How can I apply the attached vector coding equation to a matrix in matlab?

I currently am using atan2d(y,x) but I am unsure whether that is accounting for the y(i+1)-y(i) and x(i+1)-x(i) nature of the equation. x and y are defined as the two matrices I am comparing (i.e. knee versus ankle joint angles during a gait cycle).

Answer 1

[Star Strider]

It won’t account for it unless you tell it to:

Theta_vc = atan2d(diff(theta1), diff(theta2));

NOTE — This should work with your data.

[Kylie Davis]

I will try this and return to this post if I still have trouble. I appreciate your feedback thank you!

[Star Strider]

My pleasure!

My code will operate column-wise on your 2D matrices, so no loops are necessary:

theta1 = randi(9, 4, 5);
theta2 = randi(9, 4, 5);
Theta_vc = atan2d(diff(theta1), diff(theta2));

Note that because of the diff function, ‘Theta_vc’ will have one less row than ‘theta1’ and ‘theta2’.

[Kylie Davis]

Ok now I have another question because I think I made a mistake. I believe x and y are each 1D vectors, and I need to take the average across the row and not column if that makes sense. Right now I have z = atan2d(diff(y),diff(x)) but I'm not sure it's giving me what I want.

[Kylie Davis]

To be more specific... X is the ankle angle over a gait cycle, and y is the knee angle over a gait cycle. The vector coding phase angle I want is equal to tan-1(y(i+1)-y(i),x(i+1)-x(i)) for each consecutive data point (which is 101 points because data was normalized to 100% gait cycle).

[Star Strider]

My code:

Theta_vc = atan2d(diff(theta1), diff(theta2));

does exactly what the expression in your image does. See the documentation on the diff function for details.

If you just have vectors, they will work with my code whether they’re row or column vectors. I don’t understand your gait cycle coding (an area peripheral to my areas of expertise). I would use atan2 or atan2d because they reflect the correct quadrants.

If you want to convert the angles you get as Theta_vc to 0°-360° or 0-2*pi, use the appropriate one of these functions:

Angles360 = @(a) rem(360+a, 360);                        % For ‘atan2d’
Angles2pi = @(a) rem(2*pi+a, 2*pi);                      % For ‘atan2’

Answer 2

[James Tursa]

atan2d(y,x) will not do any difference calculations such as y(i+1)-y(i) or x(i+1)-x(i) as part of the calculation. So you would need to do that calculation before using atan2d (e.g. using the diff function). Are x and y 1D vectors or 2D matrices?

[Kylie Davis]

I believe it is 2D matrices. I am new to Matlab and am sorry if I'm asking a basic question. I appreciate your feedback thank you!