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Chebfun V4

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Chebfun V4

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30 Apr 2009 (Updated )

Numerical computation with functions instead of numbers.

Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

maps(varargin)
function varargout = maps(varargin)
% CHEBFUN MAPS
%  Rather than using Chebyshev polynomial interpolants, Chebfun can use
%  non-polynomial bases defined by maps. This is useful in a number of
%  circumstances, such as when working on infinite intervals, or with 
%  functions which are ill-behaved in localised regions of the interval.
%
%  The syntax for creating a chebfun using a map is
%    chebfun(@(x) f(x), 'map', {MAPNAME,MAPPARAMS});
%  where MAPNAME is a one of;
%    'LINEAR','UNBOUNDED','SING','KTE','STRIP','SAUSAGE',
%    'SLIT','SLITP', or 'MPINCH'. 
%  MAPPARAMS is a row vector containing the paramaters which define the map.
%  (An overview of some of the important maps is given below.)
%  Examples;
%    chebfun(@(x) sin(1000*x), 'map', {'kte',.9});
%    chebfun(@(x) 1 + (1-x).^sqrt(3), 'map', {'sing',[1 sqrt(3)]});
%    chebfun(@(x) tanh(100*pi*x/2), 'map', {'slit',1i/100});
%  (A keen user might want to compare the lengths of these chebfuns with
%  those not using maps!)
%
%  M = MAPS({MAPNAME,MAPPARAMS},INT) returns a map structure for the
%  built-in map type MAPNAME with parameters MAPPARAMS where INT is 2 by 1
%  vector containing the images of -1 and 1 under the map. INT may also be
%  a domain object, and is assumed to be [-1,1] if not given
%
%  The LINEAR map is simply a linear scaling and is used all the time in
%  Chebfun when working on an interval other than [-1,1]. It does not contain
%  any tunable parameters.
%
%  The UNBOUNDED map is for unbounded domains of the form [-inf,b],
%  [-inf,inf], or [a,inf]. For semi-infinite domains (here with infinity 
%  at the right boundary), this map takes the form 
%     m(y) = 15*s*(y+1)./(1-y)+a
%  where S is a scaling parameter that can be changed. By defaults it is
%  taken from mappref.parinf(1).
%  On doubly infinite domains the maps takes the form
%     m(y) = 5*s*y./(1-y.^2)+c
%  where again S is a scaling and C is a shift. These are also taken by
%  default from mappref.parinf(1:2) respectively if not supplied.
%
%  The SING map is for dealing with functions with singular endpoints that
%  cannot be dealt wf = chebfun('(1-x.^2).^.3','singmap',[.3 .3])ith with 'exps'. 
%  SINGmaps take two parameters, which correspond to the form of singularity 
%  at the left and right ends of the interval respectively. Zero (0) or one (1) 
%  corresponds to no singlarity. For example
%     m = maps({'sing',[.5,1]})
%  will be a good map for dealing with something like f(x) = sqrt(x)+1
%  Currently if singularites are required at the end, the parameter can
%  only be [.5 .5] or [.25 .25], yet such a map can still do well even when
%  these exponents aren't exactly correct. For example
%     m = maps({'sing',[.25 .25]},[-2 2])
%     f = chebfun('(4-x.^2).^.3',[-2 2],'map',m)
%  SING type maps can be called directly in the constructor via
%     f = chebfun('(4-x.^2).^.3',[-2 2],'singmap',[.25 .25])
%
%  M = MAPS(F) returns a cell structure of the maps used by the chebfun F.
%  M = MAPS(D) returns the default map for the domain D.
%
%  For help on the MAPS function from the MAPPING TOOLBOX, type
%  help([fileparts(which('aitoff')),filesep 'maps'])

%  Copyright 2011 by The University of Oxford and The Chebfun Developers. 
%  See http://www.maths.ox.ac.uk/chebfun/ for Chebfun information.

%  This code is just a wrapper for fun/maps.

% Try to resolve conflicts with the mapping toolbox.
if nargin == 1 && ischar(varargin{1}) && exist('aitoff','file')
    chebAllowedStr = {'LINEAR','UNBOUNDED','SING','KTE','STRIP','SAUSAGE', 'SLIT','SLITP', 'MPINCH'};
    if ~any(strcmpi(varargin{1},chebAllowedStr))
        try
            curDir = pwd;
            cd(fileparts(which('aitoff')));
            builtin_maps = @maps;
            cd(curDir);
            varargout = {builtin_maps(varargin{:})};
            return
        catch
            warning('CHEBFUN:maps:conflict',...
                ['Possible conflict with mapping toolbox. To ensure the mapping ', ...
            'toolbox works correctly, ensure it is higher on the MATLAB path than ', ...
            'Chebfun. See ''help path''.']);
        end
    end
end

varargout = {maps(fun,varargin{:})};

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