function HaarApprox(normalization, save)% HaarApprox(normalization, save) does a Haar wavelet decomposition of a% simple function, and plots the scaling function and wavelet coefficients.% The normalization parameter can be 'max' or 'L2'.  If save is present, the% plot is saved as an EPS file.% Settings:filename = 'haar1d-approx.ps';arrows = 0;jinf = 8;jmax = 4;jmin = 0;hspacing = 2.0; % horizontal spacing between functionshsize = 1.6;    % horizontal size of each functionvspacing = 1.2; % vertical spacing between functionsvsize = 0.5;    % vertical sizevgap = vspacing - vsize;% Set up plot:clg;hold on;axis off;axis equal;% Axes:axis1_x = [0, 0, 1];axis1_y = [1, 0, 0];axis2_x = [0, 0, nan, 0, 1];axis2_y = [0.5, -0.5, nan, 0, 0];% True function:xinf = [0:2^jinf] / 2^jinf;yinf = (10 * exp(-16*xinf/3) .* sin(8*xinf) + 1)/6;plot(axis1_x*hsize, axis1_y*vsize + vspacing*(jmax-jmin), 'w');plot(xinf*hsize, yinf*vsize + vspacing*(jmax-jmin), ':w');% Finest scaling function approximation, computed by averaging:y = zeros(1, 2^jmax);for i = 1:2^(jinf-jmax)  y = y + yinf(i:2^(jinf-jmax):2^jmax*(2^(jinf-jmax)-1)+i);end;y = y / 2^(jinf-jmax);if strcmp(normalization, 'L2')  y = y/2^(jmax/2);end;[xp, yp] = HaarCoords(y, normalization);plot(xp*hsize, yp*vsize + vspacing*(jmax-jmin), 'w', 'LineWidth', 2);if nargin > 1  % Latex stuff:  disp(['    \begin{picture}(' num2str(hspacing + hsize) ',' ...	  num2str(vspacing*(jmax-jmin+1) - vgap/2) ')(0,' ...	  num2str(-vgap/2) ')']);  disp(['      \putbl{0,0}{\psfig{file=' filename ',width=' ...	  num2str(hspacing + hsize) 'in}}']);  disp(['      \putt{' num2str(hsize/2) ',' ...	  num2str(vspacing*(jmax-jmin-0.1)) ...	  '}{\small $V^' num2str(jmax) '$ approximation}']);else  plot(hsize/2, vspacing*(jmax-jmin)-0.1, 'o');end;% Repeatedly do summing and differencing on shorter and shorter part of y.j = jmax;len = 2^j;while len >= 2  y = HaarDecompStep(y, len, normalization);  len = len/2;  j = j - 1;  [xp, yp] = HaarCoords(y(1:len), normalization);  plot(axis1_x*hsize, axis1_y*vsize + vspacing*(j-jmin), 'w');  plot(xinf*hsize, yinf*vsize + vspacing*(j-jmin), ':w');  plot(xp*hsize, yp*vsize + vspacing*(j-jmin), 'w', 'LineWidth', 2);  if nargin > 1    % Latex stuff:    if arrows      disp(['      \put(' num2str(hsize/2) ',' ...	      num2str(vspacing*(j-jmin+0.75)) ...	      '){\vector(0,-1){' num2str(0.7*vspacing-vsize) '}}']);    end;    disp(['      \putt{' num2str(hsize/2) ',' ...	    num2str(vspacing*(j-jmin)-0.1) ...	    '}{\small $V^' num2str(j) '$ approximation}']);  else    if arrows      plot([hsize/2 hsize/2], ...	  [vspacing*(j-jmin+0.75) ...	      vspacing*(j-jmin+0.75)-(0.7*vspacing-vsize)]);    end;    plot(hsize/2, vspacing*(j-jmin)-0.1, 'o');  end;  xp = [1:2:2^(j+1)-1]/2^(j+1);  yp = y(len+1:2*len);  plot(axis2_x*hsize + hspacing, ...      axis2_y*vsize + vspacing*(j-jmin) + vsize/2, 'w');  plot(xp*hsize + hspacing, 2*yp*vsize + vspacing*(j-jmin) + vsize/2, 'wo');  w = 0.5*hsize;  h = 0.7*vspacing-vsize;  slope = round(w/h);  w = h*slope;  if nargin > 1    % Latex stuff:    if arrows      disp(['      \put(' num2str(0.9*hsize) ',' ...	      num2str(vspacing*(j-jmin+0.75)) ...	      '){\vector(' num2str(slope) ...	      ',-1){' num2str(w) '}}']);    end;    disp(['      \putt{' num2str(hsize/2 + hspacing) ',' ...	    num2str(vspacing*(j-jmin)-0.1) ...	    '}{\small $W^' num2str(j) ...	    '$ detail coefficient' (j>0)*'s}'+(j==0)*'} ']);  else    if arrows      plot([0.9*hsize 0.9*hsize+w], ...	  [vspacing*(j-jmin+0.75) vspacing*(j-jmin+0.75)-(w/slope)]);      end;    plot(hsize/2 + hspacing, vspacing*(j-jmin)-0.1, 'o');  end;end;if nargin > 1  disp(['Saving EPS to "' filename '"...']);  print('-deps', filename);end;