);
    return m_storage; // dummy return
  }

◆ ncols()

template<typename _Type >

std::size_t CppNoddy::BandedMatrix< _Type >::ncols

inlinevirtual

Get the number of columns.

Returns: The number of columns in the matrix

Implements CppNoddy::Sequential_Matrix_base< _Type >.

Definition at line 222 of file BandedMatrix.h.

                                                    {
    return m_N;
  }

◆ nelts()

template<typename _Type >

std::size_t CppNoddy::BandedMatrix< _Type >::nelts

virtual

Get the number of elements.

Returns: The number of elements

Implements CppNoddy::Sequential_Matrix_base< _Type >.

Definition at line 47 of file BandedMatrix.cpp.

                                             {
    return m_storage.size();
  }

◆ noffdiag()

template<typename _Type >

std::size_t CppNoddy::BandedMatrix< _Type >::noffdiag

inline

Get the number of off-diagonal elements where the total INPUT band width is 2*noffdiag+1 since the band structure is symmetric.

Returns: The number of upper or lower offdiagonal bands; NOTE: the number of offdiagonals STORED will typically be three times this to allow for pivotting

Definition at line 227 of file BandedMatrix.h.

                                                       {
    return m_L;
  }

Referenced by CppNoddy::PDE_IBVP< _Type >::assemble_matrix_problem(), and main().

◆ nrows()

template<typename _Type >

std::size_t CppNoddy::BandedMatrix< _Type >::nrows

inlinevirtual

Get the number of rows.

Returns: The number of rows in the matrix

Implements CppNoddy::Sequential_Matrix_base< _Type >.

Definition at line 217 of file BandedMatrix.h.

                                                    {
    return m_N;
  }

◆ one_norm()

template<typename _Type >

double CppNoddy::BandedMatrix< _Type >::one_norm

Returns: The maximum one_norm of all rows

Definition at line 90 of file BandedMatrix.cpp.

                                             {
    double max(0.0);
    for(unsigned row = 0; row < m_N; ++row) {
      // copy the row into a temp vector
      DenseVector<_Type> temp(3 * m_L + 1, &m_storage[ row * (3 * m_L + 1) ]);
      max = std::max(max, temp.one_norm());
    }
    return max;
  }

References CppNoddy::DenseVector< _Type >::one_norm().

◆ operator()() [1/2]

template<typename _Type >

_Type & CppNoddy::BandedMatrix< _Type >::operator()	(	const std::size_t &	row,
		const std::size_t &	col
	)

inlinevirtual

Access operator.

Implements CppNoddy::Sequential_Matrix_base< _Type >.

Definition at line 175 of file BandedMatrix.h.

                                                                                          {
#ifdef PARANOID
    // if outside the m_Nxm_N matrix
    if((row >= m_N) || (row < 0) || (col >= m_N) || (col < 0)) {
      std::string problem;
      problem = " The operator() of BandedMatrix has been called \n";
      problem += " with a (row, col) index that is outside \n";
      problem += " the square m_Nxm_N matrix.\n";
      throw ExceptionRange(problem, m_N, m_N, row, col);
    }
    // check if the subscripts are out of the band
    if(!((col + m_L >= row) && (col <= 2*m_L + row))) {
      std::string problem;
      problem = " The operator() of BandedMatrix has been called \n";
      problem += " with a (row, col) index that is outside \n";
      problem += " the band structure.\n";
      std::cout << " m_L = " << m_L << "\n";
      std::cout << " row = " << row << "\n";
      std::cout << " col = " << col << "\n";
      throw ExceptionRange(problem, m_N, m_L, row, col);
    }
#endif
    // MOSTLY WE PUSH BANDED MATRICES TO LAPACK - so we'll keep column major
    // internal storage ... a la Fortran
    // return m_storage[ col * ( 3 * m_L + 1 ) + ( row - col ) + 2 * m_L ];
    // or equiv.
    return m_storage[ m_L * (3 * col + 2) + row ];
  }

◆ operator()() [2/2]

template<typename _Type >

const _Type & CppNoddy::BandedMatrix< _Type >::operator()	(	const std::size_t &	row,
		const std::size_t &	col
	)		const

inlinevirtual

Access operator.

Implements CppNoddy::Sequential_Matrix_base< _Type >.

Definition at line 147 of file BandedMatrix.h.

                                                                                                      {
#ifdef PARANOID
    // if outside the m_Nxm_N matrix
    if((row >= m_N) || (row < 0) || (col >= m_N) || (col < 0)) {
      std::string problem;
      problem = " The const operator() of BandedMatrix has been called \n";
      problem += " with a (row, col) index that is outside \n";
      problem += " the square m_Nxm_N matrix.\n";
      throw ExceptionGeom(problem, m_N, m_N, row, col);
    }
    // check if the subscripts are out of the band
    if(!((col + m_L >= row) && (col <= 2*m_L + row))) {
      std::string problem;
      problem = " The const operator() of BandedMatrix has been called \n";
      problem += " with a (row, col) index that is outside \n";
      problem += " the band structure. Bandwidth and offset from\n";
      problem += " the diagonal information follows.\n";
      throw ExceptionGeom(problem, m_L, col - row);
    }
#endif
    // MOSTLY WE PUSH BANDED MATRICES TO LAPACK - so we'll keep column major
    // internal storage ... a la Fortran
    // return m_storage[ col * ( 3 * m_L + 1 ) + ( row - col ) + 2 * m_L ];
    // or equiv.
    return m_storage[ m_L * (3 * col + 2) + row ];
  }

◆ operator=()

template<typename _Type >

BandedMatrix< _Type > & CppNoddy::BandedMatrix< _Type >::operator= ( const BandedMatrix< _Type > & source )

inline

Assignment operator.

Parameters

source The source object for the assignment

Returns: The newly assigned object

Definition at line 37 of file BandedMatrix.cpp.

                                                                                              {
    if(this == &source)
      return * this;
    m_storage = source.m_storage;
    m_N = source.m_N;
    m_L = source.m_L;
    return *this;
  }

◆ row_swap()

template<typename _Type >

void CppNoddy::BandedMatrix< _Type >::row_swap	(	const std::size_t &	row1,
		const std::size_t &	row2
	)

Exchange rows in the matrix.

Parameters

row1	First row to be swapped
row2	Second row to be swapped

Todo:: MAKE ME PRIVATE OR ELSE!

Definition at line 79 of file BandedMatrix.cpp.

                                                                                 {
    // WE MUST HAVE row2 > row1 & row1 must have no elements left of the diagonal!
    // only of any use to native Gaussian elimination solver
    /// \todo MAKE ME PRIVATE OR ELSE!
    for(std::size_t col = row1; col <= std::min(row1 + 2 * m_L, m_N - 1); ++col) {
      std::swap(operator()(row1, col), operator()(row2, col));
    }
  }

◆ scale()

template<typename _Type >

void CppNoddy::BandedMatrix< _Type >::scale ( const _Type & mult )

virtual

Scale all entries in the matrix by a scalar.

Parameters

mult	The scalar multiplier

Implements CppNoddy::Sequential_Matrix_base< _Type >.

Definition at line 52 of file BandedMatrix.cpp.

                                                   {
    m_storage *= mult;
  }

◆ set()

template<typename _Type >

_Type & CppNoddy::BandedMatrix< _Type >::set	(	const std::size_t &	row,
		const std::size_t &	col
	)

inlinevirtual

Access operator.

Implements CppNoddy::Sequential_Matrix_base< _Type >.

Definition at line 211 of file BandedMatrix.h.

                                               {
    return operator()(row, col);
  }

◆ transpose()

template<typename _Type >

void CppNoddy::BandedMatrix< _Type >::transpose

Transpose the matrix.

Definition at line 68 of file BandedMatrix.cpp.

                                      {
    for(std::size_t row = 0; row < m_N; ++row) {
      for(std::size_t col = std::max(0, int(row) - int(m_L)); col < row; ++col) {
        // swap elements
        std::swap(operator()(row, col), operator()(col, row));
      }
    }
  }

◆ two_norm()

template<typename _Type >

double CppNoddy::BandedMatrix< _Type >::two_norm

Returns: The maximum two_norm of all rows

Definition at line 102 of file BandedMatrix.cpp.

                                             {
    double max(0.0);
    for(unsigned row = 0; row < m_N; ++row) {
      // copy the row into a temp vector
      DenseVector<_Type> temp(3 * m_L + 1, &m_storage[ row * (3 * m_L + 1) ]);
      max = std::max(max, temp.two_norm());
    }
    return max;
  }

References CppNoddy::DenseVector< _Type >::two_norm().

Member Data Documentation

◆ m_L

template<typename _Type >

std::size_t CppNoddy::BandedMatrix< _Type >::m_L

Max number of (INPUT) bands above OR below the main diagonal.

Definition at line 138 of file BandedMatrix.h.

Referenced by CppNoddy::BandedMatrix< _Type >::BandedMatrix(), CppNoddy::BandedMatrix< _Type >::blank(), and CppNoddy::BandedMatrix< _Type >::get_elt_iter().

◆ m_N

template<typename _Type >

std::size_t CppNoddy::BandedMatrix< _Type >::m_N

The number of rows/cols in the matrix.

Definition at line 136 of file BandedMatrix.h.

Referenced by CppNoddy::BandedMatrix< _Type >::BandedMatrix(), and CppNoddy::BandedMatrix< _Type >::blank().

◆ m_storage

template<typename _Type >

DenseVector<_Type> CppNoddy::BandedMatrix< _Type >::m_storage

A contiguous vector.

Definition at line 134 of file BandedMatrix.h.

Referenced by CppNoddy::BandedMatrix< _Type >::assign(), CppNoddy::BandedMatrix< _Type >::BandedMatrix(), CppNoddy::BandedMatrix< _Type >::blank(), and CppNoddy::BandedMatrix< _Type >::get_elt_iter().

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

include/BandedMatrix.h
src/BandedMatrix.cpp

Public Types

Public Member Functions

Public Attributes

Detailed Description

Member Typedef Documentation

◆ elt_iter

Constructor & Destructor Documentation

◆ BandedMatrix() [1/3]

◆ BandedMatrix() [2/3]

◆ BandedMatrix() [3/3]

Member Function Documentation

◆ assign()

◆ base() [1/3]

◆ base() [2/3]

◆ base() [3/3]

◆ blank()

◆ dump()

◆ frob_norm()

◆ get()

◆ get_elt_iter()

◆ inf_norm()

◆ multiply()

◆ ncols()

◆ nelts()

◆ noffdiag()

◆ nrows()

◆ one_norm()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator=()

◆ row_swap()

◆ scale()

◆ set()

◆ transpose()

◆ two_norm()

Member Data Documentation

◆ m_L

◆ m_N

◆ m_storage