Use of 3D array. Find inverse of individual page

My program contains a 3x3x100 matrix. I need to find A=J\B where J is each page of the 3x3x100 matrix ( i.e. 100 numbers of 3x3 matrix) and B is a 3x1 matrix. Which would result in matrix A to be of dimension 3x100

How do i solve this. One of the ways might be to generate a loop 100 times. But i was looking for more efficient way. May by using the matrix directly. Please help.

I have attached the codes incase it helps.

    function[J]=Jacobian(t1,t2,t3)
global l1 l2 l3;
%t1 t2 and t3 would be 1x100 matrices each.
J{1,1}=-(l1+l2.*cos(t2)+l3.*cos(t2+t3)).*sin(t1);
J{1,2}=-(l2.*sin(t2)+l3.*sin(t2+t3)).*cos(t1);
J{1,3}=-l3.*sin(t2+t3).*cos(t1);
J{2,1}=(l1+l2.*cos(t2)+l3.*cos(t2+t3)).*cos(t1);
J{2,2}=-(l2.*sin(t2)+l3.*sin(t2+t3)).*sin(t1);
J{2,3}=-l3.*sin(t2+t3).*sin(t1);
J{3,1}=0;
J{3,2}=l2.*cos(t2)+l3.*cos(t2+t3);
J{3,3}=l3.*cos(t2+t3);

function[]=Support(A,B)
%.....
J=Jacobian(M1(1,:),M1(2,:),M1(3,:))
vx=(B(1)-A(1))/2.5
vy=0;
vz=0;
V=[vx;vy;vz];
Td=J\V

This is the error i get

??? Undefined function or method 'mldivide' for input arguments of type 'cell'.

Error in ==> Support at 11 Td=J\V

Answer 1

[Andrei Bobrov]

function J =Jacobian1(t)
    global l1 l2 l3;
    j1 = [-(l1+l2.*cos(t(2,:))+l3.*cos(t(2,:)+t(3,:))).*sin(t(1,:));
    -(l2.*sin(t(2,:))+l3.*sin(t(2,:)+t(3,:))).*cos(t(1,:));
    -l3.*sin(t(2,:)+t(3,:)).*cos(t(1,:));
    (l1+l2.*cos(t(2,:))+l3.*cos(t(2,:)+t(3,:))).*cos(t(1,:));
    -(l2.*sin(t(2,:))+l3.*sin(t(2,:)+t(3,:))).*sin(t(1,:));
    -l3.*sin(t(2,:)+t(3,:)).*sin(t(1,:));
    zeros(1,size(t,2));
    l2.*cos(t(2,:))+l3.*cos(t(2,:)+t(3,:));
    l3.*cos(t(2,:)+t(3,:))];
    J = permute(reshape(j1,3,3,[]),[2 1 3]);
end

J=Jacobian1(M1);
vx=(B(1)-A(1))/2.5;
vy=0;
vz=0;
V=[vx;vy;vz];
Td=cell2mat(arrayfun(@(jj)J(:,:,jj)\V,1:size(J,3),'un',0));

[Andrei Bobrov]

small corrected in row: J = permute ...

[Saurav Agarwal]

Sir Andrei,

Could you please explain the last line Td=cell2mat(arrayfun.....

the code is working fine but i couldnt understand the last line well although i went through my handbook. Please Help.

Thank you

Answer 2

[James Tursa]

See this small size linear solver by Bruno Luong:

http://www.mathworks.com/matlabcentral/fileexchange/27762-small-size-linear-solver

and you might be interested in this one as well:

http://www.mathworks.com/matlabcentral/fileexchange/24260-multiple-same-size-linear-solver