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%%        SUB-FUNCTIONS          %%
%% USED BY: VOLBET2ISO           %%
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% USE DIRECTLY AT YOUR OWN RISK ! %
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% Master sub-function:
function varargout = subfct_getvol(CHP,Z,Y,X,LIMITS)

% Limits:
%disp(strcat('Limits: ',num2str(LIMITS)));
O  = LIMITS(1);
MZ = LIMITS(2);
MY = sort( LIMITS(3:4) );
MX = sort( LIMITS(5:6) );

% Compute the volume:
[V Vmat dV] = getvol(Z,Y,X,O,MZ,MY,MX,CHP);

% Outputs:
switch nargout
 case 1
  varargout(1) = {V};
 case 2
  varargout(1) = {V};
  varargout(2) = {Vmat};
 case 3
  varargout(1) = {V};
  varargout(2) = {Vmat};
  varargout(3) = {dV};
end %switch nargout


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This function computes the volume limited southward by
% MY(1), northward by iso-O (or MY(2) if iso-O reaches it),
% eastward by MX(1), westward by MX(2) and downward by iso-O
% (or MZ if iso-O reaches it).
%
% Updates: 
% 20060615: add a default meridional gradient (negative)
%           test on x,y,z limits
%
function varargout = getvol(Z,Y,X,O,MZ,MY,MX,CHP)

%% Dim:
nz = length(Z);
ny = length(Y);
nx = length(X);
%disp(num2str([nz ny nx]));

%% Indices:
izmax = min( find( Z>MZ    ) ); if isempty(izmax),izmax=nz;end;
iymin = max( find( Y<MY(1) ) ); if isempty(iymin),iymin=1; end;
iymax = min( find( Y>MY(2) ) ); if isempty(iymax),iymax=ny;end;
ixmin = max( find( X<MX(1) ) ); if isempty(ixmin),ixmin=1; end;
ixmax = min( find( X>MX(2) ) ); if isempty(ixmax),ixmax=nx;end;
%disp(num2str([1 izmax iymin iymax ixmin ixmax]));

%% 1- determine the 3D matrix of volume elements defined by
% the grid:
dV = getdV(Z,Y,X);

%% 2- compute the 3D volume matrix where 1 means dV must be 
% counted and 0 must not:

V = ones(nz,ny,nx); % initialy keep all points

% Exclude northward iso-O limits:
% NB: here the test depends on the meridional gradient of CHP
%     if CHP increase (resp. decreases) with LAT then we must
%     keep lower (resp. higher) values than O limit
% a: determine test type:
N = iymax - iymin + 1; % Number of Y points in the domain
CHPsouth = nanmean(nanmean(squeeze(CHP(1,iymin:iymin+fix(N/2),ixmin:ixmax))));
CHPnorth = nanmean(nanmean(squeeze(CHP(1,iymin+fix(N/2):iymax,ixmin:ixmax))));
SNgrad = (CHPnorth - CHPsouth)./abs(CHPnorth - CHPsouth);
if isnan(SNgrad), SNgrad=-1; end % Assume negative gradient by default
%disp(strcat('Northward gradient sign is:',num2str(SNgrad)));
switch SNgrad
 case  1, testype = 'le'; % Less than  or equal 
 case -1, testype = 'ge'; % Greater than or equal
end %switch
% b: exclude points
for iz=1:izmax
  chpZ = squeeze(CHP(iz,:,:));
  V(iz,:,:)=double(feval(testype,chpZ,O));
end %for iz

% Exclude southward limit:
V(:,1:iymin,:) = zeros(nz,iymin,nx);

% Exclude northward limit:
V(:,iymax:ny,:) = zeros(nz,(ny-iymax)+1,nx);

% Exclude westward limit:
V(:,:,1:ixmin) = zeros(nz,ny,ixmin);

% Exclude eastward limit:
V(:,:,ixmax:nx) = zeros(nz,ny,(nx-ixmax)+1);

% Exclude downward limit:
V(izmax:nz,:,:) = zeros((nz-izmax)+1,ny,nx);


%% 3- Then compute the volume by summing dV elements 
%     for non 0 V points
Vkeep = V.*dV;
Vkeep = sum(sum(sum(Vkeep)));

%% 4- Outputs:
switch nargout
 case 1
  varargout(1) = {Vkeep}; % Volume single value
 case 2
  varargout(1) = {Vkeep};
  varargout(2) = {V};     % Logical V matrix with included/excluded points
 case 3
  varargout(1) = {Vkeep};
  varargout(2) = {V};
  varargout(3) = {dV};    % Volume elements matrix
end %switch nargout



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This function computes the 3D dV volume elements.
function dv = getdV(Z,Y,X);

nz = length(Z);
ny = length(Y);
nx = length(X);

%%% Compute the DY:
% Assuming Y is independant of ix:
d  = m_lldist([1 1]*X(1),Y);
dy = [d(1)/2  (d(2:length(d))+d(1:length(d)-1))/2 d(length(d))/2];
dy = meshgrid(dy,X)';

%%% Compute the DX:
clear d
for iy = 1 : ny
   d(:,iy) = m_lldist(X,Y([iy iy]));
end
dx = [d(1,:)/2 ;  ( d(2:size(d,1),:) + d(1:size(d,1)-1,:) )./2 ; d(size(d,1),:)/2];
dx = dx';

%% Compute the horizontal DS surface element:
ds = dx.*dy;

%% Compute the DZ:
d = diff(Z);
dz = [d(1)/2 ( d(2:length(d)) + d(1:length(d)-1) )./2 d(length(d))/2];

%% Then compute the DV volume elements:
dv = ones(nz,ny,nx)*NaN;
for iz=1:nz
  dv(iz,:,:) = dz(iz).*ds;
end