Detailed Description

Handles matrix math operations.

Author: Tony Peden, Jon Berndt, Mathias Froelich

Definition at line 69 of file FGMatrix33.h.

#include <FGMatrix33.h>

Public Types
enum	{ eRows = 3 , eColumns = 3 }

Public Member Functions
	FGMatrix33 (const double m11, const double m12, const double m13, const double m21, const double m22, const double m23, const double m31, const double m32, const double m33)
	Initialization by given values. More...

	FGMatrix33 (const FGMatrix33 &M)
	Copy constructor. More...

	FGMatrix33 (void)
	Default initializer. More...

	~FGMatrix33 (void)
	Destructor.

unsigned int	Cols (void) const
	Number of cloumns in the matrix. More...

double	Determinant (void) const
	Determinant of the matrix. More...

std::string	Dump (const std::string &delimeter) const
	Prints the contents of the matrix. More...

std::string	Dump (const std::string &delimiter, const std::string &prefix) const
	Prints the contents of the matrix. More...

double &	Entry (unsigned int row, unsigned int col)
	Write access the entries of the matrix. More...

double	Entry (unsigned int row, unsigned int col) const
	Read access the entries of the matrix. More...

FGColumnVector3	GetEuler () const
	Returns the Euler angle column vector associated with this matrix.

FGQuaternion	GetQuaternion (void) const
	Returns the quaternion associated with this direction cosine (rotation) matrix.

void	InitMatrix (const double m11, const double m12, const double m13, const double m21, const double m22, const double m23, const double m31, const double m32, const double m33)
	Initialize the matrix. More...

void	InitMatrix (void)
	Initialize the matrix. More...

FGMatrix33	Inverse (void) const
	Return the inverse of the matrix. More...

bool	Invertible (void) const
	Return if the matrix is invertible. More...

double &	operator() (unsigned int row, unsigned int col)
	Write access the entries of the matrix. More...

double	operator() (unsigned int row, unsigned int col) const
	Read access the entries of the matrix. More...

FGMatrix33	operator* (const double scalar) const
	Multiply the matrix with a scalar. More...

FGColumnVector3	operator* (const FGColumnVector3 &v) const
	Matrix vector multiplication. More...

FGMatrix33	operator* (const FGMatrix33 &B) const
	Matrix product. More...

FGMatrix33 &	operator*= (const double scalar)
	In place matrix scale. More...

FGMatrix33 &	operator*= (const FGMatrix33 &B)
	In place matrix multiplication. More...

FGMatrix33	operator+ (const FGMatrix33 &B) const
	Matrix addition. More...

FGMatrix33 &	operator+= (const FGMatrix33 &B)
	In place matrix addition. More...

FGMatrix33	operator- (const FGMatrix33 &B) const
	Matrix subtraction. More...

FGMatrix33 &	operator-= (const FGMatrix33 &B)
	In place matrix subtraction. More...

FGMatrix33	operator/ (const double scalar) const
	Multiply the matrix with 1.0/scalar. More...

FGMatrix33 &	operator/= (const double scalar)
	In place matrix scale. More...

FGMatrix33 &	operator= (const FGMatrix33 &A)
	Assignment operator. More...

FGMatrix33 &	operator= (std::initializer_list< double > lv)
	Assignment operator. More...

unsigned int	Rows (void) const
	Number of rows in the matrix. More...

void	T (void)
	Transposes this matrix. More...

FGMatrix33	Transposed (void) const
	Transposed matrix. More...

Constructor & Destructor Documentation

◆ FGMatrix33() [1/3]

FGMatrix33 ( void )

Default initializer.

Create a zero matrix.

Definition at line 58 of file FGMatrix33.cpp.

 {
   data[0] = data[1] = data[2] = data[3] = data[4] = data[5] =
     data[6] = data[7] = data[8] = 0.0;
 }

◆ FGMatrix33() [2/3]

FGMatrix33 ( const FGMatrix33 & M )

inline

Copy constructor.

Parameters

M	Matrix which is used for initialization.

Create copy of the matrix given in the argument.

Definition at line 90 of file FGMatrix33.h.

   {
     data[0] = M.data[0];
     data[1] = M.data[1];
     data[2] = M.data[2];
     data[3] = M.data[3];
     data[4] = M.data[4];
     data[5] = M.data[5];
     data[6] = M.data[6];
     data[7] = M.data[7];
     data[8] = M.data[8];
   }

◆ FGMatrix33() [3/3]

FGMatrix33	(	const double	m11,
		const double	m12,
		const double	m13,
		const double	m21,
		const double	m22,
		const double	m23,
		const double	m31,
		const double	m32,
		const double	m33
	)

inline

Initialization by given values.

Parameters

m11	value of the 1,1 Matrix element.
m12	value of the 1,2 Matrix element.
m13	value of the 1,3 Matrix element.
m21	value of the 2,1 Matrix element.
m22	value of the 2,2 Matrix element.
m23	value of the 2,3 Matrix element.
m31	value of the 3,1 Matrix element.
m32	value of the 3,2 Matrix element.
m33	value of the 3,3 Matrix element.

Create a matrix from the doubles given in the arguments.

Definition at line 117 of file FGMatrix33.h.

   {
     data[0] = m11;
     data[1] = m21;
     data[2] = m31;
     data[3] = m12;
     data[4] = m22;
     data[5] = m32;
     data[6] = m13;
     data[7] = m23;
     data[8] = m33;
   }

Member Function Documentation

◆ Cols()

unsigned int Cols ( void ) const

inline

Number of cloumns in the matrix.

Returns: the number of columns in the matrix.

Definition at line 214 of file FGMatrix33.h.

214 { return eColumns; }

◆ Determinant()

double Determinant ( void ) const

Determinant of the matrix.

Returns: the determinant of the matrix.

Definition at line 221 of file FGMatrix33.cpp.

                                          {
   return data[0]*data[4]*data[8] + data[3]*data[7]*data[2]
        + data[6]*data[1]*data[5] - data[6]*data[4]*data[2]
        - data[3]*data[1]*data[8] - data[7]*data[5]*data[0];
 }

◆ Dump() [1/2]

string Dump ( const std::string & delimeter ) const

Prints the contents of the matrix.

Parameters

delimeter the item separator (tab or comma)

Returns: a string with the delimeter-separated contents of the matrix

Definition at line 66 of file FGMatrix33.cpp.

 {
   ostringstream buffer;
   buffer << setw(12) << setprecision(10) << data[0] << delimiter;
   buffer << setw(12) << setprecision(10) << data[3] << delimiter;
   buffer << setw(12) << setprecision(10) << data[6] << delimiter;
   buffer << setw(12) << setprecision(10) << data[1] << delimiter;
   buffer << setw(12) << setprecision(10) << data[4] << delimiter;
   buffer << setw(12) << setprecision(10) << data[7] << delimiter;
   buffer << setw(12) << setprecision(10) << data[2] << delimiter;
   buffer << setw(12) << setprecision(10) << data[5] << delimiter;
   buffer << setw(12) << setprecision(10) << data[8];
   return buffer.str();
 }

◆ Dump() [2/2]

string Dump	(	const std::string &	delimiter,
		const std::string &	prefix
	)		const

Prints the contents of the matrix.

Parameters

delimeter	the item separator (tab or comma, etc.)
prefix	an additional prefix that is used to indent the 3X3 matrix printout

Returns: a string with the delimeter-separated contents of the matrix

Definition at line 83 of file FGMatrix33.cpp.

 {
   ostringstream buffer;
  
   buffer << prefix << right << fixed << setw(9) << setprecision(6) << data[0] << delimiter;
   buffer << right << fixed << setw(9) << setprecision(6) << data[3] << delimiter;
   buffer << right << fixed << setw(9) << setprecision(6) << data[6] << endl;
  
   buffer << prefix << right << fixed << setw(9) << setprecision(6) << data[1] << delimiter;
   buffer << right << fixed << setw(9) << setprecision(6) << data[4] << delimiter;
   buffer << right << fixed << setw(9) << setprecision(6) << data[7] << endl;
  
   buffer << prefix << right << fixed << setw(9) << setprecision(6) << data[2] << delimiter;
   buffer << right << fixed << setw(9) << setprecision(6) << data[5] << delimiter;
   buffer << right << fixed << setw(9) << setprecision(6) << data[8];
  
   buffer << setw(0) << left;
  
   return buffer.str();
 }

◆ Entry() [1/2]

double& Entry	(	unsigned int	row,
		unsigned int	col
	)

inline

Write access the entries of the matrix.

This function is just a shortcut for the double& operator()(unsigned int row, unsigned int col) function. It is used internally to access the elements in a more convenient way.

Note that the indices given in the arguments are unchecked.

Parameters

row	Row index.
col	Column index.

Returns: a reference to the matrix entry at the given row and column indices. Indices are counted starting with 1.

Definition at line 202 of file FGMatrix33.h.

                                                      {
      return data[(col-1)*eRows+row-1];
    }

◆ Entry() [2/2]

double Entry	(	unsigned int	row,
		unsigned int	col
	)		const

inline

Read access the entries of the matrix.

This function is just a shortcut for the double& operator()(unsigned int row, unsigned int col) function. It is used internally to access the elements in a more convenient way.

Note that the indices given in the arguments are unchecked.

Parameters

row	Row index.
col	Column index.

Returns: the value of the matrix entry at the given row and column indices. Indices are counted starting with 1.

Definition at line 185 of file FGMatrix33.h.

                                                          {
     return data[(col-1)*eRows+row-1];
   }

◆ InitMatrix() [1/2]

void InitMatrix	(	const double	m11,
		const double	m12,
		const double	m13,
		const double	m21,
		const double	m22,
		const double	m23,
		const double	m31,
		const double	m32,
		const double	m33
	)

inline

Initialize the matrix.

This function initializes a matrix to user specified values.

Definition at line 240 of file FGMatrix33.h.

   {
     data[0] = m11;
     data[1] = m21;
     data[2] = m31;
     data[3] = m12;
     data[4] = m22;
     data[5] = m32;
     data[6] = m13;
     data[7] = m23;
     data[8] = m33;
   }

◆ InitMatrix() [2/2]

void InitMatrix ( void )

Initialize the matrix.

This function initializes a matrix to all 0.0.

Definition at line 259 of file FGMatrix33.cpp.

 {
   data[0] = data[1] = data[2] = data[3] = data[4] = data[5] =
     data[6] = data[7] = data[8] = 0.0;
 }

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◆ Inverse()

FGMatrix33 Inverse ( void ) const

Return the inverse of the matrix.

Computes and returns if the inverse of the matrix. It is computed by Cramers Rule. Also there are no checks performed if the matrix is invertible. If you are not sure that it really is check this with the Invertible() call before.

Definition at line 229 of file FGMatrix33.cpp.

                                          {
   // Compute the inverse of a general matrix using Cramers rule.
   // I guess googling for cramers rule gives tons of references
   // for this. :)
  
   if (Determinant() != 0.0) {
     double rdet = 1.0/Determinant();
  
     double i11 = rdet*(data[4]*data[8]-data[7]*data[5]);
     double i21 = rdet*(data[7]*data[2]-data[1]*data[8]);
     double i31 = rdet*(data[1]*data[5]-data[4]*data[2]);
     double i12 = rdet*(data[6]*data[5]-data[3]*data[8]);
     double i22 = rdet*(data[0]*data[8]-data[6]*data[2]);
     double i32 = rdet*(data[3]*data[2]-data[0]*data[5]);
     double i13 = rdet*(data[3]*data[7]-data[6]*data[4]);
     double i23 = rdet*(data[6]*data[1]-data[0]*data[7]);
     double i33 = rdet*(data[0]*data[4]-data[3]*data[1]);
  
     return FGMatrix33( i11, i12, i13,
                        i21, i22, i23,
                        i31, i32, i33 );
   } else {
     return FGMatrix33( 0, 0, 0,
                        0, 0, 0,
                        0, 0, 0 );
   }
 }

◆ Invertible()

bool Invertible ( void ) const

inline

Return if the matrix is invertible.

Checks and returns if the matrix is nonsingular and thus invertible. This is done by simply computing the determinant and check if it is zero. Note that this test does not cover any instabilities caused by nearly singular matirces using finite arithmetics. It only checks exact singularity.

Definition at line 275 of file FGMatrix33.h.

275 { return 0.0 != Determinant(); }

◆ operator()() [1/2]

double& operator()	(	unsigned int	row,
		unsigned int	col
	)

inline

Write access the entries of the matrix.

Note that the indices given in the arguments are unchecked.

Parameters

row	Row index.
col	Column index.

Returns: a reference to the matrix entry at the given row and column indices. Indices are counted starting with 1.

Definition at line 168 of file FGMatrix33.h.

                                                          {
     return data[(col-1)*eRows+row-1];
   }

◆ operator()() [2/2]

double operator()	(	unsigned int	row,
		unsigned int	col
	)		const

inline

Read access the entries of the matrix.

Parameters

row	Row index.
col	Column index.

Returns: the value of the matrix entry at the given row and column indices. Indices are counted starting with 1.

Definition at line 155 of file FGMatrix33.h.

                                                               {
     return data[(col-1)*eRows+row-1];
   }

◆ operator*() [1/3]

FGMatrix33 operator* ( const double scalar ) const

Multiply the matrix with a scalar.

Parameters

scalar scalar factor to multiply with.

Returns: scaled matrix.

Compute and return the product of the current matrix with the scalar value scalar given in the argument.

Definition at line 333 of file FGMatrix33.cpp.

 {
   return FGMatrix33( scalar * data[0],
                      scalar * data[3],
                      scalar * data[6],
                      scalar * data[1],
                      scalar * data[4],
                      scalar * data[7],
                      scalar * data[2],
                      scalar * data[5],
                      scalar * data[8] );
 }

◆ operator*() [2/3]

FGColumnVector3 operator* ( const FGColumnVector3 & v ) const

Matrix vector multiplication.

Parameters

v	vector to multiply with.

Returns: matric vector product.

Compute and return the product of the current matrix with the vector given in the argument.

Definition at line 481 of file FGMatrix33.cpp.

 {
   double v1 = v(1);
   double v2 = v(2);
   double v3 = v(3);
  
   double tmp1 = v1*data[0];  //[(col-1)*eRows+row-1]
   double tmp2 = v1*data[1];
   double tmp3 = v1*data[2];
  
   tmp1 += v2*data[3];
   tmp2 += v2*data[4];
   tmp3 += v2*data[5];
  
   tmp1 += v3*data[6];
   tmp2 += v3*data[7];
   tmp3 += v3*data[8];
  
   return FGColumnVector3( tmp1, tmp2, tmp3 );
 }

◆ operator*() [3/3]

FGMatrix33 operator* ( const FGMatrix33 & B ) const

Matrix product.

Parameters

B	matrix to add to.

Returns: product of the matrices.

Compute and return the product of the current matrix and the matrix B given in the argument.

Definition at line 380 of file FGMatrix33.cpp.

 {
   FGMatrix33 Product;
  
   Product.data[0] = data[0]*M.data[0] + data[3]*M.data[1] + data[6]*M.data[2];
   Product.data[3] = data[0]*M.data[3] + data[3]*M.data[4] + data[6]*M.data[5];
   Product.data[6] = data[0]*M.data[6] + data[3]*M.data[7] + data[6]*M.data[8];
   Product.data[1] = data[1]*M.data[0] + data[4]*M.data[1] + data[7]*M.data[2];
   Product.data[4] = data[1]*M.data[3] + data[4]*M.data[4] + data[7]*M.data[5];
   Product.data[7] = data[1]*M.data[6] + data[4]*M.data[7] + data[7]*M.data[8];
   Product.data[2] = data[2]*M.data[0] + data[5]*M.data[1] + data[8]*M.data[2];
   Product.data[5] = data[2]*M.data[3] + data[5]*M.data[4] + data[8]*M.data[5];
   Product.data[8] = data[2]*M.data[6] + data[5]*M.data[7] + data[8]*M.data[8];
  
   return Product;
 }

◆ operator*=() [1/2]

FGMatrix33 & operator*= ( const double scalar )

In place matrix scale.

Parameters

scalar scalar value to multiply with.

Returns: reference to the current matrix.

Compute the product of the current matrix and the scalar value scalar given in the argument.

Definition at line 363 of file FGMatrix33.cpp.

 {
   data[0] *= scalar;
   data[3] *= scalar;
   data[6] *= scalar;
   data[1] *= scalar;
   data[4] *= scalar;
   data[7] *= scalar;
   data[2] *= scalar;
   data[5] *= scalar;
   data[8] *= scalar;
  
   return *this;
 }

◆ operator*=() [2/2]

FGMatrix33 & operator*= ( const FGMatrix33 & B )

In place matrix multiplication.

Parameters

B	matrix to multiply with.

Returns: reference to the current matrix.

Compute the product of the current matrix and the matrix B given in the argument.

Definition at line 399 of file FGMatrix33.cpp.

 {
   // FIXME: Make compiler friendlier
   double a,b,c;
  
   a = data[0]; b=data[3]; c=data[6];
   data[0] = a*M.data[0] + b*M.data[1] + c*M.data[2];
   data[3] = a*M.data[3] + b*M.data[4] + c*M.data[5];
   data[6] = a*M.data[6] + b*M.data[7] + c*M.data[8];
  
   a = data[1]; b=data[4]; c=data[7];
   data[1] = a*M.data[0] + b*M.data[1] + c*M.data[2];
   data[4] = a*M.data[3] + b*M.data[4] + c*M.data[5];
   data[7] = a*M.data[6] + b*M.data[7] + c*M.data[8];
  
   a = data[2]; b=data[5]; c=data[8];
   data[2] = a*M.data[0] + b*M.data[1] + c*M.data[2];
   data[5] = a*M.data[3] + b*M.data[4] + c*M.data[5];
   data[8] = a*M.data[6] + b*M.data[7] + c*M.data[8];
  
   return *this;
 }

◆ operator+()

FGMatrix33 operator+ ( const FGMatrix33 & B ) const

Matrix addition.

Parameters

B	matrix to add to.

Returns: sum of the matrices.

Compute and return the sum of the current matrix and the matrix B given in the argument.

Definition at line 301 of file FGMatrix33.cpp.

 {
   return FGMatrix33( data[0] + M.data[0],
                      data[3] + M.data[3],
                      data[6] + M.data[6],
                      data[1] + M.data[1],
                      data[4] + M.data[4],
                      data[7] + M.data[7],
                      data[2] + M.data[2],
                      data[5] + M.data[5],
                      data[8] + M.data[8] );
 }

◆ operator+=()

FGMatrix33 & operator+= ( const FGMatrix33 & B )

In place matrix addition.

Parameters

B	matrix to add.

Returns: reference to the current matrix.

Compute the sum of the current matrix and the matrix B given in the argument.

Definition at line 316 of file FGMatrix33.cpp.

 {
   data[0] += M.data[0];
   data[3] += M.data[3];
   data[6] += M.data[6];
   data[1] += M.data[1];
   data[4] += M.data[4];
   data[7] += M.data[7];
   data[2] += M.data[2];
   data[5] += M.data[5];
   data[8] += M.data[8];
  
   return *this;
 }

◆ operator-()

FGMatrix33 operator- ( const FGMatrix33 & B ) const

Matrix subtraction.

Parameters

B	matrix to add to.

Returns: difference of the matrices.

Compute and return the sum of the current matrix and the matrix B given in the argument.

Definition at line 269 of file FGMatrix33.cpp.

 {
   return FGMatrix33( data[0] - M.data[0],
                      data[3] - M.data[3],
                      data[6] - M.data[6],
                      data[1] - M.data[1],
                      data[4] - M.data[4],
                      data[7] - M.data[7],
                      data[2] - M.data[2],
                      data[5] - M.data[5],
                      data[8] - M.data[8] );
 }

◆ operator-=()

FGMatrix33 & operator-= ( const FGMatrix33 & B )

In place matrix subtraction.

Parameters

B	matrix to subtract.

Returns: reference to the current matrix.

Compute the diffence from the current matrix and the matrix B given in the argument.

Definition at line 284 of file FGMatrix33.cpp.

 {
   data[0] -= M.data[0];
   data[1] -= M.data[1];
   data[2] -= M.data[2];
   data[3] -= M.data[3];
   data[4] -= M.data[4];
   data[5] -= M.data[5];
   data[6] -= M.data[6];
   data[7] -= M.data[7];
   data[8] -= M.data[8];
  
   return *this;
 }

◆ operator/()

FGMatrix33 operator/ ( const double scalar ) const

Multiply the matrix with 1.0/scalar.

Parameters

scalar scalar factor to divide through.

Returns: scaled matrix.

Compute and return the product of the current matrix with the scalar value 1.0/scalar, where scalar is given in the argument.

Definition at line 424 of file FGMatrix33.cpp.

 {
   FGMatrix33 Quot;
  
   double tmp = 1.0/scalar;
   Quot.data[0] = data[0] * tmp;
   Quot.data[3] = data[3] * tmp;
   Quot.data[6] = data[6] * tmp;
   Quot.data[1] = data[1] * tmp;
   Quot.data[4] = data[4] * tmp;
   Quot.data[7] = data[7] * tmp;
   Quot.data[2] = data[2] * tmp;
   Quot.data[5] = data[5] * tmp;
   Quot.data[8] = data[8] * tmp;
  
   return Quot;
 }

◆ operator/=()

FGMatrix33 & operator/= ( const double scalar )

In place matrix scale.

Parameters

scalar scalar value to divide through.

Returns: reference to the current matrix.

Compute the product of the current matrix and the scalar value 1.0/scalar, where scalar is given in the argument.

Definition at line 444 of file FGMatrix33.cpp.

 {
   double tmp = 1.0/scalar;
   data[0] *= tmp;
   data[3] *= tmp;
   data[6] *= tmp;
   data[1] *= tmp;
   data[4] *= tmp;
   data[7] *= tmp;
   data[2] *= tmp;
   data[5] *= tmp;
   data[8] *= tmp;
  
   return *this;
 }

◆ operator=() [1/2]

FGMatrix33& operator= ( const FGMatrix33 & A )

inline

Assignment operator.

Parameters

A	source matrix.

Copy the content of the matrix given in the argument into *this.

Definition at line 291 of file FGMatrix33.h.

   {
     data[0] = A.data[0];
     data[1] = A.data[1];
     data[2] = A.data[2];
     data[3] = A.data[3];
     data[4] = A.data[4];
     data[5] = A.data[5];
     data[6] = A.data[6];
     data[7] = A.data[7];
     data[8] = A.data[8];
     return *this;
   }

◆ operator=() [2/2]

FGMatrix33& operator= ( std::initializer_list< double > lv )

inline

Assignment operator.

Parameters

lv	initializer list of at most 9 values.

Copy the content of the list into *this.

Definition at line 310 of file FGMatrix33.h.

   {
     double *v = data;
     for(auto& x: lv) {
       *v = x;
       v += 3;
       if (v-data > 8)
         v -= 8;
     }
  
     return *this;
   }

◆ Rows()

unsigned int Rows ( void ) const

inline

Number of rows in the matrix.

Returns: the number of rows in the matrix.

Definition at line 209 of file FGMatrix33.h.

209 { return eRows; }

◆ T()

void T ( void )

Transposes this matrix.

This function only transposes this matrix. Nothing is returned.

Definition at line 462 of file FGMatrix33.cpp.

 {
   double tmp;
  
   tmp = data[3];
   data[3] = data[1];
   data[1] = tmp;
  
   tmp = data[6];
   data[6] = data[2];
   data[2] = tmp;
  
   tmp = data[7];
   data[7] = data[5];
   data[5] = tmp;
 }

◆ Transposed()

FGMatrix33 Transposed ( void ) const

inline

Transposed matrix.

This function only returns the transpose of this matrix. This matrix itself remains unchanged.

Returns: the transposed matrix.

Definition at line 221 of file FGMatrix33.h.

                                     {
     return FGMatrix33( data[0], data[1], data[2],
                        data[3], data[4], data[5],
                        data[6], data[7], data[8] );
   }

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

Detailed Description

Public Types

Public Member Functions

Constructor & Destructor Documentation

◆ FGMatrix33() [1/3]

◆ FGMatrix33() [2/3]

◆ FGMatrix33() [3/3]

Member Function Documentation

◆ Cols()

◆ Determinant()

◆ Dump() [1/2]

◆ Dump() [2/2]

◆ Entry() [1/2]

◆ Entry() [2/2]

◆ InitMatrix() [1/2]

◆ InitMatrix() [2/2]

◆ Inverse()

◆ Invertible()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ Rows()

◆ T()

◆ Transposed()