Home > sgwt_toolbox > sgwt_cheby_eval.m

sgwt_cheby_eval

PURPOSE ^

sgwt_cheby_eval : Evaluate shifted Chebyshev polynomial on given domain

SYNOPSIS ^

function r=sgwt_cheby_eval(x,c,arange)

DESCRIPTION ^

 sgwt_cheby_eval : Evaluate shifted Chebyshev polynomial on given domain

 function r=sgwt_cheby_eval(x,c,arange)

 Compute Chebyshev polynomial of laplacian applied to input.
 This is primarily for visualization

 Inputs:
 x - input values to evaluate polynomial on
 c - Chebyshev coefficients (c(1+j) is jth coefficient)
 arange - interval of approximation. Note that x need not be inside
          arange, but the polynomial will no longer be near the
          approximated function outside of arange.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 % sgwt_cheby_eval : Evaluate shifted Chebyshev polynomial on given domain
0002 %
0003 % function r=sgwt_cheby_eval(x,c,arange)
0004 %
0005 % Compute Chebyshev polynomial of laplacian applied to input.
0006 % This is primarily for visualization
0007 %
0008 % Inputs:
0009 % x - input values to evaluate polynomial on
0010 % c - Chebyshev coefficients (c(1+j) is jth coefficient)
0011 % arange - interval of approximation. Note that x need not be inside
0012 %          arange, but the polynomial will no longer be near the
0013 %          approximated function outside of arange.
0014 
0015 % This file is part of the SGWT toolbox (Spectral Graph Wavelet Transform toolbox)
0016 % Copyright (C) 2010, David K. Hammond.
0017 %
0018 % The SGWT toolbox is free software: you can redistribute it and/or modify
0019 % it under the terms of the GNU General Public License as published by
0020 % the Free Software Foundation, either version 3 of the License, or
0021 % (at your option) any later version.
0022 %
0023 % The SGWT toolbox is distributed in the hope that it will be useful,
0024 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0025 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0026 % GNU General Public License for more details.
0027 %
0028 % You should have received a copy of the GNU General Public License
0029 % along with the SGWT toolbox.  If not, see <http://www.gnu.org/licenses/>.
0030 
0031 function r=sgwt_cheby_eval(x,c,arange)
0032 % By setting the operator L to mean (pointwise) multiplication by x,
0033 % and f to be vector of ones, p(L)f will contain p(x) at each
0034 % point. This lets us use sgwt_cheby_op to evaluate the Chebyshev polynomials.
0035 L=spdiags(x(:),0,speye(numel(x)));
0036 f=ones(size(x(:)));
0037 r=sgwt_cheby_op(f,L,c,arange);
0038 
0039 if iscell(r)
0040   for k=1:numel(r)
0041     r{k}=reshape(r{k},size(x));
0042   end
0043 else
0044   r=reshape(r,size(x));
0045 end
0046 
0047 
0048 
0049   
0050

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