Standard matrix class. More...

Public Types
typedef Eigen::Matrix< TScalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor >	Base
	the type of the ancestor class

typedef TScalar *	TBuffer
	the data type of the dynamic data buffer (pointer)

typedef Base::Index	TEigenIndex
	index type for Eigen matrices

typedef number	TScalar
	the floating point number type of a mtrix element

typedef number	TUnsignedIndex
	an unsigned index type

Public Member Functions
string	__getstate__ ()

Matrix	__neg__ () const

	__setstate_internal (string state)

char *	__str__ ()
	transforms this objects into a string, required by SWIG More...

	Add (Matrix other)
	modifies this matrix by the matrix sum A+B More...

	Add (MatrixBlock other)
	modifies this matrix by the matrix sum A+B More...

Matrix	AddCol (Matrix m)
	returns an object including new data data

Matrix	AddRow (Matrix m)

Matrix	AppendCols (Matrix m)
	returns an object with modified data More...

Matrix	AppendRows (Matrix m)
	returns an object with modified data More...

	Assign (Matrix ar)
	The assignment operator for matrices (data only) More...

	Assign (MatrixBlock ar)
	The assignment operator for blocks (data only) More...

MatrixBlock	Block (TUnsignedIndex row, TUnsignedIndex col, TUnsignedIndex numrows, TUnsignedIndex numcols)
	returns a reference to a block starting at 'row','column' with size 'numrows'*'numcols' More...

MatrixBlock	Col (TUnsignedIndex col)
	returns a reference to the 'col'th column More...

TUnsignedIndex	Cols () const

MatrixBlock	Cols (TUnsignedIndex col1, TUnsignedIndex ncol)
	returns a block containing the ncol columns starting at column index col1 More...

void	ConservativeResize (TUnsignedIndex rows, TUnsignedIndex cols=1)
	resizes the matrix to its new dimensions without destroying the contents. More...

MatrixCWise	CW ()

	Div (TScalar other)
	modifies this matrix by the scalar matrix quotient A/s More...

TScalar	Dot (Matrix other)
	returns the scalar product of two vectors (a'b) More...

TScalar	Dot (MatrixBlock other)
	returns the scalar product of two vectors (a'b) More...

TScalar	Dott (Matrix other)
	returns the weighted scalar product of this matrix and the given vector multiplied once from left and once from right (b'Ab) More...

TScalar	Dott (MatrixBlock other)
	returns the weighted scalar product of this matrix and the given vector multiplied once from left and once from right (b'Ab) More...

Matrix	GetCols (TUnsignedIndex col1, TUnsignedIndex ncol=1)
	returns an object providing copy of data

Matrix	GetCols (Matrix indices)

Matrix	GetColsThread (TUnsignedIndex col, TUnsignedIndex ncols)

Matrix	GetRows (TUnsignedIndex row1, TUnsignedIndex nrow=1)

Matrix	GetRows (Matrix indices)

Matrix	GetRowsThread (TUnsignedIndex row, TUnsignedIndex nrows)

Matrix	InnerProduct (Matrix other)
	returns the inner product of two matrices/vectors (a'*b) More...

Matrix	InnerProduct (MatrixBlock other)
	returns the inner product of two matrices/vectors (a'*b) More...

bool	IsApprox (Matrix other, TScalar s) const
	returns true if other and this are approx. identical More...

bool	IsApproxToConstant (TScalar value, TScalar s)
	returns true if array is constant and approx. equal s More...

bool	IsDiagonal (TScalar s)
	returns true if array is a diagonal matrix by precision s More...

bool	IsIdentity (TScalar s)
	returns true if array is the identity matrix by precision s More...

bool	IsLowerTriangular (TScalar s)
	returns true if array is a lower triangular matrix by precision s More...

bool	IsScalar ()

bool	IsUnitary (TScalar s)
	returns true if array is a unitary matrix by precision s (is an orthonormal basis) More...

bool	IsUpperTriangular (TScalar s)
	returns true if array is an upper triangular matrix by precision s More...

bool	IsVector ()

bool	IsZero (TScalar s)

	Matrix ()
	destructor More...

	Matrix (Matrix ar)
	copy constructor More...

	Matrix (TUnsignedIndex nrow, TUnsignedIndex ncol=1)
	constructs a matrix and allocates nrow*ncol elements More...

	Matrix (MatrixBlock x)
	constructs a matrix from a matrix block More...

	Matrix (sparse::SparseMatrix x)
	copies from a sparse matrix More...

	Matrix (sparse::SymSparseMatrix x)
	copies from a symmetric sparse matrix More...

TScalar	MaxCoeff (TEigenIndex OUTPUT, TEigenIndex OUTPUT) const

TScalar	MinCoeff (TEigenIndex OUTPUT, TEigenIndex OUTPUT) const
	find the smallest element in the array returns the minimum element in the array More...

	Mul (TScalar other)
	modifies this matrix by the scalar matrix product A*s More...

Matrix	operator* (Matrix other) const
	returns the matrix product A*B More...

Matrix	operator* (MatrixBlock other) const
	returns the matrix product A*B More...

Matrix	operator* (TScalar other) const
	returns the scalar matrix product A*s More...

Matrix	operator+ (Matrix other) const
	returns the matrix sum A+B More...

Matrix	operator+ (MatrixBlock other) const
	returns the matrix sum A+B More...

Matrix	operator- (Matrix other) const
	returns the matrix difference A-B More...

Matrix	operator- (MatrixBlock other) const
	returns the matrix difference A-B More...

Matrix	operator/ (TScalar other) const
	returns the scalar matrix quotient A/s More...

Matrix	operator< (TScalar x) const
	returns a matrix of 1 and 0 indicating which element is less than x More...

Matrix	operator= (Matrix ar)
	copy assignment operator More...

Matrix	OuterProduct (Matrix other)
	returns the outer product of two matrices/vectors (a*b') More...

Matrix	OuterProduct (MatrixBlock other)
	returns the outer product of two matrices/vectors (a*b') More...

	Print (string format="%g ", TUnsignedIndex rows=20, TUnsignedIndex cols=20) const
	prints the matrix up to the given rows and columns More...

Matrix	RemoveCol (TUnsignedIndex col)
	returns an object of corresponding smaller size

Matrix	RemoveRow (TUnsignedIndex row)

MatrixBlock	Row (TUnsignedIndex row)
	returns a reference to the 'row'th row More...

TUnsignedIndex	Rows () const

MatrixBlock	Rows (TUnsignedIndex row1, TUnsignedIndex nrow)
	returns a block containing the nrow columns starting at column index row1 More...

void	SetCols (Matrix m, TUnsignedIndex col)
	returns an object providing copy of data More...

	SetColsThread (Matrix m, TUnsignedIndex col)

	SetConstant (TScalar value)
	initializes the matrix with constant values More...

void	SetIdentity ()
	initializes the matrix as identity matrix

void	SetLinearCols (TScalar a, TScalar b)
	initializes the matrix with linear columns More...

	SetLinearRows (TScalar a, TScalar b)
	initializes the matrix with linear rows More...

void	SetOnes ()
	initializes the matrix with constant values "1"

void	SetRandom ()
	initializes the matrix with random values

void	SetRows (Matrix m, TUnsignedIndex row)

	SetRowsThread (Matrix m, TUnsignedIndex row)

void	SetZero ()
	initializes the matrix with zeros

	Sub (Matrix other)
	modifies this matrix by the matrix difference A-B More...

	Sub (MatrixBlock other)
	modifies this matrix by the matrix difference A-B More...

	Swap (Matrix ar)
	The swap operator for matrices (data only) More...

Matrix	Transpose () const

void	TransposeInPlace ()
	transposes this matrix

Public Attributes
apply	int { TEigenIndex }
	find the largest element in the array returns the maximum element in the array More...

apply int *	OUTPUT { TEigenIndex *OUTPUT }

Detailed Description

Standard matrix class.

A class that represents storage for dense linalg objects.

The storage scheme is column_major (FORTRAN). It is derived from Eigen::Matrix. Many operations have been added/overwritten for compatibility with scripting requirements. Most operations of Eigen2 are still available.

Basic Eigen linalg operators have been overloaded. To access a linalg operator from C++, for example the matrix product, type

Matrix x,y,z;
...
z = x.Base::operator*(z)

This will give you the fastest operation possible within the Eigen library. The overloaded operators have some if-clauses and do not make use of expression templates what may harm performance.

Matrix offers a handling for complex numbers which differs from Eigen: The odd columns are the real parts and the odd columns contain the imaginary parts.

Some of the underlying Eigen methods are available for SWIG. They are not integrated into the error chacking system, though! neverthelesse, ften they are the most efficient methods. To distuingish between Eigen and own methods, the Eigen methods identifiers start with a noncapital first letter, our own methods start with a capital letter.

Operators for SWIG are provided using the methods add, etc., The SWIG-operators must be safeguarded, whereas the C++-operators should be the original Eigen2 operators. Therefore they must be defined separately on C++ level.

Matrix is useing a reference counter system. It is advised not to use 'delete Matrix();' to remove it from memory, but to use removeReference.

Constructor & Destructor Documentation

◆ Matrix() [1/6]

Matrix ( )

destructor

default constructor

◆ Matrix() [2/6]

Matrix ( Matrix ar )

copy constructor

Parameters

ar	the object to be copied

◆ Matrix() [3/6]

Matrix	(	TUnsignedIndex	nrow,
		TUnsignedIndex	ncol = `1`
	)

constructs a matrix and allocates nrow*ncol elements

Parameters

nrow	the number of rows
ncol	the number of columns

◆ Matrix() [4/6]

Matrix ( MatrixBlock x )

constructs a matrix from a matrix block

Parameters

x	the object to be copied from

◆ Matrix() [5/6]

Matrix ( sparse::SparseMatrix x )

copies from a sparse matrix

Parameters

x	the object to be copied from

◆ Matrix() [6/6]

Matrix ( sparse::SymSparseMatrix x )

copies from a symmetric sparse matrix

Parameters

x	the object to be copied from

Member Function Documentation

◆ neg()

Matrix __neg__ ( ) const

Returns: unary minus (B=-A) Used by SWIG.

◆ str()

char* __str__ ( )

transforms this objects into a string, required by SWIG

Returns: a string

◆ Add() [1/2]

Add ( Matrix other )

modifies this matrix by the matrix sum A+B

Parameters

other the matrix B

◆ Add() [2/2]

Add ( MatrixBlock other )

modifies this matrix by the matrix sum A+B

Parameters

other the matrix B

◆ AppendCols()

Matrix AppendCols ( Matrix m )

returns an object with modified data

Parameters

m	the columns to be appended

Returns: Matrix with columns appended

◆ AppendRows()

Matrix AppendRows ( Matrix m )

returns an object with modified data

Parameters

m	the rows to be appended

Returns: Matrix with rows appended

◆ Assign() [1/2]

Assign ( Matrix ar )

The assignment operator for matrices (data only)

Parameters

ar	the source object

◆ Assign() [2/2]

Assign ( MatrixBlock ar )

The assignment operator for blocks (data only)

Parameters

ar	the source object

◆ Block()

MatrixBlock Block	(	TUnsignedIndex	row,
		TUnsignedIndex	col,
		TUnsignedIndex	numrows,
		TUnsignedIndex	numcols
	)

returns a reference to a block starting at 'row','column' with size 'numrows'*'numcols'

Parameters

row	the top left row index
col	the top left column index
numrows	the number of rows of the matrix part
numcols	the number of columns of the matrix part

Returns: a matrix block serving as a reference to the specified matrix part

◆ Col()

MatrixBlock Col ( TUnsignedIndex col )

returns a reference to the 'col'th column

Parameters

col	the requested column index

Returns: a matrix block serving as a reference to the column

◆ Cols() [1/2]

TUnsignedIndex Cols ( ) const

Returns: the number of cols

◆ Cols() [2/2]

MatrixBlock Cols	(	TUnsignedIndex	col1,
		TUnsignedIndex	ncol
	)

returns a block containing the ncol columns starting at column index col1

Parameters

col1	the left column index
ncol	the number of columns of the matrix part

Returns: a matrix block serving as a reference to the specified matrix part

◆ ConservativeResize()

void ConservativeResize	(	TUnsignedIndex	rows,
		TUnsignedIndex	cols = `1`
	)

resizes the matrix to its new dimensions without destroying the contents.

Parameters

rows	the number of rows after resize
cols	the number of columns after resize Internally it creates a copy of the object (nothing if memory is crucial).

◆ CW()

MatrixCWise CW ( )

Returns: an object providing cwise access

◆ Div()

Div ( TScalar other )

modifies this matrix by the scalar matrix quotient A/s

Parameters

other the scalar s

◆ Dot() [1/2]

TScalar Dot ( Matrix other )

returns the scalar product of two vectors (a'b)

Parameters

other the vector b

Returns: the result of the operation

◆ Dot() [2/2]

TScalar Dot ( MatrixBlock other )

returns the scalar product of two vectors (a'b)

Parameters

other the vector b

Returns: the result of the operation

◆ Dott() [1/2]

TScalar Dott ( Matrix other )

returns the weighted scalar product of this matrix and the given vector multiplied once from left and once from right (b'Ab)

Parameters

other the vector b

Returns: the result of the operation

◆ Dott() [2/2]

TScalar Dott ( MatrixBlock other )

returns the weighted scalar product of this matrix and the given vector multiplied once from left and once from right (b'Ab)

Parameters

other the vector b

Returns: the result of the operation

◆ InnerProduct() [1/2]

Matrix InnerProduct ( Matrix other )

returns the inner product of two matrices/vectors (a'*b)

Parameters

other the vector/matrix b

Returns: the result of the operation

◆ InnerProduct() [2/2]

Matrix InnerProduct ( MatrixBlock other )

returns the inner product of two matrices/vectors (a'*b)

Parameters

other the vector/matrix b

Returns: the result of the operation

◆ IsApprox()

bool IsApprox	(	Matrix	other,
		TScalar	s
	)		const

returns true if other and this are approx. identical

Parameters

other	the object to be compared
s	a tolerance for the equality test

Returns: the result of the operation

◆ IsApproxToConstant()

bool IsApproxToConstant	(	TScalar	value,
		TScalar	s
	)

returns true if array is constant and approx. equal s

Parameters

value	the constant value to be compared with
s	a tolerance for the equality test

Returns: the result of the operation

◆ IsDiagonal()

bool IsDiagonal ( TScalar s )

returns true if array is a diagonal matrix by precision s

Parameters

s	a tolerance for the test

Returns: the result of the operation

◆ IsIdentity()

bool IsIdentity ( TScalar s )

returns true if array is the identity matrix by precision s

Parameters

s	a tolerance for the equality test

Returns: the result of the operation

◆ IsLowerTriangular()

bool IsLowerTriangular ( TScalar s )

returns true if array is a lower triangular matrix by precision s

Parameters

s	a tolerance for the equality test

Returns: the result of the operation

◆ IsScalar()

bool IsScalar ( )

Returns: true if array is a scalar

◆ IsUnitary()

bool IsUnitary ( TScalar s )

returns true if array is a unitary matrix by precision s (is an orthonormal basis)

Parameters

s	a tolerance for the equality test

Returns: the result of the operation

◆ IsUpperTriangular()

bool IsUpperTriangular ( TScalar s )

returns true if array is an upper triangular matrix by precision s

Parameters

s	a tolerance for the equality test

Returns: the result of the operation

◆ IsVector()

bool IsVector ( )

Returns: true if array is a vector

◆ IsZero()

bool IsZero ( TScalar s )

Returns: true if array is a zero matrix by precision s

Parameters

s	a tolerance for the equality test

◆ MinCoeff()

TScalar MinCoeff	(	TEigenIndex *	OUTPUT,
		TEigenIndex *	OUTPUT
	)		const

find the smallest element in the array returns the minimum element in the array

Parameters

row	will be modified and will contain the row position of the found value on return
col	will be modified and will contain the column position of the found value on return

Returns: smallest elment

◆ Mul()

Mul ( TScalar other )

modifies this matrix by the scalar matrix product A*s

Parameters

other the scalar s

◆ operator*() [1/3]

Matrix operator* ( Matrix other ) const

returns the matrix product A*B

Parameters

other the matrix B

Returns: the result of the operation

◆ operator*() [2/3]

Matrix operator* ( MatrixBlock other ) const

returns the matrix product A*B

Parameters

other the matrix B

Returns: the result of the operation

◆ operator*() [3/3]

Matrix operator* ( TScalar other ) const

returns the scalar matrix product A*s

Parameters

other the scalar s

Returns: the result of the operation

◆ operator+() [1/2]

Matrix operator+ ( Matrix other ) const

returns the matrix sum A+B

Parameters

other the matrix B

Returns: the result of the operation

◆ operator+() [2/2]

Matrix operator+ ( MatrixBlock other ) const

returns the matrix sum A+B

Parameters

other the matrix B

Returns: the result of the operation

◆ operator-() [1/2]

Matrix operator- ( Matrix other ) const

returns the matrix difference A-B

Parameters

other the matrix B

Returns: the result of the operation

◆ operator-() [2/2]

Matrix operator- ( MatrixBlock other ) const

returns the matrix difference A-B

Parameters

other the matrix B

Returns: the result of the operation

◆ operator/()

Matrix operator/ ( TScalar other ) const

returns the scalar matrix quotient A/s

Parameters

other the scalar s

Returns: the result of the operation

◆ operator<()

Matrix operator< ( TScalar x ) const

returns a matrix of 1 and 0 indicating which element is less than x

Parameters

x	the scalar x

Returns: the result of the operation

◆ operator=()

Matrix operator= ( Matrix ar )

copy assignment operator

Parameters

ar	the object to be copy-assigned

◆ OuterProduct() [1/2]

Matrix OuterProduct ( Matrix other )

returns the outer product of two matrices/vectors (a*b')

Parameters

other the vector/matrix b

Returns: the result of the operation

◆ OuterProduct() [2/2]

Matrix OuterProduct ( MatrixBlock other )

returns the outer product of two matrices/vectors (a*b')

Parameters

other the vector/matrix b

Returns: the result of the operation

◆ Print()

Print	(	string	format = `"%g "`,
		TUnsignedIndex	rows = `20`,
		TUnsignedIndex	cols = `20`
	)		const

prints the matrix up to the given rows and columns

Parameters

format	the format according to printf()
rows	the maximum number of rows to be printed
cols	the maximum number of columns to be printed

◆ Row()

MatrixBlock Row ( TUnsignedIndex row )

returns a reference to the 'row'th row

Parameters

row	the requested row index

Returns: a matrix block serving as a reference to the row

◆ Rows() [1/2]

TUnsignedIndex Rows ( ) const

Returns: the number of rows

◆ Rows() [2/2]

MatrixBlock Rows	(	TUnsignedIndex	row1,
		TUnsignedIndex	nrow
	)

returns a block containing the nrow columns starting at column index row1

Parameters

row1	the right row index
nrow	the number of rows of the matrix part

Returns: a matrix block serving as a reference to the specified matrix part

◆ SetCols()

void SetCols	(	Matrix	m,
		TUnsignedIndex	col
	)

returns an object providing copy of data

changes object data in place

◆ SetConstant()

SetConstant ( TScalar value )

initializes the matrix with constant values

Parameters

value the scalar value of the matrix

◆ SetLinearCols()

void SetLinearCols	(	TScalar	a,
		TScalar	b
	)

initializes the matrix with linear columns

Parameters

a	the value of the first row
b	the value of the last row

◆ SetLinearRows()

SetLinearRows	(	TScalar	a,
		TScalar	b
	)

initializes the matrix with linear rows

Parameters

a	the value of the first column
b	the value of the last column

◆ Sub() [1/2]

Sub ( Matrix other )

modifies this matrix by the matrix difference A-B

Parameters

other the matrix B

◆ Sub() [2/2]

Sub ( MatrixBlock other )

modifies this matrix by the matrix difference A-B

Parameters

other the matrix B

◆ Swap()

Swap ( Matrix ar )

The swap operator for matrices (data only)

Parameters

ar	the other object. On output this will contain the input value of ar while ar contains the input value of this.

◆ Transpose()

Matrix Transpose ( ) const

Returns: the transpose

Member Data Documentation

◆ int

apply int { TEigenIndex }

find the largest element in the array returns the maximum element in the array

Parameters

row	will be modified and will contain the row position of the found value on return
col	will be modified and will contain the column position of the found value on return

Returns: largest elment

Matrix Class Reference

Public Types

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Matrix() [1/6]

◆ Matrix() [2/6]

◆ Matrix() [3/6]

◆ Matrix() [4/6]

◆ Matrix() [5/6]

◆ Matrix() [6/6]

Member Function Documentation

◆ __neg__()

◆ __str__()

◆ Add() [1/2]

◆ Add() [2/2]

◆ AppendCols()

◆ AppendRows()

◆ Assign() [1/2]

◆ Assign() [2/2]

◆ Block()

◆ Col()

◆ Cols() [1/2]

◆ Cols() [2/2]

◆ ConservativeResize()

◆ CW()

◆ Div()

◆ Dot() [1/2]

◆ Dot() [2/2]

◆ Dott() [1/2]

◆ Dott() [2/2]

◆ InnerProduct() [1/2]

◆ InnerProduct() [2/2]

◆ IsApprox()

◆ IsApproxToConstant()

◆ IsDiagonal()

◆ IsIdentity()

◆ IsLowerTriangular()

◆ IsScalar()

◆ IsUnitary()

◆ IsUpperTriangular()

◆ IsVector()

◆ IsZero()

◆ MinCoeff()

◆ Mul()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator/()

◆ operator<()

◆ operator=()

◆ OuterProduct() [1/2]

◆ OuterProduct() [2/2]

◆ Print()

◆ Row()

◆ Rows() [1/2]

◆ Rows() [2/2]

◆ SetCols()

◆ SetConstant()

◆ SetLinearCols()

◆ SetLinearRows()

◆ Sub() [1/2]

◆ Sub() [2/2]

◆ Swap()

◆ Transpose()

Member Data Documentation

◆ int

Connect with Ansys

◆ neg()

◆ str()