Index Position 1 is invalid. Newton's method program

When I run the following code, I keep getting errors of either Index Position 1 is invalid or out of range subscript depending on my values for x0. Not sure what to do.

x0=[1,1,1,1,1,1,1,1,1]';   %enter estimates

I defined 9 functions (f1-f9)

J=sym(zeros(9));
for j=1:length(vars)    %create Jacobian matrix
    J(1,j)=diff(f1,vars(j));
    J(2,j)=diff(f2,vars(j));
    J(....
end
x=[x0];
for i=1:10
    x(:,i+1)=x(:,i)-inv(J(x(1,i),x(2,i),x(3,i),x(4,i),x(5,i),x(6,i),x(7,i),x(8,i),x(9,i)))*f(x(1,i),x(2,i),x(3,i),x(4,i),x(5,i),x(6,i),x(7,i),x(8,i),x(9,i))';    %solve for x
end

Answer 1

[Walter Roberson]

You are invoking J as if it is a function with 9 inputs. But it is not a function: it is a 9 x 9 array of symbolic expressions.

You should create

F = [f1, f2, f3, f4, f5, f6, f7, f8, f9];
Jmat = jacobian(F, vars);
J = matlabFunction(Jmat, 'vars', {vars});

x(:,i) - J(x(:,i))\f(x(1,i),x(2,i),x(3,i),x(4,i),x(5,i),x(6,i),x(7,i),x(8,i),x(9,i))

and easier yet would be if you used matlabFunction() to turn f (whatever it is) into an anonymous function that accepted a vector of inputs.

What is the relationship between f and your f1, f2, and so on?

[Hunter Crittenden]

Hi Walter,

So the f1-f9 are symbolic functions that represent a system of equations I'm attempting to solve. f is the entire system of equations put together (this code is trying to execute Newton's method to solve them). When I turn J into a function like you said, I'm getting this error:

Index in position 2 exceeds array bounds (must not exceed 1).

Error in

symengine>@(in1)reshape([0.0,0.0,0.0,-1.0,1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,0.0,1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,-1.0,0.0,1.0,4.0e-2,0.0,0.0,in1(:,4).*-1.0e+5,0.0,0.0,0.0,0.0,0.0,-1.0e-2,1.0e-2,0.0,0.0,in1(:,5).*-1.0e+5,0.0,0.0,0.0,0.0,-1.0e-2,0.0,1.0e-2,0.0,0.0,in1(:,6).*-1.0e+5,0.0,0.0,0.0,0.0,-4.0e-2,4.0e-2,0.0,0.0,0.0,in1(:,7).*-5.0e+4,0.0,0.0,0.0,-1.0e-2,0.0,0.0,0.0,0.0,0.0,in1(:,8).*-1.0e+5,0.0,0.0,0.0,-1.0e-2,0.0,0.0,0.0,0.0,0.0,in1(:,9).*-1.0e+5],[9,9])

Error in CompHW5 (line 44)

x(:,i+1)=x(:,i)-inv(J(x(:,i)))*f(x(:,i))'; %solve for x

[Walter Roberson]

Jmat = jacobian(f, vars);
J = matlabFunction(Jmat, 'vars', {vars.'});

x(:,i) - J(x(:,i))\f(x(1,i),x(2,i),x(3,i),x(4,i),x(5,i),x(6,i),x(7,i),x(8,i),x(9,i))

[Hunter Crittenden]

That worked! Thank you so much!