adding files

adding files

bisect.m

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+function [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,varargin)
+% bisect: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses bisection method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4||isempty(es), es=0.0001;end
+if nargin<5||isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  xr = (xl + xu)/2;
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es || iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:});

falsepos.m

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+function [root,fx,ea,iter]=falsepos(func,xl,xu,es,maxit,varargin)
+% bisect: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses bisection method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4|isempty(es), es=0.0001;end
+if nargin<5|isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  xr = (xl + xu)/2;
+  % xr = (xl + xu)/2; % bisect method
+  xr=xu - (f_m(xu)*(xl-xu))/(f_m(xl)-f_m(xu)); % false position method
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es | iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:});

goldmin.m

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+function [x,fx,ea,iter]=goldmin(f,xl,xu,es,maxit,varargin)
+% goldmin: minimization golden section search
+%   [x,fx,ea,iter]=goldmin(f,xl,xu,es,maxit,p1,p2,...):
+%     uses golden section search to find the minimum of f
+% input:
+%   f = name of function
+%   xl, xu = lower and upper guesses
+%   es = desired relative error (default = 0.0001%)
+%   maxit = maximum allowable iterations (default = 50)
+%   p1,p2,... = additional parameters used by f
+% output:
+%   x = location of minimum
+%   fx = minimum function value
+%   ea = approximate relative error (%)
+%   iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+if nargin<4|isempty(es), es=0.0001;end
+if nargin<5|isempty(maxit), maxit=50;end
+phi=(1+sqrt(5))/2;
+iter=0;
+while(1)
+  d = (phi-1)*(xu - xl);
+  x1 = xl + d;
+  x2 = xu - d;
+  if f(x1,varargin{:}) < f(x2,varargin{:})
+    xopt = x1;
+    xl = x2;
+  else
+    xopt = x2;
+    xu = x1;
+  end
+  iter=iter+1;
+  if xopt~=0, ea = (2 - phi) * abs((xu - xl) / xopt) * 100;end
+  if ea <= es | iter >= maxit,break,end
+end
+x=xopt;fx=f(xopt,varargin{:});

mod_secant.m

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+function [root,ea,iter]=mod_secant(func,dx,xr,es,maxit,varargin)
+% newtraph: Modified secant root location zeroes
+% [root,ea,iter]=mod_secant(func,dfunc,xr,es,maxit,p1,p2,...):
+%   uses modified secant method to find the root of func
+% input:
+%   func = name of function
+%   dx = perturbation fraction
+%   xr = initial guess
+%   es = desired relative error (default = 0.0001%)
+%   maxit = maximum allowable iterations (default = 50)
+%   p1,p2,... = additional parameters used by function
+% output:
+%   root = real root
+%   ea = approximate relative error (%)
+%   iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+if nargin<4 || isempty(es),es=0.0001;end
+if nargin<5 || isempty(maxit),maxit=50;end
+iter = 0;
+while (1)
+  xrold = xr;
+  dfunc=(func(xr+dx)-func(xr))./dx;
+  xr = xr - func(xr)/dfunc;
+  iter = iter + 1;
+  if xr ~= 0 
+    ea = abs((xr - xrold)/xr) * 100;
+  end
+  if ea <= es || iter >= maxit, break, end
+end
+root = xr;