Unable to get correct 2θ value from tan2θ = (2*a12)/(a11-a22) by writing as p= A(1,1) - A(2,2) q= 2 * A(1,2) theta = atan (p/q).Please help

Unable to get correct 2θ value from tan2θ = (2*a12)/(a11-a22) by writing as

p= A(1,1) - A(2,2)

q= 2 * A(1,2)

theta = atan (p/q) for a (2 x 2) matrix.My code and output are

INPUT >>>>>

% Write down Matrix elements in [A(1,1)	A(1,2);A(2,1) A(2,2)] format
Matrix = 'Write down Matrix elements.'
A = input(Matrix)
if ne(A(1,2),A(2,1))
    disp('This is a asymmetric matrix')
else
    disp('1.This is a symmetric matrix')
% Write down Matrix elements in [A(1,1),A(1,2);A(2,1),A(2,2)] format
     p= A(1,1) - A(2,2)
	 q= 2 * A(1,2)
	 theta = atan (p/q)
end

OUTPUT >>>>>

Matrix =

    'Write down Matrix elements.'

Write down Matrix elements.
[1 2;2 4]

A =

     1     2
     2     4

1.This is a symmetric matrix

p =  -3
q =  4
theta =  -0.6435 

while correct value from calculator is -0.9272 rad.

Please help me.

Answer 1

[Geoff Hayes]

Amar - I think that you should have q/p instead so that

theta = atan (q / p)

and theta will be -0.9272. Not sure if you still need to divide that result by two since you really have

2*theta = atan(q / p)

[Amar Kumar]

A lots of thanks sir.I have got right answer.

one more question.when i am trying to write 2*theta by simple expression like 2*theta = atan (2 * A(1,2)/A(1,1) - A(2,2))

i have got as input and output ----

% Write down Matrix elements in [A(1,1) A(1,2);A(2,1) A(2,2)] format

Matrix = 'Write down Matrix elements.'

A = input(Matrix)

if ne(A(1,2),A(2,1))

disp('This is a asymmetric matrix')

else

disp('1.This is a symmetric matrix')

% Write down Matrix elements in [A(1,1),A(1,2);A(2,1),A(2,2)] format

theta = atan (2 * A(1,2)/A(1,1) - A(2,2))

end

Matrix =

'Write down Matrix elements.'

Write down Matrix elements.

[1 2 ; 2 4]

A =

1 2

2 4

1.This is a symmetric matrix

theta =

0

[Geoff Hayes]

Amar - I think that you are missing some brackets around the denominator

theta = (atan (2 * A(1,2)/(A(1,1) - A(2,2)))) / 2.0;