gmaze_pv/subfct/subfct_getvol.m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%        SUB-FUNCTIONS          %%
%% USED BY: VOLBET2ISO           %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% USE DIRECTLY AT YOUR OWN RISK ! %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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: 
% 20060616: bug fixed in CHPsouth, CHPnorth nanmean
% 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)),1),2);
CHPnorth = nanmean(nanmean(squeeze(CHP(1,iymin+fix(N/2):iymax,ixmin:ixmax)),1),2);
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

1	gmaze	1.1	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2			%% SUB-FUNCTIONS %%
3			%% USED BY: VOLBET2ISO %%
4			%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5			% USE DIRECTLY AT YOUR OWN RISK ! %
6			%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7
8
9			%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
10			% Master sub-function:
11			function varargout = subfct_getvol(CHP,Z,Y,X,LIMITS)
12
13			% Limits:
14			%disp(strcat('Limits: ',num2str(LIMITS)));
15			O = LIMITS(1);
16			MZ = LIMITS(2);
17			MY = sort( LIMITS(3:4) );
18			MX = sort( LIMITS(5:6) );
19
20			% Compute the volume:
21			[V Vmat dV] = getvol(Z,Y,X,O,MZ,MY,MX,CHP);
22
23			% Outputs:
24			switch nargout
25			case 1
26			varargout(1) = {V};
27			case 2
28			varargout(1) = {V};
29			varargout(2) = {Vmat};
30			case 3
31			varargout(1) = {V};
32			varargout(2) = {Vmat};
33			varargout(3) = {dV};
34			end %switch nargout
35
36
37			%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
38			% This function computes the volume limited southward by
39			% MY(1), northward by iso-O (or MY(2) if iso-O reaches it),
40			% eastward by MX(1), westward by MX(2) and downward by iso-O
41			% (or MZ if iso-O reaches it).
42			%
43			% Updates:
44			% 20060616: bug fixed in CHPsouth, CHPnorth nanmean
45			% 20060615: add a default meridional gradient (negative)
46			% test on x,y,z limits
47			%
48			function varargout = getvol(Z,Y,X,O,MZ,MY,MX,CHP)
49
50			%% Dim:
51			nz = length(Z);
52			ny = length(Y);
53			nx = length(X);
54			%disp(num2str([nz ny nx]));
55
56			%% Indices:
57			izmax = min( find( Z>MZ ) ); if isempty(izmax),izmax=nz;end;
58			iymin = max( find( Y<MY(1) ) ); if isempty(iymin),iymin=1; end;
59			iymax = min( find( Y>MY(2) ) ); if isempty(iymax),iymax=ny;end;
60			ixmin = max( find( X<MX(1) ) ); if isempty(ixmin),ixmin=1; end;
61			ixmax = min( find( X>MX(2) ) ); if isempty(ixmax),ixmax=nx;end;
62			%disp(num2str([1 izmax iymin iymax ixmin ixmax]));
63
64			%% 1- determine the 3D matrix of volume elements defined by
65			% the grid:
66			dV = getdV(Z,Y,X);
67
68			%% 2- compute the 3D volume matrix where 1 means dV must be
69			% counted and 0 must not:
70
71			V = ones(nz,ny,nx); % initialy keep all points
72
73			% Exclude northward iso-O limits:
74			% NB: here the test depends on the meridional gradient of CHP
75			% if CHP increase (resp. decreases) with LAT then we must
76			% keep lower (resp. higher) values than O limit
77			% a: determine test type:
78			N = iymax - iymin + 1; % Number of Y points in the domain
79			CHPsouth = nanmean(nanmean(squeeze(CHP(1,iymin:iymin+fix(N/2),ixmin:ixmax)),1),2);
80			CHPnorth = nanmean(nanmean(squeeze(CHP(1,iymin+fix(N/2):iymax,ixmin:ixmax)),1),2);
81			SNgrad = (CHPnorth - CHPsouth)./abs(CHPnorth - CHPsouth);
82			if isnan(SNgrad), SNgrad=-1; end % Assume negative gradient by default
83			%disp(strcat('Northward gradient sign is:',num2str(SNgrad)));
84			switch SNgrad
85			case 1, testype = 'le'; % Less than or equal
86			case -1, testype = 'ge'; % Greater than or equal
87			end %switch
88			% b: exclude points
89			for iz=1:izmax
90			chpZ = squeeze(CHP(iz,:,:));
91			V(iz,:,:)=double(feval(testype,chpZ,O));
92			end %for iz
93
94			% Exclude southward limit:
95			V(:,1:iymin,:) = zeros(nz,iymin,nx);
96
97			% Exclude northward limit:
98			V(:,iymax:ny,:) = zeros(nz,(ny-iymax)+1,nx);
99
100			% Exclude westward limit:
101			V(:,:,1:ixmin) = zeros(nz,ny,ixmin);
102
103			% Exclude eastward limit:
104			V(:,:,ixmax:nx) = zeros(nz,ny,(nx-ixmax)+1);
105
106			% Exclude downward limit:
107			V(izmax:nz,:,:) = zeros((nz-izmax)+1,ny,nx);
108
109
110			%% 3- Then compute the volume by summing dV elements
111			% for non 0 V points
112			Vkeep = V.*dV;
113			Vkeep = sum(sum(sum(Vkeep)));
114
115			%% 4- Outputs:
116			switch nargout
117			case 1
118			varargout(1) = {Vkeep}; % Volume single value
119			case 2
120			varargout(1) = {Vkeep};
121			varargout(2) = {V}; % Logical V matrix with included/excluded points
122			case 3
123			varargout(1) = {Vkeep};
124			varargout(2) = {V};
125			varargout(3) = {dV}; % Volume elements matrix
126			end %switch nargout
127
128
129
130			%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
131			% This function computes the 3D dV volume elements.
132			function dv = getdV(Z,Y,X);
133
134			nz = length(Z);
135			ny = length(Y);
136			nx = length(X);
137
138			%%% Compute the DY:
139			% Assuming Y is independant of ix:
140			d = m_lldist([1 1]*X(1),Y);
141			dy = [d(1)/2 (d(2:length(d))+d(1:length(d)-1))/2 d(length(d))/2];
142			dy = meshgrid(dy,X)';
143
144			%%% Compute the DX:
145			clear d
146			for iy = 1 : ny
147			d(:,iy) = m_lldist(X,Y([iy iy]));
148			end
149			dx = [d(1,:)/2 ; ( d(2:size(d,1),:) + d(1:size(d,1)-1,:) )./2 ; d(size(d,1),:)/2];
150			dx = dx';
151
152			%% Compute the horizontal DS surface element:
153			ds = dx.*dy;
154
155			%% Compute the DZ:
156			d = diff(Z);
157			dz = [d(1)/2 ( d(2:length(d)) + d(1:length(d)-1) )./2 d(length(d))/2];
158
159			%% Then compute the DV volume elements:
160			dv = ones(nz,ny,nx)*NaN;
161			for iz=1:nz
162			dv(iz,:,:) = dz(iz).*ds;
163			end
164