Home > sgwt_toolbox > sgwt_kernel_abspline3.m

sgwt_kernel_abspline3

PURPOSE ^

sgwt_kernel_abspline3 : Monic polynomial / cubic spline / power law decay kernel

SYNOPSIS ^

function r = sgwt_kernel_abspline3(x,alpha,beta,t1,t2)

DESCRIPTION ^

 sgwt_kernel_abspline3 : Monic polynomial / cubic spline / power law decay kernel

 function r = sgwt_kernel_abspline3(x,alpha,beta,t1,t2)

 defines function g(x) with g(x) = c1*x^alpha for 0<x<x1
 g(x) = c3/x^beta for x>t2
 cubic spline for t1<x<t2,
 Satisfying g(t1)=g(t2)=1

 Inputs :
 x : array of independent variable values
 alpha : exponent for region near origin
 beta : exponent decay
 t1, t2 : determine transition region

 Outputs :
 r - result (same size as x)

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 % sgwt_kernel_abspline3 : Monic polynomial / cubic spline / power law decay kernel
0002 %
0003 % function r = sgwt_kernel_abspline3(x,alpha,beta,t1,t2)
0004 %
0005 % defines function g(x) with g(x) = c1*x^alpha for 0<x<x1
0006 % g(x) = c3/x^beta for x>t2
0007 % cubic spline for t1<x<t2,
0008 % Satisfying g(t1)=g(t2)=1
0009 %
0010 % Inputs :
0011 % x : array of independent variable values
0012 % alpha : exponent for region near origin
0013 % beta : exponent decay
0014 % t1, t2 : determine transition region
0015 %
0016 % Outputs :
0017 % r - result (same size as x)
0018 
0019 % This file is part of the SGWT toolbox (Spectral Graph Wavelet Transform toolbox)
0020 % Copyright (C) 2010, David K. Hammond.
0021 %
0022 % The SGWT toolbox is free software: you can redistribute it and/or modify
0023 % it under the terms of the GNU General Public License as published by
0024 % the Free Software Foundation, either version 3 of the License, or
0025 % (at your option) any later version.
0026 %
0027 % The SGWT toolbox is distributed in the hope that it will be useful,
0028 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0029 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0030 % GNU General Public License for more details.
0031 %
0032 % You should have received a copy of the GNU General Public License
0033 % along with the SGWT toolbox.  If not, see <http://www.gnu.org/licenses/>.
0034 
0035 function r = sgwt_kernel_abspline3(x,alpha,beta,t1,t2)
0036   r=zeros(size(x));
0037   % compute spline coefficients
0038   % M a = v
0039   M=[[1 t1 t1^2 t1^3];...
0040      [1 t2 t2^2 t2^3];...
0041      [0 1 2*t1 3*t1^2];...
0042      [0 1 2*t2 3*t2^2]];
0043   %v=[t1^alpha ; t2^(-beta) ; alpha*t1^(alpha-1) ; -beta*t2^(-beta-1)];
0044   v=[1 ; 1 ; t1^(-alpha)*alpha*t1^(alpha-1) ; -beta*t2^(-beta-1)*t2^beta];
0045   a=M\v;
0046 
0047   r1=find(x>=0 & x<t1);
0048   r2=find(x>=t1 & x<t2);
0049   r3=find(x>=t2);
0050   r(r1)=x(r1).^alpha*t1^(-alpha);
0051   r(r3)=x(r3).^(-beta)*t2^(beta);
0052   
0053   x2=x(r2);
0054   r(r2)=a(1)+a(2)*x2+a(3)*x2.^2+a(4)*x2.^3;
0055 %  tmp=polyval(flipud(a),x2);
0056 %  keyboard

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