This class is a multi level toeplitz matrix whose leaf block are dense matrix of dimension D and with size S=D x D. More...

#include <MATH_GlobalMultiLevelsPolynomialToeplitzMatrix.h>

Inheritance diagram for MATH_GlobalMultiLevelsPolynomialToeplitzMatrix:

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Collaboration diagram for MATH_GlobalMultiLevelsPolynomialToeplitzMatrix:

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Public Member Functions
virtual SP::MATH_MultiLevelsToeplitzMatrix	NewInstance () const
	new instance More...

virtual void	copy (const MATH_MultiLevelsToeplitzMatrix &mat)
	copy the instance mat More...

virtual void	clear ()
	clear the matrix clear the data creating when building the spectral space More...

virtual tULLInt	getMemorySize () const
	return the memory size in byte More...

FFTW_FFT &	getDFTProjector () const
	return the projector for vector into the spectral space More...

virtual void	vectorProduct (const tUIndex &N, const tReal X, tReal Y) const
	do the vector product of the circular matrix C with Y by an FFT method More...

virtual void	vectorProduct (const CORE_RealArray &X, CORE_RealArray &Y) const
	do the vector product of the circular matrix C with Y by an FFT method More...

const tFFTWComplex &	operator() (const tUIndex &i, const tUIndex &j) const
	get the value of the matrix at row i and column j More...

tFFTWComplex &	operator() (const tUIndex &i, const tUIndex &j)
	get the value of the matrix at row i and column j More...

virtual void	setLeafBlockDimension (const tUIndex &n)
	set the dimension of leaf block More...

virtual void	setLevels (const tUSInt &levelsNumber, const tUIndex levels[], const tUIndex &nD)
	set the levels of the matrix More...

void	setLevels (const tUSInt &levelsNumber, const tUIndex levels[])
	set the levels of the matrix More...

tReal	getRealValue (const tUIndex &i, const tUIndex &j) const
	get the real value at row i and column j More...

const tUIndex &	getDimension () const
	get the dimension of the matrix More...

const tUIndex &	getRowsNumber () const
	get the dimension of the matrix More...

const tUIndex &	getColumnsNumber () const
	get the dimension of the matrix More...

FFTW_ComplexArray &	getValues ()
	get the values of the matrix More...

const FFTW_ComplexArray &	getValues () const
	get the values of the matrix More...

const tFFTWComplex *	getLeafBlockValues (const tIndex indices[]) const
	get the values of the leaf block More...

tFFTWComplex *	getLeafBlockValues (const tIndex indices[])
	get the values of the leaf block More...

const CORE_UIndexArray &	getLevels () const
	get the level of the matrix More...

tUSInt	getLevelsNumber () const
	get the number of levels of the matrix More...

const tUIndex &	getCanonicalSpaceSize () const
	get canonical space size More...

tUIndex	getLeafBlockSize () const
	return the size of the leaf block matrix More...

const tUIndex &	getLeafBlockDimension () const
	return the dimension of the leaf block matrix More...

tUIndex	getBlocksNumber () const
	get the blocks number More...

tUIndex	getBlocksNumber (const tUIndex &l) const
	get the blocks number at the level More...

const tUIndex &	getBlocksNumberPerRow (const tUSInt &l) const
	get the blocks number per row or column at the level More...

const tFlag &	getSpace () const
	get the space of the matrix More...

const MATH_LeafBlockMatrixStorage &	getStorage () const
	get the storage of the leaf matrices More...

MATH_LeafBlockMatrixStorage &	getStorage ()
	get the storage of the leaf matrices More...

tUIndex	getIndex (const tUIndex &i, const tUIndex &j) const
	return the index in values of the matrix value at row i and column j More...

tUIndex	getToeplitzBlockIndex (const tUSInt &nLevels, const tUIndex N[], const tIndex I[]) const
	get the block index corresponding to indices More...

tUIndex	getToeplitzBlockIndex (const tIndex I[]) const
	get the block index corresponding to indices More...

void	projection (const tFlag &space)
	make the projection in the space More...

virtual tString	toString () const
	return string More...

void	getSharedPointer (SP::CORE_Object &p)
	get the shared pointer of this class into p More...

void	getSharedPointer (SPC::CORE_Object &p) const
	get the shared pointer of this class into p More...

tString	getClassName () const
	return the class name of the object More...

tString	getIdentityString () const
	return the identity string of the object of the form className_at_address More...

tString	getPointerAddress () const
	return the identity string of the object More...

template<class T >
tBoolean	isInstanceOf () const
	test if the clas T is an instance of this class More...

tBoolean	isInstanceOf (const tString &name) const
	test if the object is an instance of className More...

Static Public Member Functions
static SP::MATH_GlobalMultiLevelsPolynomialToeplitzMatrix	New ()
	build a new instance of class More...

static void	setIsMemoryChecked (const tBoolean &v)
	set if the memory checking is used More...

static void	setOut (SP::CORE_Out out)
	set the output stream More...

static void	resetOut ()
	reset the output stream More...

static void	setThread (SP::CORE_Thread thread)
	set the thread More...

static void	resetThread ()
	reset the output stream More...

static CORE_Out &	out ()
	get the output More...

static SP::CORE_Out	getOut ()
	get the output More...

static CORE_Thread &	getThread ()
	get the profilier More...

static const tBoolean &	isMemoryChecked ()
	get if the memory checking is used More...

static tString	getClassName (const tString &identityString)
	return the class name of the object More...

template<class T >
static tString	getTypeName ()
	get type name More...

static tBoolean	is64Architecture ()
	return true if the machine is a 64 bits machine More...

static tBoolean	is32Architecture ()
	return true if the machine is a 32 bits machine More...

static tString	pointer2String (const void *obj)
	return the string representation of a pointer More...

static void	printObjectsInMemory (ostream &f)
	print object in memory More...

static void	printObjectsInMemory ()
	print object in memory in the standart output More...

static tChar	getMaxChar ()
	get the max value for tChar type More...

static tChar	getMinChar ()
	get the min value for tChar type More...

static tUChar	getMaxUChar ()
	get the max value for tUChar type More...

static tUChar	getMinUChar ()
	get the min value for tUChar type More...

static tSInt	getMaxSInt ()
	get the max value for tSInt type More...

static tSInt	getMinSInt ()
	get the min value for tSInt type More...

static tUSInt	getMaxUSInt ()
	get the max value for tUSInt type More...

static tUSInt	getMinUSInt ()
	get the min value for tUSInt type More...

static tInt	getMaxInt ()
	get the max value for tInt type More...

static tInt	getMinInt ()
	get the min value for tInt type More...

static tUInt	getMaxUInt ()
	get the max value for tUInt type More...

static tUInt	getMinUInt ()
	get the min value for tUInt type More...

static tLInt	getMaxLInt ()
	get the max value for tLInt type More...

static tLInt	getMinLInt ()
	get the min value for tLInt type More...

static tULInt	getMaxULInt ()
	get the max value for tULInt type More...

static tULInt	getMinULInt ()
	get the min value for tULInt type More...

static tLLInt	getMaxLLInt ()
	get the max value for tULInt type More...

static tLLInt	getMinLLInt ()
	get the min value for tLLInt type More...

static tULLInt	getMaxULLInt ()
	get the max value for tULLInt type More...

static tULLInt	getMinULLInt ()
	get the min value for tULLInt type More...

static tFloat	getMaxFloat ()
	get the max value for tFloat type More...

static tFloat	getMinFloat ()
	get the min value for tFloat type More...

template<class T >
static T	getEpsilon ()
	get the epsilon value for T type More...

template<class T >
static T	getInfinity ()
	get the infinity for T type More...

static tFloat	getFloatEpsilon ()
	get the epsilon value for tFloat type More...

static tFloat	getFloatInfinity ()
	get the infinity value for tFloat type More...

static tDouble	getMaxDouble ()
	get the max value for tDouble type More...

static tDouble	getMinDouble ()
	get the min value for tDouble type More...

static tDouble	getDoubleInfinity ()
	get the infinity value for tFloat type More...

static tDouble	getDoubleEpsilon ()
	get the epsilon value for tDouble type More...

static tLDouble	getMinLDouble ()
	get the min value for tLDouble type More...

static tLDouble	getMaxLDouble ()
	get the max value for tLDouble type More...

static tLDouble	getLDoubleEpsilon ()
	get the epsilon value for tLDouble type More...

static tDouble	getLDoubleInfinity ()
	get the infinity value for tDouble type More...

static tIndex	getMaxIndex ()
	get the max value for the array/vector indexing type More...

static tIndex	getMinIndex ()
	get the min value for the array/vector indexing type More...

static tUIndex	getMaxUIndex ()
	get the max value for difference the array/vector indexing type More...

static tUIndex	getMinUIndex ()
	get the min value for difference the array/vector indexing type More...

static tFlag	getMaxFlag ()
	get the max value for the tFlag type More...

static tFlag	getMinFlag ()
	get the min value for the tFlag type More...

static tUInteger	getMaxUInteger ()
	get the max value for the unsigned integer type More...

static tUInteger	getMinUInteger ()
	get the min value for the unsigned integer type More...

static tInteger	getMaxInteger ()
	get the max value for the integer type More...

static tInteger	getMinInteger ()
	get the min value for the integer type More...

static tReal	getMaxReal ()
	get the max value for the real type More...

static tReal	getMinReal ()
	get the min value for the real type More...

static tReal	getRealEpsilon ()
	get the eps which is the difference between 1 and the least value greater than 1 that is representable. More...

static tReal	getRealInfinity ()
	get the infinity value More...

template<class T >
static T	computeEpsilon ()
	compute epsilon More...

Static Public Attributes
static const tFlag	CANONICAL_SPACE =0

static const tFlag	SPECTRAL_SPACE =1

Protected Member Functions
	MATH_GlobalMultiLevelsPolynomialToeplitzMatrix (void)
	create a multi level toeplitz matrix More...

virtual	~MATH_GlobalMultiLevelsPolynomialToeplitzMatrix (void)
	destroy a multi level toeplitz matrix More...

virtual void	buildSpectralVectorProjector (FFTW_FFT &proj) const
	build the projector of vector in spectral spce More...

virtual void	buildSpectralSpace ()
	build the spectral space More...

virtual void	recoverCanonicalSpace ()
	recover the canonical space from the spectral space More...

virtual void	buildColumnLeadingDimensions ()
	build the column leading dimensions More...

virtual void	buildRowLeadingDimensions ()
	build the row indices More...

virtual void	vectorProductInSpectralSpace (const FFTW_FFT &A, FFTW_FFT &Z) const
	make the vector product in spectral space More...

virtual void	projectIntoSpectralSpace (const tUIndex &N, const tReal *X) const
	project the vector X from initial space to multi levels space More...

virtual void	recoverFromSpectralSpace (const tUIndex &N, tReal *X) const
	recover from multi levels space to the initial space More...

void	setSpectralSpaceSize (const tUIndex &n)
	set the spectral space size More...

const CORE_UIndexArray &	getColumnLeadingDimensions () const
	get the leading dimension of columns from the spectral space More...

CORE_UIndexArray &	getColumnLeadingDimensions ()
	get the leading dimension of columns from the spectral space More...

const CORE_UIndexArray &	getRowLeadingDimensions () const
	get the index of the row i and column 0 from the spectral space More...

CORE_UIndexArray &	getRowLeadingDimensions ()
	get the index of the row i and column 0 from the spectral space More...

const tUIndex &	getSpectralSpaceSize () const
	get the spectral space size More...

virtual void	diagonalize ()
	diagonalize the matrix projection of the matrix in the SPECTRAL_SPACE More...

virtual void	recover ()
	projection of the matrix in the CANONICAL SPACE More...

tFFTWComplex &	operator[] (const tUIndex &k)
	get the value at index k More...

const tFFTWComplex &	operator[] (const tUIndex &k) const
	get the value at index k More...

void	setSpace (const tFlag &space)
	set the space of the multi level block matrix More...

void	setStorage (SP::MATH_LeafBlockMatrixStorage storage)
	set the storage of the matrix More...

void	setDFT (SP::FFTW_FFT dft)
	set the DFT class More...

const FFTW_FFT &	getDFT () const
	get the FFT class More...

FFTW_FFT &	getDFT ()
	get the FFT class More...

tUIndex	getBlockIndex (const tUIndex &ib, const tUIndex &jb, const tUIndex &N) const
	get the index of the block in the block list More...

void	setThis (SP::CORE_Object p)
	set this weak shared pointer called toDoAfterThis setting method More...

virtual void	toDoAfterThisSetting ()
	method called after setThis() method this method can oly be called once. More...

Private Member Functions
	SP_OBJECT (MATH_GlobalMultiLevelsPolynomialToeplitzMatrix)

Detailed Description

This class is a multi level toeplitz matrix whose leaf block are dense matrix of dimension D and with size S=D x D.

The matrix vector product T. U = W is modelized as a polynomial product thanks to Discrete Fourier Transform method. This work is based on the article of B. E. Barrows, F. L. Teixeira and J.A. Kong .

We consider T as a L-Multi levels matrix with $ N_l $ blocks per row. The dimension of the dense leaf block matrix is f.

The L-multi levels toplitz matrix dimension (number of rows or columns) is $\displaystyle N=D. \prod_{l=1}^{l=L} N_l$ . So the dimension of U is N.

The L-multi levels toeplitz values is presented as a vector of size $\displaystyle P=f^2.\prod_{l=1}^{l=L} (2.N_l-1)$ .

The elements of the leaf block matrix are stored from right to left and from top to bottom in order to be compatible with the way to save the values of the multi-levels toeplitz matrix.

$B = \left[ {\begin{array}{ccc} B_{0,0} & ... & D_{0,D-1} \\ B_{1,0} & ... & D_{1,D-1} \\ ... & ... & ... \\ B_{D-1,0} & ... & B_{D-1,D-1} \end{array} } \right]$ are stored in a vector $(B_{0,D-1},...,B_{0,0},B_{1,D-1},..,B_{1,0},...,B_{D-1,0} )$ .

The values of T are stored as explained in the MATH_MultiLevelsToeplitzMatrix class :

$T = \left[ {\begin{array}{ccccc} T^k_0 & T^k_{-1} & T^k_{-1} & ... & T^k_{1-N_k} \\ T^k_1 & T^k_0 & ... & ... & T^k_{2-N_k} \\ ... & ... & ... & ... & ... \\ T^k_{N_k-1} & T^k_{N_k-2} & ... & ... & T^k_0 \end{array} } \right]$

The blocks at level k are saved in the list ${T^k_{1-N_k},...,T^k_{-2},T^k_{-1},T^k_0,T^k_1,...,T^k_{N_k-2},T^k_{N_k-1}}$ . Each toeplitz block block $T^k_{i}$ are stored in the same way.

So the values of the matrix is a vector V of size N. We associate the polynom $\displaystyle V(x)=\sum_{i=0}^{i=P-1} V_i x^i$ .

The polynom associate to U is $\displaystyle U(x)=\sum_{i=0}^{i=P-1} u_i x^{c(0)-c(i)}$ where $ c(i) $ is the index of the value of the T matrix at first row and i-th column in its V vector values. c is decreasing .

If we denote by $ r(i) $ the index of the value of the T matrix at first column and i-th row in its V vector values. r is increasing. We note that $ r(0)=c(0) $ .

$\displaystyle W(x)=V(x).U(x)=\sum_{i=0}^{i=P+c(0)-c(N-1)-1} W_i x^i$ . The values of $ W = T. U $ is $(W_{r(0)},W_{r(1)+}...,W_{r(N-1)})$

So the matrix . vector product is reduced to a multiplication of polynoms $\displaystyle \forall j in [0,N[, W_j=\sum_{k=0}^{k=j} V_k . U_{c(0)-c(N-1)-k}$ which is a convolution product of V and U which is well known to be of cost N. log(N) by Discrete Fourier Transform.

So the algorithm to make the product $ T.X=Y $ :

The size of the polynom V is P. Increase the size to M such that $M=2^m \geq P > 2^{m-1}$ for better efficiency on Discrete Fast Fourier Transform. Complete by 0 the added values. (done in buildSpectralSpace() )
build the functions c and r (done in buildColumnLeadingDimensions() & buildRowLeadingDimensions() )
compute $\tilde V= DFT_M(V)$ with M the size of the Discrete Fourier Transform FFTW_DFT (done in diagonalize() )
build projection U of X in the spectral space : $U[c(0)-c(i)]= X[i] \forall i \in [0,N[$ and $U[j]=0 \forall j in [0,M[ j \ni {c(0)-c(i)}$ (see projectIntoSpectralSpace() )
compute $\tilde U= DFT_M(U)$ (done in projectIntoSpectralSpace() )
make the product W of the diagonal matrix in the spectral space $\tilde V$ with the projection of U in the spectral space $\tilde U$ : $W[i]= \tilde U[i] \cdot \tilde V[i]$ (done in vectorProduct() )
build projection R of W in the canonical space $R=DFT_M^{-1}(W)$ . (done in recoverFromSpectralSpace())
extract the corresponding value Y from R : . (done in recoverFromSpectralSpace())

Note that in fact the c does not store the index of the element (0,i) but the positive number of elements between 2 successive index except for its first element :

c(i)=indexOfT(0,i-1)-indexOfT(0,i)
c(0)=indexOfT(0,0). r is built in a similar way in order to be more efficent in the computations.

For example :

Consider the matrix 2x2x2 levels matrix with leaf block matrix of size 1 :

the values of the matrix is (completed by 0 until size 32) : V=(27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 09 08 07 06 05 04 03 02 01 0 0 0 0 0)
the index of each element of V is (0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 )
the c and r functions are c=(13,12,10,9,4,3,1,0) r=(13,14,16,17,22,23,25,26) or more precisly c=(13,1,2,1,5,1,2,1) r=(13,1,2,1,5,1,2,1)
build U from X=(1,2,3,4,5,6,7,8) bu using the c function : U=(1,2,0,3,4,0,0,0,0,5,6,0,7,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
compute W= DFT(U)*DFT(V)
compute $R=DFT^{-1}(W)$ , $R=(R_0,...,R_{31})$ R={190,217,188,240,316,285,260,235,217,342,489,468,636,824,788,752,716,680,644,608,572,536,500,464,428,392,356,320,285,252,219,189}
restore with the r function $Y=(R_{13},R_{14},R_{16},R_{17},R_{22},R_{23},R_{25},R_{26})=[824,788,716,680,500,464,392,356]$

Now if we consider the matrix 2x2 of levels 2 with leaf block matrix of size 2:

the values of the matrix is (completed by 0 until size 64) : V=(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 0 ... 0 )
the c and r function c=[17,1,3,1,7,1,3,1] r=[17,2,2,2,6,2,2,2]
build U with the c function from X=(1,2,3,4,5,6,7,8), U={1,2,0,0,3,4,0,0,0,0,0,0,5,6,0,0,7,8,0..,0}
compute W= DFT(U)*DFT(V)
compute R=DFT^{-1}(W) $R=(R_0,...,R_{63})$ R={1,4,7,10,16,26,36,46,56,66,76,86,101,122,143,164,192,228,264,300,336,372,408,444,480,552,588,624,660,696,732,768,804,840,876,....}.
restore with the r function $Y=(R_{17},R_{19},R_{21},R_{23},R_{29},R_{31},R_{33},R_{35})=[228,300,372,444,660,732,804,876]$

Author: Stéphane Despréaux

Version: 1.0

Constructor & Destructor Documentation

◆ MATH_GlobalMultiLevelsPolynomialToeplitzMatrix()

MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::MATH_GlobalMultiLevelsPolynomialToeplitzMatrix ( void )

protected

create a multi level toeplitz matrix

References CORE_Run::getClassFactory(), NewInstance(), and MATH_MultiLevelsToeplitzMatrix::setDFT().

Referenced by New().

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◆ ~MATH_GlobalMultiLevelsPolynomialToeplitzMatrix()

MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::~MATH_GlobalMultiLevelsPolynomialToeplitzMatrix ( void )

protectedvirtual

destroy a multi level toeplitz matrix

Member Function Documentation

◆ buildColumnLeadingDimensions()

void MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::buildColumnLeadingDimensions ( )

protectedvirtual

build the column leading dimensions

register the index in CANONICAL space of the values corresponding to element at row 0 & column 0
register the leading dimension between column i+1 and column i at row 0

Implements MATH_MultiLevelsFFTToeplitzMatrix.

References MATH_MultiLevelsFFTToeplitzMatrix::getColumnLeadingDimensions(), MATH_MultiLevelsToeplitzMatrix::getDimension(), MATH_MultiLevelsToeplitzMatrix::getIndex(), CORE_Array< T >::setSize(), and tUIndex.

Referenced by buildSpectralSpace(), and buildSpectralVectorProjector().

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◆ buildRowLeadingDimensions()

void MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::buildRowLeadingDimensions ( )

protectedvirtual

build the row indices

register the index in CANONICAL space of the values corresponding to element at colunm 0 & row i
- register the leading dimension between row i+1 and row i at column 0

Implements MATH_MultiLevelsFFTToeplitzMatrix.

References MATH_MultiLevelsToeplitzMatrix::getDimension(), MATH_MultiLevelsToeplitzMatrix::getIndex(), MATH_MultiLevelsFFTToeplitzMatrix::getRowLeadingDimensions(), CORE_Array< T >::setSize(), and tUIndex.

Referenced by buildSpectralSpace(), and buildSpectralVectorProjector().

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◆ buildSpectralSpace()

void MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::buildSpectralSpace ( )

protectedvirtual

build the spectral space

build the spectral space size
create a DFT class

Implements MATH_MultiLevelsFFTToeplitzMatrix.

References buildColumnLeadingDimensions(), buildRowLeadingDimensions(), FFTW_Object::FORWARD, FFTW_FFT::getArray(), MATH_MultiLevelsToeplitzMatrix::getCanonicalSpaceSize(), MATH_MultiLevelsToeplitzMatrix::getDFT(), FFTW_FFT::setFFT(), FFTW_FFT::setFFTsNumber(), FFTW_FFT::setPointsNumber(), MATH_MultiLevelsFFTToeplitzMatrix::setSpectralSpaceSize(), tFFTWComplex, and tUIndex.

Referenced by buildSpectralVectorProjector().

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◆ buildSpectralVectorProjector()

virtual void MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::buildSpectralVectorProjector ( FFTW_FFT & proj ) const

inlineprotectedvirtual

build the projector of vector in spectral spce

Parameters

proj	the DFT projector built

Reimplemented from MATH_MultiLevelsFFTToeplitzMatrix.

References buildColumnLeadingDimensions(), buildRowLeadingDimensions(), buildSpectralSpace(), MATH_MultiLevelsFFTToeplitzMatrix::buildSpectralVectorProjector(), and recoverCanonicalSpace().

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◆ clear()

void MATH_MultiLevelsFFTToeplitzMatrix::clear ( )

virtualinherited

clear the matrix clear the data creating when building the spectral space

Reimplemented from MATH_MultiLevelsToeplitzMatrix.

References MATH_MultiLevelsToeplitzMatrix::clear(), CORE_Array< T >::clear(), MATH_MultiLevelsFFTToeplitzMatrix::mColumnLeadingDimensions, MATH_MultiLevelsFFTToeplitzMatrix::mDFTProjector, MATH_MultiLevelsFFTToeplitzMatrix::mRowLeadingDimensions, MATH_MultiLevelsFFTToeplitzMatrix::mSpectralSpaceSize, and null.

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◆ computeEpsilon()

template<class T >

static T CORE_Object::computeEpsilon ( )

inlinestaticinherited

compute epsilon

Returns: the epsilon value eps=10^{-p/3} where p is defined by getEpsilon()=10^{-p}

◆ copy()

virtual void MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::copy ( const MATH_MultiLevelsToeplitzMatrix & mat )

inlinevirtual

copy the instance mat

Parameters

mat	the instance to copy

Reimplemented from MATH_MultiLevelsFFTToeplitzMatrix.

References MATH_MultiLevelsToeplitzMatrix::copy().

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◆ diagonalize()

void MATH_MultiLevelsFFTToeplitzMatrix::diagonalize ( )

protectedvirtualinherited

diagonalize the matrix projection of the matrix in the SPECTRAL_SPACE

build the spectral space : calls buildSpectralSpace()
create a projector to spectral space for vector projection : calls buildSpectralVectorProjector()
transforms the valus of the toeplitz matrix into its diagonal value by Discrete Fourier Transform: getDFT()

Implements MATH_MultiLevelsToeplitzMatrix.

References MATH_MultiLevelsFFTToeplitzMatrix::buildSpectralSpace(), MATH_MultiLevelsFFTToeplitzMatrix::buildSpectralVectorProjector(), CORE_Out::ERROR_MSG, MATH_MultiLevelsToeplitzMatrix::getDFT(), CORE_Exception::getMessage(), MATH_MultiLevelsFFTToeplitzMatrix::mDFTProjector, FFTW_FFT::NewInstance(), CORE_Object::out(), CORE_Out::println(), and FFTW_FFT::runFFT().

Referenced by MATH_MultiLevelsFFTToeplitzMatrix::buildSpectralVectorProjector().

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◆ getBlockIndex()

tUIndex MATH_MultiLevelsToeplitzMatrix::getBlockIndex	(	const tUIndex &	ib,
		const tUIndex &	jb,
		const tUIndex &	N
	)		const

inlineprotectedinherited

get the index of the block in the block list

Parameters

ib	row index of the block
jb	colum index of the block
N	size of the level the list are $\{ T_{-N+1},...,T_{-1},T_0,T_1,.....T_{N-1} \}$ N=the number of columns (or rows corresponding to the matrix:

$T = \left[ {\begin{array}{ccccc} T_0 & T_{-1} & T_{-1} & ... & T_{1-N} \\ T_1 & T_0 & ... & ... & T_{2-N} \\ ... & ... & ... & ...& ... \\ T_{N-1} & T_{N-2} & ... & ... & T_0 \end{array} } \right]$

Returns: the block index in the blocks list of $T_{ib-jb}$ which is ib-jb+N-1

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::getElementIndex(), and MATH_MultiLevelsToeplitzMatrix::getIndex().

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◆ getBlocksNumber() [1/2]

tUIndex MATH_MultiLevelsToeplitzMatrix::getBlocksNumber ( ) const

inlineinherited

get the blocks number

Returns: the number of blocks

References MATH_MultiLevelsToeplitzMatrix::getLeafBlockSize().

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::buildSpectralSpace(), MATH_ElementaryMultiLevelsCircularToeplitzMatrix::buildSpectralSpace(), MATH_ElementaryMultiLevelsToeplitzMatrix::recoverCanonicalSpace(), and MATH_ElementaryMultiLevelsCircularToeplitzMatrix::recoverCanonicalSpace().

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◆ getBlocksNumber() [2/2]

tUIndex MATH_MultiLevelsToeplitzMatrix::getBlocksNumber ( const tUIndex & l ) const

inlineinherited

get the blocks number at the level

Parameters

l	index of the level

Returns: the number of blocks

◆ getBlocksNumberPerRow()

const tUIndex& MATH_MultiLevelsToeplitzMatrix::getBlocksNumberPerRow ( const tUSInt & l ) const

inlineinherited

get the blocks number per row or column at the level

Parameters

l	index of the level >=1

Returns: the number of blocks at the level l per row (or column) l=1 is the levels which contains the leaf block levels whise level is 0

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::getElementIndex().

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◆ getCanonicalSpaceSize()

const tUIndex& MATH_MultiLevelsToeplitzMatrix::getCanonicalSpaceSize ( ) const

inlineinherited

get canonical space size

Returns: the memory size of the canonical space getLeafBlockSize()*getBlocksNumber();

References MATH_MultiLevelsToeplitzMatrix::mCanonicalSpaceSize.

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::buildSpectralSpace(), buildSpectralSpace(), MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::buildSpectralSpace(), MATH_MultiLevelsToeplitzMatrix::copy(), MATH_ElementaryMultiLevelsToeplitzMatrix::recoverCanonicalSpace(), recoverCanonicalSpace(), MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::recoverCanonicalSpace(), and MATH_ToeplitzTest::toeplitzTest().

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◆ getClassName() [1/2]

tString CORE_Object::getClassName ( ) const

inherited

return the class name of the object

Returns: the class name of the object

References tString.

Referenced by CORE_Object::getIdentityString(), EMM_Operator::getName(), and CORE_Object::isMemoryChecked().

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◆ getClassName() [2/2]

static tString CORE_Object::getClassName ( const tString & identityString )

inlinestaticinherited

return the class name of the object

Parameters

identityString the identity string of the object

Returns: the class name

◆ getColumnLeadingDimensions() [1/2]

const CORE_UIndexArray& MATH_MultiLevelsFFTToeplitzMatrix::getColumnLeadingDimensions ( ) const

inlineprotectedinherited

get the leading dimension of columns from the spectral space

Returns

the leading dimension of the column from the spectral space

index 0: the index corresponding to the first column in the spectral space
index i where i>0 : the leading dimension betwen column i and column i-1

References MATH_MultiLevelsFFTToeplitzMatrix::mColumnLeadingDimensions.

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::buildColumnLeadingDimensions(), MATH_ElementaryMultiLevelsCircularToeplitzMatrix::buildColumnLeadingDimensions(), buildColumnLeadingDimensions(), MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::buildColumnLeadingDimensions(), MATH_MultiLevelsFFTToeplitzMatrix::copy(), MATH_ElementaryMultiLevelsToeplitzMatrix::projectIntoSpectralSpace(), and projectIntoSpectralSpace().

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◆ getColumnLeadingDimensions() [2/2]

CORE_UIndexArray& MATH_MultiLevelsFFTToeplitzMatrix::getColumnLeadingDimensions ( )

inlineprotectedinherited

get the leading dimension of columns from the spectral space

Returns

the leading dimension of the column from the spectral space

index 0: the index corresponding to the first column in the spectral space
index i where i>0 : the leading dimension betwen column i and column i-1

References MATH_MultiLevelsFFTToeplitzMatrix::mColumnLeadingDimensions.

◆ getColumnsNumber()

const tUIndex& MATH_MultiLevelsToeplitzMatrix::getColumnsNumber ( ) const

inlineinherited

get the dimension of the matrix

Returns: the number of rows or columns of the matrix

References MATH_MultiLevelsToeplitzMatrix::mDimension.

Referenced by MATH_MultiLevelsToeplitzMatrix::toString().

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◆ getDFT() [1/2]

const FFTW_FFT& MATH_MultiLevelsToeplitzMatrix::getDFT ( ) const

inlineprotectedinherited

get the FFT class

Returns: the fft class

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◆ getDFT() [2/2]

FFTW_FFT& MATH_MultiLevelsToeplitzMatrix::getDFT ( )

inlineprotectedinherited

get the FFT class

Returns: the fft class

◆ getDFTProjector()

FFTW_FFT& MATH_MultiLevelsFFTToeplitzMatrix::getDFTProjector ( ) const

inlineinherited

return the projector for vector into the spectral space

Returns: the projector to spectral space

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::projectIntoSpectralSpace(), projectIntoSpectralSpace(), MATH_ElementaryMultiLevelsToeplitzMatrix::recoverFromSpectralSpace(), recoverFromSpectralSpace(), and MATH_MultiLevelsFFTToeplitzMatrix::vectorProduct().

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◆ getDimension()

const tUIndex& MATH_MultiLevelsToeplitzMatrix::getDimension ( ) const

inlineinherited

get the dimension of the matrix

Returns: the number of rows or columns of the matrix

References MATH_MultiLevelsToeplitzMatrix::mDimension.

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::buildColumnLeadingDimensions(), buildColumnLeadingDimensions(), MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::buildLeadingDimensions(), MATH_ElementaryMultiLevelsToeplitzMatrix::buildRowLeadingDimensions(), buildRowLeadingDimensions(), MATH_MultiLevelsToeplitzMatrix::copy(), MATH_ToeplitzTest::emicrom411ncTest(), MATH_ToeplitzTest::emicrom411Test(), MATH_ToeplitzTest::emicrom441Test(), MATH_ToeplitzTest::emicrom444Test(), MATH_ToeplitzTest::emicromTest(), MATH_ElementaryMultiLevelsToeplitzMatrix::getElementIndex(), and MATH_ToeplitzTest::toeplitzTest().

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◆ getDoubleEpsilon()

static tDouble CORE_Object::getDoubleEpsilon ( )

inlinestaticinherited

get the epsilon value for tDouble type

Returns: the epsilon value for tDouble type

Referenced by CORE_Test::testType().

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◆ getDoubleInfinity()

static tDouble CORE_Object::getDoubleInfinity ( )

inlinestaticinherited

get the infinity value for tFloat type

Returns: the intinity value for tFloat type

◆ getEpsilon()

template<class T >

static T CORE_Object::getEpsilon ( )

inlinestaticinherited

get the epsilon value for T type

Returns: the epsilon value for T type

◆ getFloatEpsilon()

static tFloat CORE_Object::getFloatEpsilon ( )

inlinestaticinherited

get the epsilon value for tFloat type

Returns: the epsilon value for tFloat type

Referenced by CORE_Test::testType().

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◆ getFloatInfinity()

static tFloat CORE_Object::getFloatInfinity ( )

inlinestaticinherited

get the infinity value for tFloat type

Returns: the intinity value for tFloat type

◆ getIdentityString()

tString CORE_Object::getIdentityString ( ) const

inlineinherited

return the identity string of the object of the form className_at_address

Returns: the identity string of the object

References CORE_Object::getClassName(), CORE_Object::pointer2String(), and tString.

Referenced by MATH_GaussLegendreIntegration::copy(), EMM_MultiScaleGrid::initialize(), CORE_Object::isInstanceOf(), CORE_Object::printObjectsInMemory(), MATH_Matrix::toString(), EMMG_SLPeriodicMultiScale::toString(), EMM_Stepper::toString(), EMM_AnisotropyDirectionsField::toString(), EMM_BlockMassMatrix::toString(), CORE_Object::toString(), EMM_Tensors::toString(), EMM_MultiScaleGrid::toString(), EMM_MatterField::toString(), EMM_Grid3D::toString(), and EMM_LandauLifschitzSystem::toString().

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◆ getIndex()

tUIndex MATH_MultiLevelsToeplitzMatrix::getIndex	(	const tUIndex &	i,
		const tUIndex &	j
	)		const

inlineinherited

return the index in values of the matrix value at row i and column j

Parameters

i	index of row in [0,getDimension()[
j	index of column in [0,getDimension(){

Returns: the index of the element in the values

References MATH_MultiLevelsToeplitzMatrix::getRowsNumber(), CORE_Array< T >::getSize(), MATH_MultiLevelsToeplitzMatrix::getToeplitzBlockIndex(), tIndex, tUIndex, and tUSInt.

Referenced by buildColumnLeadingDimensions(), buildRowLeadingDimensions(), MATH_MultiLevelsToeplitzMatrix::getIndex(), MATH_MultiLevelsToeplitzMatrix::getToeplitzBlockIndex(), and MATH_MultiLevelsToeplitzMatrix::operator()().

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◆ getInfinity()

template<class T >

static T CORE_Object::getInfinity ( )

inlinestaticinherited

get the infinity for T type

Returns: the infinity value for T type

◆ getLDoubleEpsilon()

static tLDouble CORE_Object::getLDoubleEpsilon ( )

inlinestaticinherited

get the epsilon value for tLDouble type

Returns: the epsilon value for tLDouble type

Referenced by CORE_Test::testType().

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◆ getLDoubleInfinity()

static tDouble CORE_Object::getLDoubleInfinity ( )

inlinestaticinherited

get the infinity value for tDouble type

Returns: the infinity value for tDouble type

◆ getLeafBlockDimension()

const tUIndex& MATH_MultiLevelsToeplitzMatrix::getLeafBlockDimension ( ) const

inlineinherited

return the dimension of the leaf block matrix

Returns: the number of rows or columns of the leaf block matrix

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::buildColumnLeadingDimensions(), MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::buildLeadingDimensions(), MATH_ElementaryMultiLevelsToeplitzMatrix::buildRowLeadingDimensions(), MATH_ElementaryMultiLevelsToeplitzMatrix::buildSpectralVectorProjector(), MATH_ElementaryMultiLevelsToeplitzMatrix::getElementIndex(), and MATH_MultiLevelsToeplitzMatrix::setLevels().

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◆ getLeafBlockSize()

tUIndex MATH_MultiLevelsToeplitzMatrix::getLeafBlockSize ( ) const

inlineinherited

return the size of the leaf block matrix

Returns: the memory size of the leaf block matrix

Referenced by MATH_MultiLevelsToeplitzMatrix::getBlocksNumber(), and MATH_MultiLevelsToeplitzMatrix::setLevels().

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◆ getLeafBlockValues() [1/2]

const tFFTWComplex* MATH_MultiLevelsToeplitzMatrix::getLeafBlockValues ( const tIndex indices[] ) const

inlineinherited

get the values of the leaf block

Parameters

indices indices of the block

Returns: a pointer to the values of size getLeafBlockSize()

References CORE_Array< T >::getSize(), MATH_MultiLevelsToeplitzMatrix::getToeplitzBlockIndex(), and MATH_MultiLevelsToeplitzMatrix::getValues().

Referenced by MATH_ToeplitzTest::toeplitzTest().

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◆ getLeafBlockValues() [2/2]

tFFTWComplex* MATH_MultiLevelsToeplitzMatrix::getLeafBlockValues ( const tIndex indices[] )

inlineinherited

get the values of the leaf block

Parameters

indices indices of the block

Returns: a pointer to the values of size getLeafBlockSize()

References CORE_Array< T >::getSize(), MATH_MultiLevelsToeplitzMatrix::getToeplitzBlockIndex(), and MATH_MultiLevelsToeplitzMatrix::getValues().

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◆ getLevels()

const CORE_UIndexArray& MATH_MultiLevelsToeplitzMatrix::getLevels ( ) const

inlineinherited

get the level of the matrix

Returns: the levels array

References MATH_MultiLevelsToeplitzMatrix::mLevels.

Referenced by MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::buildLeadingDimensions(), MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::buildSpectralSpace(), MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::computeSpectralSpaceSizePerDimension(), MATH_MultiLevelsToeplitzMatrix::copy(), and MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::recoverCanonicalSpace().

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◆ getLevelsNumber()

tUSInt MATH_MultiLevelsToeplitzMatrix::getLevelsNumber ( ) const

inlineinherited

get the number of levels of the matrix

References CORE_Array< T >::getSize().

Referenced by MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::buildSpectralSpace(), MATH_ElementaryMultiLevelsToeplitzMatrix::getElementIndex(), and MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::recoverCanonicalSpace().

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◆ getMaxChar()

static tChar CORE_Object::getMaxChar ( )

inlinestaticinherited

get the max value for tChar type

Returns: the max value for tChar type

Referenced by CORE_Test::testType().

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◆ getMaxDouble()

static tDouble CORE_Object::getMaxDouble ( )

inlinestaticinherited

get the max value for tDouble type

Returns: the max value for tDouble type

Referenced by CORE_Test::testType().

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◆ getMaxFlag()

static tFlag CORE_Object::getMaxFlag ( )

inlinestaticinherited

get the max value for the tFlag type

Returns: the max value for the tFlag type

Referenced by CORE_Test::testType().

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◆ getMaxFloat()

static tFloat CORE_Object::getMaxFloat ( )

inlinestaticinherited

get the max value for tFloat type

Returns: the max value for tFloat type

Referenced by CORE_Test::testType().

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◆ getMaxIndex()

static tIndex CORE_Object::getMaxIndex ( )

inlinestaticinherited

get the max value for the array/vector indexing type

Returns: the max value for the array/vector indexing type

Referenced by CORE_Test::testType().

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◆ getMaxInt()

static tInt CORE_Object::getMaxInt ( )

inlinestaticinherited

get the max value for tInt type

Returns: the max value for tInt type

Referenced by MATSGN_FFT::fastFourierTransform3D_FFTW(), and CORE_Test::testType().

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◆ getMaxInteger()

static tInteger CORE_Object::getMaxInteger ( )

inlinestaticinherited

get the max value for the integer type

Returns: the max value for the integer type

Referenced by CORE_Test::testType().

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◆ getMaxLDouble()

static tLDouble CORE_Object::getMaxLDouble ( )

inlinestaticinherited

get the max value for tLDouble type

Returns: the max value for tLDouble type

Referenced by CORE_Test::testType().

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◆ getMaxLInt()

static tLInt CORE_Object::getMaxLInt ( )

inlinestaticinherited

get the max value for tLInt type

Returns: the max value for tLInt type

Referenced by CORE_Test::testType().

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◆ getMaxLLInt()

static tLLInt CORE_Object::getMaxLLInt ( )

inlinestaticinherited

get the max value for tULInt type

Returns: the max value for tULInt type

Referenced by CORE_Test::testType().

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◆ getMaxReal()

static tReal CORE_Object::getMaxReal ( )

inlinestaticinherited

get the max value for the real type

Returns: he max value for the real type

Referenced by EMM_MatterField::adimensionize(), and CORE_Test::testType().

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◆ getMaxSInt()

static tSInt CORE_Object::getMaxSInt ( )

inlinestaticinherited

get the max value for tSInt type

Returns: the max value for tSInt type

Referenced by CORE_Test::testType().

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◆ getMaxUChar()

static tUChar CORE_Object::getMaxUChar ( )

inlinestaticinherited

get the max value for tUChar type

Returns: the max value for tUChar type

Referenced by CORE_Test::testType().

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◆ getMaxUIndex()

static tUIndex CORE_Object::getMaxUIndex ( )

inlinestaticinherited

get the max value for difference the array/vector indexing type

Returns: the max value for difference the array/vector indexing type

Referenced by CORE_Vector< T >::addAfterIndices(), CORE_Vector< T >::search(), CORE_Test::testType(), CORE_Integer::toHexString(), and CORE_Integer::toString().

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◆ getMaxUInt()

static tUInt CORE_Object::getMaxUInt ( )

inlinestaticinherited

get the max value for tUInt type

Returns: the max value for tUInt type

Referenced by EMM_Array< tCellFlag >::loadFromFile(), EMM_RealField::loadFromFile(), and CORE_Test::testType().

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◆ getMaxUInteger()

static tUInteger CORE_Object::getMaxUInteger ( )

inlinestaticinherited

get the max value for the unsigned integer type

Returns: the max value for the unsigned integer type

Referenced by MATH_Pn::computeExtrenums(), EMM_MultiScaleGrid::computeLevelsNumber(), EMM_Input::restoreBackup(), MATH_P0::solve(), and CORE_Test::testType().

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◆ getMaxULInt()

static tULInt CORE_Object::getMaxULInt ( )

inlinestaticinherited

get the max value for tULInt type

Returns: the max value for tULInt type

Referenced by CORE_Test::testType().

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◆ getMaxULLInt()

static tULLInt CORE_Object::getMaxULLInt ( )

inlinestaticinherited

get the max value for tULLInt type

Returns: the max value for tULLInt type

Referenced by CORE_Test::testType().

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◆ getMaxUSInt()

static tUSInt CORE_Object::getMaxUSInt ( )

inlinestaticinherited

get the max value for tUSInt type

Returns: the max value for tUSInt type

Referenced by CORE_Test::testType().

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◆ getMemorySize()

virtual tULLInt MATH_MultiLevelsFFTToeplitzMatrix::getMemorySize ( ) const

inlinevirtualinherited

return the memory size in byte

Returns: the memory size of the storage in bytes 1 Kb = 1024 bytes 1 Mb = 1024 Kb 1 Gb = 1024 Mb 1 Tb = 1024 Gb 1 Hb = 1024 Tb

Reimplemented from MATH_MultiLevelsToeplitzMatrix.

Reimplemented in MATH_ElementaryMultiLevelsToeplitzMatrix.

References MATH_MultiLevelsToeplitzMatrix::getMemorySize(), CORE_Array< T >::getMemorySize(), and null.

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::getMemorySize().

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◆ getMinChar()

static tChar CORE_Object::getMinChar ( )

inlinestaticinherited

get the min value for tChar type

Returns: the min value for tChar type

Referenced by CORE_Test::testType().

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◆ getMinDouble()

static tDouble CORE_Object::getMinDouble ( )

inlinestaticinherited

get the min value for tDouble type

Returns: the min value for tDouble type

Referenced by CORE_Test::testType().

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◆ getMinFlag()

static tFlag CORE_Object::getMinFlag ( )

inlinestaticinherited

get the min value for the tFlag type

Returns: the min value for the tFlag type

Referenced by CORE_Test::testType().

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◆ getMinFloat()

static tFloat CORE_Object::getMinFloat ( )

inlinestaticinherited

get the min value for tFloat type

Returns: the min value for tFloat type

Referenced by CORE_Test::testType().

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◆ getMinIndex()

static tIndex CORE_Object::getMinIndex ( )

inlinestaticinherited

get the min value for the array/vector indexing type

Returns: the min value for the array/vector indexing type

Referenced by CORE_Test::testType().

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◆ getMinInt()

static tInt CORE_Object::getMinInt ( )

inlinestaticinherited

get the min value for tInt type

Returns: the min value for tInt type

Referenced by CORE_Test::testType().

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◆ getMinInteger()

static tInteger CORE_Object::getMinInteger ( )

inlinestaticinherited

get the min value for the integer type

Returns: the minin value for the integer type

Referenced by CORE_Test::testType().

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◆ getMinLDouble()

static tLDouble CORE_Object::getMinLDouble ( )

inlinestaticinherited

get the min value for tLDouble type

Returns: the min value for tLDouble type

Referenced by CORE_Test::testType().

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◆ getMinLInt()

static tLInt CORE_Object::getMinLInt ( )

inlinestaticinherited

get the min value for tLInt type

Returns: the min value for tLInt type

Referenced by CORE_Test::testType().

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◆ getMinLLInt()

static tLLInt CORE_Object::getMinLLInt ( )

inlinestaticinherited

get the min value for tLLInt type

Returns: the min value for tLLInt type

Referenced by CORE_Test::testType().

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◆ getMinReal()

static tReal CORE_Object::getMinReal ( )

inlinestaticinherited

get the min value for the real type

Returns: the min value for the real type

Referenced by CORE_Test::testType().

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◆ getMinSInt()

static tSInt CORE_Object::getMinSInt ( )

inlinestaticinherited

get the min value for tSInt type

Returns: the min value for tSInt type

Referenced by CORE_Test::testType().

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◆ getMinUChar()

static tUChar CORE_Object::getMinUChar ( )

inlinestaticinherited

get the min value for tUChar type

Returns: the min value for tUChar type

Referenced by CORE_Test::testType().

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◆ getMinUIndex()

static tUIndex CORE_Object::getMinUIndex ( )

inlinestaticinherited

get the min value for difference the array/vector indexing type

Returns: the min value for difference the array/vector indexing type

Referenced by CORE_Test::testType().

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◆ getMinUInt()

static tUInt CORE_Object::getMinUInt ( )

inlinestaticinherited

get the min value for tUInt type

Returns: the min value for tUInt type

Referenced by CORE_Test::testType().

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◆ getMinUInteger()

static tUInteger CORE_Object::getMinUInteger ( )

inlinestaticinherited

get the min value for the unsigned integer type

Returns: the min value for the unsigned integer type

Referenced by CORE_Test::testType().

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◆ getMinULInt()

static tULInt CORE_Object::getMinULInt ( )

inlinestaticinherited

get the min value for tULInt type

Returns: the min value for tULInt type

Referenced by CORE_Test::testType().

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◆ getMinULLInt()

static tULLInt CORE_Object::getMinULLInt ( )

inlinestaticinherited

get the min value for tULLInt type

Returns: the min value for tULLInt type

Referenced by CORE_Test::testType().

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◆ getMinUSInt()

static tUSInt CORE_Object::getMinUSInt ( )

inlinestaticinherited

get the min value for tUSInt type

Returns: the min value for tUSInt type

Referenced by CORE_Test::testType().

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◆ getOut()

static SP::CORE_Out CORE_Object::getOut ( )

inlinestaticinherited

get the output

Returns: the shared pointer to the output stream

References CORE_Object::OUT.

◆ getPointerAddress()

tString CORE_Object::getPointerAddress ( ) const

inlineinherited

return the identity string of the object

Returns: the identity string of the object

References CORE_Object::pointer2String().

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◆ getRealEpsilon()

static tReal CORE_Object::getRealEpsilon ( )

inlinestaticinherited

get the eps which is the difference between 1 and the least value greater than 1 that is representable.

Returns: the eps which is the difference between 1 and the least value greater than 1 that is representable.

Referenced by MATH_P4::solveP4De(), and CORE_Test::testType().

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◆ getRealInfinity()

static tReal CORE_Object::getRealInfinity ( )

inlinestaticinherited

get the infinity value

Returns: the inifinity value for the real type

Referenced by BrentFunction::BrentFunction(), EMM_OperatorsTest::compareDiscretizedData(), EMM_IterativeTimeStep::EMM_IterativeTimeStep(), EMM_SLElementaryDemagnetizedMatrix::Kxy(), NRFunction::NRFunction(), EMM_PolynomialInterpolationTimeStep::optimizeTimeFunction(), and CORE_Test::testType().

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◆ getRealValue()

tReal MATH_MultiLevelsToeplitzMatrix::getRealValue	(	const tUIndex &	i,
		const tUIndex &	j
	)		const

inlineinherited

get the real value at row i and column j

Returns: the real part of the complex at row i and rows j

Referenced by MATH_MultiLevelsToeplitzMatrix::toString().

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◆ getRowLeadingDimensions() [1/2]

const CORE_UIndexArray& MATH_MultiLevelsFFTToeplitzMatrix::getRowLeadingDimensions ( ) const

inlineprotectedinherited

get the index of the row i and column 0 from the spectral space

Returns

the indices of rows of the first column in the spectral space

index 0: the index corresponding to the first row in the spectral space
index i where i>0 : the leading dimension betwen row i and row i-1

References MATH_MultiLevelsFFTToeplitzMatrix::mRowLeadingDimensions.

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::buildRowLeadingDimensions(), MATH_ElementaryMultiLevelsCircularToeplitzMatrix::buildRowLeadingDimensions(), buildRowLeadingDimensions(), MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::buildRowLeadingDimensions(), MATH_MultiLevelsFFTToeplitzMatrix::copy(), MATH_ElementaryMultiLevelsToeplitzMatrix::recoverFromSpectralSpace(), and recoverFromSpectralSpace().

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◆ getRowLeadingDimensions() [2/2]

CORE_UIndexArray& MATH_MultiLevelsFFTToeplitzMatrix::getRowLeadingDimensions ( )

inlineprotectedinherited

get the index of the row i and column 0 from the spectral space

Returns

the indices of rows of the first column in the spectral space

index 0: the index corresponding to the first row in the spectral space
index i where i>0 : the leading dimension betwen row i and row i-1

References MATH_MultiLevelsFFTToeplitzMatrix::mRowLeadingDimensions.

◆ getRowsNumber()

const tUIndex& MATH_MultiLevelsToeplitzMatrix::getRowsNumber ( ) const

inlineinherited

get the dimension of the matrix

Returns: the number of rows or columns of the matrix

References MATH_MultiLevelsToeplitzMatrix::mDimension.

Referenced by MATH_MultiLevelsToeplitzMatrix::getIndex(), MATH_ToeplitzTest::toeplitzTest(), and MATH_MultiLevelsToeplitzMatrix::toString().

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◆ getSharedPointer() [1/2]

void CORE_Object::getSharedPointer ( SP::CORE_Object & p )

inlineinherited

get the shared pointer of this class into p

Parameters

p	: shared pointer of the class This

Referenced by CORE_Map< Key, Value >::getSharedPointer(), CORE_ArrayList< tString >::getSharedPointer(), EMM_Array< tCellFlag >::getSharedPointer(), CORE_Array< tCellFlag >::getSharedPointer(), CORE_MorseArray< tUChar >::getSharedPointer(), CORE_Vector< T >::getSharedPointer(), and CORE_Object::printObjectsInMemory().

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◆ getSharedPointer() [2/2]

void CORE_Object::getSharedPointer ( SPC::CORE_Object & p ) const

inlineinherited

get the shared pointer of this class into p

Parameters

p	: shared pointer of the class This

◆ getSpace()

const tFlag& MATH_MultiLevelsToeplitzMatrix::getSpace ( ) const

inlineinherited

get the space of the matrix

Returns

the space of the matrix in :

CANONICAL_SPACE
SPECTRAL_SPACE

References MATH_MultiLevelsToeplitzMatrix::mSpace.

Referenced by MATH_MultiLevelsToeplitzMatrix::copy(), MATH_MultiLevelsToeplitzMatrix::projection(), and MATH_MultiLevelsFFTToeplitzMatrix::vectorProduct().

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◆ getSpectralSpaceSize()

const tUIndex& MATH_MultiLevelsFFTToeplitzMatrix::getSpectralSpaceSize ( ) const

inlineprotectedinherited

get the spectral space size

Returns: the memory size of the spectral space

References MATH_MultiLevelsFFTToeplitzMatrix::mSpectralSpaceSize.

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◆ getStorage() [1/2]

const MATH_LeafBlockMatrixStorage& MATH_MultiLevelsToeplitzMatrix::getStorage ( ) const

inlineinherited

get the storage of the leaf matrices

Returns: the storage of the leaf block matrix

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◆ getStorage() [2/2]

MATH_LeafBlockMatrixStorage& MATH_MultiLevelsToeplitzMatrix::getStorage ( )

inlineinherited

get the storage of the leaf matrices

Returns: the storage of the leaf block matrix

◆ getThread()

static CORE_Thread& CORE_Object::getThread ( )

inlinestaticinherited

get the profilier

Returns: the profiler

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◆ getToeplitzBlockIndex() [1/2]

tUIndex MATH_MultiLevelsToeplitzMatrix::getToeplitzBlockIndex	(	const tUSInt &	nLevels,
		const tUIndex	N[],
		const tIndex	I[]
	)		const

inherited

get the block index corresponding to indices

Parameters

nLevels	number of levels
N	: number of element by level of size nLevels
I	index of element at each level i[l] in ]-N[l],N[l][

Returns: the index of element as follow: index = (i_0+N_0-1+(2*N_0-1)*(i_1+N_1-1+(2*N_1-1)*(i_2+N_2-1+...)))

References tIndex, tUIndex, and tUSInt.

Referenced by MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::buildSpectralSpace(), MATH_MultiLevelsToeplitzMatrix::getIndex(), MATH_MultiLevelsToeplitzMatrix::getLeafBlockValues(), MATH_MultiLevelsToeplitzMatrix::getToeplitzBlockIndex(), and MATH_ToeplitzTest::toeplitzTest().

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◆ getToeplitzBlockIndex() [2/2]

tUIndex MATH_MultiLevelsToeplitzMatrix::getToeplitzBlockIndex ( const tIndex I[] ) const

inlineinherited

get the block index corresponding to indices

Parameters

I	index of element at each level i[l] in ]-N[l],N[l][

Returns: the index of element as follow: index = (i_0+N_0-1+(2*N_0-1)*(i_1+N_1-1+(2*N_1-1)*(i_2+N_2-1+...)))

References MATH_MultiLevelsToeplitzMatrix::getIndex(), CORE_Array< T >::getSize(), MATH_MultiLevelsToeplitzMatrix::getToeplitzBlockIndex(), tUIndex, and tUSInt.

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◆ getTypeName()

template<class T >

static tString CORE_Object::getTypeName ( )

inlinestaticinherited

get type name

Returns: the type name of the class

References tString.

◆ getValues() [1/2]

FFTW_ComplexArray& MATH_MultiLevelsToeplitzMatrix::getValues ( )

inlineinherited

get the values of the matrix

Returns: the values array

Referenced by MATH_ToeplitzTest::emicromTest(), MATH_MultiLevelsToeplitzMatrix::getLeafBlockValues(), and MATH_ToeplitzTest::toeplitzTest().

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◆ getValues() [2/2]

const FFTW_ComplexArray& MATH_MultiLevelsToeplitzMatrix::getValues ( ) const

inlineinherited

get the values of the matrix

Returns: the values array

◆ is32Architecture()

static tBoolean CORE_Object::is32Architecture ( )

inlinestaticinherited

return true if the machine is a 32 bits machine

Returns: true is the computing is done in a 32 bits machine

References CORE_Object::pointer2String(), CORE_Object::printObjectsInMemory(), and tString.

Referenced by CORE_Test::testType().

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◆ is64Architecture()

static tBoolean CORE_Object::is64Architecture ( )

inlinestaticinherited

return true if the machine is a 64 bits machine

Returns: true is the computing is done in a 64 bits machine

Referenced by EMM_VTK::getVTKType(), and CORE_Test::testType().

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◆ isInstanceOf() [1/2]

template<class T >

tBoolean CORE_Object::isInstanceOf ( ) const

inlineinherited

test if the clas T is an instance of this class

Returns: true if the object is an instance of T

References null.

Referenced by MATH_ToeplitzTest::toeplitzTest().

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◆ isInstanceOf() [2/2]

tBoolean CORE_Object::isInstanceOf ( const tString & name ) const

inlineinherited

test if the object is an instance of className

Parameters

name	name of the class

Returns: true if the object is an instance of class Name

References CORE_Object::getIdentityString().

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◆ isMemoryChecked()

static const tBoolean& CORE_Object::isMemoryChecked ( )

inlinestaticinherited

get if the memory checking is used

Returns: true: if the memory checking is used.

References CORE_Object::getClassName(), CORE_Object::mIsMemoryTesting, and tString.

Referenced by main().

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◆ New()

static SP::MATH_GlobalMultiLevelsPolynomialToeplitzMatrix MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::New ( )

inlinestatic

build a new instance of class

Returns: the shared pointer to the matrix

References MATH_GlobalMultiLevelsPolynomialToeplitzMatrix().

Referenced by MATH_ToeplitzTest::globalPolynomialToeplitzTests(), MATH_ToeplitzClassFactory::NewInstance(), NewInstance(), and EMM_DemagnetizedOperator::setStorage().

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◆ NewInstance()

virtual SP::MATH_MultiLevelsToeplitzMatrix MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::NewInstance ( ) const

inlinevirtual

new instance

Returns: a New instance of this

Implements MATH_MultiLevelsToeplitzMatrix.

References New().

Referenced by MATH_GlobalMultiLevelsPolynomialToeplitzMatrix().

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◆ operator()() [1/2]

const tFFTWComplex& MATH_MultiLevelsToeplitzMatrix::operator()	(	const tUIndex &	i,
		const tUIndex &	j
	)		const

inlineinherited

get the value of the matrix at row i and column j

Parameters

i	the index of the row [0,getDimension()[
j	the index of the column in [0,getDimension()[ return the value at element (i,j)

References MATH_MultiLevelsToeplitzMatrix::getIndex().

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◆ operator()() [2/2]

tFFTWComplex& MATH_MultiLevelsToeplitzMatrix::operator()	(	const tUIndex &	i,
		const tUIndex &	j
	)

inlineinherited

get the value of the matrix at row i and column j

Parameters

i	the index of the row [0,getDimension()[
j	the index of the column in [0,getDimension()[ return the value at element (i,j)

References MATH_MultiLevelsToeplitzMatrix::clear(), MATH_MultiLevelsToeplitzMatrix::copy(), and MATH_MultiLevelsToeplitzMatrix::getIndex().

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◆ operator[]() [1/2]

tFFTWComplex& MATH_MultiLevelsToeplitzMatrix::operator[] ( const tUIndex & k )

inlineprotectedinherited

get the value at index k

Parameters

k	index of the value in [0,getSpectralSpaceDimension()[ return the value at index k

◆ operator[]() [2/2]

const tFFTWComplex& MATH_MultiLevelsToeplitzMatrix::operator[] ( const tUIndex & k ) const

inlineprotectedinherited

get the value at index k

Parameters

k	index of the value in [0,etSpectralSpaceDimension()()[ return the value at index k

◆ out()

static CORE_Out& CORE_Object::out ( )

inlinestaticinherited

get the output

Returns: the output stream

Referenced by EMM_Matter::adimensionize(), EMM_DisplacementFVMOperator::backup(), EMM_DisplacementOperator::backup(), MATH_ElementaryMultiLevelsToeplitzMatrix::buildSpectralVectorProjector(), EMM_Test::caseTest(), EMM_Test::caseTests(), EMM_MatterField::computeAnisotropyDirectionsField(), EMM_OptimalTimeStep::computeOptimalTimeStep(), MATH_MultiLevelsToeplitzMatrix::copy(), CORE_Exception::CORE_Exception(), EMM_MatterField::createAnisotropyOperator(), CORE_Run::createIO(), EMM_ElementaryTest::defaultBackupTest(), EMM_ElementaryTest::defaultTest(), MATH_MultiLevelsFFTToeplitzMatrix::diagonalize(), EMM_DisplacementFVMOperator::discretize(), EMM_MagnetostrictionOperator::discretize(), EMM_DisplacementFEMOperator::discretize(), EMM_4SymmetricTensors::doubleDot(), EMM_4Tensors::doubleDotCrossDoubleDotScalar(), EMM_TensorsTest::doubleDotCrossDoubleDotScalarTests(), EMM_4Tensors::doubleDotCrossProduct(), EMM_TensorsTest::doubleDotCrossProductTests(), EMM_4Tensors::doubleDotCrossSquaredScalar(), EMM_TensorsTest::doubleDotCrossSquaredScalarTests(), EMM_4Tensors::doubleDotProduct(), EMM_TensorsTest::doubleDotProductTests(), EMM_DisplacementWaveTest::elasticWaveTest(), EMM_Test::elementaryTests(), FFTW_Test::fftwTutorial(), MATH_IntegrationTest::gaussLegendreTest(), EMM_MagnetostrictionTest::HComputingTest(), EMM_DemagnetizedPeriodicalTest::HTest(), EMMH_HysteresisTest::hysteresisDefaultCycleTest(), EMM_TensorsTest::initializationTests(), EMM_MultiScaleGrid::initialize(), EMM_MultiScaleSDGrid::initialize(), EMM_MatterField::loadFromANIFile(), EMM_AnisotropyDirectionsField::loadFromFile(), EMM_Matter::loadFromFile(), EMM_Grid3D::loadFromGEOFile(), EMM_MatterField::loadFromLOCFile(), EMM_Array< tCellFlag >::loadFromStream(), EMM_Matter::loadFromStream(), EMM_Matter::loadMattersFromFile(), EMM_Run::loadSystemFromOptions(), EMM_ElementaryTest::magnetostrictionBackupTest(), CORE_Run::make(), EMMH_Run::makeHysteresis(), EMM_Run::makeRun(), CORE_Run::makeType(), EMM_ElementaryTest::optionsTest(), MATH_PolynomialTest::P4Tests(), EMM_Test::primaryTests(), EMM_LandauLifschitzSystem::printLog(), CORE_Run::printOptions(), EMM_2PackedSymmetricTensors::product(), EMMG_SLDemagnetizedOperator::projectionOnSpectralSpace(), CORE_Run::readOptionsFromCommandLine(), CORE_Test::readVectorTest(), EMM_DemagnetizedPeriodicalTest::relaxationTest(), EMM_DisplacementFVMOperator::restore(), EMM_DisplacementOperator::restore(), EMM_Input::restoreBackup(), EMMH_Hysteresis::run(), EMM_Output::save(), EMM_AnisotropyDirectionsField::saveToFile(), EMM_MatterField::saveToFile(), EMM_Grid3D::saveToGEOFile(), CORE_IOTest::searchTest(), EMMH_Hysteresis::setInitialMagnetizationField(), MATH_MultiLevelsToeplitzMatrix::setLevels(), EMM_4SymmetricTensors::squaredDoubleDot(), EMM_4Tensors::squaredDoubleDotCrossScalar(), EMM_TensorsTest::squaredDoubleDotCrossScalarTests(), EMM_4Tensors::squaredDoubleDotScalar(), EMM_TensorsTest::squaredDoubleDotScalarTests(), EMM_TensorsTest::squaredDoubleDotTests(), EMM_MatterTest::testAdimensionize(), EMM_MatterTest::testANIFile(), CORE_Test::testComplex(), CORE_Test::testDateWeek(), FFTW_Test::testDFT(), EMM_MatterTest::testIO(), EMM_ODETest::testODE(), CORE_Test::testOut(), CORE_Test::testReal(), EMM_FieldTest::testRealArray(), EMM_Grid3DTest::testSegment(), EMM_Grid3DTest::testThinSheet(), CORE_Test::testTime(), CORE_Test::testType(), MATH_FullMatrix::toString(), EMM_DemagnetizedPeriodicalTest::xyPeriodicalCubeSDGTest(), and EMM_DemagnetizedPeriodicalTest::xyPeriodicalSheetSDGTest().

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◆ pointer2String()

tString CORE_Object::pointer2String ( const void * obj )

staticinherited

return the string representation of a pointer

Parameters

obj	: oject to get the string pointer

Returns: the string pointer of the object

References tString.

Referenced by CORE_Object::CORE_Object(), CORE_Object::getIdentityString(), CORE_Object::getPointerAddress(), CORE_Object::is32Architecture(), and CORE_Object::~CORE_Object().

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◆ printObjectsInMemory() [1/2]

void CORE_Object::printObjectsInMemory ( ostream & f )

staticinherited

print object in memory

Parameters

f	: output to print the objects in memory

References CORE_Object::getIdentityString(), CORE_Object::getSharedPointer(), CORE_Object::mIsMemoryTesting, CORE_Object::mObjects, and tInteger.

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◆ printObjectsInMemory() [2/2]

static void CORE_Object::printObjectsInMemory ( )

inlinestaticinherited

print object in memory in the standart output

Referenced by CORE_Object::is32Architecture(), and main().

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◆ projectIntoSpectralSpace()

void MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::projectIntoSpectralSpace	(	const tUIndex &	N,
		const tReal *	X
	)		const

protectedvirtual

project the vector X from initial space to multi levels space

Parameters

N	size of X
X	the input vector in initial dimension

Implements MATH_MultiLevelsFFTToeplitzMatrix.

References FFTW_FFT::getArray(), MATH_MultiLevelsFFTToeplitzMatrix::getColumnLeadingDimensions(), MATH_MultiLevelsFFTToeplitzMatrix::getDFTProjector(), FFTW_FFT::runFFT(), tFFTWComplex, tReal, and tUIndex.

Referenced by vectorProductInSpectralSpace().

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◆ projection()

void MATH_MultiLevelsToeplitzMatrix::projection ( const tFlag & space )

inlineinherited

make the projection in the space

Parameters

space

space of projection

SPECTRAL_SPACE: for diagonalization of the matrix
CANONICAL_SPACE: for the canonical space

References MATH_MultiLevelsToeplitzMatrix::CANONICAL_SPACE, MATH_MultiLevelsToeplitzMatrix::diagonalize(), MATH_MultiLevelsToeplitzMatrix::getSpace(), MATH_MultiLevelsToeplitzMatrix::recover(), MATH_MultiLevelsToeplitzMatrix::setSpace(), and MATH_MultiLevelsToeplitzMatrix::SPECTRAL_SPACE.

Referenced by MATH_ToeplitzTest::emicrom411ncTest(), MATH_ToeplitzTest::emicrom411Test(), MATH_ToeplitzTest::emicrom441Test(), MATH_ToeplitzTest::emicrom444Test(), MATH_ToeplitzTest::emicromTest(), and MATH_ToeplitzTest::toeplitzTest().

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◆ recover()

void MATH_MultiLevelsFFTToeplitzMatrix::recover ( )

protectedvirtualinherited

projection of the matrix in the CANONICAL SPACE

transforms the values of the diagonal toeplitz values into its initial state by running an inverse Discrete FastFourier.
recover the canonical space which is the reverse procedure of building spectral space : calls recoverCanonicalSpace()

Implements MATH_MultiLevelsToeplitzMatrix.

References MATH_MultiLevelsToeplitzMatrix::getDFT(), MATH_MultiLevelsFFTToeplitzMatrix::recoverCanonicalSpace(), and FFTW_FFT::runFFT().

Referenced by MATH_MultiLevelsFFTToeplitzMatrix::buildSpectralVectorProjector().

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◆ recoverCanonicalSpace()

void MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::recoverCanonicalSpace ( )

protectedvirtual

recover the canonical space from the spectral space

Implements MATH_MultiLevelsFFTToeplitzMatrix.

References FFTW_FFT::getArray(), MATH_MultiLevelsToeplitzMatrix::getCanonicalSpaceSize(), MATH_MultiLevelsToeplitzMatrix::getDFT(), FFTW_ComplexArray::getSize(), tFFTWComplex, and tUIndex.

Referenced by buildSpectralVectorProjector().

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◆ recoverFromSpectralSpace()

void MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::recoverFromSpectralSpace	(	const tUIndex &	N,
		tReal *	X
	)		const

protectedvirtual

recover from multi levels space to the initial space

Parameters

N	size of X
X	the output vector in the inial space

Implements MATH_MultiLevelsFFTToeplitzMatrix.

References FFTW_FFT::getArray(), MATH_MultiLevelsFFTToeplitzMatrix::getDFTProjector(), MATH_MultiLevelsFFTToeplitzMatrix::getRowLeadingDimensions(), FFTW_FFT::runFFT(), tFFTWComplex, tReal, and tUIndex.

Referenced by vectorProductInSpectralSpace().

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◆ resetOut()

static void CORE_Object::resetOut ( )

inlinestaticinherited

reset the output stream

Referenced by run().

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◆ resetThread()

static void CORE_Object::resetThread ( )

inlinestaticinherited

reset the output stream

Referenced by run().

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◆ setDFT()

void MATH_MultiLevelsToeplitzMatrix::setDFT ( SP::FFTW_FFT dft )

inlineprotectedinherited

set the DFT class

Parameters

dft	Discrete Fourier Transform class to set

References null.

Referenced by MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix::MATH_ElementaryMultiLevelsCircularTensorToeplitzMatrix(), MATH_ElementaryMultiLevelsToeplitzMatrix::MATH_ElementaryMultiLevelsToeplitzMatrix(), and MATH_GlobalMultiLevelsPolynomialToeplitzMatrix().

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◆ setIsMemoryChecked()

static void CORE_Object::setIsMemoryChecked ( const tBoolean & v )

inlinestaticinherited

set if the memory checking is used

Parameters

v	: true to check memory

Referenced by main().

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◆ setLeafBlockDimension()

virtual void MATH_MultiLevelsToeplitzMatrix::setLeafBlockDimension ( const tUIndex & n )

inlinevirtualinherited

set the dimension of leaf block

Parameters

n	number of rows or columns of the leaf square matrix

Referenced by MATH_MultiLevelsToeplitzMatrix::setLevels().

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◆ setLevels() [1/2]

virtual void MATH_MultiLevelsToeplitzMatrix::setLevels	(	const tUSInt &	levelsNumber,
		const tUIndex	levels[],
		const tUIndex &	nD
	)

inlinevirtualinherited

set the levels of the matrix

Parameters

levelsNumber	the number of levels
levels	levels[k] is the number of Toeplitz matrices at each row which composed the level k in [0,levelsNumber[
nD	dimension of the block matrix (1D,2D,3D,..nD)

The level 0 contains the leaf matrices

The level levelsNumber contains the last level.

References MATH_MultiLevelsToeplitzMatrix::setLeafBlockDimension(), tUIndex, and tUSInt.

Referenced by MATH_ToeplitzTest::emicrom411ncTest(), MATH_ToeplitzTest::emicrom411Test(), MATH_ToeplitzTest::emicrom441Test(), MATH_ToeplitzTest::emicrom444Test(), MATH_ToeplitzTest::emicromTest(), and MATH_ToeplitzTest::toeplitzTest().

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◆ setLevels() [2/2]

void MATH_MultiLevelsToeplitzMatrix::setLevels	(	const tUSInt &	levelsNumber,
		const tUIndex	levels[]
	)

inherited

set the levels of the matrix

Parameters

levelsNumber	the number of levels
levels	levels[k] is the number of Toeplitz matrices at each row which composed the level k in [0,levelsNumber[

The Level 0 contains the leaf matrices

The level levelsNumber contains the last level.

Builds the structure of the matrix

the number of toeplitz matrices at each level
the canonical space size
the dimension of the matrix (number of columns or rows)
initialize the space to CANONICAL_SPACE

References CORE_Out::ERROR_MSG, MATH_MultiLevelsToeplitzMatrix::getLeafBlockDimension(), MATH_MultiLevelsToeplitzMatrix::getLeafBlockSize(), CORE_Exception::getMessage(), MATH_MultiLevelsToeplitzMatrix::mCanonicalSpaceSize, MATH_MultiLevelsToeplitzMatrix::mDimension, MATH_MultiLevelsToeplitzMatrix::mFFT, MATH_MultiLevelsToeplitzMatrix::mLevels, CORE_Object::out(), CORE_Out::println(), CORE_Array< T >::setSize(), tUIndex, and tUSInt.

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◆ setOut()

static void CORE_Object::setOut ( SP::CORE_Out out )

inlinestaticinherited

set the output stream

Parameters

out	: the shared pointer to the new output stream

References null.

◆ setSpace()

void MATH_MultiLevelsToeplitzMatrix::setSpace ( const tFlag & space )

inlineprotectedinherited

set the space of the multi level block matrix

Parameters

space

the space of the matrix:

CANONICAL_SPACE: the space of rows and column
SPECTRAL_SPACE: the spectral space i which the matrix is diagonalized

Referenced by MATH_MultiLevelsToeplitzMatrix::projection().

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◆ setSpectralSpaceSize()

void MATH_MultiLevelsFFTToeplitzMatrix::setSpectralSpaceSize ( const tUIndex & n )

inlineprotectedinherited

set the spectral space size

Parameters

n	: the spectral space size

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::buildSpectralSpace(), and buildSpectralSpace().

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◆ setStorage()

void MATH_MultiLevelsToeplitzMatrix::setStorage ( SP::MATH_LeafBlockMatrixStorage storage )

inlineprotectedinherited

set the storage of the matrix

Referenced by MATH_ElementaryMultiLevelsToeplitzMatrix::setStorage().

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◆ setThis()

void CORE_Object::setThis ( SP::CORE_Object p )

inlineprotectedinherited

set this weak shared pointer called toDoAfterThis setting method

Parameters

p	: shared pointer of the class This

References CORE_Object::toDoAfterThisSetting().

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◆ setThread()

static void CORE_Object::setThread ( SP::CORE_Thread thread )

inlinestaticinherited

set the thread

Parameters

thread the shared pointer to the thread

References null.

Referenced by EMM_Run::EMM_Run(), EMM_TensorsRun::EMM_TensorsRun(), and MATH_SolverRun::MATH_SolverRun().

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◆ SP_OBJECT()

MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::SP_OBJECT ( MATH_GlobalMultiLevelsPolynomialToeplitzMatrix )

private

◆ toDoAfterThisSetting()

virtual void CORE_Object::toDoAfterThisSetting ( )

inlineprotectedvirtualinherited

method called after setThis() method this method can oly be called once.

Reimplemented in EMM_DisplacementOperator, EMM_DisplacementFVMOperator, EMM_GaussLegendreRelaxation, EMM_GradGaussLegendreRelaxation, and EMM_Object.

Referenced by CORE_Object::setThis().

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◆ toString()

tString MATH_MultiLevelsToeplitzMatrix::toString ( ) const

virtualinherited

return string

Reimplemented from CORE_Object.

References MATH_MultiLevelsToeplitzMatrix::getColumnsNumber(), MATH_MultiLevelsToeplitzMatrix::getRealValue(), MATH_MultiLevelsToeplitzMatrix::getRowsNumber(), FFTW_ComplexArray::getSize(), MATH_MultiLevelsToeplitzMatrix::mFFT, null, CORE_Real::toString(), CORE_Integer::toString(), tString, and tUIndex.

Referenced by MATH_MultiLevelsToeplitzMatrix::vectorProduct().

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◆ vectorProduct() [1/2]

void MATH_MultiLevelsFFTToeplitzMatrix::vectorProduct	(	const tUIndex &	N,
		const tReal *	X,
		tReal *	Y
	)		const

virtualinherited

do the vector product of the circular matrix C with Y by an FFT method

Parameters

N	the siz eof X & Y
X	the vector value
Y	the result

The Toeplitz matrix must be diagonalized before.

computes T.X=Y :

projects X on the spectral space : calls projectIntoSpectralSpace()
makes the vector prodcut of the diagonal values and the projection of X : calls vectorProductInSpectralSpace()
recovers the value of X from its values in the spectral space calls recoverFromSpectralSpace()

Implements MATH_MultiLevelsToeplitzMatrix.

References MATH_MultiLevelsToeplitzMatrix::getDFT(), MATH_MultiLevelsFFTToeplitzMatrix::getDFTProjector(), MATH_MultiLevelsToeplitzMatrix::getSpace(), MATH_MultiLevelsFFTToeplitzMatrix::projectIntoSpectralSpace(), MATH_MultiLevelsFFTToeplitzMatrix::recoverFromSpectralSpace(), MATH_MultiLevelsToeplitzMatrix::SPECTRAL_SPACE, and MATH_MultiLevelsFFTToeplitzMatrix::vectorProductInSpectralSpace().

Referenced by MATH_MultiLevelsFFTToeplitzMatrix::buildSpectralVectorProjector(), and MATH_ToeplitzTest::toeplitzTest().

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◆ vectorProduct() [2/2]

virtual void MATH_MultiLevelsFFTToeplitzMatrix::vectorProduct	(	const CORE_RealArray &	X,
		CORE_RealArray &	Y
	)		const

inlinevirtualinherited

do the vector product of the circular matrix C with Y by an FFT method

Parameters

X	the vector value
Y	the result

The Toeplitz matrix must be diagonalized before.

computes T.X=Y :

projects X on the spectral space : calls projectIntoSpectralSpace()
makes the vector prodcut of the diagonal values and the projection of X : calls vectorProductInSpectralSpace()
recovers the value of X from its values in the spectral space calls recoverFromSpectralSpace()

Reimplemented from MATH_MultiLevelsToeplitzMatrix.

References MATH_MultiLevelsFFTToeplitzMatrix::projectIntoSpectralSpace(), MATH_MultiLevelsFFTToeplitzMatrix::recoverFromSpectralSpace(), tReal, tUIndex, MATH_MultiLevelsToeplitzMatrix::vectorProduct(), and MATH_MultiLevelsFFTToeplitzMatrix::vectorProductInSpectralSpace().

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◆ vectorProductInSpectralSpace()

virtual void MATH_GlobalMultiLevelsPolynomialToeplitzMatrix::vectorProductInSpectralSpace	(	const FFTW_FFT &	A,
		FFTW_FFT &	Z
	)		const

inlineprotectedvirtual

make the vector product in spectral space

Parameters

A	the diagonal values of the matrix in spectral space
Z	in input : the values of the vector in spectral space in output : the values of the result vector Z:=A*Z

Implements MATH_MultiLevelsFFTToeplitzMatrix.

References FFTW_FFT::multiply(), projectIntoSpectralSpace(), recoverFromSpectralSpace(), tReal, and tUIndex.

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Member Data Documentation

◆ CANONICAL_SPACE

const tFlag MATH_MultiLevelsToeplitzMatrix::CANONICAL_SPACE =0

staticinherited

Referenced by MATH_MultiLevelsToeplitzMatrix::clear(), MATH_ToeplitzTest::emicrom411ncTest(), MATH_ToeplitzTest::emicrom411Test(), MATH_ToeplitzTest::emicrom441Test(), MATH_ToeplitzTest::emicrom444Test(), MATH_ToeplitzTest::emicromTest(), MATH_MultiLevelsToeplitzMatrix::MATH_MultiLevelsToeplitzMatrix(), MATH_MultiLevelsToeplitzMatrix::projection(), and MATH_ToeplitzTest::toeplitzTest().

◆ SPECTRAL_SPACE

const tFlag MATH_MultiLevelsToeplitzMatrix::SPECTRAL_SPACE =1

staticinherited

Referenced by MATH_ToeplitzTest::emicrom411ncTest(), MATH_ToeplitzTest::emicrom411Test(), MATH_ToeplitzTest::emicrom441Test(), MATH_ToeplitzTest::emicrom444Test(), MATH_ToeplitzTest::emicromTest(), MATH_MultiLevelsToeplitzMatrix::projection(), MATH_ToeplitzTest::toeplitzTest(), and MATH_MultiLevelsFFTToeplitzMatrix::vectorProduct().

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

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ MATH_GlobalMultiLevelsPolynomialToeplitzMatrix()

◆ ~MATH_GlobalMultiLevelsPolynomialToeplitzMatrix()

Member Function Documentation

◆ buildColumnLeadingDimensions()

◆ buildRowLeadingDimensions()

◆ buildSpectralSpace()

◆ buildSpectralVectorProjector()

◆ clear()

◆ computeEpsilon()

◆ copy()

◆ diagonalize()

◆ getBlockIndex()

◆ getBlocksNumber() [1/2]

◆ getBlocksNumber() [2/2]

◆ getBlocksNumberPerRow()

◆ getCanonicalSpaceSize()

◆ getClassName() [1/2]

◆ getClassName() [2/2]

◆ getColumnLeadingDimensions() [1/2]

◆ getColumnLeadingDimensions() [2/2]

◆ getColumnsNumber()

◆ getDFT() [1/2]

◆ getDFT() [2/2]

◆ getDFTProjector()

◆ getDimension()

◆ getDoubleEpsilon()

◆ getDoubleInfinity()

◆ getEpsilon()

◆ getFloatEpsilon()

◆ getFloatInfinity()

◆ getIdentityString()

◆ getIndex()

◆ getInfinity()

◆ getLDoubleEpsilon()

◆ getLDoubleInfinity()

◆ getLeafBlockDimension()

◆ getLeafBlockSize()

◆ getLeafBlockValues() [1/2]

◆ getLeafBlockValues() [2/2]

◆ getLevels()

◆ getLevelsNumber()

◆ getMaxChar()

◆ getMaxDouble()

◆ getMaxFlag()

◆ getMaxFloat()

◆ getMaxIndex()

◆ getMaxInt()

◆ getMaxInteger()

◆ getMaxLDouble()

◆ getMaxLInt()

◆ getMaxLLInt()

◆ getMaxReal()

◆ getMaxSInt()

◆ getMaxUChar()

◆ getMaxUIndex()

◆ getMaxUInt()

◆ getMaxUInteger()

◆ getMaxULInt()

◆ getMaxULLInt()

◆ getMaxUSInt()

◆ getMemorySize()

◆ getMinChar()

◆ getMinDouble()

◆ getMinFlag()

◆ getMinFloat()

◆ getMinIndex()

◆ getMinInt()

◆ getMinInteger()

◆ getMinLDouble()

◆ getMinLInt()

◆ getMinLLInt()

◆ getMinReal()

◆ getMinSInt()