I get complex numbers while using "acosd" function

Hello everyone,

I would get complexe number when I use acosd function to caclulate cosine inverse of a value, which I am pressty sure is in the range of [-1,1]. Look at the example below. Can anyone let me know where the problem is?

GRD_u=[-0.6372,1.7170];
A_s_uniqe=[0.3479,-0.9375];
y=acosd(dot(GRD_u,A_s_uniqe)/sqrt(sum(GRD_u.^2))/sqrt(sum(A_s_uniqe.^2)))

Answer 1

[VBBV]

Probably you might have evaluated the equation using incorrect parenthesis enclosing only the dot product for acosd function and dividing the rest of terms in sqrt function as shown below

GRD_u=[-0.6372,1.7170];
A_s_uniqe=[0.3479,-0.9375];
% the dot product is out of range [-1 1] 
dot(GRD_u,A_s_uniqe)

ans = -1.8314

% you might have used incorrect parenthesis while evaluating equation
%------------------------->>>
y=acosd(dot(GRD_u,A_s_uniqe))/sqrt(sum(GRD_u.^2))/sqrt(sum(A_s_uniqe.^2))

y = 98.2871 -37.9687i

y=acosd(dot(GRD_u,A_s_uniqe)/sqrt(sum(GRD_u.^2))/sqrt(sum(A_s_uniqe.^2)))

y = 179.9990

Otherwise, it seems to return real value

Answer 2

[Mrinal Anand]

You are getting a complex number because the acosd() function is only defined for values in the range of [-1, 1]. If the function argument is outside this range, it will return a complex number.

In your code, the argument passed to acosd() is calculated as the dot product of GRD_u and A_s_uniqe divided by the product of their magnitudes. If the magnitude of either GRD_u or A_s_uniqe is less than the dot product of the two vectors, then the argument passed to acosd() will be greater than 1, which is outside the defined range.

[VBBV]

@Mrinal Anand, The magnitude of both GRD_u or A_s_uniqe vectors are not less than dot product but its the usage of incorrect parenthesis in equation that would result in complex valued number

GRD_u=[-0.6372,1.7170];
A_s_uniqe=[0.3479,-0.9375];

% dot product 
dot(GRD_u,A_s_uniqe)

ans = -1.8314

% Magnitude if both vectors 
Mag1 = sqrt(GRD_u(1)^2 + GRD_u(2)^2)

Mag1 = 1.8314

Mag2 = sqrt(A_s_uniqe(1)^2 + A_s_uniqe(2)^2)

Mag2 = 1.0000

Answer 3

[dpb]

GRD_u=[-0.6372,1.7170];
A_s_uniqe=[0.3479,-0.9375];
y=acosd(dot(GRD_u,A_s_uniqe)/sqrt(sum(GRD_u.^2))/sqrt(sum(A_s_uniqe.^2)))

y = 179.9990

format longE
arg=dot(GRD_u,A_s_uniqe)/sqrt(sum(GRD_u.^2))/sqrt(sum(A_s_uniqe.^2))

arg = 
    -9.999999998594938e-01

The particular set of values does't cause the problem, but argument is pretty close to -1; it's possible rounding error in floating point numbers could cause a calculation to be just on the other side for a given case.

I'm also guessing that the numbers above are rounded manual inputs from a set of calculations and that for the actual computed values, the above issue occurred -- but the lack of precision with only four decimal places changes the results.

Would have to post the exact values/code that created the problem, but I'll bet if you put the calc in a try...catch block and verify the actual value when it errors or assert() that the abs(value) is <=1 before the call you'll find it's close, but on the wrong side of the tracks.

[dpb]

The solution will be to use acosd(sign(x)*min(abs(x),1)) in order to bound the calculation to be within [-1,1].

You probably also want to wrap that inside a test to confirm that it is only a rounding isse and not that the code has gone completely off the rails so that you're not just silently passing through nonsensical results.