matlab中cape,Lorentz matlab实现

【实例简介】

该项目包含使用Lorentz＆Rossler技术调整图像大小的matlab脚本。

【实例截图】

【核心代码】

function [x,y,z]=lorentz(n,level,s,r,b,x0,y0,z0,h)

%Syntax: [x,y,z]=lorentz(n,level,s,r,b,x0,y0,z0,h)

%_________________________________________________

%

% Simulation of the Lorentz ODE.

%    dx/dt=s*(y-x)

%    dy/dt=r*x-y-xz

%    dz/dt=x*y-b*z;

%

% x, y, and z are the simulated time series.

% n is the number of the simulated points.

% level is the noise standard deviation divided by the standard deviation of the

%   noise-free time series. We assume Gaussian noise with zero mean.

% s, r, b, and s are the parameters

% x0 is the initial value for x.

% y0 is the initial value for y.

% z0 is the initial value for z.

% h is the step size.

%

%

% Notes:

% The time is n*h.

% The integration is obtained by the Euler's method.

%

%

% Reference:

%

% Lorentz E N (1963): Deterministic nonperiodic flow. Journal of the

% Atmosphairic Sciences 20: 130-141

%

%

% Alexandros Leontitsis

% Department of Education

% University of Ioannina

% 45110 - Dourouti

% Ioannina

% Greece

%

% University e-mail: me00743@cc.uoi.gr

% Lifetime e-mail: leoaleq@yahoo.com

% Homepage: http://www.geocities.com/CapeCanaveral/Lab/1421

%

% 16 Nov 2001

if nargin<1 | isempty(n)==1

n=500;

else

% n must be scalar

if sum(size(n))>2

error('n must be scalar.');

end

% n must be positive

if n<0

error('n must be positive.');

end

% n must be an integer

if round(n)-n~=0

error('n must be an integer.');

end

end

if nargin<2 | isempty(level)==1

level=0;

else

% level must be scalar

if sum(size(level))>2

error('level must be scalar.');

end

% level must be positive

if level<0

error('level must be positive.');

end

end

if nargin<3 | isempty(s)==1

s=16;

else

% s must be scalar

if sum(size(s))>2

error('s must be scalar.');

end

end

if nargin<4 | isempty(r)==1

r=45.92;

else

% r must be scalar

if sum(size(r))>2

error('r must be scalar.');

end

end

if nargin<5 | isempty(b)==1

b=4;

else

% b must be scalar

if sum(size(b))>2

error('b must be scalar.');

end

end

if nargin<6 | isempty(x0)==1

x0=0.1;

else

% x0 must be scalar

if sum(size(x0))>2

error('x0 must be scalar.');

end

end

if nargin<7 | isempty(y0)==1

y0=0.1;

else

% y0 must be scalar

if max(size(y0))>2

error('y0 must be scalar.');

end

end

if nargin<8 | isempty(z0)==1

z0=0.1;

else

% z0 must be scalar

if max(size(z0))>2

error('z0 must be scalar.');

end

end

if nargin<9 | isempty(h)==1

h=0.01;

else

% h must be scalar

if max(size(h))>2

error('h must be scalar.');

end

% h must be positive

if h<0

error('h must be positive.');

end

end

% Initialize

y(1,:)=[x0 y0 z0];

% Simulate

for i=2:n

ydot(1)=s*(y(i-1,2)-y(i-1,1));

ydot(2)=r*y(i-1,1)-y(i-1,2)-y(i-1,1)*y(i-1,3);

ydot(3)=y(i-1,1)*y(i-1,2)-b*y(i-1,3);

y(i,:)=y(i-1,:) h*ydot;

end

% Separate the solutions

x=y(:,1);

z=y(:,3);

y=y(:,2);

% Add normal white noise

x=x randn(n,1)*level*std(x);

y=y randn(n,1)*level*std(y);

z=z randn(n,1)*level*std(z);