Add assumption to pinv solution

Hi all,

I want to find a solution to this equation with adding an assumption:

 A * X = d

I know the solution which is :

 X=pinv(M)* d; where X = (x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12)

But I want a solution with these assumptions :

dot([ x1 x4 x7],[ x2 x5 x8])=0
dot([ x1 x4 x7],[ x3 x6 x9])=0
dot([ x3 x6 x9],[ x2 x5 x8])=0

How can I find it using the assumeAlso(condition) function?

Any help please?

Answer 1

[Matt J]

You would use fmincon to solve the constrained minimization problem

min ||A*x-d||^2

subject to constraints 

    dot([ x1 x4 x7],[ x2 x5 x8])=0

    dot([ x1 x4 x7],[ x3 x6 x9])=0

    dot([ x3 x6 x9],[ x2 x5 x8])=0

Your constraints are nonlinear, so you would specify them as described here.

[Matt J]

Mokhtar commented

Hi, Thank you for your reply. Can you give me more detail please or example ?

Thank you, Mokhtar.

[Matt J]

The documentation for FMINCON is here and an example using nonlinear constraints is here.