Alter magnitude of vector - matlab

Question

I'm trying to extend or subtract a magnitude from vectors in an array. The code to call the function is:
v_set = {[1;0],[0;2],[1;1]};
v_extensions = [1,-.5,1];
v_set_extended = vector_set_extend(v_set, v_extensions);
And the function itself is below. What I have adds the magnitude to both x and y, but I want it to add the magnitude in the direction of that the vector is pointing, if that makes sense.
function v_set_extended = vector_set_extend(v_set,v_extensions)
% Takes a set of vectors and a set of lengths by which to extend them.
% Returns a set of extended vectors
%
% Inputs:
%
% v_set: a cell array, each element of which is a vector
%
% v_extensions: a vector of the same dimensions as v_set, containing
% lengths which should be added to the vectors
%
% Outputs:
%
% v_set_extended: cell array of the same size as v_set, each element of
% which is the vector with its new length
%%%%%%%%
% Use the 'cell' and 'size' commands to create the output
% v_set_extended as an empty cell of the same size as v_set
v_set_extended = cell(size(v_set))
%%%%%%%%
% Loop over the vectors and extensions, adding the extension to the
% length of the vector, and then storing the result in the
% corresponding entry of v_set_extended
for idx = 1:numel(v_set_extended)
v_set_extended{idx} = v_set{idx}+v_extensions(idx);
end
end

Answer 1

This is mostly a trigonometry problem. You have your vector, let's call it v, with components v_x, v_y. Let's say now that you want to add w to the magnitude of your vector.
The magnitude of v is sqrt(v_x^2 + v_y^2), and its angle is theta = tan(v_y/v_x).
What you want to do is then create a new vector of magnitude m = sqrt(v_x^2 + v_y^2) + w but with the same direction. Once you know the new magnitude, the angle is the same and the new components of the vector are v1_x = m*cos(theta) and v1_y = m*sin(theta).
You shouldn't have any problem implementing this, just pay attention to the difference between sin/sind in Matlab.

Answer 2

The solution is rather simple but it is more complex since you are using cell array. Please avoid cell array and prefer normal array as much as possible. So first we convert v_set into a matrix:
v_mat = cell2mat(v_set)
Then you want to extend the vector so that the magnitude of the new vector is extended by some value. Compute first the magnitude of the vectors:
mag_v_mat = vecnorm(v_mat);
And finally make new vectors all at once:
v_extended = v_mat.*(mag_v_mat+v_extensions)./mag_v_mat;
Dotted operators are here to vectorize the operations along the vectors.
In one-line, it may be written as:
v_extended = cell2mat(v_set).*(1+v_extensions./vecnorm(cell2mat(v_set)));

Answer 3

Please refer to the comments for explanation, and easy way to stick to your current structure is to just compute a unit vector and scale it, rather than directly adding the extension...
for idx = 1:numel(v_set_extended)
% Compute the unit vector (magnitude 1) in the same direction
uvec = v_set{idx} / vecnorm(v_set{idx});
% Create a vector of the extension length in the unit direction
ext = uvec * v_extensions(idx);
% Add the extension
v_set_extended{idx} = v_set{idx} + ext;
end
You can sanity check this by validating the vecnorm (magnitude) values
cellfun( #vecnorm, v_set ) % = [1, 2.0, 1.4142]
cellfun( #vecnorm, v_set_extended ) % = [2, 1.5, 2.4142]
% difference = [1,-0.5, 1]