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Octave version #8

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e255019
Specifying double datatype in multiple locations. This is necessary d…
rakoczi-h Nov 5, 2024
ec57a56
specifying that this is an Octave version
rakoczi-h Nov 5, 2024
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2 changes: 1 addition & 1 deletion README.md
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Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
# Global Spherical Harmonic package (GSH)

GSH is a MATLAB package to do **Global Spherical Harmonic Analyses** (GSHA) and **Synthesis** (GSHS) for Crust1.0.
GSH is a MATLAB package to do **Global Spherical Harmonic Analyses** (GSHA) and **Synthesis** (GSHS) for Crust1.0. This version supports running the scripts with Octave.


## Requirements
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183 changes: 91 additions & 92 deletions Tools/GSHA.m
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function cs = GSHA(f,lmax)

% GSHA global spherical harmonic analysis (wls)
%
% HOW cs = gsha(f,method,grid)
%
% IN f - global field of size N*2N
% lmax - maximum degree of development
% OUT cs - Clm & Slm in |C\S| format
%
%--------------------------------------------------------------------------
% uses Legendre_functions, SC2CS
%--------------------------------------------------------------------------

%--------------------------------------------------------------------------
% Grid definition
%--------------------------------------------------------------------------
[rows,cols] = size(f);

n = rows;
dt = 180 / n;
theta = (dt/2:dt:180)';
lam = (dt/2:dt:360); % dt = dlam

%--------------------------------------------------------------------------
% further diagnostics
%--------------------------------------------------------------------------
if lmax > n
error('Maximum degree of development is higher than number of rows of input.')
end

if lmax == n
error('max. degree 180 is not possible for block grid, problem for m = 0')
end
%--------------------------------------------------------------------------
% Init.
%--------------------------------------------------------------------------
% L = n;
L = lmax;
clm = zeros(L+1,L+1);
slm = zeros(L+1,L+1);

%--------------------------------------------------------------------------
% 1st step analysis: Am(theta) & Bm(theta)
%--------------------------------------------------------------------------
m = 0:L;
c = cos(lam'*m*pi/180);
s = sin(lam'*m*pi/180);

% preserving the orthogonality

c = c/rows;
s = s/rows;

c(:,1) = c(:,1)/2;
s(:,L+1) = s(:,L+1)/2; % not sure if this is needed? Need to take a look at the equations
%c(:,L+1) = zeros(2*n,1); % this line is not needed otherwise Clamx,lamx is not computed.
s(:,1) = zeros(2*n,1);

a = f * c;
b = f * s;

%--------------------------------------------------------------------------
% 2nd step analysis: Clm & Slm
%--------------------------------------------------------------------------

% predefine weights for the weighted least squares analysis
si = sin(theta*pi/180);
si = 2*si/sum(si);

% loop over the order of the Spherical Harmonics
for m = 0:L
% construct the legendre polynomials
p = Legendre_functions(m:L,m,theta);
% Select particular colum of the signal
ai = a(:,m+1);
bi = b(:,m+1);
d = 1:length(theta);
pts = p' * sparse(d,d,si);

% Estimate the coefficients
clm(m+1:L+1,m+1) = (pts * p) \ pts * ai;
slm(m+1:L+1,m+1) = (pts * p) \ pts * bi;
end

%--------------------------------------------------------------------------
% Write the coefficients Clm & Slm in |C\S| format
%--------------------------------------------------------------------------
slm = fliplr(slm);
%sc = [slm(:,1:L) clm];
cs = sc2cs([slm(:,1:L) clm]);
cs = cs(1:lmax+1,1:lmax+1);
function cs = GSHA(f,lmax)

% GSHA global spherical harmonic analysis (wls)
%
% HOW cs = gsha(f,method,grid)
%
% IN f - global field of size N*2N
% lmax - maximum degree of development
% OUT cs - Clm & Slm in |C\S| format
%
%--------------------------------------------------------------------------
% uses Legendre_functions, SC2CS
%--------------------------------------------------------------------------

%--------------------------------------------------------------------------
% Grid definition
%--------------------------------------------------------------------------
[rows,cols] = size(f);
n = rows;
dt = double(180 / n);
theta = double((dt/2:dt:180))';
lam = double((dt/2:dt:360)); % dt = dlam
%--------------------------------------------------------------------------
% further diagnostics
%--------------------------------------------------------------------------
if lmax > n
error('Maximum degree of development is higher than number of rows of input.')
end

if lmax == n
error('max. degree 180 is not possible for block grid, problem for m = 0')
end
%--------------------------------------------------------------------------
% Init.
%--------------------------------------------------------------------------
% L = n;
L = lmax;
clm = zeros(L+1,L+1);
slm = zeros(L+1,L+1);

%--------------------------------------------------------------------------
% 1st step analysis: Am(theta) & Bm(theta)
%--------------------------------------------------------------------------
m = double(0:L);

c = cos(lam'*m*pi/180);
s = sin(lam'*m*pi/180);

% preserving the orthogonality

c = c/rows;
s = s/rows;

c(:,1) = c(:,1)/2;
s(:,L+1) = s(:,L+1)/2; % not sure if this is needed? Need to take a look at the equations
%c(:,L+1) = zeros(2*n,1); % this line is not needed otherwise Clamx,lamx is not computed.
s(:,1) = zeros(2*n,1);

a = f * c;
b = f * s;

%--------------------------------------------------------------------------
% 2nd step analysis: Clm & Slm
%--------------------------------------------------------------------------

% predefine weights for the weighted least squares analysis
si = sin(theta*pi/180);
si = 2*si/sum(si);

%% loop over the order of the Spherical Harmonics
for m = double(0:L)
% construct the legendre polynomials
p = Legendre_functions(m:L,m,theta);
% Select particular colum of the signal
ai = a(:,m+1);
bi = b(:,m+1);
d = 1:length(theta);
pts = p' * sparse(d,d,si);

% Estimate the coefficients
clm(m+1:L+1,m+1) = (pts * p) \ (pts * ai);
slm(m+1:L+1,m+1) = (pts * p) \ (pts * bi);
end

%--------------------------------------------------------------------------
% Write the coefficients Clm & Slm in |C\S| format
%--------------------------------------------------------------------------
slm = fliplr(slm);
%sc = [slm(:,1:L) clm];
cs = sc2cs([slm(:,1:L) clm]);
cs = cs(1:lmax+1,1:lmax+1);
9 changes: 4 additions & 5 deletions Tools/GSHS.m
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Expand Up @@ -53,9 +53,8 @@
end

% prepare coordinates
th = sort(th(:));
lam = lam(:).*pi/180;

th = double(sort(th(:)));
lam = double(lam(:).*pi/180);
% use the desired degree
if nargin < 5 || isempty(ldesired), ldesired = lmax; end
if ldesired < lmax
Expand All @@ -68,7 +67,7 @@
[row,~] = size(field);

% prepare cosine and sine --> cos(m*lam) and sin(m*lam)
m = 0:lmax;
m = double(0:lmax);
l = m';
mlam = (lam*m)';
cosmlam = cos(mlam);
Expand All @@ -81,7 +80,7 @@
%----------------------------------------------------------------------------
% CALCULATION
%----------------------------------------------------------------------------
for m = 0:row-1
for m = double(0:row-1)
if m==0
Cnm = field(:,row+m); % get column with order 0
Snm = zeros(row,1); % there are no Sn0 coefficients
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