N x N symmetric matrix. More...

#include <JMatrixNS.hh>

Inheritance diagram for JMATH::JMatrixNS:

Public Member Functions
	JMatrixNS ()
	Default constructor.

	JMatrixNS (const size_t size)
	Constructor (identity matrix).

	JMatrixNS (const JMatrixND &A)
	Contructor.

JMatrixNS &	operator= (const JMatrixNS &A)
	Assignment operator.

void	invert ()
	Invert matrix according LDU decomposition.

template<class JVectorND_t >
void	solve (JVectorND_t &u)
	Get solution of equation `A x = b`.

void	update (const size_t k, const double value)
	Update inverted matrix at given diagonal element.

void	resize (const size_t size)
	Resize matrix.

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

JMatrixND &	setIdentity ()
	Set to identity matrix.

JMatrixND &	negate ()
	Negate matrix.

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

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

JMatrixND &	mul (const double factor)
	Scale matrix.

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

JMatrixND &	mul (const JSecond_t &object)
	Multiply with object.

JMatrixND &	div (const double factor)
	Scale matrix.

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

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

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

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

void	clear ()
	Clear memory.

void	set (const JMatrixND_t &A)
	Set matrix.

void	swap (JMatrixND_t &A)
	Swap matrices.

JMatrixND_t &	transpose ()
	Transpose.

size_t	size () const
	Get dimension of matrix.

size_t	capacity () const
	Get capacity of dimension.

bool	empty () const
	Check emptyness.

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

double *	data ()
	Get pointer to data.

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

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

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

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

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

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

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

void	rswap (size_t r1, size_t r2)

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

Protected Attributes
JMatrixND_t	ws

double *	__p
	pointer to data

size_t	__n
	dimension of matrix

size_t	__m
	capacity of matrix

Private Attributes
std::vector< int >	P
	permutation matrix

Detailed Description

N x N symmetric matrix.

Definition at line 28 of file JMatrixNS.hh.

Constructor & Destructor Documentation

◆ JMatrixNS() [1/3]

JMATH::JMatrixNS::JMatrixNS ( )

inline

Default constructor.

Definition at line 34 of file JMatrixNS.hh.

                :
      JMatrixND()
    {}

◆ JMatrixNS() [2/3]

JMATH::JMatrixNS::JMatrixNS ( const size_t size )

inline

Constructor (identity matrix).

Parameters

size dimension

Definition at line 44 of file JMatrixNS.hh.

                                 :
      JMatrixND(size)
    {}

◆ JMatrixNS() [3/3]

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

inline

Contructor.

Parameters

A matrix

Definition at line 54 of file JMatrixNS.hh.

                                  :
      JMatrixND(A)
    {}

Member Function Documentation

◆ operator=()

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

inline

Assignment operator.

Parameters

A matrix

Definition at line 64 of file JMatrixNS.hh.

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

◆ invert()

void JMATH::JMatrixNS::invert ( )

inline

Invert matrix according LDU decomposition.

Definition at line 75 of file JMatrixNS.hh.

    {
      using namespace std;
 
      size_t  i, row, col, root;
 
      double* p0;
      double* p1;
      double* p2;
      double* p3;
 
      const double* c0;
 
      double v0;
      double v1;
      double v2;
      double v3;
 
      double w0;
 
      P.resize(this->size());
 
      // LDU decomposition
 
      for (root = 0; root != this->size(); ++root) {
 
        double value = (*this)(root, root);
        size_t pivot = root;
 
        for (row = root; ++row != this->size(); ) {
          if (fabs((*this)(row, root)) > fabs(value)) {
            value = (*this)(row, root);
            pivot = row;
          }
        }
 
        if (value == 0.0) {
          THROW(JDivisionByZero, "LDU decomposition zero pivot at " << root);
        }
 
        if (pivot != root) {
          this->rswap(root, pivot);
        }
 
        P[root] = pivot;
 
        for (row = root + 1; row + 4 <= this->size(); row += 4) {            // process rows by four
 
          p0 = (*this)[row + 0]  +  root;
          p1 = (*this)[row + 1]  +  root;
          p2 = (*this)[row + 2]  +  root;
          p3 = (*this)[row + 3]  +  root;
 
          v0 = (*p0++ /= value);
          v1 = (*p1++ /= value);
          v2 = (*p2++ /= value);
          v3 = (*p3++ /= value);
 
          c0 = (*this)[root] + root + 1;
 
          for (i = root + 1; i + 4 <= this->size(); i += 4, p0 += 4, p1 += 4, p2 += 4, p3 += 4, c0 += 4) {
            p0[0] -= v0 * c0[0];  p0[1] -= v0 * c0[1];  p0[2] -= v0 * c0[2];  p0[3] -= v0 * c0[3];
            p1[0] -= v1 * c0[0];  p1[1] -= v1 * c0[1];  p1[2] -= v1 * c0[2];  p1[3] -= v1 * c0[3];
            p2[0] -= v2 * c0[0];  p2[1] -= v2 * c0[1];  p2[2] -= v2 * c0[2];  p2[3] -= v2 * c0[3];
            p3[0] -= v3 * c0[0];  p3[1] -= v3 * c0[1];  p3[2] -= v3 * c0[2];  p3[3] -= v3 * c0[3];
          }
 
          for ( ; i != this->size(); ++i, ++p0, ++p1, ++p2, ++p3, ++c0) {
            *p0 -= v0 * (*c0);
            *p1 -= v1 * (*c0);
            *p2 -= v2 * (*c0);
            *p3 -= v3 * (*c0);
          }
        }
 
        for ( ; row != this->size(); ++row) {                                // remaining rows
 
          p0 = (*this)[row + 0]  +  root;
 
          v0 = (*p0++ /= value);
 
          c0 = (*this)[root] + root + 1;
 
          for (i = root + 1; i + 4 <= this->size(); i += 4, p0 += 4, c0 += 4) {
            *p0 -= v0 * c0[0];  p0[1] -= v0 * c0[1];  p0[2] -= v0 * c0[2];  p0[3] -= v0 * c0[3];
          }
 
          for ( ; i != this->size(); ++i, ++p0, ++c0) {
            *p0 -= v0 * (*c0);
          }
        }
      }
 
 
      JMatrixND_t& A = getInstance();
 
      A.reset();
 
      for (i = 0; i != this->size(); ++i) {
        A(i,i) = 1.0;
      }
 
 
      // forward substitution
 
      col = 0;
      
      for ( ; col + 4 <= this->size(); col += 4) {
          
        for (row = 0; row != this->size(); ++row) {
 
          p0 = A[col + 0];
          p1 = A[col + 1];
          p2 = A[col + 2];
          p3 = A[col + 3];
 
          i  = P[row];
 
          v0 = p0[i];
          v1 = p1[i];
          v2 = p2[i];
          v3 = p3[i];
 
          p0[i] = p0[row];
          p1[i] = p1[row];
          p2[i] = p2[row];
          p3[i] = p3[row];
 
          for (i = 0, c0 = (*this)[row]; i != row; ++c0, ++p0, ++p1, ++p2, ++p3, ++i) {
            v0 -= (*c0) * (*p0);
            v1 -= (*c0) * (*p1);
            v2 -= (*c0) * (*p2);
            v3 -= (*c0) * (*p3);
          }
 
          A[col + 0][row] = v0;
          A[col + 1][row] = v1;
          A[col + 2][row] = v2;
          A[col + 3][row] = v3;
        }
      }
 
      for ( ; col != this->size(); ++col) {
 
        for (row = 0; row != this->size(); ++row) {
 
          p0 = A[col];
          
          i  = P[row];
 
          v0 = p0[i];
 
          p0[i] = p0[row];
 
          for (i = 0, c0 = (*this)[row] + i; i != row; ++c0, ++p0, ++i) {
            v0 -= (*c0) * (*p0);
          }
 
          A[col][row] = v0;
        }
      }
 
      // backward substitution
 
      col = 0;
      
      for ( ; col + 4 <= this->size(); col += 4) {
 
        for (int row = this->size() - 1; row >= 0; --row) {
 
          p0 = A[col + 0] + row;
          p1 = A[col + 1] + row;
          p2 = A[col + 2] + row;
          p3 = A[col + 3] + row;
 
          v0 = *p0;
          v1 = *p1;
          v2 = *p2;
          v3 = *p3;
 
          ++p0;
          ++p1;
          ++p2;
          ++p3;
 
          for (i = row + 1, c0 = (*this)[row] + i; i != this->size(); ++c0, ++p0, ++p1, ++p2, ++p3, ++i) {
            v0 -= (*c0) * (*p0);
            v1 -= (*c0) * (*p1);
            v2 -= (*c0) * (*p2);
            v3 -= (*c0) * (*p3);
          }
 
          w0 = 1.0 / (*this)[row][row];
 
          A[col + 0][row] = v0 * w0;
          A[col + 1][row] = v1 * w0;
          A[col + 2][row] = v2 * w0;
          A[col + 3][row] = v3 * w0;
        }
      }
     
      for ( ; col != this->size(); ++col) {
 
        for (int row = this->size() - 1; row >= 0; --row) {
 
          p0 = A[col] + row;
 
          v0 = *p0;
 
          ++p0;
 
          for (i = row + 1, c0 = (*this)[row] + i; i != this->size(); ++c0, ++p0, ++i) {
            v0 -= (*c0) * (*p0);
          }
 
          w0 = 1.0 / (*this)[row][row];
 
          A[col][row] = v0 * w0;
        }
      }
 
      A.transpose();
 
      this->swap(A);
    }

◆ solve()

template<class JVectorND_t >

void JMATH::JMatrixNS::solve ( JVectorND_t & u )

inline

Get solution of equation A x = b.

Parameters

u	column vector; b on input, x on output(I/O)

Definition at line 308 of file JMatrixNS.hh.

    {
      using namespace std;
 
      size_t  i, row, root;
 
      double* p0;
      double* p1;
      double* p2;
      double* p3;
 
      const double* c0;
 
      double v0;
      double v1;
      double v2;
      double v3;
 
      P.resize(this->size());
 
      // LDU decomposition
 
      for (root = 0; root != this->size(); ++root) {
 
        double value = (*this)(root, root);
        size_t pivot = root;
 
        for (row = root; ++row != this->size(); ) {
          if (fabs((*this)(row, root)) > fabs(value)) {
            value = (*this)(row, root);
            pivot = row;
          }
        }
 
        if (value == 0.0) {
          THROW(JDivisionByZero, "LDU decomposition zero pivot at " << root);
        }
 
        if (pivot != root) {
          this->rswap(root, pivot);
        }
 
        P[root] = pivot;
 
        for (row = root + 1; row + 4 <= this->size(); row += 4) {            // process rows by four
 
          p0 = (*this)[row + 0]  +  root;
          p1 = (*this)[row + 1]  +  root;
          p2 = (*this)[row + 2]  +  root;
          p3 = (*this)[row + 3]  +  root;
 
          v0 = (*p0++ /= value);
          v1 = (*p1++ /= value);
          v2 = (*p2++ /= value);
          v3 = (*p3++ /= value);
 
          c0 = (*this)[root] + root + 1;
 
          for (i = root + 1; i + 4 <= this->size(); i += 4, p0 += 4, p1 += 4, p2 += 4, p3 += 4, c0 += 4) {
            p0[0] -= v0 * c0[0];  p0[1] -= v0 * c0[1];  p0[2] -= v0 * c0[2];  p0[3] -= v0 * c0[3];
            p1[0] -= v1 * c0[0];  p1[1] -= v1 * c0[1];  p1[2] -= v1 * c0[2];  p1[3] -= v1 * c0[3];
            p2[0] -= v2 * c0[0];  p2[1] -= v2 * c0[1];  p2[2] -= v2 * c0[2];  p2[3] -= v2 * c0[3];
            p3[0] -= v3 * c0[0];  p3[1] -= v3 * c0[1];  p3[2] -= v3 * c0[2];  p3[3] -= v3 * c0[3];
          }
 
          for ( ; i != this->size(); ++i, ++p0, ++p1, ++p2, ++p3, ++c0) {
            *p0 -= v0 * (*c0);
            *p1 -= v1 * (*c0);
            *p2 -= v2 * (*c0);
            *p3 -= v3 * (*c0);
          }
        }
 
        for ( ; row != this->size(); ++row) {                                // remaining rows
 
          p0 = (*this)[row + 0]  +  root;
 
          v0 = (*p0++ /= value);
 
          c0 = (*this)[root] + root + 1;
 
          for (i = root + 1; i + 4 <= this->size(); i += 4, p0 += 4, c0 += 4) {
            *p0 -= v0 * c0[0];  p0[1] -= v0 * c0[1];  p0[2] -= v0 * c0[2];  p0[3] -= v0 * c0[3];
          }
 
          for ( ; i != this->size(); ++i, ++p0, ++c0) {
            *p0 -= v0 * (*c0);
          }
        }
      }
 
      // forward substitution
 
      for (row = 0; row != this->size(); ++row) {
 
        i      = P[row];
        v0     = u[i];
        u[i]   = u[row];
 
        for (i = 0, c0 = (*this)[row] + i; i != row; ++c0, ++i) {
          v0 -= *c0 * u[i];
        }
 
        u[row] = v0;
      }
 
      // backward substitution
 
      for (int row = this->size() - 1; row >= 0; --row) {
 
        v0     = u[row];
 
        for (i = row + 1, c0 = (*this)[row] + i; i < this->size(); ++c0, ++i) {
          v0 -= *c0 * u[i];
        }
 
        u[row] = v0 / (*this)[row][row];
      }
    }

◆ update()

void JMATH::JMatrixNS::update	(	const size_t	k,
		const double	value )

inline

Update inverted matrix at given diagonal element.

If A is the original matrix and A' is such that for each (i,j) != (k,k):

      A'[i][j] = A[i][j]
      A'[k][k] = A[k][k] + value

then JMatrixNS::update(k, value) will modify the already inverted matrix of A such that it will be the inverse of A'.

See also arXiv.
This algorithm can be considered a special case of the Sherman–Morrison formula.

Parameters

k	index of diagonal element
value	value to add

Definition at line 446 of file JMatrixNS.hh.

    {
      if (k >= this->size()) {
        THROW(JIndexOutOfRange, "JMatrixNS::update(): index out of range " << k);
      }
 
      size_t  i, row;
      double* col;
 
      const double del  =  (*this)(k,k);
      const double din  =  1.0 / (1.0 + value * del);
 
      double* root = (*this)[k];
 
      for (row = 0; row != this->size(); ++row) {
 
        if (row != k) {
 
          const double val = (*this)(row, k);
 
          for (i = 0, col = (*this)[row]; i != this->size(); ++i, ++col) {
            if (i != k) {
              (*col) -= val * root[i] * value * din;
            }
          }
 
          (*this)(row, k) *= din;
        }
      }
 
      for (i = 0, col = root; i != this->size(); ++i, ++col) {
        if (i != k) {
          (*col) *= din;
        }
      }
 
      root[k] = del * din;
    }

◆ getInstance()

JMatrixND_t & JMATH::JMatrixND::getInstance ( )

inlineprotectedinherited

Get work space.

Returns: work space

Definition at line 361 of file JMatrixND.hh.

    {
      return ws;
    }

◆ resize()

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

inlineinherited

Resize matrix.

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

Parameters

size dimension

Definition at line 446 of file JMatrixND.hh.

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

◆ reset()

JMatrixND & JMATH::JMatrixND::reset ( )

inlineinherited

Set matrix to the null matrix.

Returns: this matrix

Definition at line 459 of file JMatrixND.hh.

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

◆ setIdentity()

JMatrixND & JMATH::JMatrixND::setIdentity ( )

inlineinherited

Set to identity matrix.

Returns: this matrix

Definition at line 476 of file JMatrixND.hh.

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

◆ negate()

JMatrixND & JMATH::JMatrixND::negate ( )

inlineinherited

Negate matrix.

Returns: this matrix

Definition at line 493 of file JMatrixND.hh.

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

◆ add()

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

inlineinherited

Matrix addition.

Parameters

A matrix

Returns: this matrix

Definition at line 511 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;
    }

◆ sub()

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

inlineinherited

Matrix subtraction.

Parameters

A matrix

Returns: this matrix

Definition at line 536 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;
    }

◆ mul() [1/3]

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

inlineinherited

Scale matrix.

Parameters

factor factor

Returns: this matrix

Definition at line 561 of file JMatrixND.hh.

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

◆ mul() [2/3]

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

inlineinherited

Matrix multiplication.

Parameters

A	matrix
B	matrix

Returns: this matrix

Definition at line 598 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;
    }

◆ mul() [3/3]

JMatrixND & JMATH::JMath< JMatrixND, JSecond_t >::mul ( const JSecond_t & 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);
    }

◆ div()

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

inlineinherited

Scale matrix.

Parameters

factor factor

Returns: this matrix

Definition at line 579 of file JMatrixND.hh.

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

◆ equals()

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

inlineinherited

Equality.

Parameters

A	matrix
eps	numerical precision

Returns: true if matrices identical; else false

Definition at line 695 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());
      }
    }

◆ isIdentity()

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

inlineinherited

Test identity.

Parameters

eps	numerical precision

Returns: true if identity matrix; else false

Definition at line 726 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;
    }

◆ isSymmetric()

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

inlineinherited

Test symmetry.

Parameters

eps	numerical precision

Returns: true if symmetric matrix; else false

Definition at line 751 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;
    }

◆ getDot()

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

inlineinherited

Get dot product.

The dot product corresponds to

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

.

Parameters

v vector

Returns: dot product

Definition at line 773 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;
    }

◆ rswap()

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

inlineprotectedinherited

Definition at line 873 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));
    }

◆ cswap()

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

inlineprotectedinherited

Swap columns.

Parameters

c1	column
c2	column

Definition at line 891 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);
      }
    }

◆ clear()

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;
    }

◆ set()

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

inlineinherited

Set matrix.

Parameters

A matrix

Definition at line 155 of file JMatrixND.hh.

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

◆ swap()

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

inlineinherited

Swap matrices.

Parameters

A matrix

Definition at line 168 of file JMatrixND.hh.

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

◆ transpose()

JMatrixND_t & JMATH::JMatrixND_t::transpose ( )

inlineinherited

Transpose.

Returns: this matrix

Definition at line 183 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()

size_t JMATH::JMatrixND_t::size ( ) const

inlineinherited

Get dimension of matrix.

Returns: dimension

Definition at line 202 of file JMatrixND.hh.

    {
      return __n;
    }

◆ capacity()

size_t JMATH::JMatrixND_t::capacity ( ) const

inlineinherited

Get capacity of dimension.

Returns: capacity

Definition at line 213 of file JMatrixND.hh.

    {
      return __m;
    }

◆ empty()

bool JMATH::JMatrixND_t::empty ( ) const

inlineinherited

Check emptyness.

Returns: true if empty; else false

Definition at line 224 of file JMatrixND.hh.

    {
      return __n == 0;
    }

◆ data() [1/2]

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

inlineinherited

Get pointer to data.

Returns: pointer to data.

Definition at line 235 of file JMatrixND.hh.

    {
      return __p;
    }

◆ data() [2/2]

double * JMATH::JMatrixND_t::data ( )

inlineinherited

Get pointer to data.

Returns: pointer to data.

Definition at line 246 of file JMatrixND.hh.

    {
      return __p;
    }

◆ operator[]() [1/2]

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 258 of file JMatrixND.hh.

    {
      return __p + row*__n;
    }

◆ operator[]() [2/2]

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

inlineinherited

Get row data.

Parameters

row	row number

Returns: pointer to row data

Definition at line 270 of file JMatrixND.hh.

    {
      return __p + row*__n;
    }

◆ operator()() [1/2]

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 283 of file JMatrixND.hh.

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

◆ operator()() [2/2]

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 296 of file JMatrixND.hh.

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

◆ at() [1/2]

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 309 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);
    }

◆ at() [2/2]

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 327 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);
    }

Member Data Documentation

◆ P

std::vector<int> JMATH::JMatrixNS::P

private

permutation matrix

Definition at line 486 of file JMatrixNS.hh.

◆ ws

JMatrixND_t JMATH::JMatrixND::ws

protectedinherited

Definition at line 354 of file JMatrixND.hh.

◆ __p

double* JMATH::JMatrixND_t::__p

protectedinherited

pointer to data

Definition at line 339 of file JMatrixND.hh.

◆ __n

size_t JMATH::JMatrixND_t::__n

protectedinherited

dimension of matrix

Definition at line 340 of file JMatrixND.hh.

◆ __m

size_t JMATH::JMatrixND_t::__m

protectedinherited

capacity of matrix

Definition at line 341 of file JMatrixND.hh.

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

JMatrixNS.hh

Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ JMatrixNS() [1/3]

◆ JMatrixNS() [2/3]

◆ JMatrixNS() [3/3]

Member Function Documentation

◆ operator=()

◆ invert()

◆ solve()

◆ update()

◆ getInstance()

◆ resize()

◆ reset()

◆ setIdentity()

◆ negate()

◆ add()

◆ sub()

◆ mul() [1/3]

◆ mul() [2/3]

◆ mul() [3/3]

◆ div()

◆ equals()

◆ isIdentity()

◆ isSymmetric()

◆ getDot()

◆ rswap()

◆ cswap()

◆ clear()

◆ set()

◆ swap()

◆ transpose()

◆ size()

◆ capacity()

◆ empty()

◆ data() [1/2]

◆ data() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ at() [1/2]

◆ at() [2/2]

Member Data Documentation

◆ P

◆ ws

◆ __p

◆ __n

◆ __m