MonomialIterator: Create list of d-dim monomials. More...

Detailed Description

MonomialIterator: Create list of d-dim monomials.

For a given dimension, this class produces an infinite list of monomials which increase in degree as all monomials of the last degree have been listed. The natural ordering of the monomials is degree first, then lexographically. Example for d=3: \(0,z,x,y,zz,zy,zx,yy,yx,xx,zzz,zzy,zzx,zyy,zyx\ldots\)

Note that the zero-monomial is not included in the list, however, it can be accessed via the extra method getNullMonomial.

Author: Daniel Wirtz

Date: 2012-01-20

New in 0.6:: (Daniel Wirtz, 2012-01-20) Added this class.

This class is part of the framework

KerMor - Model Order Reduction using Kernels

Homepage http://www.morepas.org/software/index.html
Documentation http://www.morepas.org/software/kermor/index.html
License KerMor license conditions

Definition at line 17 of file MonomialIterator.m.

Public Member Functions
	MonomialIterator (integer dim)
	Creates a new monomial iterator. More...

function colvec < double > alpha =	getNullMonomial ()
	Get the monomial of degree zero. More...

function [ colvec< double > alpha , int32 deg , exps ] =	nextMonomial ()
	Returns the next monomial in the sequence. More...

function colvec< int32 > alpha =	getRandMonomial (int32 deg)
	Returns a random monomial. More...

Static Public Member Functions
static function logical res =	test_MonomialIterator ()
	Tests the MonomialIterator for two test cases. More...

Public Attributes
	Dim

Public Attributes inherited from handle
	addlistener
	Creates a listener for the specified event and assigns a callback function to execute when the event occurs. More...

	notify
	Broadcast a notice that a specific event is occurring on a specified handle object or array of handle objects. More...

	delete
	Handle object destructor method that is called when the object's lifecycle ends. More...

	disp
	Handle object disp method which is called by the display method. See the MATLAB disp function. More...

	display
	Handle object display method called when MATLAB software interprets an expression returning a handle object that is not terminated by a semicolon. See the MATLAB display function. More...

	findobj
	Finds objects matching the specified conditions from the input array of handle objects. More...

	findprop
	Returns a meta.property objects associated with the specified property name. More...

	fields
	Returns a cell array of string containing the names of public properties. More...

	fieldnames
	Returns a cell array of string containing the names of public properties. See the MATLAB fieldnames function. More...

	isvalid
	Returns a logical array in which elements are true if the corresponding elements in the input array are valid handles. This method is Sealed so you cannot override it in a handle subclass. More...

	eq
	Relational functions example. See details for more information. More...

	transpose
	Transposes the elements of the handle object array. More...

	permute
	Rearranges the dimensions of the handle object array. See the MATLAB permute function. More...

	reshape
	hanges the dimensions of the handle object array to the specified dimensions. See the MATLAB reshape function. More...

	sort
	ort the handle objects in any array in ascending or descending order. More...

Constructor & Destructor Documentation

MonomialIterator.MonomialIterator ( integer dim )

Creates a new monomial iterator.

Parameters

dim	The target dimension \(d\in\N\)

Definition at line 62 of file MonomialIterator.m.

References Dim.

Referenced by test_MonomialIterator().

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Member Function Documentation

function colvec< double > alpha = MonomialIterator.getNullMonomial ( )

Get the monomial of degree zero.

Return values

alpha The multiindex of size \(1\times d\) with zero entries, corresponding to the zero degree monomial.

Definition at line 80 of file MonomialIterator.m.

References Dim.

function colvec< int32 > alpha = MonomialIterator.getRandMonomial ( int32 deg )

Returns a random monomial.

Parameters

deg	The degree \(p = \|\alpha\|\) of the monomial.

Return values

alpha The multiindex \(\alpha\in\Z^d\) corresponding to the exponents of the current monomial

Definition at line 141 of file MonomialIterator.m.

References Dim.

function [ colvec< double > alpha , int32 deg , exps ] = MonomialIterator.nextMonomial ( )

Returns the next monomial in the sequence.

Return values

alpha	The multiindex \(\alpha\in\Z^d\) corresponding to the exponents of the current monomial
deg	The degree \(p = \|\alpha\|\) of the monomial
exps	(Debug) The indices of \((1 \ldots d)\) at which an exponent is to be added.
Connection	A histogram search of exps with bins \((1 \ldots d)\) results in \(\alpha\)

Definition at line 92 of file MonomialIterator.m.

References Dim, and t.

function logical res = MonomialIterator.test_MonomialIterator ( )

static

Tests the MonomialIterator for two test cases.

Return values