NxN matrix. More...

#include <JMatrixND.hh>

Inheritance diagram for JMATH::JMatrixND:

Public Member Functions
	JMatrixND ()
	Default constructor. More...

	JMatrixND (const size_t size)
	Constructor. More...

	JMatrixND (const JMatrixND &A)
	Copy constructor. More...

	JMatrixND (JMatrixND &&A)
	Move constructor. More...

JMatrixND &	operator= (const JMatrixND &A)
	Assignment operator. More...

JMatrixND &	operator= (JMatrixND &&A)
	Move assignment operator. More...

void	resize (const size_t size)
	Resize matrix. More...

JMatrixND &	reset ()
	Set matrix to the null matrix. More...

JMatrixND &	setIdentity ()
	Set to identity matrix. More...

JMatrixND &	negate ()
	Negate matrix. More...

JMatrixND &	add (const JMatrixND &A)
	Matrix addition. More...

JMatrixND &	sub (const JMatrixND &A)
	Matrix subtraction. More...

JMatrixND &	mul (const double factor)
	Scale matrix. More...

JMatrixND &	div (const double factor)
	Scale matrix. More...

JMatrixND &	mul (const JMatrixND &A, const JMatrixND &B)
	Matrix multiplication. More...

bool	equals (const JMatrixND &A, const double eps=std::numeric_limits< double >::min()) const
	Equality. More...

bool	isIdentity (const double eps=std::numeric_limits< double >::min()) const
	Test identity. More...

bool	isSymmetric (const double eps=std::numeric_limits< double >::min()) const
	Test symmetry. More...

double	getDot (const JVectorND &v) const
	Get dot product. More...

void	clear ()
	Clear memory. More...

void	set (const JMatrixND_t &A)
	Set matrix. More...

void	swap (JMatrixND_t &A)
	Swap matrices. More...

JMatrixND_t &	transpose ()
	Transpose. More...

size_t	size () const
	Get dimension of matrix. More...

size_t	capacity () const
	Get capacity of dimension. More...

bool	empty () const
	Check emptyness. More...

const double *	data () const
	Get pointer to data. More...

double *	data ()
	Get pointer to data. More...

const double *	operator[] (size_t row) const
	Get row data. More...

double *	operator[] (size_t row)
	Get row data. More...

double	operator() (const size_t row, const size_t col) const
	Get matrix element. More...

double &	operator() (const size_t row, const size_t col)
	Get matrix element. More...

double	at (size_t row, size_t col) const
	Get matrix element. More...

double &	at (size_t row, size_t col)
	Get matrix element. More...

JMatrixND &	mul (const JNullType &object)
	Multiply with object. More...

Protected Member Functions
JMatrixND_t &	getInstance ()
	Get work space. More...

void	rswap (size_t r1, size_t r2)

void	cswap (size_t c1, size_t c2)
	Swap columns. More...

Protected Attributes
JMatrixND_t	ws

double *	__p
	pointer to data More...

size_t	__n
	dimension of matrix More...

size_t	__m
	capacity of matrix More...

Friends
JReader &	operator>> (JReader &in, JMatrixND &A)
	Read matrix from input. More...

JWriter &	operator<< (JWriter &out, const JMatrixND &A)
	Write matrix to output. More...

std::ostream &	operator<< (std::ostream &out, const JMatrixND &A)
	Print ASCII formatted output. More...

Detailed Description

NxN matrix.

Definition at line 345 of file JMatrixND.hh.

Constructor & Destructor Documentation

JMATH::JMatrixND::JMatrixND ( )

inline

Default constructor.

Definition at line 370 of file JMatrixND.hh.

371 {}

JMATH::JMatrixND::JMatrixND ( const size_t size )

inline

Constructor.

The matrix is set to zero.

Parameters

size dimension

Definition at line 381 of file JMatrixND.hh.

     {
       resize(size);
       reset();
     }

JMATH::JMatrixND::JMatrixND ( const JMatrixND & A )

inline

Copy constructor.

Parameters

A matrix

Definition at line 393 of file JMatrixND.hh.

     {
       set(A);
     }

JMATH::JMatrixND::JMatrixND ( JMatrixND && A )

inline

Move constructor.

Parameters

A matrix

Definition at line 404 of file JMatrixND.hh.

     {
       swap(A);
     }

Member Function Documentation

JMatrixND_t& JMATH::JMatrixND::getInstance ( )

inlineprotected

Get work space.

Returns: work space

Definition at line 358 of file JMatrixND.hh.

     {
       return ws;
     }

JMatrixND& JMATH::JMatrixND::operator= ( const JMatrixND & A )

inline

Assignment operator.

Parameters

A matrix

Definition at line 415 of file JMatrixND.hh.

     {
       this->set(A);
 
       return *this;
     }

JMatrixND& JMATH::JMatrixND::operator= ( JMatrixND && A )

inline

Move assignment operator.

Parameters

A matrix

Definition at line 428 of file JMatrixND.hh.

     {
       this->swap(A);
 
       return *this;
     }

void JMATH::JMatrixND::resize ( const size_t size )

inline

Resize matrix.

Note that this method does not maintain data in the matrix.

Parameters

size dimension

Definition at line 443 of file JMatrixND.hh.

     {
       static_cast<JMatrixND_t&>(*this).resize(size);
 
       getInstance().resize(size);
     }

JMatrixND& JMATH::JMatrixND::reset ( )

inline

Set matrix to the null matrix.

Returns: this matrix

Definition at line 456 of file JMatrixND.hh.

     {
       JMatrixND_t::reset();
 
       JMatrixND_t& A = getInstance();
 
       A.resize(this->size());
 
       return *this;
     }

JMatrixND& JMATH::JMatrixND::setIdentity ( )

inline

Set to identity matrix.

Returns: this matrix

Definition at line 473 of file JMatrixND.hh.

     {
       reset();
 
       for (size_t i = 0; i != this->size(); ++i) {
         (*this)(i,i) = 1.0;
       }
 
       return *this;
     }

JMatrixND& JMATH::JMatrixND::negate ( )

inline

Negate matrix.

Returns: this matrix

Definition at line 490 of file JMatrixND.hh.

     {
       double* p = this->data();
 
       for (size_t i = this->size()*this->size(); i != 0; --i, ++p) {
         *p = -*p;
       }
 
       return *this;
     }

JMatrixND& JMATH::JMatrixND::add ( const JMatrixND & A )

inline

Matrix addition.

Parameters

A matrix

Returns: this matrix

Definition at line 508 of file JMatrixND.hh.

     {
       if (this->size() == A.size()) {
 
         double*       p = this->data();
         const double* q = A.data();
 
         for (size_t i = this->size()*this->size(); i != 0; --i, ++p, ++q) {
           *p += *q;
         }
 
       } else {
         THROW(JException, "JMatrixND::add() inconsistent matrix dimensions " << this->size() << ' ' << A.size());
       }
 
       return *this;
     }

JMatrixND& JMATH::JMatrixND::sub ( const JMatrixND & A )

inline

Matrix subtraction.

Parameters

A matrix

Returns: this matrix

Definition at line 533 of file JMatrixND.hh.

     {
       if (this->size() == A.size()) {
 
         double*       p = this->data();
         const double* q = A.data();
 
         for (size_t i = this->size()*this->size(); i != 0; --i, ++p, ++q) {
           *p -= *q;
         }
 
       } else {
         THROW(JException, "JMatrixND::sub() inconsistent matrix dimensions " << this->size() << ' ' << A.size());
       }
 
       return *this;
     }

JMatrixND& JMATH::JMatrixND::mul ( const double factor )

inline

Scale matrix.

Parameters

factor factor

Returns: this matrix

Definition at line 558 of file JMatrixND.hh.

     {
       double* p = this->data();
 
       for (size_t i = this->size()*this->size(); i != 0; --i, ++p) {
         *p *= factor;
       }
 
       return *this;
     }

JMatrixND& JMATH::JMatrixND::div ( const double factor )

inline

Scale matrix.

Parameters

factor factor

Returns: this matrix

Definition at line 576 of file JMatrixND.hh.

     {
       double* p = this->data();
 
       for (size_t i = this->size()*this->size(); i != 0; --i, ++p) {
         *p /= factor;
       }
 
       return *this;
     }

JMatrixND& JMATH::JMatrixND::mul	(	const JMatrixND &	A,
		const JMatrixND &	B
	)

inline

Matrix multiplication.

Parameters

A	matrix
B	matrix

Returns: this matrix

Definition at line 595 of file JMatrixND.hh.

     {
       if (A.size() == B.size()) {
 
         this->resize(A.size());
 
         if (!this->empty()) {
 
           JMatrixND_t& C = getInstance();
           
           C.set(B);
           C.transpose();
 
           size_t i, row;
 
           for (row = 0; row + 4 <= this->size(); row += 4) {              // process rows by four
 
             double* p0 = (*this)[row + 0];
             double* p1 = (*this)[row + 1];
             double* p2 = (*this)[row + 2];
             double* p3 = (*this)[row + 3];
 
             for (size_t col = 0; col != this->size(); ++col, ++p0, ++p1, ++p2, ++p3) {
 
               double w0 = 0.0;
               double w1 = 0.0;
               double w2 = 0.0;
               double w3 = 0.0;
 
               const double* a0 =  A[row + 0];
               const double* a1 =  A[row + 1];
               const double* a2 =  A[row + 2];
               const double* a3 =  A[row + 3];
 
               const double* c0 =  C[col];
 
               for (i = 0; i + 4 <= this->size(); i += 4, a0 += 4, a1 += 4, a2 += 4, a3 += 4, c0 += 4) {
                 w0  +=  a0[0] * c0[0]  +  a0[1] * c0[1]  +  a0[2] * c0[2]  +  a0[3] * c0[3];
                 w1  +=  a1[0] * c0[0]  +  a1[1] * c0[1]  +  a1[2] * c0[2]  +  a1[3] * c0[3];
                 w2  +=  a2[0] * c0[0]  +  a2[1] * c0[1]  +  a2[2] * c0[2]  +  a2[3] * c0[3];
                 w3  +=  a3[0] * c0[0]  +  a3[1] * c0[1]  +  a3[2] * c0[2]  +  a3[3] * c0[3];
               }
 
               for ( ; i != this->size(); ++i, ++a0, ++a1, ++a2, ++a3, ++c0) {
                 w0  +=  (*a0) * (*c0);
                 w1  +=  (*a1) * (*c0);
                 w2  +=  (*a2) * (*c0);
                 w3  +=  (*a3) * (*c0);
               }
 
               *p0 = w0;
               *p1 = w1;
               *p2 = w2;
               *p3 = w3;
             }
           }
 
           for ( ; row != this->size(); ++row) {                  // remaining rows
 
             double* p0 = (*this)[row + 0];
 
             for (size_t col = 0; col != this->size(); ++col, ++p0) {
 
               double w0 = 0.0;
 
               const double* a0 =  A[row + 0];
               const double* c0 =  C[col];
 
               for (i = 0; i + 4 <= this->size(); i += 4, a0 += 4, c0 += 4) {
                 w0  +=  a0[0] * c0[0]  +  a0[1] * c0[1]  +  a0[2] * c0[2]  +  a0[3] * c0[3];
               }
 
               for ( ; i != this->size(); ++i, ++a0, ++c0) {
                 w0  +=  (*a0) * (*c0);
               }
 
               *p0 = w0;
             }
           }
         }
 
       } else {
         THROW(JException, "JMatrixND::mul() inconsistent matrix dimensions " << A.size() << ' ' << B.size());
       }
 
       return *this;
     }

bool JMATH::JMatrixND::equals	(	const JMatrixND &	A,
		const double	eps = `std::numeric_limits<double>::min()`
	)		const

inline

Equality.

Parameters

A	matrix
eps	numerical precision

Returns: true if matrices identical; else false

Definition at line 692 of file JMatrixND.hh.

     {
       if (this->size() == A.size()) {
 
         for (size_t row = 0; row != this->size(); ++row) {
 
           const double* p = (*this)[row];
           const double* q = A      [row];
 
           for (size_t i = this->size(); i != 0; --i, ++p, ++q) {
             if (fabs(*p - *q) > eps) {
               return false;
             }
           }
         }
 
         return true;
 
       } else {
         THROW(JException, "JMatrixND::equals() inconsistent matrix dimensions " << this->size() << ' ' << A.size());
       }
     }

bool JMATH::JMatrixND::isIdentity ( const double eps = std::numeric_limits<double>::min() ) const

inline

Test identity.

Parameters

eps	numerical precision

Returns: true if identity matrix; else false

Definition at line 723 of file JMatrixND.hh.

     {
       for (size_t i = 0; i != this->size(); ++i) {
 
         if (fabs(1.0 - (*this)(i,i)) > eps) {
           return false;
         };
 
         for (size_t j = 0; j != i; ++j) {
           if (fabs((*this)(i,j)) > eps || fabs((*this)(j,i)) > eps) {
             return false;
           };
         }
       }
 
       return true;
     }

bool JMATH::JMatrixND::isSymmetric ( const double eps = std::numeric_limits<double>::min() ) const

inline

Test symmetry.

Parameters

eps	numerical precision

Returns: true if symmetric matrix; else false

Definition at line 748 of file JMatrixND.hh.

     {
       for (size_t i = 0; i != this->size(); ++i) {
         for (size_t j = 0; j != i; ++j) {
           if (fabs((*this)(i,j) - (*this)(j,i)) > eps) {
             return false;
           };
         }
       }
 
       return true;
     }

double JMATH::JMatrixND::getDot ( const JVectorND & v ) const

inline

Get dot product.

The dot product corresponds to

$v^{T} \times A \times v$

.

Parameters

v vector

Returns: dot product

Definition at line 770 of file JMatrixND.hh.

     {
       double dot = 0.0;
 
       for (size_t i = 0; i != v.size(); ++i) {
 
         const double* p = (*this)[i];
 
         double w = 0.0;
 
         for (JVectorND::const_iterator y = v.begin(); y != v.end(); ++y, ++p) {
           w += (*p) * (*y);
         }
 
         dot += v[i] * w;
       }
 
       return dot;
     }

void JMATH::JMatrixND::rswap	(	size_t	r1,
		size_t	r2
	)

inlineprotected

Definition at line 870 of file JMatrixND.hh.

     {
       JMatrixND_t& A = getInstance();
 
       A.resize(this->size());
       
       memcpy(A.data(),    (*this)[r1], this->size() * sizeof(double));
       memcpy((*this)[r1], (*this)[r2], this->size() * sizeof(double));
       memcpy((*this)[r2], A.data(),    this->size() * sizeof(double));
     }

void JMATH::JMatrixND::cswap	(	size_t	c1,
		size_t	c2
	)

inlineprotected

Swap columns.

Parameters

c1	column
c2	column

Definition at line 888 of file JMatrixND.hh.

     {
       using std::swap;
 
       double* p1 = this->data() + c1;
       double* p2 = this->data() + c2;
 
       for (size_t i = this->size(); i != 0; --i, p1 += this->size(), p2 += this->size()) {
         swap(*p1, *p2);
       }
     }

void JMATH::JMatrixND_t::clear ( )

inlineinherited

Clear memory.

Definition at line 83 of file JMatrixND.hh.

     {
       if (__p != NULL) {
         delete [] __p;
       }
 
       __p = NULL;
       __n = 0;
       __m = 0;
     }

void JMATH::JMatrixND_t::set ( const JMatrixND_t & A )

inlineinherited

Set matrix.

Parameters

A matrix

Definition at line 152 of file JMatrixND.hh.

     {
       this->resize(A.size());
 
       memcpy(this->data(), A.data(), A.size() * A.size() * sizeof(double));
     }

void JMATH::JMatrixND_t::swap ( JMatrixND_t & A )

inlineinherited

Swap matrices.

Parameters

A matrix

Definition at line 165 of file JMatrixND.hh.

     {
       using std::swap;
 
       swap(this->__p, A.__p);
       swap(this->__n, A.__n);
       swap(this->__m, A.__m);
     }

JMatrixND_t& JMATH::JMatrixND_t::transpose ( )

inlineinherited

Transpose.

Returns: this matrix

Definition at line 180 of file JMatrixND.hh.

     {
       using std::swap;
 
       for (size_t row = 0; row != this->size(); ++row) {
         for (size_t col = 0; col != row; ++col) {
           swap((*this)(row,col), (*this)(col,row));
         }
       }
 
       return *this;
     }

size_t JMATH::JMatrixND_t::size ( ) const

inlineinherited

Get dimension of matrix.

Returns: dimension

Definition at line 199 of file JMatrixND.hh.

     {
       return __n;
     }

size_t JMATH::JMatrixND_t::capacity ( ) const

inlineinherited

Get capacity of dimension.

Returns: capacity

Definition at line 210 of file JMatrixND.hh.

     {
       return __m;
     }

bool JMATH::JMatrixND_t::empty ( ) const

inlineinherited

Check emptyness.

Returns: true if empty; else false

Definition at line 221 of file JMatrixND.hh.

     {
       return __n == 0;
     }

const double* JMATH::JMatrixND_t::data ( ) const

inlineinherited

Get pointer to data.

Returns: pointer to data.

Definition at line 232 of file JMatrixND.hh.

     {
       return __p;
     }

double* JMATH::JMatrixND_t::data ( )

inlineinherited

Get pointer to data.

Returns: pointer to data.

Definition at line 243 of file JMatrixND.hh.

     {
       return __p;
     }

const double* JMATH::JMatrixND_t::operator[] ( size_t row ) const

inlineinherited

Get row data.

Parameters

row	row number

Returns: pointer to row data

Definition at line 255 of file JMatrixND.hh.

     {
       return __p + row*__n;
     }

double* JMATH::JMatrixND_t::operator[] ( size_t row )

inlineinherited

Get row data.

Parameters

row	row number

Returns: pointer to row data

Definition at line 267 of file JMatrixND.hh.

     {
       return __p + row*__n;
     }

double JMATH::JMatrixND_t::operator()	(	const size_t	row,
		const size_t	col
	)		const

inlineinherited

Get matrix element.

Parameters

row	row number
col	column number

Returns: matrix element at (row,col)

Definition at line 280 of file JMatrixND.hh.

     {
       return *(__p + row*__n + col);
     }

double& JMATH::JMatrixND_t::operator()	(	const size_t	row,
		const size_t	col
	)

inlineinherited

Get matrix element.

Parameters

row	row number
col	column number

Returns: matrix element at (row,col)

Definition at line 293 of file JMatrixND.hh.

     {
       return *(__p + row*__n + col);
     }

double JMATH::JMatrixND_t::at	(	size_t	row,
		size_t	col
	)		const

inlineinherited

Get matrix element.

Parameters

row	row number
col	column number

Returns: matrix element at (row,col)

Definition at line 306 of file JMatrixND.hh.

     {
       if (row >= this->size() ||
           col >= this->size()) {
         THROW(JIndexOutOfRange, "JMatrixND::at(" << row << "," << col << "): index out of range.");
       }
 
       return (*this)(row, col);
     }

double& JMATH::JMatrixND_t::at	(	size_t	row,
		size_t	col
	)

inlineinherited

Get matrix element.

Parameters

row	row number
col	column number

Returns: matrix element at (row,col)

Definition at line 324 of file JMatrixND.hh.

     {
       if (row >= this->size() ||
           col >= this->size()) {
         THROW(JIndexOutOfRange, "JMatrixND::at(" << row << "," << col << "): index out of range.");
       }
 
       return (*this)(row, col);
     }

JMatrixND & JMATH::JMath< JMatrixND , JNullType >::mul ( const JNullType & object )

inlineinherited

Multiply with object.

Parameters

object object

Returns: result object

Definition at line 354 of file JMath.hh.

     {
       return static_cast<JFirst_t&>(*this) = JFirst_t().mul(static_cast<const JFirst_t&>(*this), object);
     }

Friends And Related Function Documentation

JReader& operator>>	(	JReader &	in,
		JMatrixND &	A
	)

friend

Read matrix from input.

Parameters

in	reader
A	matrix

Returns: reader

Definition at line 798 of file JMatrixND.hh.

     {
       size_t size;
 
       in >> size;
 
       A.resize(size);
 
       size_t n = A.size() * A.size();      
 
       for (double* p = A.data(); n != 0; --n, ++p) {
         in >> *p;
       }
 
       return in;
     }

JWriter& operator<<	(	JWriter &	out,
		const JMatrixND &	A
	)

friend

Write matrix to output.

Parameters

out	writer
A	matrix

Returns: writer

Definition at line 823 of file JMatrixND.hh.

     {
       out << A.size();
 
       size_t n = A.size() * A.size();
 
       for (const double* p = A.data(); n != 0; --n, ++p) {
         out << *p;
       }
 
       return out;
     }

std::ostream& operator<<	(	std::ostream &	out,
		const JMatrixND &	A
	)

friend

Print ASCII formatted output.

Parameters

out	output stream
A	matrix

Returns: output stream

Definition at line 844 of file JMatrixND.hh.

     {
       using namespace std;
 
       const JFormat format(out, getFormat<JMatrixND>(JFormat_t(10, 3, std::ios::fixed | std::ios::showpos)));
 
       for (size_t row = 0; row != A.size(); ++row) {
 
         for (size_t col = 0; col != A.size(); ++col) {
           out << format << A(row,col) << ' ';
         }
 
         out << endl;
       }
 
       return out;
     }

Member Data Documentation

JMatrixND_t JMATH::JMatrixND::ws

protected

Definition at line 351 of file JMatrixND.hh.

double* JMATH::JMatrixND_t::__p

protectedinherited

pointer to data

Definition at line 336 of file JMatrixND.hh.

size_t JMATH::JMatrixND_t::__n

protectedinherited

dimension of matrix

Definition at line 337 of file JMatrixND.hh.

size_t JMATH::JMatrixND_t::__m

protectedinherited

capacity of matrix

Definition at line 338 of file JMatrixND.hh.

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

JMatrixND.hh

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation