Levenberg–Marquardt algorithm with fixing the last row of solution

Hi all, I am using Levenberg–Marquardt algorithm to do an optimization(I use lsqnonlin function). In fact I want to get a solution that I fix its last row. In fact my solution has this following forme :

    X=[ x11 x12 x13 x14 ;
    x21 x22 x23 x24 ;
    x31 x32 x33 x34 ;
    0    0   0   1  ]

So I want to get a solution using Levenberg–Marquardt with fixing its last row to [0 0 0 1] Any help please ?

Answer 1

[Walter Roberson]

g = @(x) YourFunction( reshape([reshape(x, 3, 4); 0 0 0 1], [], 1) )

then optimize g

[Matt J]

Accepted.

Although, I think the 2nd reshape must be omitted if YourFunction() expects matrix input.

[Walter Roberson]

YourFunction should not expect matrix input:

http://www.mathworks.com/help/optim/ug/lsqnonlin.html#inputarg_fun

"fun is a function that accepts a vector x and returns a vector F, the objective functions evaluated at x"

"If the user-defined values for x and F are matrices, they are converted to a vector using linear indexing."

[Matt J]

I think that's a mis-phrasing. In the following example, the objective expects matrix input and it works just fine

>> X=lsqnonlin(  @(X) X-eye(3)  ,  2*eye(3))

This is also consistent with the more general link on Matrix Inputs, which says

When x0 is a matrix, solvers pass x as a matrix of the same size as x0 to both the objective function and to any nonlinear constraint function.

Answer 2

[Mokhtar Bouain]

Hi Walter, Thank you for your reply. Can you explain more your solution? why two functions reshape?

[Walter Roberson]

lsqnonlin passes in a vector. You need to make that vector into 3 x 4 so that you can paste on a bottom row. Then you make it a column vector again. The new output would look like

 old(1,1)
 old(2,1)
 old(3,1)
 new 0
 old(1,2)
 old(2,2)
 old(3,2)
 new 0

and so on, so it is not a simple manner of appending some values on to the end of it. The double reshape is the easiest way to inject the values in the places they are needed.