JMATH::JMatrix4S Class Reference

4 x 4 symmetric matrix More...

#include <JMatrix4S.hh>

Inheritance diagram for JMATH::JMatrix4S:

Public Member Functions
	JMatrix4S ()
	Default constructor. More...
	JMatrix4S (const JMatrix4D &A)
	Contructor. More...
	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. More...
void	invert ()
	Invert matrix. More...
JMatrix4D &	setIdentity ()
	Set to identity matrix. More...
void	set (const JMatrix4D &A)
	Set matrix. More...
JMatrix4D &	reset ()
	Set matrix to the null matrix. More...
JMatrix4D &	transpose ()
	Transpose. More...
JMatrix4D &	negate ()
	Negate matrix. More...
JMatrix4D &	add (const JMatrix4D &A)
	Matrix addition. More...
JMatrix4D &	sub (const JMatrix4D &A)
	Matrix subtraction. More...
JMatrix4D &	mul (const double factor)
	Scale matrix. More...
const JMatrix4D &	mul (const JMatrix4D &A, const JMatrix4D &B)
	Matrix multiplication. More...
JMatrix4D &	mul (const JSecond_t &object)
	Multiply with object. More...
JMatrix4D &	div (const double factor)
	Scale matrix. More...
bool	equals (const JMatrix4D &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...
double	getDeterminant () const
	Get determinant of matrix. More...
void	transform (double &__x0, double &__x1, double &__x2, double &__x3) const
	Transform. More...

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

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 273 of file JMath.hh.

    {
      return static_cast<JFirst_t&>(*this) = JCalculator<JFirst_t>::calculator.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