I had a problem coding in MATLAB. I am trying to use the Newton Raphson iteration here. I want to find lambda_init after the first iteration and the third iteration and compare the two. Also, I want to subtract the DCM from the third iteration to the first to see the difference. I could always just copy and paste the for loop and run it for 1 iterations to compare the difference, but is there an easier way? S = B_mat + B_mat'; kappa = trace(adjoint(S)); % Characteristic Equation (Eqn. 3.73) f = @(x) (x^2 - trace(B_mat)^2 + kappa) * (x^2 - trace(B_mat)^2 - ... dot(z, z)) -(x - trace(B_mat)) * (z'Sz + det(S)) -... z'(S'S)z; % Derivative of the characteristic equation df =@(x) 2x(x^2 - trace(B_mat)^2 - dot(z , z)) + ... 2x(x^2 - trace(B_mat)^2 + kappa) + (z'Sz + det(S)) ; % Calculate the eigenvalue Newton-Raphson iteration lambda_init = 95; lambdas = zeros(4, 1); lambdas(1) = lambda_init; step = zeros(3 ,1); quat = zeros (4, 3); DCM = zeros (3, 3, 3); for i = 1:3 Xn = f(lambda_init) / df(lambda_init); lambda_init = lambda_init - Xn; % get the corresponding attitude estimates rho = lambda_init + trace(B_mat); rho_mat = rho eye (3) - S; q_unit = [adjoint(rho_mat) * z ; det(rho_mat)]; q_unit = q_unit / norm(q_unit); % store the step size and attitude estimate step(i) = Xn; lambdas(i + 1) = lambda_init; quat(:, i) = q_unit; DCM(:, :, i) = q_DCM(q_unit); end

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter5: Control Structures Ii (repetition)

Section: Chapter Questions

Problem 34SA

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I had a problem coding in MATLAB. I am trying to use the Newton Raphson iteration here. I want to find lambda_init after the first iteration and the third iteration and compare the two. Also, I want to subtract the DCM from the third iteration to the first to see the difference. I could always just copy and paste the for loop and run it for 1 iterations to compare the difference, but is there an easier way?

S = B_mat + B_mat';

kappa = trace(adjoint(S));

% Characteristic Equation (Eqn. 3.73)

f = @(x) (x^2 - trace(B_mat)^2 + kappa) * (x^2 - trace(B_mat)^2 - ...

dot(z, z)) -(x - trace(B_mat)) * (z'*S*z + det(S)) -...

z'*(S'*S)*z;

% Derivative of the characteristic equation

df =@(x) 2*x*(x^2 - trace(B_mat)^2 - dot(z , z)) + ...

2*x*(x^2 - trace(B_mat)^2 + kappa) + (z'*S*z + det(S)) ;

% Calculate the eigenvalue Newton-Raphson iteration

lambda_init = 95;

lambdas = zeros(4, 1);

lambdas(1) = lambda_init;

step = zeros(3 ,1);

quat = zeros (4, 3);

DCM = zeros (3, 3, 3);

for i = 1:3

Xn = f(lambda_init) / df(lambda_init);

lambda_init = lambda_init - Xn;

% get the corresponding attitude estimates

rho = lambda_init + trace(B_mat);

rho_mat = rho * eye (3) - S;

q_unit = [adjoint(rho_mat) * z ; det(rho_mat)];

q_unit = q_unit / norm(q_unit);

% store the step size and attitude estimate

step(i) = Xn;

lambdas(i + 1) = lambda_init;

quat(:, i) = q_unit;

DCM(:, :, i) = q_DCM(q_unit);

end

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