I am trying to write a MATLAB code of the Levenberg-Marquardt Algorithm based on Section III in the paper "Training Feedforward networks with the Marquardt Algorithm" by Matin.T.Hagan. So considering I have a set of training inputs and a set of Target inputs, my question is

- How do I calculate the Jacobian Matrix ? I understand that it is a matrix of the partial derivatives of the vector being calculated. But am not sure how do I actually use the Jacobian command that is in MATLAB to compute the jacobian matrix ? .

hoping somone can help me out. Thank you .

I would be very surprised if there is such a command.

The Jacobian is a matrix of partial derivatives of the

function you attempt to optimize. If you have an analytic

expression for the fucntion, compute the partial derivatives

analytically and arrange in a matrix.

If you can't find the analytic expressions for the partial

derivatives, you can come up with all kinds of numerical

estimates. But be aware that not all such estimates are

very good. In which case you might prefer to use a method

that does not require the Jacobian at all.

All this is standard material in an intro class on

numerical optimization. Find a textbook and read.

Rune

MATLAB has two potentially relevant commands. The jacobian function

in the symbolic computation toolbox computes a symbolic Jacobian. The

numjac command uses finite difference approximations to compute the

jacobian of a function at a particular point.

in the symbolic computation toolbox computes a symbolic Jacobian. The

numjac command uses finite difference approximations to compute the

jacobian of a function at a particular point.

================

jacobian() is a command in the Symbolic Math Toolbox, so first off, you have to have that. If you do have that, its usage is documented here, with an example:

http://www.mathworks.com/access/helpdesk/help/toolbox/symbolic/jacobian.html

Hello Mr.Mano Samuel,

I am also trying to write own code for Levenberg-Marquardt Algorithm for feed forward neural network, i hope you would have programmed it so can you please help me out in programming the same. i am new in using matlab so can you please help me out to program for Levenberg-Marquardt Algorithm

Thanking you

raj

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Do not start a new thread, stick to the original thread as long as you discuss the same problem. Junfeng Chen wrote: > > > Dear all, > > First of all, a special thank you to Marcelo Marazzi, who have gave > me tremendous help in the previous message. Here I would like to > further and detail the problem I encounter: > > As was described in the last letter, "When I use the function > lsqnonlin(...) provided by MATLAB to solve > the nonlinear least-squares problems, the first thing I need to do > is > to provide a problem-dependent function that will be passed to > lsqnonlin. Here, I have > > F = SUM(||mi - Mi||^2), where Mi = 1/(h3*vi')*[h1*vi', h2*vi']', > where h1, h2, h3, vi are all vectors of the same size, and both mi > and Mi are vectors with two elements. > > Although I have tried millions of times, there is still something > wrong with the expression I used to calculate F in the function." > > Source code > %//////////////////////////////////////////////////////// > % The maximum likelihood estimate function of homography > %//////////////////////////////////////////////////////// > function F = HMaxLikeFunc(H, dataFileName0, dataFileNameN) > % Initialize: extend the data points' dimension to 3D by assuming > Z=1 > > f0 = load(dataFileName0); > fn = load(dataFileNameN); > data_0 = zeros(4,3); > data_0(:,3) = 1; > data_n = zeros(4,2); > for i = 1:4, > data_0(i,1) = f0(i,1); > data_0(i,2) = f0(i,2); > data_n(i,1) = fn(i,1); > data_n(i,2) = fn(i,2); > end > k = 1:4; > F = data_n(k,:) - 1 ./ (H(3,:) * data_0(k,:)') * [H(1,:) * > data_0(k,:)', H(2,:) * data_0(k,:)']; > > %The very place I call the above function > %//////////////////////////////////////////////////////// > % Obtain the homography: dataFileName0 is the data from > % the model plane while dataFileNameN from the nth image > %//////////////////////////////////////////////////////// > function H = GetH(dataFileName0, dataFileNameN) > % Obtain the initial estimate of the homography > H0 = zeros(3,3); > H0 = GetHInit(dataFileName0, dataFileNameN); > % Calculate the homography by solving the nonlinear least squares > % with the Levenberg-Marquardt algorithm > H = zeros(3,3); > Z = []; > H = lsqnonlin(@HMaxLikeFunc, H0, Z, Z, Z, > dataFileName0,dataFileNameN); > > ///////////////////////////////////////////////////////////// > And here is the error I get: > > Error using ==> * > Inner matrix dimensions must agree. > > Error in ==> C:\MATLAB6p5\toolbox\optim\lsqnonlin.m > On line 121 ==> [x,Resnorm,FVAL,EXITFLAG,OUTPUT,LAMBDA,JACOB] = > ... > > Error in ==> D:\RESEARCH\MATLAB\TEST\getHomography.m (GetH) > On line 136 ==> H = lsqnonlin(@HMaxLikeFunc, H0, Z, Z, Z, > dataFileName0,dataFileNameN); > > Error in ==> D:\RESEARCH\MATLAB\TEST\getHomography.m > On line 4 ==> H = GetH(dataFileName0,dataFileNameN); > > ////////////////////////////////////////////////////////////// > > In the F expression, the part "1 ./ (H(3,:) * data_0(k,:)')" is > supposed to return a scalar, while it actually becomes a vector, > and > I really can't figure out what's going on here. > > > The above formula is the least-squares problem I need to solve. > Hopefully all the information presented here is adequate for you. > Thank you very much for your time and patience.