function [Q, sigma_deg] = normalisation_laplacian(number_clusters, ...						  power_lin, AS_deg, delta_phi_deg)% [Q, sigma_deg] = normalisation_laplacian(number_clusters,%                  power_lin, AS_deg, delta_phi_deg)%% Computes the variances sigma_k and the power normalising% coefficients Q_k such that the Power Azimuth Spectrum (PAS) can% be regarded as a probability distribution function (pdf), that is% to say int_{-\pi}^{pi} PAS(\phi) d\phi = 1.%%% STANDARD DISCLAIMER%% CSys is furnishing this item "as is". CSys does not provide any% warranty of the item whatsoever, whether express, implied, or% statutory, including, but not limited to, any warranty of% merchantability or fitness for a particular purpose or any% warranty that the contents of the item will be error-free.%% In no respect shall CSys incur any liability for any damages,% including, but limited to, direct, indirect, special, or% consequential damages arising out of, resulting from, or any way% connected to the use of the item, whether or not based upon% warranty, contract, tort, or otherwise; whether or not injury was% sustained by persons or property or otherwise; and whether or not% loss was sustained from, or arose out of, the results of, the% item, or any services that may be provided by CSys.%% (c) Laurent Schumacher, AAU-TKN/IES/KOM/CPK/CSys - July 2001%% Computation of sigma%load AS2sigma_laplacian tmp;for k=1:number_clusters  if ((AS_deg(k) < min(tmp(:,1))) | (AS_deg(k) >= max(tmp(:,1))))    disp('Look-up table AS -> sigma incomplete.');    disp('Please regenerate with AS_vs_sigma_laplacian.m');    return;  end;  pos          = find(tmp(:,1)>=AS_deg(k));  sigma_deg(k) = ((tmp(pos(1),1)-AS_deg(k))*tmp(pos(1)-1,2) + ...		  (AS_deg(k) - tmp(pos(1)-1,1))*tmp(pos(1),2))/ ...      (tmp(pos(1),1)-tmp(pos(1)-1,1));end;% Conversion degree -> radAS_rad    = AS_deg.*(pi/180);sigma_rad = sigma_deg.*(pi/180);% Domain definitiondelta_phi_rad = delta_phi_deg.*(pi/180);%% Computation of Q%if (number_clusters == 1)  Q = 1/(1-exp(((-1)*sqrt(2)*delta_phi_rad)/sigma_rad));else  A = zeros(number_clusters);  A(1:number_clusters-1,1) = 1/(sigma_rad(1)*power_lin(1));  for k=2:number_clusters    A(k-1,k) = (-1)/(sigma_rad(k)*power_lin(k));  end;  A(number_clusters,:) = ones(1,number_clusters)-exp(((-1).* ...						 sqrt(2).* ...						 delta_phi_rad)./ ...						 sigma_rad);  b = zeros(number_clusters,1);  b(number_clusters,1) = 1;  Q = (inv(A)*b).';end;%% Validation%if ~(sum((ones(1,number_clusters)-exp(((-1).*sqrt(2).* ...				       delta_phi_rad)./sigma_rad))*Q.')-1 ...     < 1e-15)  disp('Normalisation of laplacian distribution failed!');  return;end;