math_Matrix Class Reference

This class implements the real matrix abstract data type. Matrixes can have an arbitrary range which must be defined at the declaration and cannot be changed after this declaration math_Matrix(-3,5,2,4); //a vector with range [-3..5, 2..4] Matrix values may be initialized and retrieved using indexes which must lie within the range of definition of the matrix. Matrix objects follow "value semantics", that is, they cannot be shared and are copied through assignment Matrices are copied through assignment: More...

#include <math_Matrix.hxx>

Public Member Functions
	math_Matrix (const int LowerRow, const int UpperRow, const int LowerCol, const int UpperCol)
	Constructs a non-initialized matrix of range [LowerRow..UpperRow, LowerCol..UpperCol] For the constructed matrix:
	math_Matrix (const int LowerRow, const int UpperRow, const int LowerCol, const int UpperCol, const double InitialValue)
	constructs a non-initialized matrix of range [LowerRow..UpperRow, LowerCol..UpperCol] whose values are all initialized with the value InitialValue.
	math_Matrix (void *const Tab, const int LowerRow, const int UpperRow, const int LowerCol, const int UpperCol)
	constructs a matrix of range [LowerRow..UpperRow, LowerCol..UpperCol] Sharing data with a "C array" pointed by Tab.
	math_Matrix (const math_Matrix &Other)
	constructs a matrix for copy in initialization. An exception is raised if the matrixes have not the same dimensions.
	math_Matrix (math_Matrix &&Other) noexcept
	Move constructor.
void	Init (const double InitialValue) noexcept
	Initialize all the elements of a matrix to InitialValue.
int	RowNumber () const noexcept
	Returns the number of rows of this matrix. Note that for a matrix A you always have the following relations:
int	ColNumber () const noexcept
	Returns the number of rows of this matrix. Note that for a matrix A you always have the following relations:
int	LowerRow () const noexcept
	Returns the value of the Lower index of the row range of a matrix.
int	UpperRow () const noexcept
	Returns the Upper index of the row range of a matrix.
int	LowerCol () const noexcept
	Returns the value of the Lower index of the column range of a matrix.
int	UpperCol () const noexcept
	Returns the value of the upper index of the column range of a matrix.
double	Determinant () const
	Computes the determinant of a matrix. An exception is raised if the matrix is not a square matrix.
void	Transpose ()
	Transposes a given matrix. An exception is raised if the matrix is not a square matrix.
void	Invert ()
	Inverts a matrix using Gauss algorithm. Exception NotSquare is raised if the matrix is not square. Exception SingularMatrix is raised if the matrix is singular.
void	Multiply (const double Right) noexcept
	Sets this matrix to the product of the matrix Left, and the matrix Right. Example math_Matrix A (1, 3, 1, 3); math_Matrix B (1, 3, 1, 3); // A = ... , B = ... math_Matrix C (1, 3, 1, 3); C.Multiply(A, B); Exceptions Standard_DimensionError if matrices are of incompatible dimensions, i.e. if:
void	operator*= (const double Right) noexcept
math_Matrix	Multiplied (const double Right) const noexcept
	multiplies all the elements of a matrix by the value <Right>.
math_Matrix	operator* (const double Right) const noexcept
math_Matrix	TMultiplied (const double Right) const noexcept
	Sets this matrix to the product of the transposed matrix TLeft, and the matrix Right. Example math_Matrix A (1, 3, 1, 3); math_Matrix B (1, 3, 1, 3); // A = ... , B = ... math_Matrix C (1, 3, 1, 3); C.Multiply(A, B); Exceptions Standard_DimensionError if matrices are of incompatible dimensions, i.e. if:
void	Divide (const double Right)
	divides all the elements of a matrix by the value <Right>. An exception is raised if <Right> = 0.
void	operator/= (const double Right)
math_Matrix	Divided (const double Right) const
	divides all the elements of a matrix by the value <Right>. An exception is raised if <Right> = 0.
math_Matrix	operator/ (const double Right) const
void	Add (const math_Matrix &Right)
	adds the matrix <Right> to a matrix. An exception is raised if the dimensions are different. Warning In order to save time when copying matrices, it is preferable to use operator += or the function Add whenever possible.
void	operator+= (const math_Matrix &Right)
math_Matrix	Added (const math_Matrix &Right) const
	adds the matrix <Right> to a matrix. An exception is raised if the dimensions are different.
math_Matrix	operator+ (const math_Matrix &Right) const
void	Add (const math_Matrix &Left, const math_Matrix &Right)
	sets a matrix to the addition of <Left> and <Right>. An exception is raised if the dimensions are different.
void	Subtract (const math_Matrix &Right)
	Subtracts the matrix <Right> from <me>. An exception is raised if the dimensions are different. Warning In order to avoid time-consuming copying of matrices, it is preferable to use operator -= or the function Subtract whenever possible.
void	operator-= (const math_Matrix &Right)
math_Matrix	Subtracted (const math_Matrix &Right) const
	Returns the result of the subtraction of <Right> from <me>. An exception is raised if the dimensions are different.
math_Matrix	operator- (const math_Matrix &Right) const
void	Set (const int I1, const int I2, const int J1, const int J2, const math_Matrix &M)
	Sets the values of this matrix,.
void	SetRow (const int Row, const math_VectorBase<> &V)
	Sets the row of index Row of a matrix to the vector <V>. An exception is raised if the dimensions are different. An exception is raises if <Row> is inferior to the lower row of the matrix or <Row> is superior to the upper row.
void	SetCol (const int Col, const math_VectorBase<> &V)
	Sets the column of index Col of a matrix to the vector <V>. An exception is raised if the dimensions are different. An exception is raises if <Col> is inferior to the lower column of the matrix or <Col> is superior to the upper column.
void	SetDiag (const double Value)
	Sets the diagonal of a matrix to the value . An exception is raised if the matrix is not square.
math_VectorBase	Row (const int Row) const
	Returns the row of index Row of a matrix.
math_VectorBase	Col (const int Col) const
	Returns the column of index <Col> of a matrix.
void	SwapRow (const int Row1, const int Row2)
	Swaps the rows of index Row1 and Row2. An exception is raised if <Row1> or <Row2> is out of range.
void	SwapCol (const int Col1, const int Col2)
	Swaps the columns of index <Col1> and <Col2>. An exception is raised if <Col1> or <Col2> is out of range.
math_Matrix	Transposed () const
	Teturns the transposed of a matrix. An exception is raised if the matrix is not a square matrix.
math_Matrix	Inverse () const
	Returns the inverse of a matrix. Exception NotSquare is raised if the matrix is not square. Exception SingularMatrix is raised if the matrix is singular.
math_Matrix	TMultiply (const math_Matrix &Right) const
	Returns the product of the transpose of a matrix with the matrix <Right>. An exception is raised if the dimensions are different.
void	Multiply (const math_VectorBase<> &Left, const math_VectorBase<> &Right)
	Computes a matrix as the product of 2 vectors. An exception is raised if the dimensions are different. <me> = <Left> * <Right>.
void	Multiply (const math_Matrix &Left, const math_Matrix &Right)
	Computes a matrix as the product of 2 matrixes. An exception is raised if the dimensions are different.
void	TMultiply (const math_Matrix &TLeft, const math_Matrix &Right)
	Computes a matrix to the product of the transpose of the matrix <TLeft> with the matrix <Right>. An exception is raised if the dimensions are different.
void	Subtract (const math_Matrix &Left, const math_Matrix &Right)
	Sets a matrix to the Subtraction of the matrix <Right> from the matrix <Left>. An exception is raised if the dimensions are different.
const double &	Value (const int Row, const int Col) const
	Accesses the value of index <Row> and <Col> of a matrix. An exception is raised if <Row> and <Col> are not in the correct range.
double &	Value (const int Row, const int Col)
	Accesses (in read or write mode) the value of index <Row> and <Col> of a matrix. An exception is raised if <Row> and <Col> are not in the correct range.
const double &	operator() (const int Row, const int Col) const
double &	operator() (const int Row, const int Col)
math_Matrix &	Initialized (const math_Matrix &Other)
	Matrixes are copied through assignment. An exception is raised if the dimensions are different.
math_Matrix &	operator= (const math_Matrix &Other)
math_Matrix &	operator= (math_Matrix &&Other)
	Move assignment operator.
void	Multiply (const math_Matrix &Right)
	Returns the product of 2 matrices. An exception is raised if the dimensions are different.
void	operator*= (const math_Matrix &Right)
math_Matrix	Multiplied (const math_Matrix &Right) const
	Returns the product of 2 matrices. An exception is raised if the dimensions are different.
math_Matrix	operator* (const math_Matrix &Right) const
math_VectorBase	Multiplied (const math_VectorBase<> &Right) const
	Returns the product of a matrix by a vector. An exception is raised if the dimensions are different.
math_VectorBase	operator* (const math_VectorBase<> &Right) const
math_Matrix	Opposite () const
	Returns the opposite of a matrix. An exception is raised if the dimensions are different.
math_Matrix	operator- () const
void	Dump (Standard_OStream &o) const
	Prints information on the current state of the object. Is used to redefine the operator <<.

Protected Member Functions
void	SetLowerRow (const int LowerRow) noexcept
	The new lower row of the matrix is set to <LowerRow>
void	SetLowerCol (const int LowerCol) noexcept
	The new lower column of the matrix is set to the column of range <LowerCol>.
void	SetLower (const int LowerRow, const int LowerCol) noexcept
	The new lower row of the matrix is set to <LowerRow> and the new lower column of the matrix is set to the column of range <LowerCol>.

Detailed Description

This class implements the real matrix abstract data type. Matrixes can have an arbitrary range which must be defined at the declaration and cannot be changed after this declaration math_Matrix(-3,5,2,4); //a vector with range [-3..5, 2..4] Matrix values may be initialized and retrieved using indexes which must lie within the range of definition of the matrix. Matrix objects follow "value semantics", that is, they cannot be shared and are copied through assignment Matrices are copied through assignment:

math_Matrix M2(1, 9, 1, 3);
...
M2 = M1;
M1(1) = 2.0;//the matrix M2 will not be modified.

The exception RangeError is raised when trying to access outside the range of a matrix :

M1(11, 1)=0.0// --> will raise RangeError.

The exception DimensionError is raised when the dimensions of two matrices or vectors are not compatible.

math_Matrix M3(1, 2, 1, 2);
M3 = M1;   // will raise DimensionError
M1.Add(M3) // --> will raise DimensionError.

A Matrix can be constructed with a pointer to "c array". It allows to carry the bounds inside the matrix. Example :

double tab1[10][20];
double tab2[200];
 
math_Matrix A (tab1[0][0], 1, 10, 1, 20);
math_Matrix B (tab2[0],    1, 10, 1, 20);

Constructor & Destructor Documentation

math_Matrix() [1/5]

math_Matrix::math_Matrix ( const int LowerRow, const int UpperRow, const int LowerCol, const int UpperCol )

inline

Constructs a non-initialized matrix of range [LowerRow..UpperRow, LowerCol..UpperCol] For the constructed matrix:

• LowerRow and UpperRow are the indexes of the lower and upper bounds of a row, and
• LowerCol and UpperCol are the indexes of the lower and upper bounds of a column.

math_Matrix() [2/5]

math_Matrix::math_Matrix ( const int LowerRow, const int UpperRow, const int LowerCol, const int UpperCol, const double InitialValue )

inline

constructs a non-initialized matrix of range [LowerRow..UpperRow, LowerCol..UpperCol] whose values are all initialized with the value InitialValue.

math_Matrix() [3/5]

math_Matrix::math_Matrix ( void *const Tab, const int LowerRow, const int UpperRow, const int LowerCol, const int UpperCol )

inline

constructs a matrix of range [LowerRow..UpperRow, LowerCol..UpperCol] Sharing data with a "C array" pointed by Tab.

math_Matrix() [4/5]

math_Matrix::math_Matrix ( const math_Matrix & Other )

inline

constructs a matrix for copy in initialization. An exception is raised if the matrixes have not the same dimensions.

math_Matrix() [5/5]

math_Matrix::math_Matrix ( math_Matrix && Other )

inlinenoexcept

Move constructor.

Member Function Documentation

Add() [1/2]

void math_Matrix::Add ( const math_Matrix & Left, const math_Matrix & Right )

inline

sets a matrix to the addition of <Left> and <Right>. An exception is raised if the dimensions are different.

Add() [2/2]

void math_Matrix::Add ( const math_Matrix & Right )

inline

adds the matrix <Right> to a matrix. An exception is raised if the dimensions are different. Warning In order to save time when copying matrices, it is preferable to use operator += or the function Add whenever possible.

Added()

math_Matrix math_Matrix::Added ( const math_Matrix & Right ) const

inline

adds the matrix <Right> to a matrix. An exception is raised if the dimensions are different.

Col()

math_VectorBase math_Matrix::Col

(

const int

Col

)

const

Returns the column of index <Col> of a matrix.

ColNumber()

int math_Matrix::ColNumber ( ) const

noexcept

Returns the number of rows of this matrix. Note that for a matrix A you always have the following relations:

• A.RowNumber() = A.UpperRow() - A.LowerRow() + 1
• A.ColNumber() = A.UpperCol() - A.LowerCol() + 1
• the length of a row of A is equal to the number of columns of A,
• the length of a column of A is equal to the number of rows of A.returns the row range of a matrix.

Determinant()

double math_Matrix::Determinant

(

)

const

Computes the determinant of a matrix. An exception is raised if the matrix is not a square matrix.

Divide()

void math_Matrix::Divide ( const double Right )

inline

divides all the elements of a matrix by the value <Right>. An exception is raised if <Right> = 0.

Divided()

math_Matrix math_Matrix::Divided ( const double Right ) const

inline

divides all the elements of a matrix by the value <Right>. An exception is raised if <Right> = 0.

Dump()

void math_Matrix::Dump ( Standard_OStream & o ) const

inline

Prints information on the current state of the object. Is used to redefine the operator <<.

Init()

void math_Matrix::Init ( const double InitialValue )

inlinenoexcept

Initialize all the elements of a matrix to InitialValue.

Initialized()

math_Matrix & math_Matrix::Initialized ( const math_Matrix & Other )

inline

Matrixes are copied through assignment. An exception is raised if the dimensions are different.

Inverse()

math_Matrix math_Matrix::Inverse

(

)

const

Returns the inverse of a matrix. Exception NotSquare is raised if the matrix is not square. Exception SingularMatrix is raised if the matrix is singular.

Invert()

void math_Matrix::Invert

(

)

Inverts a matrix using Gauss algorithm. Exception NotSquare is raised if the matrix is not square. Exception SingularMatrix is raised if the matrix is singular.

LowerCol()

int math_Matrix::LowerCol ( ) const

noexcept

Returns the value of the Lower index of the column range of a matrix.

LowerRow()

int math_Matrix::LowerRow ( ) const

noexcept

Returns the value of the Lower index of the row range of a matrix.

Multiplied() [1/3]

math_Matrix math_Matrix::Multiplied ( const double Right ) const

inlinenoexcept

multiplies all the elements of a matrix by the value <Right>.

Multiplied() [2/3]

math_Matrix math_Matrix::Multiplied ( const math_Matrix & Right ) const

inline

Returns the product of 2 matrices. An exception is raised if the dimensions are different.

Multiplied() [3/3]

math_VectorBase math_Matrix::Multiplied

(

const math_VectorBase<> &

Right

)

const

Returns the product of a matrix by a vector. An exception is raised if the dimensions are different.

Multiply() [1/4]

void math_Matrix::Multiply ( const double Right )

inlinenoexcept

Sets this matrix to the product of the matrix Left, and the matrix Right. Example math_Matrix A (1, 3, 1, 3); math_Matrix B (1, 3, 1, 3); // A = ... , B = ... math_Matrix C (1, 3, 1, 3); C.Multiply(A, B); Exceptions Standard_DimensionError if matrices are of incompatible dimensions, i.e. if:

• the number of columns of matrix Left, or the number of rows of matrix TLeft is not equal to the number of rows of matrix Right, or
• the number of rows of matrix Left, or the number of columns of matrix TLeft is not equal to the number of rows of this matrix, or
• the number of columns of matrix Right is not equal to the number of columns of this matrix.

Multiply() [2/4]

void math_Matrix::Multiply ( const math_Matrix & Left, const math_Matrix & Right )

inline

Computes a matrix as the product of 2 matrixes. An exception is raised if the dimensions are different.

Multiply() [3/4]

void math_Matrix::Multiply ( const math_Matrix & Right )

inline

Returns the product of 2 matrices. An exception is raised if the dimensions are different.

Multiply() [4/4]

void math_Matrix::Multiply	(	const math_VectorBase<> &	Left,
		const math_VectorBase<> &	Right )

Computes a matrix as the product of 2 vectors. An exception is raised if the dimensions are different. <me> = <Left> * <Right>.

operator()() [1/2]

double & math_Matrix::operator() ( const int Row, const int Col )

inline

operator()() [2/2]

const double & math_Matrix::operator() ( const int Row, const int Col ) const

inline

operator*() [1/3]

math_Matrix math_Matrix::operator* ( const double Right ) const

inlinenoexcept

operator*() [2/3]

math_Matrix math_Matrix::operator* ( const math_Matrix & Right ) const

inline

operator*() [3/3]

math_VectorBase math_Matrix::operator*

(

const math_VectorBase<> &

Right

)

const

operator*=() [1/2]

void math_Matrix::operator*= ( const double Right )

inlinenoexcept

operator*=() [2/2]

void math_Matrix::operator*= ( const math_Matrix & Right )

inline

operator+()

math_Matrix math_Matrix::operator+ ( const math_Matrix & Right ) const

inline

operator+=()

void math_Matrix::operator+= ( const math_Matrix & Right )

inline

operator-() [1/2]

math_Matrix math_Matrix::operator- ( ) const

inline

operator-() [2/2]

math_Matrix math_Matrix::operator- ( const math_Matrix & Right ) const

inline

operator-=()

void math_Matrix::operator-= ( const math_Matrix & Right )

inline

operator/()

math_Matrix math_Matrix::operator/ ( const double Right ) const

inline

operator/=()

void math_Matrix::operator/= ( const double Right )

inline

operator=() [1/2]

math_Matrix & math_Matrix::operator= ( const math_Matrix & Other )

inline

operator=() [2/2]

math_Matrix & math_Matrix::operator= ( math_Matrix && Other )

inline

Move assignment operator.

Opposite()

math_Matrix math_Matrix::Opposite ( ) const

inline

Returns the opposite of a matrix. An exception is raised if the dimensions are different.

Row()

math_VectorBase math_Matrix::Row

(

const int

Row

)

const

Returns the row of index Row of a matrix.

RowNumber()

int math_Matrix::RowNumber ( ) const

noexcept

Returns the number of rows of this matrix. Note that for a matrix A you always have the following relations:

• A.RowNumber() = A.UpperRow() - A.LowerRow() + 1
• A.ColNumber() = A.UpperCol() - A.LowerCol() + 1
• the length of a row of A is equal to the number of columns of A,
• the length of a column of A is equal to the number of rows of A.returns the row range of a matrix.

Set()

void math_Matrix::Set ( const int I1, const int I2, const int J1, const int J2, const math_Matrix & M )

inline

Sets the values of this matrix,.

• from index I1 to index I2 on the row dimension, and
• from index J1 to index J2 on the column dimension, to those of matrix M. Exceptions Standard_DimensionError if:
• I1 is less than the index of the lower row bound of this matrix, or
• I2 is greater than the index of the upper row bound of this matrix, or
• J1 is less than the index of the lower column bound of this matrix, or
• J2 is greater than the index of the upper column bound of this matrix, or
• I2 - I1 + 1 is not equal to the number of rows of matrix M, or
• J2 - J1 + 1 is not equal to the number of columns of matrix M.

SetCol()

void math_Matrix::SetCol	(	const int	Col,
		const math_VectorBase<> &	V )

Sets the column of index Col of a matrix to the vector <V>. An exception is raised if the dimensions are different. An exception is raises if <Col> is inferior to the lower column of the matrix or <Col> is superior to the upper column.

SetDiag()

void math_Matrix::SetDiag ( const double Value )

inline

Sets the diagonal of a matrix to the value . An exception is raised if the matrix is not square.

SetLower()

void math_Matrix::SetLower ( const int LowerRow, const int LowerCol )

protectednoexcept

The new lower row of the matrix is set to <LowerRow> and the new lower column of the matrix is set to the column of range <LowerCol>.

SetLowerCol()

void math_Matrix::SetLowerCol ( const int LowerCol )

inlineprotectednoexcept

The new lower column of the matrix is set to the column of range <LowerCol>.

SetLowerRow()

void math_Matrix::SetLowerRow ( const int LowerRow )

inlineprotectednoexcept

The new lower row of the matrix is set to <LowerRow>

SetRow()

void math_Matrix::SetRow	(	const int	Row,
		const math_VectorBase<> &	V )

Sets the row of index Row of a matrix to the vector <V>. An exception is raised if the dimensions are different. An exception is raises if <Row> is inferior to the lower row of the matrix or <Row> is superior to the upper row.

Subtract() [1/2]

void math_Matrix::Subtract ( const math_Matrix & Left, const math_Matrix & Right )

inline

Sets a matrix to the Subtraction of the matrix <Right> from the matrix <Left>. An exception is raised if the dimensions are different.

Subtract() [2/2]

void math_Matrix::Subtract ( const math_Matrix & Right )

inline

Subtracts the matrix <Right> from <me>. An exception is raised if the dimensions are different. Warning In order to avoid time-consuming copying of matrices, it is preferable to use operator -= or the function Subtract whenever possible.

Subtracted()

math_Matrix math_Matrix::Subtracted ( const math_Matrix & Right ) const

inline

Returns the result of the subtraction of <Right> from <me>. An exception is raised if the dimensions are different.

SwapCol()

void math_Matrix::SwapCol	(	const int	Col1,
		const int	Col2 )

Swaps the columns of index <Col1> and <Col2>. An exception is raised if <Col1> or <Col2> is out of range.

SwapRow()

void math_Matrix::SwapRow	(	const int	Row1,
		const int	Row2 )

Swaps the rows of index Row1 and Row2. An exception is raised if <Row1> or <Row2> is out of range.

TMultiplied()

math_Matrix math_Matrix::TMultiplied ( const double Right ) const

inlinenoexcept

Sets this matrix to the product of the transposed matrix TLeft, and the matrix Right. Example math_Matrix A (1, 3, 1, 3); math_Matrix B (1, 3, 1, 3); // A = ... , B = ... math_Matrix C (1, 3, 1, 3); C.Multiply(A, B); Exceptions Standard_DimensionError if matrices are of incompatible dimensions, i.e. if:

• the number of columns of matrix Left, or the number of rows of matrix TLeft is not equal to the number of rows of matrix Right, or
• the number of rows of matrix Left, or the number of columns of matrix TLeft is not equal to the number of rows of this matrix, or
• the number of columns of matrix Right is not equal to the number of columns of this matrix.

TMultiply() [1/2]

math_Matrix math_Matrix::TMultiply ( const math_Matrix & Right ) const

inline

Returns the product of the transpose of a matrix with the matrix <Right>. An exception is raised if the dimensions are different.

TMultiply() [2/2]

void math_Matrix::TMultiply ( const math_Matrix & TLeft, const math_Matrix & Right )

inline

Computes a matrix to the product of the transpose of the matrix <TLeft> with the matrix <Right>. An exception is raised if the dimensions are different.

Transpose()

void math_Matrix::Transpose ( )

inline

Transposes a given matrix. An exception is raised if the matrix is not a square matrix.

Transposed()

math_Matrix math_Matrix::Transposed ( ) const

inline

Teturns the transposed of a matrix. An exception is raised if the matrix is not a square matrix.

UpperCol()

int math_Matrix::UpperCol ( ) const

noexcept

Returns the value of the upper index of the column range of a matrix.

UpperRow()

int math_Matrix::UpperRow ( ) const

noexcept

Returns the Upper index of the row range of a matrix.

Value() [1/2]

double & math_Matrix::Value	(	const int	Row,
		const int	Col )

Accesses (in read or write mode) the value of index <Row> and <Col> of a matrix. An exception is raised if <Row> and <Col> are not in the correct range.

Value() [2/2]

const double & math_Matrix::Value	(	const int	Row,
		const int	Col ) const

Accesses the value of index <Row> and <Col> of a matrix. An exception is raised if <Row> and <Col> are not in the correct range.

---

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

• math_Matrix.hxx