How to use Newton-Ramphson method to find an equation root?

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zayed 2011-12-1

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/22787-how-to-use-newton-ramphson-method-to-find-an-equation-root

Hi, I want to make all of them one M-file by making the second and the third M-file as anonymous functions in the main M-file( f and df are defined as anonymous functions).

THE CURRENT MAIN CODE

        function [p0,err,k,y]=newtonlab(f,df,p0,delta,epsilon,max1)
%Input    - f is the object function 
%            - df is the derivative of f 
%            - p0 is the initial approximation to a zero of f
%           - delta is the tolerance for p0
%           - epsilon is the tolerance for the function values y
%           - max1 is the maximum number of iterations
%Output - p0 is the Newton-Raphson approximation to the zero
%           - err is the error estimate for p0
%           - k is the number of iterations
%           - y is the function value f(p0)
%If f and df are defined as M-file functions use the @ notation
% call [p0,err,k,y]=newton(@f,@df,p0,delta,epsilon,max1).
%If f and df are defined as anonymous functions use the
% call  [p0,err,k,y]=newton(f,df,p0,delta,epsilon,max1).
%  NUMERICAL METHODS: Matlab Programs
for k=1:max1  
  p1=p0-f(p0)/df(p0);  
  err=abs(p1-p0);
  relerr=2*err/(abs(p1)+delta);
  p0=p1;
  y=f(p0);
  if (err<delta)|(relerr<delta)|(abs(y)<epsilon),break,end
end
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

*SECOND M_FILE *_ITALIC TEXT_

      function y=f(x)
%%input to function
    format short e;
            Params = load('saved_data.mat');
            theta = pi/2;
            zeta = cos(theta);
            I = eye(Params.n,Params.n);
            Q = zeta*I-Params.p*Params.p';
%T is a matrix(5,5)
            Mroot = Params.M.^(1/2);  %optimization
            T = Mroot*Q*Mroot;
  %find the eigen values
            E =real( eig(T));
%find the negative eigen values -- %find the smallest negative eigen value
            gamma = min(E);  
%now solve for lambda
          M_inv = inv(Params.M);  %optimization
          zm = Params.zm;
           y= zm'*M_inv*inv(M_inv+x.*Q)*M_inv*zm;

THE THIRD M_FILE:

      function y1=df(x)
%%%%input to the equation
   Params = load('saved_data.mat');
          theta = pi/2;
          zeta = cos(theta);
          I = eye(Params.n,Params.n);
          Q = zeta*I-Params.p*Params.p';
%T is a matrix(5,5)
            Mroot = Params.M.^(1/2);  %optimization
            T = Mroot*Q*Mroot;
%find the eigen values
            E =real( eig(T));
    %find the negative eigen values -- %find the smallest negative eigen value
            gamma = min(E);  
  %now solve for lambda
             M_inv = inv(Params.M);  %optimization
            zm = Params.zm;
            y1=-zm'*M_inv*inv(M_inv+x.*Q)*Q*M_inv*zm;

1 个评论
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Walter Roberson 2011-12-1

Is this question asking something different than your previous question, http://www.mathworks.com/matlabcentral/answers/22711-newton-raphson-method ? If not then the two should be merged together and one of them deleted.

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采纳的回答

Walter Roberson 2011-12-1

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/22787-how-to-use-newton-ramphson-method-to-find-an-equation-root#answer_29980

在 MATLAB Online 中打开

λ is not a valid variable name in MATLAB. This code would never have passed m-lint. Please do basic error checking on your code before you post it.

It is fairly unlikely that a program would use both fzero() and Newton Raphson.

[EDIT: Dec 4 2011 17:42 CDT - put in explicit merged code]

function newtonlab_driver
  [p0, err, k, y] = newtonlab(@f, @df, 0, 100, 1e-8, 1000);
  fprintf(1, 'Best answer was %g at lambda = %g\n', p0, y);
        function [p0,err,k,y]=newtonlab(f,df,p0,delta,epsilon,max1)
%Input    - f is the object function 
%            - df is the derivative of f 
%            - p0 is the initial approximation to a zero of f
%           - delta is the tolerance for p0
%           - epsilon is the tolerance for the function values y
%           - max1 is the maximum number of iterations
%Output - p0 is the Newton-Raphson approximation to the zero
%           - err is the error estimate for p0
%           - k is the number of iterations
%           - y is the function value f(p0)
%If f and df are defined as M-file functions use the @ notation
% call [p0,err,k,y]=newton(@f,@df,p0,delta,epsilon,max1).
%If f and df are defined as anonymous functions use the
% call  [p0,err,k,y]=newton(f,df,p0,delta,epsilon,max1).
%  NUMERICAL METHODS: Matlab Programs
for k=1:max1  
  p1=p0-f(p0)/df(p0);  
  err=abs(p1-p0);
  relerr=2*err/(abs(p1)+delta);
  p0=p1;
  y=f(p0);
  if (err<delta)|(relerr<delta)|(abs(y)<epsilon),break,end
end
      function y=f(x)
%%input to function
    format short e;
            Params = load('saved_data.mat');
            theta = pi/2;
            zeta = cos(theta);
            I = eye(Params.n,Params.n);
            Q = zeta*I-Params.p*Params.p';
%T is a matrix(5,5)
            Mroot = Params.M.^(1/2);  %optimization
            T = Mroot*Q*Mroot;
  %find the eigen values
            E =real( eig(T));
%find the negative eigen values -- %find the smallest negative eigen value
            gamma = min(E);  
%now solve for lambda
          M_inv = inv(Params.M);  %optimization
          zm = Params.zm;
           y= zm'*M_inv*inv(M_inv+x.*Q)*M_inv*zm;
      function y1=df(x)
%%%%input to the equation
   Params = load('saved_data.mat');
          theta = pi/2;
          zeta = cos(theta);
          I = eye(Params.n,Params.n);
          Q = zeta*I-Params.p*Params.p';
%T is a matrix(5,5)
            Mroot = Params.M.^(1/2);  %optimization
            T = Mroot*Q*Mroot;
%find the eigen values
            E =real( eig(T));
    %find the negative eigen values -- %find the smallest negative eigen value
            gamma = min(E);  
  %now solve for lambda
             M_inv = inv(Params.M);  %optimization
            zm = Params.zm;
            y1=-zm'*M_inv*inv(M_inv+x.*Q)*Q*M_inv*zm;

28 个评论
显示 26更早的评论隐藏 26更早的评论

Walter Roberson 2011-12-1

In your previous threads, the version with the Q and the minus sign was what you were trying to find the zero of. Are you saying now that that expression is for the derivative, and thus before you were solving for the derivative being 0, but now you are instead solving for "the original function" being 0 ?

Your calculation of the initial value of f and df is equivalent to calculating with lambda = 0, which you had determined in your previous thread leads to a complex result. As your code has lost its lambda, it is not surprising that your f/df stays complex and thus that you are always dealing with complex.

Your code should have the lambda still in it, and the x of the Newton formula should be rewritten with a change of variable to use lambda.

Really, though, it would have been easier if you had stayed with the earlier code version that calculated all the way down to the Lz function handle, and passed that handle in to a generic Newton-Raphson routine. You would have had to construct a second function to calculate the derivative, but at least then you would not be getting so confused in your code about what x is and what xi is.

Your code really should not be adding 1 to x !

zayed 2011-12-5

So I should put 'load file and do the next step involving calculating gamma and also (I,Q,M_inv) to get rid of duplication, on the line after the first line (function newtonlab_driver) in the edited code

zayed 2011-12-6

How can I call the result of the FUNCTION (newtonlab_driver) -in the thread below-into another code.Also I need to change the intial value guess p0 to changed as gamma changed .

http://www.mathworks.com/matlabcentral/answers/22787-how-to-use-newton-ramphson-method-to-find-an-equation-root

Thanks

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