Class with mathematical matrix operations. More...

#include <densematrix.hh>

Public Types
typedef std::size_t	size_type
	Type used for array indices.

typedef std::vector< REAL >	VType

typedef VType::const_iterator	ConstVectorIterator

typedef VType::iterator	VectorIterator

Public Member Functions
	DenseMatrix ()
	default constructor (empty Matrix)

	DenseMatrix (const std::size_t _rows, const std::size_t _cols, const REAL def_val=0)
	constructor

	DenseMatrix (const std::initializer_list< std::initializer_list< REAL > > &v)
	constructor from initializer list

	DenseMatrix (const hdnum::SparseMatrix< REAL > &other)
	constructor from hdnum::SparseMatrix

void	addNewRow (const hdnum::Vector< REAL > &rowvector)

size_t	rowsize () const
	get number of rows of the matrix

size_t	colsize () const
	get number of columns of the matrix

bool	scientific () const

void	scientific (bool b) const
	Switch between floating point (default=true) and fixed point (false) display.

std::size_t	iwidth () const
	get index field width for pretty-printing

std::size_t	width () const
	get data field width for pretty-printing

std::size_t	precision () const
	get data precision for pretty-printing

void	iwidth (std::size_t i) const
	set index field width for pretty-printing

void	width (std::size_t i) const
	set data field width for pretty-printing

void	precision (std::size_t i) const
	set data precision for pretty-printing

REAL &	operator() (const std::size_t row, const std::size_t col)
	(i,j)-operator for accessing entries of a (m x n)-matrix directly

const REAL &	operator() (const std::size_t row, const std::size_t col) const
	read-access on matrix element A_ij using A(i,j)

const ConstVectorIterator	operator[] (const std::size_t row) const
	read-access on matrix element A_ij using A[i][j]

VectorIterator	operator[] (const std::size_t row)
	write-access on matrix element A_ij using A[i][j]

DenseMatrix &	operator= (const DenseMatrix &A)
	assignment operator

DenseMatrix &	operator= (const REAL value)
	assignment from a scalar value

DenseMatrix	sub (size_type i, size_type j, size_type rows, size_type cols)
	Submatrix extraction.

DenseMatrix	transpose () const
	Transposition.

DenseMatrix &	operator+= (const DenseMatrix &B)
	Addition assignment.

DenseMatrix &	operator-= (const DenseMatrix &B)
	Subtraction assignment.

DenseMatrix &	operator*= (const REAL s)
	Scalar multiplication assignment.

DenseMatrix &	operator/= (const REAL s)
	Scalar division assignment.

void	update (const REAL s, const DenseMatrix &B)
	Scaled update of a Matrix.

template<class V >
void	mv (Vector< V > &y, const Vector< V > &x) const
	matrix vector product y = A*x

template<class V >
void	umv (Vector< V > &y, const Vector< V > &x) const
	update matrix vector product y += A*x

template<class V >
void	umv (Vector< V > &y, const V &s, const Vector< V > &x) const
	update matrix vector product y += sA*x

void	mm (const DenseMatrix< REAL > &A, const DenseMatrix< REAL > &B)
	assign to matrix product C = A*B to matrix C

void	umm (const DenseMatrix< REAL > &A, const DenseMatrix< REAL > &B)
	add matrix product A*B to matrix C

void	sc (const Vector< REAL > &x, std::size_t k)
	set column: make x the k'th column of A

void	sr (const Vector< REAL > &x, std::size_t k)
	set row: make x the k'th row of A

REAL	norm_infty () const
	compute row sum norm

REAL	norm_1 () const
	compute column sum norm

Vector< REAL >	operator* (const Vector< REAL > &x) const
	vector = matrix * vector

DenseMatrix	operator* (const DenseMatrix &x) const
	matrix = matrix * matrix

DenseMatrix	operator+ (const DenseMatrix &x) const
	matrix = matrix + matrix

DenseMatrix	operator- (const DenseMatrix &x) const
	matrix = matrix - matrix

Related Symbols
(Note that these are not member symbols.)
template<class T >
void	identity (DenseMatrix< T > &A)

template<typename REAL >
void	spd (DenseMatrix< REAL > &A)

template<typename REAL >
void	vandermonde (DenseMatrix< REAL > &A, const Vector< REAL > x)

template<typename REAL >
void	readMatrixFromFileDat (const std::string &filename, DenseMatrix< REAL > &A)
	Read matrix from a text file.

template<typename REAL >
void	readMatrixFromFileMatrixMarket (const std::string &filename, DenseMatrix< REAL > &A)
	Read matrix from a matrix market file.

Detailed Description

template<typename REAL>
class hdnum::DenseMatrix< REAL >

Class with mathematical matrix operations.

Member Function Documentation

◆ colsize()

template<typename REAL >

size_t hdnum::DenseMatrix< REAL >::colsize ( ) const

inline

get number of columns of the matrix

Example:

hdnum::DenseMatrix<double> A(4,5);
size_t nColumns = A.colsize();
std::cout << "Matrix A has " << nColumns << " columns." << std::endl;

Output:

Matrix A has 5 columns.

◆ mm()

template<typename REAL >

void hdnum::DenseMatrix< REAL >::mm	(	const DenseMatrix< REAL > &	A,
		const DenseMatrix< REAL > &	B )

inline

assign to matrix product C = A*B to matrix C

Implements C = A*B where A and B are matrices

Parameters

[in]	A	constant reference to a DenseMatrix
[in]	B	constant reference to a DenseMatrix

Example:

hdnum::DenseMatrix<double> A(2,6,1.0);
hdnum::DenseMatrix<double> B(6,3,-1.0);
 
A.scientific(false); // fixed point representation for all DenseMatrix
objects A.width(6);          // use at least 6 columns for displaying
matrix entries A.precision(3);      // display 3 digits behind the point
 
std::cout << "A =" << A << std::endl;
std::cout << "B =" << B << std::endl;
 
hdnum::DenseMatrix<double> C(2,3);
C.mm(A,B);
std::cout << "C = A*B =" << C << std::endl;

Output:

A =
0      1      2      3      4      5
0   1.000  1.000  1.000  1.000  1.000  1.000
1   1.000  1.000  1.000  1.000  1.000  1.000

B =
0      1      2
0  -1.000 -1.000 -1.000
1  -1.000 -1.000 -1.000
2  -1.000 -1.000 -1.000
3  -1.000 -1.000 -1.000
4  -1.000 -1.000 -1.000
5  -1.000 -1.000 -1.000

C = A*B =
0      1      2
0  -6.000 -6.000 -6.000
1  -6.000 -6.000 -6.000

◆ mv()

template<typename REAL >

template<class V >

void hdnum::DenseMatrix< REAL >::mv	(	Vector< V > &	y,
		const Vector< V > &	x ) const

inline

matrix vector product y = A*x

Implements y = A*x where x and y are a vectors and A is a matrix

Parameters

[in]	y	reference to the resulting Vector
[in]	x	constant reference to a Vector

Example:

hdnum::Vector<double> x(3,10.0);
hdnum::Vector<double> y(2);
hdnum::DenseMatrix<double> A(2,3,1.0);
 
x.scientific(false); // fixed point representation for all Vector objects
A.scientific(false); // fixed point representation for all DenseMatrix
objects
 
std::cout << "A =" << A << std::endl;
std::cout << "x =" << x << std::endl;
A.mv(y,x);
std::cout << "y = A*x =" << y << std::endl;

Output:

A =
0          1          2
0       1.000      1.000      1.000
1       1.000      1.000      1.000

x =
[ 0]     10.0000000
[ 1]     10.0000000
[ 2]     10.0000000

y = A*x =
[ 0]     30.0000000
[ 1]     30.0000000

◆ operator()()

template<typename REAL >

REAL & hdnum::DenseMatrix< REAL >::operator()	(	const std::size_t	row,
		const std::size_t	col )

inline

(i,j)-operator for accessing entries of a (m x n)-matrix directly

Parameters

[in]	row	row index (0...m-1)
[in]	col	column index (0...n-1)

Example:

hdnum::DenseMatrix<double> A(4,4);
A.scientific(false); // fixed point representation for all DenseMatrix
objects A.width(8); A.precision(3);
 
identity(A);  // Defines the identity matrix of the same dimension
std::cout << "A=" << A << std::endl;
 
std::cout << "reading A(0,0)=" << A(0,0) << std::endl;
 
std::cout << "resetting A(0,0) and A(2,3)..." << std::endl;
A(0,0) = 1.234;
A(2,3) = 432.1;
 
std::cout << "A=" << A << std::endl;

Output:

A=
0        1        2        3
0     1.000    0.000    0.000    0.000
1     0.000    1.000    0.000    0.000
2     0.000    0.000    1.000    0.000
3     0.000    0.000    0.000    1.000

reading A(0,0)=1.000
resetting A(0,0) and A(2,3)...
A=
0        1        2        3
0     1.234    0.000    0.000    0.000
1     0.000    1.000    0.000    0.000
2     0.000    0.000    1.000  432.100
3     0.000    0.000    0.000    1.000

◆ operator*() [1/2]

template<typename REAL >

DenseMatrix hdnum::DenseMatrix< REAL >::operator* ( const DenseMatrix< REAL > & x ) const

inline

matrix = matrix * matrix

Parameters

[in] x constant reference to a DenseMatrix

Example:

hdnum::DenseMatrix<double> A(3,3,2.0);
hdnum::DenseMatrix<double> B(3,3,4.0);
hdnum::DenseMatrix<double> C(3,3);
 
A.scientific(false); // fixed point representation for all DenseMatrix
objects A.width(8); A.precision(1);
 
std::cout << "A=" << A << std::endl;
std::cout << "B=" << B << std::endl;
C=A*B;
std::cout << "C=A*B=" << C << std::endl;

Output:

A=
0        1        2
0       2.0      2.0      2.0
1       2.0      2.0      2.0
2       2.0      2.0      2.0

B=
0        1        2
0       4.0      4.0      4.0
1       4.0      4.0      4.0
2       4.0      4.0      4.0

C=A*B=
0        1        2
0      24.0     24.0     24.0
1      24.0     24.0     24.0
2      24.0     24.0     24.0

◆ operator*() [2/2]

template<typename REAL >

Vector< REAL > hdnum::DenseMatrix< REAL >::operator* ( const Vector< REAL > & x ) const

inline

vector = matrix * vector

Parameters

[in] x constant reference to a Vector

Example:

hdnum::Vector<double> x(3,4.0);
hdnum::DenseMatrix<double> A(3,3,2.0);
hdnum::Vector<double> y(3);
 
A.scientific(false); // fixed point representation for all DenseMatrix
objects A.width(8); A.precision(1);
 
x.scientific(false); // fixed point representation for all Vector objects
x.width(8);
x.precision(1);
 
 
std::cout << "A=" << A << std::endl;
std::cout << "x=" << x << std::endl;
y=A*x;
std::cout << "y=A*x" << y << std::endl;

Output:

A=
0        1        2
0       2.0      2.0      2.0
1       2.0      2.0      2.0
2       2.0      2.0      2.0

x=
[ 0]     4.0
[ 1]     4.0
[ 2]     4.0

y=A*x
[ 0]    24.0
[ 1]    24.0
[ 2]    24.0

◆ operator*=()

template<typename REAL >

DenseMatrix & hdnum::DenseMatrix< REAL >::operator*= ( const REAL s )

inline

Scalar multiplication assignment.

Implements A *= s where s is a scalar

Parameters

[in] s scalar value to multiply with

Example:

double s = 0.5;
hdnum::DenseMatrix<double> A(2,3,1.0);
std::cout << "A=" << A << std::endl;
A *= s;
std::cout << "A=" << A << std::endl;

Output:

A=
0          1          2
0   1.000e+00  1.000e+00  1.000e+00
1   1.000e+00  1.000e+00  1.000e+00

0.5*A =
0          1          2
0   5.000e-01  5.000e-01  5.000e-01
1   5.000e-01  5.000e-01  5.000e-01

◆ operator+()

template<typename REAL >

DenseMatrix hdnum::DenseMatrix< REAL >::operator+ ( const DenseMatrix< REAL > & x ) const

inline

matrix = matrix + matrix

Parameters

[in] x constant reference to a DenseMatrix

Example:

hdnum::DenseMatrix<double> A(3,3,2.0);
hdnum::DenseMatrix<double> B(3,3,4.0);
hdnum::DenseMatrix<double> C(3,3);
 
A.scientific(false); // fixed point representation for all DenseMatrix
objects A.width(8); A.precision(1);
 
std::cout << "A=" << A << std::endl;
std::cout << "B=" << B << std::endl;
C=A+B;
std::cout << "C=A+B=" << C << std::endl;

Output:

A=
0        1        2
0       2.0      2.0      2.0
1       2.0      2.0      2.0
2       2.0      2.0      2.0

B=
0        1        2
0       4.0      4.0      4.0
1       4.0      4.0      4.0
2       4.0      4.0      4.0

C=A+B=
0        1        2
0       6.0      6.0      6.0
1       6.0      6.0      6.0
2       6.0      6.0      6.0

◆ operator+=()

template<typename REAL >

DenseMatrix & hdnum::DenseMatrix< REAL >::operator+= ( const DenseMatrix< REAL > & B )

inline

Addition assignment.

Implements A += B matrix addition

Parameters

[in] B another Matrix

◆ operator-()

template<typename REAL >

DenseMatrix hdnum::DenseMatrix< REAL >::operator- ( const DenseMatrix< REAL > & x ) const

inline

matrix = matrix - matrix

Parameters

[in] x constant reference to a DenseMatrix

Example:

hdnum::DenseMatrix<double> A(3,3,2.0);
hdnum::DenseMatrix<double> B(3,3,4.0);
hdnum::DenseMatrix<double> C(3,3);
 
A.scientific(false); // fixed point representation for all DenseMatrix
objects A.width(8); A.precision(1);
 
std::cout << "A=" << A << std::endl;
std::cout << "B=" << B << std::endl;
C=A-B;
std::cout << "C=A-B=" << C << std::endl;

Output:

A=
0        1        2
0       2.0      2.0      2.0
1       2.0      2.0      2.0
2       2.0      2.0      2.0

B=
0        1        2
0       4.0      4.0      4.0
1       4.0      4.0      4.0
2       4.0      4.0      4.0

C=A-B=
0        1        2
0      -2.0     -2.0     -2.0
1      -2.0     -2.0     -2.0
2      -2.0     -2.0     -2.0

◆ operator-=()

template<typename REAL >

DenseMatrix & hdnum::DenseMatrix< REAL >::operator-= ( const DenseMatrix< REAL > & B )

inline

Subtraction assignment.

Implements A -= B matrix subtraction

Parameters

[in] B another matrix

◆ operator/=()

template<typename REAL >

DenseMatrix & hdnum::DenseMatrix< REAL >::operator/= ( const REAL s )

inline

Scalar division assignment.

Implements A /= s where s is a scalar

Parameters

[in] s scalar value to multiply with

Example:

double s = 0.5;
hdnum::DenseMatrix<double> A(2,3,1.0);
std::cout << "A=" << A << std::endl;
A /= s;
std::cout << "A=" << A << std::endl;

Output:

A=
0          1          2
0   1.000e+00  1.000e+00  1.000e+00
1   1.000e+00  1.000e+00  1.000e+00

A/0.5 =
0          1          2
0   2.000e+00  2.000e+00  2.000e+00
1   2.000e+00  2.000e+00  2.000e+00

◆ operator=() [1/2]

template<typename REAL >

DenseMatrix & hdnum::DenseMatrix< REAL >::operator= ( const DenseMatrix< REAL > & A )

inline

assignment operator

Example:

hdnum::DenseMatrix<double> A(4,4);
spd(A);
hdnum::DenseMatrix<double> B(4,4);
B = A;
std::cout << "B=" << B << std::endl;

Output:

B=
0          1          2          3
0   4.000e+00 -1.000e+00 -2.500e-01 -1.111e-01
1  -1.000e+00  4.000e+00 -1.000e+00 -2.500e-01
2  -2.500e-01 -1.000e+00  4.000e+00 -1.000e+00
3  -1.111e-01 -2.500e-01 -1.000e+00  4.000e+00

◆ operator=() [2/2]

template<typename REAL >

DenseMatrix & hdnum::DenseMatrix< REAL >::operator= ( const REAL value )

inline

assignment from a scalar value

Example:

hdnum::DenseMatrix<double> A(2,3);
A = 5.432;
A.scientific(false); // fixed point representation for all DenseMatrix
objects A.width(8); A.precision(3); std::cout << "A=" << A << std::endl;

Output:

A=
0        1        2
0     5.432    5.432    5.432
1     5.432    5.432    5.432

◆ rowsize()

template<typename REAL >

size_t hdnum::DenseMatrix< REAL >::rowsize ( ) const

inline

get number of rows of the matrix

Example:

hdnum::DenseMatrix<double> A(4,5);
size_t nRows = A.rowsize();
std::cout << "Matrix A has " << nRows << " rows." << std::endl;

Output:

Matrix A has 4 rows.

◆ sc()

template<typename REAL >

void hdnum::DenseMatrix< REAL >::sc	(	const Vector< REAL > &	x,
		std::size_t	k )

inline

set column: make x the k'th column of A

Parameters

[in]	x	constant reference to a Vector
[in]	k	number of the column of A to be set

Example:

hdnum::Vector<double> x(2,434.0);
hdnum::DenseMatrix<double> A(2,6);
 
A.scientific(false); // fixed point representation for all DenseMatrix
objects A.width(8); A.precision(1);
 
std::cout << "original A=" << A << std::endl;
A.sc(x,3);   // redefine fourth column of the matrix
std::cout << "modified A=" << A << std::endl;

Output:

original A=
0        1        2        3        4        5
0       0.0      0.0      0.0      0.0      0.0      0.0
1       0.0      0.0      0.0      0.0      0.0      0.0

modified A=
0        1        2        3        4        5
0       0.0      0.0      0.0    434.0      0.0      0.0
1       0.0      0.0      0.0    434.0      0.0      0.0

◆ scientific()

template<typename REAL >

void hdnum::DenseMatrix< REAL >::scientific ( bool b ) const

inline

Switch between floating point (default=true) and fixed point (false) display.

Example:

hdnum::DenseMatrix<double> A(4,4);
A.scientific(false); // fixed point representation for all DenseMatrix
objects A.width(8); A.precision(3); identity(A);  // Defines the identity
matrix of the same dimension std::cout << "A=" << A << std::endl; 

Output:

A=
0        1        2        3
0     1.000    0.000    0.000    0.000
1     0.000    1.000    0.000    0.000
2     0.000    0.000    1.000    0.000
3     0.000    0.000    0.000    1.000

◆ sr()

template<typename REAL >

void hdnum::DenseMatrix< REAL >::sr	(	const Vector< REAL > &	x,
		std::size_t	k )

inline

set row: make x the k'th row of A

Parameters

[in]	x	constant reference to a Vector
[in]	k	number of the row of A to be set

Example:

hdnum::Vector<double> x(3,434.0);
hdnum::DenseMatrix<double> A(3,3);
 
A.scientific(false); // fixed point representation for all DenseMatrix
objects A.width(8); A.precision(1);
 
std::cout << "original A=" << A << std::endl;
A.sr(x,1);   // redefine second row of the matrix
std::cout << "modified A=" << A << std::endl;

Output:

original A=
0        1        2
0       0.0      0.0      0.0
1       0.0      0.0      0.0
2       0.0      0.0      0.0

modified A=
0        1        2
0       0.0      0.0      0.0
1     434.0    434.0    434.0
2       0.0      0.0      0.0

◆ sub()

template<typename REAL >

DenseMatrix hdnum::DenseMatrix< REAL >::sub	(	size_type	i,
		size_type	j,
		size_type	rows,
		size_type	cols )

inline

Submatrix extraction.

Returns a new matrix that is a subset of the components of the given matrix.

Parameters

[in]	i	first row index of the new matrix
[in]	j	first column index of the new matrix
[in]	rows	row size of the new matrix, i.e. it has components [i,i+rows-1]
[in]	cols	column size of the new matrix, i.e. it has components [j,j+cols-1]

◆ transpose()

template<typename REAL >

DenseMatrix hdnum::DenseMatrix< REAL >::transpose ( ) const

inline

Transposition.

Return the transposed as a new matrix.

◆ umm()

template<typename REAL >

void hdnum::DenseMatrix< REAL >::umm	(	const DenseMatrix< REAL > &	A,
		const DenseMatrix< REAL > &	B )

inline

add matrix product A*B to matrix C

Implements C += A*B where A, B and C are matrices

Parameters

[in]	A	constant reference to a DenseMatrix
[in]	B	constant reference to a DenseMatrix

Example:

hdnum::DenseMatrix<double> A(2,6,1.0);
hdnum::DenseMatrix<double> B(6,3,-1.0);
hdnum::DenseMatrix<double> C(2,3,0.5);
 
A.scientific(false); // fixed point representation for all DenseMatrix
objects A.width(6); A.precision(3);
 
std::cout << "C =" << C << std::endl;
std::cout << "A =" << A << std::endl;
std::cout << "B =" << B << std::endl;
 
C.umm(A,B);
std::cout << "C + A*B =" << C << std::endl;

Output:

C =
0      1      2
0   0.500  0.500  0.500
1   0.500  0.500  0.500

A =
0      1      2      3      4      5
0   1.000  1.000  1.000  1.000  1.000  1.000
1   1.000  1.000  1.000  1.000  1.000  1.000

B =
0      1      2
0  -1.000 -1.000 -1.000
1  -1.000 -1.000 -1.000
2  -1.000 -1.000 -1.000
3  -1.000 -1.000 -1.000
4  -1.000 -1.000 -1.000
5  -1.000 -1.000 -1.000

C + A*B =
0      1      2
0  -5.500 -5.500 -5.500
1  -5.500 -5.500 -5.500

◆ umv() [1/2]

template<typename REAL >

template<class V >

void hdnum::DenseMatrix< REAL >::umv	(	Vector< V > &	y,
		const V &	s,
		const Vector< V > &	x ) const

inline

update matrix vector product y += sA*x

Implements y += sA*x where s is a scalar value, x and y are a vectors and A is a matrix

Parameters

[in]	y	reference to the resulting Vector
[in]	s	constant reference to a number type
[in]	x	constant reference to a Vector

Example:

double s=0.5;
hdnum::Vector<double> x(3,10.0);
hdnum::Vector<double> y(2,5.0);
hdnum::DenseMatrix<double> A(2,3,1.0);
 
x.scientific(false); // fixed point representation for all Vector objects
A.scientific(false); // fixed point representation for all DenseMatrix
objects
 
std::cout << "y =" << y << std::endl;
std::cout << "A =" << A << std::endl;
std::cout << "x =" << x << std::endl;
A.umv(y,s,x);
std::cout << "y = s*A*x =" << y << std::endl;

Output:

y =
[ 0]      5.0000000
[ 1]      5.0000000

A =
0          1          2
0       1.000      1.000      1.000
1       1.000      1.000      1.000

x =
[ 0]     10.0000000
[ 1]     10.0000000
[ 2]     10.0000000

y = s*A*x =
[ 0]     20.0000000
[ 1]     20.0000000

◆ umv() [2/2]

template<typename REAL >

template<class V >

void hdnum::DenseMatrix< REAL >::umv	(	Vector< V > &	y,
		const Vector< V > &	x ) const

inline

update matrix vector product y += A*x

Implements y += A*x where x and y are a vectors and A is a matrix

Parameters

[in]	y	reference to the resulting Vector
[in]	x	constant reference to a Vector

Example:

hdnum::Vector<double> x(3,10.0);
hdnum::Vector<double> y(2,5.0);
hdnum::DenseMatrix<double> A(2,3,1.0);
 
x.scientific(false); // fixed point representation for all Vector objects
A.scientific(false); // fixed point representation for all DenseMatrix
objects
 
std::cout << "y =" << y << std::endl;
std::cout << "A =" << A << std::endl;
std::cout << "x =" << x << std::endl;
A.umv(y,x);
std::cout << "y = A*x =" << y << std::endl;

Output:

y =
[ 0]      5.0000000
[ 1]      5.0000000

A =
0          1          2
0       1.000      1.000      1.000
1       1.000      1.000      1.000

x =
[ 0]     10.0000000
[ 1]     10.0000000
[ 2]     10.0000000

y + A*x =
[ 0]     35.0000000
[ 1]     35.0000000

◆ update()

template<typename REAL >

void hdnum::DenseMatrix< REAL >::update	(	const REAL	s,
		const DenseMatrix< REAL > &	B )

inline

Scaled update of a Matrix.

Implements A += s*B where s is a scalar and B a matrix

Parameters

[in]	s	scalar value to multiply with
[in]	B	another matrix

Example:

double s = 0.5;
hdnum::DenseMatrix<double> A(2,3,1.0);
hdnum::DenseMatrix<double> B(2,3,2.0);
A.update(s,B);
std::cout << "A + s*B =" << A << std::endl;

Output:

A + s*B =
0          1          2
0       1.500      1.500      1.500
1       1.500      1.500      1.500

Friends And Related Symbol Documentation

◆ identity()

template<class T >

void identity ( DenseMatrix< T > & A )

template<class T>

inline void identity (DenseMatrix<T> &A)

Parameters

[in] A reference to a DenseMatrix that shall be filled with entries

Example:

hdnum::DenseMatrix<double> A(4,4);
identity(A);
 
A.scientific(false); // fixed point representation for all DenseMatrix objects
A.width(10);
A.precision(5);
 
std::cout << "A=" << A << std::endl;

Output:

A=
0          1          2          3
0     1.00000    0.00000    0.00000    0.00000
1     0.00000    1.00000    0.00000    0.00000
2     0.00000    0.00000    1.00000    0.00000
3     0.00000    0.00000    0.00000    1.00000

◆ readMatrixFromFileDat()

template<typename REAL >

void readMatrixFromFileDat	(	const std::string &	filename,
		DenseMatrix< REAL > &	A )

Parameters

[in]	filename	name of the text file
[in,out]	A	reference to a DenseMatrix

Example:

hdnum::DenseMatrix<number> L;
readMatrixFromFile("matrixL.dat", L );
std::cout << "L=" << L << std::endl;

Output:

Contents of "matrixL.dat":
1.000e+00  0.000e+00  0.000e+00
2.000e+00  1.000e+00  0.000e+00
3.000e+00  2.000e+00  1.000e+00

would give:
L=
0          1          2
0   1.000e+00  0.000e+00  0.000e+00
1   2.000e+00  1.000e+00  0.000e+00
2   3.000e+00  2.000e+00  1.000e+00

◆ readMatrixFromFileMatrixMarket()

template<typename REAL >

void readMatrixFromFileMatrixMarket	(	const std::string &	filename,
		DenseMatrix< REAL > &	A )

Parameters

[in]	filename	name of the text file
[in,out]	A	reference to a DenseMatrix

Example:

hdnum::DenseMatrix<number> L;
readMatrixFromFile("matrixL.mtx", L );
std::cout << "L=" << L << std::endl;

Output:

Contents of "matrixL.mtx":
3 3 6
1 1 1
2 1 2
2 2 1
3 1 3
3 2 2
3 3 1

would give:
L=
0          1          2
0   1.000e+00  0.000e+00  0.000e+00
1   2.000e+00  1.000e+00  0.000e+00
2   3.000e+00  2.000e+00  1.000e+00

◆ spd()

template<typename REAL >

void spd ( DenseMatrix< REAL > & A )

template<typename REAL>

inline void spd (DenseMatrix<REAL> &A)

Parameters

[in] A reference to a DenseMatrix that shall be filled with entries

Example:

hdnum::DenseMatrix<double> A(4,4);
spd(A);
 
A.scientific(false); // fixed point representation for all DenseMatrix objects
A.width(10);
A.precision(5);
 
std::cout << "A=" << A << std::endl;

Output:

A=
0          1          2          3
0     4.00000   -1.00000   -0.25000   -0.11111
1    -1.00000    4.00000   -1.00000   -0.25000
2    -0.25000   -1.00000    4.00000   -1.00000
3    -0.11111   -0.25000   -1.00000    4.00000

◆ vandermonde()

template<typename REAL >

void vandermonde	(	DenseMatrix< REAL > &	A,
		const Vector< REAL >	x )

template<typename REAL>

inline void vandermonde (DenseMatrix<REAL> &A, const Vector<REAL> x)

hdnum::DenseMatrix::vandermonde

void vandermonde(DenseMatrix< REAL > &A, const Vector< REAL > x)

Definition densematrix.hh:1344

Parameters

[in]	A	reference to a DenseMatrix that shall be filled with entries
[in]	x	constant reference to a Vector

Example:

hdnum::Vector<double> x(4);
fill(x,2.0,1.0);
hdnum::DenseMatrix<double> A(4,4);
vandermonde(A,x);
 
A.scientific(false); // fixed point representation for all DenseMatrix objects
A.width(10);
A.precision(5);
 
x.scientific(false); // fixed point representation for all Vector objects
x.width(10);
x.precision(5);
 
std::cout << "x=" << x << std::endl;
std::cout << "A=" << A << std::endl;

Output:

x=
[ 0]   2.00000
[ 1]   3.00000
[ 2]   4.00000
[ 3]   5.00000

A=
0          1          2          3
0     1.00000    2.00000    4.00000    8.00000
1     1.00000    3.00000    9.00000   27.00000
2     1.00000    4.00000   16.00000   64.00000
3     1.00000    5.00000   25.00000  125.00000

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

src/densematrix.hh

Public Types

Public Member Functions

Related Symbols

Detailed Description

Member Function Documentation

◆ colsize()

◆ mm()

◆ mv()

◆ operator()()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ rowsize()

◆ sc()

◆ scientific()

◆ sr()

◆ sub()

◆ transpose()

◆ umm()

◆ umv() [1/2]

◆ umv() [2/2]

◆ update()

Friends And Related Symbol Documentation

◆ identity()

◆ readMatrixFromFileDat()

◆ readMatrixFromFileMatrixMarket()

◆ spd()

◆ vandermonde()