4 x 4 symmetric matrix More...

#include <JMatrix4S.hh>

Inheritance diagram for JMATH::JMatrix4S:

Public Member Functions
	JMatrix4S ()
	Default constructor.

	JMatrix4S (const JMatrix4D &A)
	Contructor.

	JMatrix4S (const double __a00, const double __a10, const double __a11, const double __a20, const double __a21, const double __a22, const double __a30, const double __a31, const double __a32, const double __a33)
	Contructor.

void	invert ()
	Invert matrix.

JMatrix4D &	setIdentity ()
	Set to identity matrix.

void	set (const JMatrix4D &A)
	Set matrix.

JMatrix4D &	reset ()
	Set matrix to the null matrix.

JMatrix4D &	transpose ()
	Transpose.

JMatrix4D &	negate ()
	Negate matrix.

JMatrix4D &	add (const JMatrix4D &A)
	Matrix addition.

JMatrix4D &	sub (const JMatrix4D &A)
	Matrix subtraction.

JMatrix4D &	mul (const double factor)
	Scale matrix.

const JMatrix4D &	mul (const JMatrix4D &A, const JMatrix4D &B)
	Matrix multiplication.

JMatrix4D &	mul (const JSecond_t &object)
	Multiply with object.

JMatrix4D &	div (const double factor)
	Scale matrix.

bool	equals (const JMatrix4D &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 &__x0, double &__x1, double &__x2, double &__x3) const
	Transform.

Static Public Member Functions
static const JMatrix4D &	getInstance ()
	Get reference to unique instance of this class object.

static const JMatrix4D &	getIdentity ()
	Get reference to unique instance of this class object.

Public Attributes
double	a00

double	a01

double	a02

double	a03

double	a10

double	a11

double	a12

double	a13

double	a20

double	a21

double	a22

double	a23

double	a30

double	a31

double	a32

double	a33

Detailed Description

4 x 4 symmetric matrix

Definition at line 26 of file JMatrix4S.hh.

Constructor & Destructor Documentation

◆ JMatrix4S() [1/3]

JMATH::JMatrix4S::JMatrix4S ( )

inline

Default constructor.

Definition at line 33 of file JMatrix4S.hh.

                :
      JMatrix4D()
    {}

◆ JMatrix4S() [2/3]

JMATH::JMatrix4S::JMatrix4S ( const JMatrix4D & A )

inline

Contructor.

Parameters

A matrix

Definition at line 43 of file JMatrix4S.hh.

                                  :
      JMatrix4D(A)
    {}

◆ JMatrix4S() [3/3]

JMATH::JMatrix4S::JMatrix4S	(	const double	__a00,
		const double	__a10,
		const double	__a11,
		const double	__a20,
		const double	__a21,
		const double	__a22,
		const double	__a30,
		const double	__a31,
		const double	__a32,
		const double	__a33 )

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)
__a30	(3,0)
__a31	(3,1)
__a32	(3,2)
__a33	(3,3)

Definition at line 63 of file JMatrix4S.hh.

                                                                                              :
      JMatrix4D(__a00, __a10, __a20, __a30,
                __a10, __a11, __a21, __a31,
                __a20, __a21, __a22, __a32,
                __a30, __a31, __a32, __a33)
    {}

Member Function Documentation

◆ invert()

void JMATH::JMatrix4S::invert ( )

inline

Invert matrix.

Definition at line 77 of file JMatrix4S.hh.

    {
      using std::swap;
 
      // LDU decomposition
 
      int    p0 = 0; // permute row 0
      int    p1 = 0; // permute row 1
      int    p2 = 0; // permute row 2
 
      double val;
 
      val = a00;
 
      if (fabs(a10) > fabs(val)) {
        p0  = 1;
        val = a10;
      }
 
      if (fabs(a20) > fabs(val)) {
        p0  = 2;
        val = a20;
      }
 
      if (fabs(a30) > fabs(val)) {
        p0  = 3;
        val = a30;
      }
 
      switch (p0) {
 
      case 1:
        swap(a00,a10);
        swap(a01,a11);
        swap(a02,a12);
        swap(a03,a13);
        break;
 
      case 2:
        swap(a00,a20);
        swap(a01,a21);
        swap(a02,a22);
        swap(a03,a23);
        break;
 
      case 3:
        swap(a00,a30);
        swap(a01,a31);
        swap(a02,a32);
        swap(a03,a33);
        break;
      }
 
      if (val == 0) {
        throw JDivisionByZero("LDU decomposition zero pivot");  
      }
 
      a10 /= val;
      a11 -= a10 * a01;
      a12 -= a10 * a02;
      a13 -= a10 * a03;
 
      a20 /= val;
      a21 -= a20 * a01;
      a22 -= a20 * a02;
      a23 -= a20 * a03;
 
      a30 /= val;
      a31 -= a30 * a01;
      a32 -= a30 * a02;
      a33 -= a30 * a03;
 
      val = a11;
 
      if (fabs(a21) > fabs(val)) {
        p1  = 2;
        val = a21;
      }
 
      if (fabs(a31) > fabs(val)) {
        p1  = 3;
        val = a31;
      }
 
      switch (p1) {
 
      case 2:
        swap(a10,a20);
        swap(a11,a21);
        swap(a12,a22);
        swap(a13,a23);
        break;
 
      case 3:
        swap(a10,a30);
        swap(a11,a31);
        swap(a12,a32);
        swap(a13,a33);
        break;
      }
 
      if (val == 0) {
        throw JDivisionByZero("LDU decomposition zero pivot");
      }
 
      a21 /= val;
      a22 -= a21 * a12;
      a23 -= a21 * a13;
 
      a31 /= val;
      a32 -= a31 * a12;
      a33 -= a31 * a13;
 
      val = a22;
 
      if (fabs(a32) > fabs(val)) {
        p2  = 3;
        val = a32;
      }
 
      switch (p2) {
 
      case 3:
        swap(a20,a30);
        swap(a21,a31);
        swap(a22,a32);
        swap(a23,a33);
        break;
      }
 
      if (val == 0) {
        throw JDivisionByZero("LDU decomposition zero pivot");
      }
 
      a32 /= val;
      a33 -= a32 * a23;
 
      // invert D
 
      if (a33 == 0) {
        throw JDivisionByZero("D matrix not invertable");
      }
      
      a00  = 1.0 / a00;
      a11  = 1.0 / a11;
      a22  = 1.0 / a22;
      a33  = 1.0 / a33;
 
      // invert U
 
      a01 *= -a00;
      a01 *=  a11;
 
      a02 *= -a00;
      a02 -=  a01 * a12;
      a02 *=  a22;
 
      a03 *= -a00;
      a03 -=  a01 * a13;
      a03 -=  a02 * a23;
      a03 *=  a33;
 
      a12 *= -a11;
      a12 *=  a22;
 
      a13 *= -a11;
      a13 -=  a12 * a23;
      a13 *=  a33;
 
      a23 *= -a22;
      a23 *=  a33;
 
      // invert L
 
      a32  = -a32;
 
      a31  = -a31;
      a31 -=  a32 * a21;
 
      a30  = -a30;
      a30 -=  a31 * a10;
      a30 -=  a32 * a20;
 
      a21  = -a21;
      a20  = -a20;
      a20 -=  a21 * a10;
      a10  = -a10;
 
      // U^-1 x L^-1
 
      a00 += a01 * a10  +  a02 * a20  +  a03 * a30;
      a01 += a02 * a21  +  a03 * a31;
      a02 += a03 * a32;
 
      a10 *= a11;
      a10 += a12 * a20  +  a13 * a30;
      a11 += a12 * a21  +  a13 * a31;
      a12 += a13 * a32;
 
      a20 *= a22;
      a20 += a23 * a30;
      a21 *= a22;
      a21 += a23 * a31;
      a22 += a23 * a32;
 
      a30 *= a33;
      a31 *= a33;
      a32 *= a33;
 
      switch (p2) {
 
      case 3:
        swap(a02,a03);
        swap(a12,a13);
        swap(a22,a23);
        swap(a32,a33);
        break;
      }
 
      switch (p1) {
 
      case 2:
        swap(a01,a02);
        swap(a11,a12);
        swap(a21,a22);
        swap(a31,a32);
        break;
 
      case 3:
        swap(a01,a03);
        swap(a11,a13);
        swap(a21,a23);
        swap(a31,a33);
        break;
      }
 
      switch (p0) {
 
      case 1:
        swap(a00,a01);
        swap(a10,a11);
        swap(a20,a21);
        swap(a30,a31);
        break;
 
      case 2:
        swap(a00,a02);
        swap(a10,a12);
        swap(a20,a22);
        swap(a30,a32);
        break;
 
      case 3:
        swap(a00,a03);
        swap(a10,a13);
        swap(a20,a23);
        swap(a30,a33);
        break;
      }
    }

◆ getInstance()

static const JMatrix4D & JMATH::JMatrix4D::getInstance ( )

inlinestaticinherited

Get reference to unique instance of this class object.

Returns: zero matrix

Definition at line 89 of file JMatrix4D.hh.

    {
      static JMatrix4D matrix;
 
      return matrix;
    }

◆ setIdentity()

JMatrix4D & JMATH::JMatrix4D::setIdentity ( )

inlineinherited

Set to identity matrix.

Returns: this matrix

Definition at line 102 of file JMatrix4D.hh.

    {
      a00 = 1.0;  a01 = 0.0;  a02 = 0.0;  a03 = 0.0;  
      a10 = 0.0;  a11 = 1.0;  a12 = 0.0;  a13 = 0.0;  
      a20 = 0.0;  a21 = 0.0;  a22 = 1.0;  a23 = 0.0;  
      a30 = 0.0;  a31 = 0.0;  a32 = 0.0;  a33 = 1.0;  
 
      return *this;
    }

◆ getIdentity()

static const JMatrix4D & JMATH::JMatrix4D::getIdentity ( )

inlinestaticinherited

Get reference to unique instance of this class object.

Returns: identity matrix

Definition at line 118 of file JMatrix4D.hh.

    {
      static JMatrix4D matrix(JMatrix4D().setIdentity());
 
      return matrix;
    }

◆ set()

void JMATH::JMatrix4D::set ( const JMatrix4D & A )

inlineinherited

Set matrix.

Parameters

A matrix

Definition at line 131 of file JMatrix4D.hh.

    {
      static_cast<JMatrix4D&>(*this) = A;
    }

◆ reset()

JMatrix4D & JMATH::JMatrix4D::reset ( )

inlineinherited

Set matrix to the null matrix.

Returns: this matrix

Definition at line 142 of file JMatrix4D.hh.

    {
      *this = JMatrix4D();
 
      return *this;
    }

◆ transpose()

JMatrix4D & JMATH::JMatrix4D::transpose ( )

inlineinherited

Transpose.

Returns: this matrix

Definition at line 155 of file JMatrix4D.hh.

    {
      using std::swap;
 
      swap(a10, a01);
      swap(a20, a02);
      swap(a21, a12);
      swap(a30, a03);
      swap(a31, a13);
      swap(a32, a23);
 
      return *this;
    }

◆ negate()

JMatrix4D & JMATH::JMatrix4D::negate ( )

inlineinherited

Negate matrix.

Returns: -this matrix

Definition at line 175 of file JMatrix4D.hh.

    {
      a00 = -a00;  a01 = -a01;  a02 = -a02;  a03 = -a03;
      a10 = -a10;  a11 = -a11;  a12 = -a12;  a13 = -a13;
      a20 = -a20;  a21 = -a21;  a22 = -a22;  a13 = -a23;
      a30 = -a30;  a31 = -a31;  a32 = -a32;  a33 = -a33;
 
      return *this;
    }

◆ add()

JMatrix4D & JMATH::JMatrix4D::add ( const JMatrix4D & A )

inlineinherited

Matrix addition.

Parameters

A matrix

Returns: this matrix + A

Definition at line 192 of file JMatrix4D.hh.

    {
      a00 += A.a00;  a01 += A.a01;  a02 += A.a02;  a03 += A.a03;
      a10 += A.a10;  a11 += A.a11;  a12 += A.a12;  a13 += A.a13;
      a20 += A.a20;  a21 += A.a21;  a22 += A.a22;  a23 += A.a23;
      a30 += A.a30;  a31 += A.a31;  a32 += A.a32;  a33 += A.a33;
  
      return *this;
    }

◆ sub()

JMatrix4D & JMATH::JMatrix4D::sub ( const JMatrix4D & A )

inlineinherited

Matrix subtraction.

Parameters

A matrix

Returns: this matrix - A

Definition at line 209 of file JMatrix4D.hh.

    {
      a00 -= A.a00;  a01 -= A.a01;  a02 -= A.a02;  a03 -= A.a03;
      a10 -= A.a10;  a11 -= A.a11;  a12 -= A.a12;  a13 -= A.a13;
      a20 -= A.a20;  a21 -= A.a21;  a22 -= A.a22;  a23 -= A.a23;
      a30 -= A.a30;  a31 -= A.a31;  a32 -= A.a32;  a33 -= A.a33;
  
      return *this;
    }

◆ mul() [1/3]

JMatrix4D & JMATH::JMatrix4D::mul ( const double factor )

inlineinherited

Scale matrix.

Parameters

factor factor

Returns: this matrix * factor

Definition at line 226 of file JMatrix4D.hh.

    {
      a00 *= factor; a01 *= factor; a02 *= factor; a03 *= factor;
      a10 *= factor; a11 *= factor; a12 *= factor; a13 *= factor;
      a20 *= factor; a21 *= factor; a22 *= factor; a23 *= factor;
      a30 *= factor; a31 *= factor; a32 *= factor; a33 *= factor;
 
      return *this;
    }

◆ mul() [2/3]

const JMatrix4D & JMATH::JMatrix4D::mul	(	const JMatrix4D &	A,
		const JMatrix4D &	B )

inlineinherited

Matrix multiplication.

Parameters

A	matrix
B	matrix

Returns: this matrix

Definition at line 261 of file JMatrix4D.hh.

    {
      a00 = A.a00 * B.a00  +  A.a01 * B.a10  +  A.a02 * B.a20  +  A.a03 * B.a30;
      a01 = A.a00 * B.a01  +  A.a01 * B.a11  +  A.a02 * B.a21  +  A.a03 * B.a31;
      a02 = A.a00 * B.a02  +  A.a01 * B.a12  +  A.a02 * B.a22  +  A.a03 * B.a32;
      a03 = A.a00 * B.a03  +  A.a01 * B.a13  +  A.a02 * B.a23  +  A.a03 * B.a33;
      
      a10 = A.a10 * B.a00  +  A.a11 * B.a10  +  A.a12 * B.a20  +  A.a13 * B.a30;
      a11 = A.a10 * B.a01  +  A.a11 * B.a11  +  A.a12 * B.a21  +  A.a13 * B.a31;
      a12 = A.a10 * B.a02  +  A.a11 * B.a12  +  A.a12 * B.a22  +  A.a13 * B.a32;
      a13 = A.a10 * B.a03  +  A.a11 * B.a13  +  A.a12 * B.a23  +  A.a13 * B.a33;
      
      a20 = A.a20 * B.a00  +  A.a21 * B.a10  +  A.a22 * B.a20  +  A.a23 * B.a30;
      a21 = A.a20 * B.a01  +  A.a21 * B.a11  +  A.a22 * B.a21  +  A.a23 * B.a31;
      a22 = A.a20 * B.a02  +  A.a21 * B.a12  +  A.a22 * B.a22  +  A.a23 * B.a32;
      a23 = A.a20 * B.a03  +  A.a21 * B.a13  +  A.a22 * B.a23  +  A.a23 * B.a33;
      
      a30 = A.a30 * B.a00  +  A.a31 * B.a10  +  A.a32 * B.a20  +  A.a33 * B.a30;
      a31 = A.a30 * B.a01  +  A.a31 * B.a11  +  A.a32 * B.a21  +  A.a33 * B.a31;
      a32 = A.a30 * B.a02  +  A.a31 * B.a12  +  A.a32 * B.a22  +  A.a33 * B.a32;
      a33 = A.a30 * B.a03  +  A.a31 * B.a13  +  A.a32 * B.a23  +  A.a33 * B.a33;
      
      return *this;
    }

◆ mul() [3/3]

JMatrix4D & JMATH::JMath< JMatrix4D, 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()

JMatrix4D & JMATH::JMatrix4D::div ( const double factor )

inlineinherited

Scale matrix.

Parameters

factor factor

Returns: this matrix / factor

Definition at line 243 of file JMatrix4D.hh.

    {
      a00 /= factor; a01 /= factor; a02 /= factor; a03 /= factor;
      a10 /= factor; a11 /= factor; a12 /= factor; a13 /= factor;
      a20 /= factor; a21 /= factor; a22 /= factor; a23 /= factor;
      a30 /= factor; a31 /= factor; a32 /= factor; a33 /= factor;
 
      return *this;
    }

◆ equals()

bool JMATH::JMatrix4D::equals	(	const JMatrix4D &	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 295 of file JMatrix4D.hh.

    {
      return (fabs(a00 - A.a00) <= eps  &&
              fabs(a01 - A.a01) <= eps  &&
              fabs(a02 - A.a02) <= eps  &&
              fabs(a03 - A.a03) <= eps  &&
              fabs(a10 - A.a10) <= eps  &&
              fabs(a11 - A.a11) <= eps  &&
              fabs(a12 - A.a12) <= eps  &&
              fabs(a13 - A.a13) <= eps  &&
              fabs(a20 - A.a20) <= eps  &&
              fabs(a21 - A.a21) <= eps  &&
              fabs(a22 - A.a22) <= eps  &&
              fabs(a23 - A.a23) <= eps  &&
              fabs(a30 - A.a30) <= eps  &&
              fabs(a31 - A.a31) <= eps  &&
              fabs(a32 - A.a32) <= eps  &&
              fabs(a33 - A.a33) <= eps);
    }

◆ isIdentity()

bool JMATH::JMatrix4D::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 323 of file JMatrix4D.hh.

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

◆ getDeterminant()

double JMATH::JMatrix4D::getDeterminant ( ) const

inlineinherited

Get determinant of matrix.

Returns: determinant of matrix

Definition at line 334 of file JMatrix4D.hh.

    {
      double det = 0.0;
 
      det += a00 * JMatrix3D(a11, a12, a13,
                             a21, a22, a23,
                             a31, a32, a33).getDeterminant();
 
      det -= a01 * JMatrix3D(a10, a12, a13,
                             a20, a22, a23,
                             a30, a32, a33).getDeterminant();
 
      det += a02 * JMatrix3D(a10, a11, a13,
                             a20, a21, a23,
                             a30, a31, a33).getDeterminant();
 
      det -= a03 * JMatrix3D(a10, a11, a12,
                             a20, a21, a22,
                             a30, a31, a32).getDeterminant();
 
      return det;
    }

◆ transform()

void JMATH::JMatrix4D::transform	(	double &	__x0,
		double &	__x1,
		double &	__x2,
		double &	__x3 ) const

inlineinherited

Transform.

Parameters

__x0	x0 value
__x1	x1 value
__x2	x2 value
__x3	x3 value

Definition at line 366 of file JMatrix4D.hh.

    {
      const double x0 = a00 * __x0  +  a01 * __x1  +  a02 * __x2  +  a03 * __x3;
      const double x1 = a10 * __x0  +  a11 * __x1  +  a12 * __x2  +  a13 * __x3;
      const double x2 = a20 * __x0  +  a21 * __x1  +  a22 * __x2  +  a23 * __x3;
      const double x3 = a30 * __x0  +  a31 * __x1  +  a32 * __x2  +  a33 * __x3;
 
      __x0 = x0;
      __x1 = x1;
      __x2 = x2;
      __x3 = x3;
    }

Member Data Documentation

◆ a00

double JMATH::JMatrix4D::a00

inherited

Definition at line 438 of file JMatrix4D.hh.

◆ a01

double JMATH::JMatrix4D::a01

inherited

Definition at line 438 of file JMatrix4D.hh.

◆ a02

double JMATH::JMatrix4D::a02

inherited

Definition at line 438 of file JMatrix4D.hh.

◆ a03

double JMATH::JMatrix4D::a03

inherited

Definition at line 438 of file JMatrix4D.hh.

◆ a10

double JMATH::JMatrix4D::a10

inherited

Definition at line 439 of file JMatrix4D.hh.

◆ a11

double JMATH::JMatrix4D::a11

inherited

Definition at line 439 of file JMatrix4D.hh.

◆ a12

double JMATH::JMatrix4D::a12

inherited

Definition at line 439 of file JMatrix4D.hh.

◆ a13

double JMATH::JMatrix4D::a13

inherited

Definition at line 439 of file JMatrix4D.hh.

◆ a20

double JMATH::JMatrix4D::a20

inherited

Definition at line 440 of file JMatrix4D.hh.

◆ a21

double JMATH::JMatrix4D::a21

inherited

Definition at line 440 of file JMatrix4D.hh.

◆ a22

double JMATH::JMatrix4D::a22

inherited

Definition at line 440 of file JMatrix4D.hh.

◆ a23

double JMATH::JMatrix4D::a23

inherited

Definition at line 440 of file JMatrix4D.hh.

◆ a30

double JMATH::JMatrix4D::a30

inherited

Definition at line 441 of file JMatrix4D.hh.

◆ a31

double JMATH::JMatrix4D::a31

inherited

Definition at line 441 of file JMatrix4D.hh.

◆ a32

double JMATH::JMatrix4D::a32

inherited

Definition at line 441 of file JMatrix4D.hh.

◆ a33

double JMATH::JMatrix4D::a33

inherited

Definition at line 441 of file JMatrix4D.hh.

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

JMatrix4S.hh

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ JMatrix4S() [1/3]

◆ JMatrix4S() [2/3]

◆ JMatrix4S() [3/3]

Member Function Documentation

◆ invert()

◆ 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

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