lab2 вроде / func_Brownian_field

function [field1,field2,tx,ty] = func_Brownian_field(H,n)
%% simulate Fractional Brownian field on unit disk, with Hurst parameter 'H';
% Note that the covariance function is isotropic, see reference below.
% INPUTS:
% - 'H' is the Hurst parameter of the Gaussian process
% - 'n' is the number of grid points, where 'n' is a power of 2;
% if the 'n' supplied is not a power of two,
% then we set n=2^ceil(log2(n)); default is n=2^8;
% OUTPUT:
% - two statistically independent fields 'field1' and 'field2'
% over unit disk; if not output requested, then function
% outputs a figure of one of the fields
% - vectors 'tx' and 'ty' so that the field is plotted via
% surf(tx,ty,field1,'EdgeColor','none')
if (H>1)|(H<0) % Hurst parameter error check
error('Hurst parameter must be between 0 and 1')
end
if nargin<2
n = 2^8; % default value of points
else
n = 2^ceil(log2(n));
end
R = 2; % [0,R]^2 grid, may have to extract only [0,R/2]^2
m = n; % size of grid is m*n; covariance matrix is m^2*n^2
tx = [1:n]/n*R; ty=[1:m]/m*R; % create grid for field
Rows = zeros(m,n);
for i = 1:n
for j = 1:m % rows of blocks of cov matrix
Rows(j,i)=rho([tx(i),ty(j)],[tx(1),ty(1)],R,2*H);
end
end
BlkCirc_row = [Rows, Rows(:,end-1:-1:2);
Rows(end-1:-1:2,:), Rows(end-1:-1:2,end-1:-1:2)];
% compute eigen-values
lam = real(fft2(BlkCirc_row))/(4*(m-1)*(n-1));
lam = sqrt(lam);
% generate field with covariance given by block circular matrix
Z = complex(randn(2*(m-1),2*(n-1)),randn(2*(m-1),2*(n-1)));
F = fft2(lam.*Z);
F = F(1:m,1:n); % extract sub-block with desired covariance
[out,c0,c2] = rho([0,0],[0,0],R,2*H);
field1 = real(F); field2 = imag(F); % two independent fields
field1 = field1-field1(1,1); % set field zero at origin
field2 = field2-field2(1,1); % set field zero at origin
% make correction for embedding with a term c2*r^2
field1 = field1 + kron(ty'*randn,tx*randn)*sqrt(2*c2);
field2 = field2 + kron(ty'*randn,tx*randn)*sqrt(2*c2);
[X,Y] = meshgrid(tx,ty);
field1((X.^2+Y.^2)>1) = nan; field2((X.^2+Y.^2)>1)=nan;
field1=field1(1:n/2,1:m/2); field2=field2(1:n/2,1:m/2);
tx=tx(1:n/2);ty=ty(1:m/2);
if nargout==0
surf(tx,ty,field1,'EdgeColor','none')
title('Fractional Gaussian Field on Unit Disk')
colormap bone
end
end