3 x 3 symmetric matrix More...

#include <JMatrix3S.hh>

Inheritance diagram for JMATH::JMatrix3S:

Public Types
typedef std::array< double, 3 >	eigen_values
	Type definition of Eigen values.

Public Member Functions
	JMatrix3S ()
	Default constructor.

	JMatrix3S (const JMatrix3D &A)
	Contructor.

	JMatrix3S (const double __a00, const double __a10, const double __a11, const double __a20, const double __a21, const double __a22)
	Contructor.

void	invert ()
	Invert matrix.

eigen_values	getEigenValues (const double epsilon=1e-6) const
	Get eigen values.

JMatrix3D &	setIdentity ()
	Set to identity matrix.

void	set (const JMatrix3D &A)
	Set matrix.

JMatrix3D &	reset ()
	Set matrix to the null matrix.

JMatrix3D &	transpose ()
	Transpose.

JMatrix3D &	negate ()
	Negate matrix.

JMatrix3D &	add (const JMatrix3D &A)
	Matrix addition.

JMatrix3D &	sub (const JMatrix3D &A)
	Matrix subtraction.

JMatrix3D &	mul (const double factor)
	Scale matrix.

JMatrix3D &	mul (const JMatrix3D &A, const JMatrix3D &B)
	Matrix multiplication.

JMatrix3D &	mul (const JSecond_t &object)
	Multiply with object.

JMatrix3D &	div (const double factor)
	Scale matrix.

bool	equals (const JMatrix3D &A, const double eps=std::numeric_limits< double >::min()) const
	Equality.

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

double	getDeterminant () const
	Get determinant of matrix.

void	transform (double &__x, double &__y, double &__z) const
	Transform.

Static Public Member Functions
static const JMatrix3D &	getInstance ()
	Get reference to unique instance of this class object.

static const JMatrix3D &	getIdentity ()
	Get reference to unique instance of this class object.

Public Attributes
double	a00

double	a01

double	a02

double	a10

double	a11

double	a12

double	a20

double	a21

double	a22

Detailed Description

3 x 3 symmetric matrix

Definition at line 29 of file JMatrix3S.hh.

Member Typedef Documentation

◆ eigen_values

std::array<double, 3> JMATH::JMatrix3S::eigen_values

Type definition of Eigen values.

Definition at line 36 of file JMatrix3S.hh.

Constructor & Destructor Documentation

◆ JMatrix3S() [1/3]

JMATH::JMatrix3S::JMatrix3S ( )

inline

Default constructor.

Definition at line 42 of file JMatrix3S.hh.

                :
      JMatrix3D()
    {}

◆ JMatrix3S() [2/3]

JMATH::JMatrix3S::JMatrix3S ( const JMatrix3D & A )

inline

Contructor.

Parameters

A matrix

Definition at line 52 of file JMatrix3S.hh.

                                  :
      JMatrix3D(A)
    {}

◆ JMatrix3S() [3/3]

JMATH::JMatrix3S::JMatrix3S	(	const double	__a00,
		const double	__a10,
		const double	__a11,
		const double	__a20,
		const double	__a21,
		const double	__a22 )

inline

Contructor.

The upper triangle is internally set.

Parameters

__a00	(0,0)
__a10	(1,0)
__a11	(1,1)
__a20	(2,0)
__a21	(2,1)
__a22	(2,2)

Definition at line 68 of file JMatrix3S.hh.

                                                                          :
      JMatrix3D(__a00, __a10, __a20,
                __a10, __a11, __a21,
                __a20, __a21, __a22)
    {}

Member Function Documentation

◆ invert()

void JMATH::JMatrix3S::invert ( )

inline

Invert matrix.

Definition at line 80 of file JMatrix3S.hh.

    {
      using std::swap;
 
      // LDU decomposition
 
      int    p0 = 0; // permute row 0
      int    p1 = 0; // permute row 1
 
      double val;
 
      val = a00;
 
      if (fabs(a10) > fabs(val)) {
        p0  = 1;
        val = a10;
      }
 
      if (fabs(a20) > fabs(val)) {
        p0  = 2;
        val = a20;
      }
 
      switch (p0) {
 
      case 1:
        swap(a00,a10);
        swap(a01,a11);
        swap(a02,a12);
        break;
 
      case 2:
        swap(a00,a20);
        swap(a01,a21);
        swap(a02,a22);
        break;
      }
 
      if (val == 0) {
        throw JDivisionByZero("LDU decomposition zero pivot");  
      }
 
      a10 /= val;
      a11 -= a10 * a01;
      a12 -= a10 * a02;
 
      a20 /= val;
      a21 -= a20 * a01;
      a22 -= a20 * a02;
 
      val = a11;
 
      if (fabs(a21) > fabs(val)) {
        p1  = 2;
        val = a21;
      }
 
      switch (p1) {
 
      case 2:
        swap(a10,a20);
        swap(a11,a21);
        swap(a12,a22);
        break;
      }
 
      if (val == 0) {
        throw JDivisionByZero("LDU decomposition zero pivot");
      }
 
      a21 /= val;
      a22 -= a21 * a12;
 
      // invert D
 
      if (a22 == 0) {
        throw JDivisionByZero("D matrix not invertable");
      }
 
      a00  = 1.0 / a00;
      a11  = 1.0 / a11;
      a22  = 1.0 / a22;
 
      // invert U
 
      a01 *= -a00;
      a01 *=  a11;
 
      a02 *= -a00;
      a02 -=  a01 * a12;
      a02 *=  a22;
 
      a12 *= -a11;
      a12 *=  a22;
 
      // invert L
 
      a21  = -a21;
      a20  = -a20;
      a20 -=  a21 * a10;
      a10  = -a10;
 
      // U^-1 x L^-1
 
      a00 += a01 * a10  +  a02 * a20;
      a01 += a02 * a21;
      a10 *= a11;
      a10 += a12 * a20;
      a11 += a12 * a21;
      a20 *= a22;
      a21 *= a22;
 
      switch (p1) {
 
      case 2:
        swap(a01,a02);
        swap(a11,a12);
        swap(a21,a22);
        break;
      }
 
      switch (p0) {
 
      case 1:
        swap(a00,a01);
        swap(a10,a11);
        swap(a20,a21);
        break;
 
      case 2:
        swap(a00,a02);
        swap(a10,a12);
        swap(a20,a22);
        break;
      }
    }

◆ getEigenValues()

eigen_values JMATH::JMatrix3S::getEigenValues ( const double epsilon = 1e-6 ) const

inline

Get eigen values.

The eigen values sorted in decreasing order of absolute values.
Algorithm taken from "Eigenvalues of a symmetric 3x3 matrix"
by Oliver K. Smith; see reference.

Parameters

epsilon precision

Returns: eigen values

Definition at line 227 of file JMatrix3S.hh.

    {
      using namespace std;
 
      eigen_values eigenvalues;
 
      const double p1 = a01*a01 + a02*a02 + a12*a12;
 
      if (fabs(p1 - 1.0) > epsilon) {
      
        const double q  = (a00 + a11 + a22) / 3.0;
        const double p2 = (a00 - q)*(a00 - q) + (a11 - q)*(a11 - q) + (a22 - q)*(a22 - q) + 2*p1;
        const double p  = sqrt(p2 / 6.0);
 
        JMatrix3S B(*this);
 
        B.sub(q * JMatrix3D::getIdentity());
        B.div(p);
 
        const double r   = B.getDeterminant() / 2.0;
        const double phi = (r < -1.0 ? PI / 3.0 : (r >  1.0 ? 0.0 : acos(r) / 3.0));
 
        eigenvalues[0] = q + 2*p*cos(phi);
        eigenvalues[2] = q + 2*p*cos(phi + 2*PI/3.0);
        eigenvalues[1] = 3 * q - eigenvalues[0] - eigenvalues[2];
 
      } else {
 
        eigenvalues = eigen_values{ a00, a11, a12 };
      }
 
      // sort absolute values in descending order
 
      if (fabs(eigenvalues[0]) < fabs(eigenvalues[1])) {
        swap(eigenvalues[0], eigenvalues[1]);
      }
 
      if (fabs(eigenvalues[1]) < fabs(eigenvalues[2])) {
 
        swap(eigenvalues[1], eigenvalues[2]);
 
        if (fabs(eigenvalues[0]) < fabs(eigenvalues[1])) {
          swap(eigenvalues[0], eigenvalues[1]);
        }
      }
 
      return eigenvalues;
    }

◆ getInstance()

static const JMatrix3D & JMATH::JMatrix3D::getInstance ( )

inlinestaticinherited

Get reference to unique instance of this class object.

Returns: zero matrix

Definition at line 78 of file JMath/JMatrix3D.hh.

    {
      static JMatrix3D matrix;
 
      return matrix;
    }

◆ setIdentity()

JMatrix3D & JMATH::JMatrix3D::setIdentity ( )

inlineinherited

Set to identity matrix.

Returns: this matrix

Definition at line 91 of file JMath/JMatrix3D.hh.

    {
      a00 = 1.0;  a01 = 0.0;  a02 = 0.0;
      a10 = 0.0;  a11 = 1.0;  a12 = 0.0;
      a20 = 0.0;  a21 = 0.0;  a22 = 1.0;
 
      return *this;
    }

◆ getIdentity()

static const JMatrix3D & JMATH::JMatrix3D::getIdentity ( )

inlinestaticinherited

Get reference to unique instance of this class object.

Returns: identity matrix

Definition at line 106 of file JMath/JMatrix3D.hh.

    {
      static JMatrix3D matrix(JMatrix3D().setIdentity());
 
      return matrix;
    }

◆ set()

void JMATH::JMatrix3D::set ( const JMatrix3D & A )

inlineinherited

Set matrix.

Parameters

A matrix

Definition at line 119 of file JMath/JMatrix3D.hh.

    {
      static_cast<JMatrix3D&>(*this) = A;
    }

◆ reset()

JMatrix3D & JMATH::JMatrix3D::reset ( )

inlineinherited

Set matrix to the null matrix.

Returns: this matrix

Definition at line 130 of file JMath/JMatrix3D.hh.

    {
      *this = JMatrix3D();
 
      return *this;
    }

◆ transpose()

JMatrix3D & JMATH::JMatrix3D::transpose ( )

inlineinherited

Transpose.

Returns: this matrix

Definition at line 143 of file JMath/JMatrix3D.hh.

    {
      using std::swap;
 
      swap(a10, a01);
      swap(a20, a02);
      swap(a21, a12);
 
      return *this;
    }

◆ negate()

JMatrix3D & JMATH::JMatrix3D::negate ( )

inlineinherited

Negate matrix.

Returns: -this matrix

Definition at line 160 of file JMath/JMatrix3D.hh.

    {
      a00 = -a00;  a01 = -a01;  a02 = -a02;
      a10 = -a10;  a11 = -a11;  a12 = -a12;
      a20 = -a20;  a21 = -a21;  a22 = -a22;
 
      return *this;
    }

◆ add()

JMatrix3D & JMATH::JMatrix3D::add ( const JMatrix3D & A )

inlineinherited

Matrix addition.

Parameters

A matrix

Returns: this matrix + A

Definition at line 176 of file JMath/JMatrix3D.hh.

    {
      a00 += A.a00;  a01 += A.a01;  a02 += A.a02;
      a10 += A.a10;  a11 += A.a11;  a12 += A.a12;
      a20 += A.a20;  a21 += A.a21;  a22 += A.a22;
  
      return *this;
    }

◆ sub()

JMatrix3D & JMATH::JMatrix3D::sub ( const JMatrix3D & A )

inlineinherited

Matrix subtraction.

Parameters

A matrix

Returns: this matrix - A

Definition at line 192 of file JMath/JMatrix3D.hh.

    {
      a00 -= A.a00;  a01 -= A.a01;  a02 -= A.a02;
      a10 -= A.a10;  a11 -= A.a11;  a12 -= A.a12;
      a20 -= A.a20;  a21 -= A.a21;  a22 -= A.a22;
  
      return *this;
    }

◆ mul() [1/3]

JMatrix3D & JMATH::JMatrix3D::mul ( const double factor )

inlineinherited

Scale matrix.

Parameters

factor factor

Returns: this matrix * factor

Definition at line 208 of file JMath/JMatrix3D.hh.

    {
      a00 *= factor; a01 *= factor; a02 *= factor;
      a10 *= factor; a11 *= factor; a12 *= factor;
      a20 *= factor; a21 *= factor; a22 *= factor;
 
      return *this;
    }

◆ mul() [2/3]

JMatrix3D & JMATH::JMatrix3D::mul	(	const JMatrix3D &	A,
		const JMatrix3D &	B )

inlineinherited

Matrix multiplication.

Parameters

A	matrix
B	matrix

Returns: this matrix

Definition at line 241 of file JMath/JMatrix3D.hh.

    {
      a00 = A.a00 * B.a00  +  A.a01 * B.a10  +  A.a02 * B.a20;
      a01 = A.a00 * B.a01  +  A.a01 * B.a11  +  A.a02 * B.a21;
      a02 = A.a00 * B.a02  +  A.a01 * B.a12  +  A.a02 * B.a22;
      
      a10 = A.a10 * B.a00  +  A.a11 * B.a10  +  A.a12 * B.a20;
      a11 = A.a10 * B.a01  +  A.a11 * B.a11  +  A.a12 * B.a21;
      a12 = A.a10 * B.a02  +  A.a11 * B.a12  +  A.a12 * B.a22;
      
      a20 = A.a20 * B.a00  +  A.a21 * B.a10  +  A.a22 * B.a20;
      a21 = A.a20 * B.a01  +  A.a21 * B.a11  +  A.a22 * B.a21;
      a22 = A.a20 * B.a02  +  A.a21 * B.a12  +  A.a22 * B.a22;
      
      return *this;
    }

◆ mul() [3/3]

JMatrix3D & JMATH::JMath< JMatrix3D, 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()

JMatrix3D & JMATH::JMatrix3D::div ( const double factor )

inlineinherited

Scale matrix.

Parameters

factor factor

Returns: this matrix / factor

Definition at line 224 of file JMath/JMatrix3D.hh.

    {
      a00 /= factor; a01 /= factor; a02 /= factor;
      a10 /= factor; a11 /= factor; a12 /= factor;
      a20 /= factor; a21 /= factor; a22 /= factor;
 
      return *this;
    }

◆ equals()

bool JMATH::JMatrix3D::equals	(	const JMatrix3D &	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 267 of file JMath/JMatrix3D.hh.

    {
      return (fabs(a00 - A.a00) <= eps  &&
              fabs(a01 - A.a01) <= eps  &&
              fabs(a02 - A.a02) <= eps  &&
              fabs(a10 - A.a10) <= eps  &&
              fabs(a11 - A.a11) <= eps  &&
              fabs(a12 - A.a12) <= eps  &&
              fabs(a20 - A.a20) <= eps  &&
              fabs(a21 - A.a21) <= eps  &&
              fabs(a22 - A.a22) <= eps);
    }

◆ isIdentity()

bool JMATH::JMatrix3D::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 288 of file JMath/JMatrix3D.hh.

    {
      return equals(getIdentity(), eps);
    }

◆ getDeterminant()

double JMATH::JMatrix3D::getDeterminant ( ) const

inlineinherited

Get determinant of matrix.

Returns: determinant of matrix

Definition at line 299 of file JMath/JMatrix3D.hh.

    {
      double det = 0.0;
 
      det += a00 * (a11 * a22 - a21 * a12);
      det -= a01 * (a10 * a22 - a20 * a12);
      det += a02 * (a10 * a21 - a20 * a11);
 
      return det;
    }

◆ transform()

void JMATH::JMatrix3D::transform	(	double &	__x,
		double &	__y,
		double &	__z ) const

inlineinherited

Transform.

Parameters

__x	x value
__y	y value
__z	z value

Definition at line 318 of file JMath/JMatrix3D.hh.

    {
      const double x = a00 * __x  +  a01 * __y  +  a02 * __z;
      const double y = a10 * __x  +  a11 * __y  +  a12 * __z;
      const double z = a20 * __x  +  a21 * __y  +  a22 * __z;
 
      __x = x;
      __y = y;
      __z = z;
    }

Member Data Documentation

◆ a00

double JMATH::JMatrix3D::a00

inherited

Definition at line 385 of file JMath/JMatrix3D.hh.

◆ a01

double JMATH::JMatrix3D::a01

inherited

Definition at line 385 of file JMath/JMatrix3D.hh.

◆ a02

double JMATH::JMatrix3D::a02

inherited

Definition at line 385 of file JMath/JMatrix3D.hh.

◆ a10

double JMATH::JMatrix3D::a10

inherited

Definition at line 386 of file JMath/JMatrix3D.hh.

◆ a11

double JMATH::JMatrix3D::a11

inherited

Definition at line 386 of file JMath/JMatrix3D.hh.

◆ a12

double JMATH::JMatrix3D::a12

inherited

Definition at line 386 of file JMath/JMatrix3D.hh.

◆ a20

double JMATH::JMatrix3D::a20

inherited

Definition at line 387 of file JMath/JMatrix3D.hh.

◆ a21

double JMATH::JMatrix3D::a21

inherited

Definition at line 387 of file JMath/JMatrix3D.hh.

◆ a22

double JMATH::JMatrix3D::a22

inherited

Definition at line 387 of file JMath/JMatrix3D.hh.

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

JMatrix3S.hh

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Member Typedef Documentation

◆ eigen_values

Constructor & Destructor Documentation

◆ JMatrix3S() [1/3]

◆ JMatrix3S() [2/3]

◆ JMatrix3S() [3/3]

Member Function Documentation

◆ invert()

◆ getEigenValues()

◆ getInstance()

◆ setIdentity()

◆ getIdentity()

◆ set()

◆ reset()

◆ transpose()

◆ negate()

◆ add()

◆ sub()

◆ mul() [1/3]

◆ mul() [2/3]

◆ mul() [3/3]

◆ div()

◆ equals()

◆ isIdentity()

◆ getDeterminant()

◆ transform()

Member Data Documentation

◆ a00

◆ a01

◆ a02

◆ a10

◆ a11

◆ a12

◆ a20

◆ a21

◆ a22