I'm trying to figure out what rows 3 and 4 of the e matrix in the MATLAB pdetool represent.
According to the documentation:
e(3,k) is the parameter value at the first point of edge k. The
parameter value is related to the arc length along the geometric
edge.
e(4,k) is the parameter value at the second point of edge k.
Even with the definition, I can't understand it.
Related
I am trying to solve some equations on Matlab using Binary Integer Programming.
I have 3 sets of equations:
Ma.X=1
Mp.X<=1
Mr.X<=m*
Where, Ma is a known matrix with size 5*12
X is unknown set with size 12*1
Also Mp is known matrix with size 5*12
and Mr is a known matrix with size 4*12.
1 in the equations is an unity matrix with size 5*1 in both sets(1&2)
m* is a given known matrix with size 4*1
I'm trying to use command bintprog but how to put 1 equality and 2 inequalities
to get values of X. Also I don't have Function f to insert, I just have set of equations. Given that X unknown values with values 1 or 0.
I tried this command bintprog([],Ma,One51,Mp,One51)
but it gives me The problem is infeasible. with zeros answer matrix.
Please help me to solve this on Matlab
The correct syntax for bintprog is X = bintprog(f,A,b,Aeq,beq).
If you don't have f (which means you just want any feasible point), you can set it to []. However, for the others, your syntax is slightly wrong.
I am assuming that the + in your constraints is actually a * since otherwise, the matrix algebra doesn't quite make sense.
Try this:
X = bintprog([],[Mp;Mr],[ones(5,1);mstar],Ma,ones(5,1))
If even then it tells you that the problem is infeasible; it might as well be true that there are no Xs that can satisfy all your constraints.
I am using SIMULINK and I needed to define a Rotation Matrix 3,3,N where N is the number of Robots which I am trying to simulate. To do that, because I am also using the Simulink Coder I had to define the signal related to this matrix as Variable Size and I had to define the upper-bound in the following way:
The problem is that when I want to use only one robot (I set n_robots to 1) I get the following error.
Cannot initialize dimensions of 'R' of 'test_pos_ctrl_target/rotation matrix to Euler angles' to [3x3x1]. When the number of dimensions of a matrix exceeds 2, the size of the trailing dimension must be greater than 1.
Someone could help me?
thanks a lot.
You can't have the last dimension as 1 because MATLAB treats any matrix of dimension [m,n,1] as [m,n]. See size() returns 1 where matrix dimension should not exist for more details.
Try defining R of size [n_robots,3,3] and then re-arrange the matrix inside your code (I assume you are using a MATLAB Function block).
Okay, so I'm working on a problem related to quantum chaos and one of the things I need to do is to map the unit cube in n-dimensions to a parallelepiped in n-dimensions and find all integer points in the interior of this parallelepiped. I have been trying to do this using the following scheme:
Given the linear map B and the dimension of the cube n, we find the coordinates of the corners of the unit hypercube by converting numbers j from 0 to (2^n -1) into their binary representation and turning them into vectors that describe the vertices of the cube.
The next step was to apply the map B to each of these vectors, which gives me a set of 2^n vectors describing the coordinates of the vertices of the parallelepiped in n dimensions
Now, we take the maximum and minimum value attained by any of these vertices in each coordinate direction, i.e the first element of my vectors might have a maximum value of 4 across all of the vertices and a minimum value of -3 etc. This gives me an n-dimensional rectangular prism that contains my parallelepiped and some extra unwanted space.
I now find all points with integer coordinates in this bounding rectangular prism described as vectors in n dimensions
Finally, I apply the inverse of the map B to each of the points and throw away any points that have any coefficients greater than 1 as they must originally have lain outside my unit hypercube.
My issue arises in step 4, I'm struggling to come up with a way of generating all vectors with integer coordinates in my rectangular hyper-prism such that I can change the number of dimensions n on the fly. Ideally, i'd like to be able to increase n at will until it becomes too computationally heavy to do so, but every method of finding all integer points in the prism i've tried so far has relied on n for loops to permute each element and thus I need to rewrite the code every time.
So I guess my question is this, is there any way to code this up so that I can change n on the fly? Also, any thoughts on the idea of the algorithm itself would be appreciated :) It wouldn't surprise me if i've overcomplicated things massively...
EDIT:
Of course as soon as I post the question I see a lovely little link in the side-bar where a clever method has been given already for how to do this: Generate a matrix containing all combinations of elements taken from n vectors
I'll leave this up for the moment just in case anyone has any comments on the method in general, but otherwise (since I can't upvote yet I'll just say it here) Luis Mendo, you are a hero!
The commands
a = magic(3);
b = pascal(3);
c = cat(4,a,b);
produce a 3-by-3-by-1-by-2 array.
Why is the result 3-3-1-2 when the dimension is 4?
Both a and b are two-dimensional matrices of size 3-by-3. When you concatenate them along a fourth dimension, the intervening third dimension is singleton (i.e. 1). So c(:,:,1,1) will be your matrix a and c(:,:,1,2) will be your matrix b.
Here's a link to some documentation that may help with understanding multidimensional arrays.
EDIT:
Perhaps it will help to think of these four dimensions in terms that us humans can more easily relate to...
Let's assume that the four dimensions in the example represent three dimensions in space (x, y, and z) plus a fourth dimension time. Imagine that I'm sampling the temperature in the air at a number of points in space at one given time. I can sample the air temperature in a grid that comprises all combinations of three x positions, three y positions, and one z position. That will give me a 3-by-3-by-1 grid. Normally, we'd probably just say that the data is in a 3-by-3 grid, ignoring the trailing singleton dimension.
However, let's say that I now take another set of samples at these points at a later time. I therefore get another 3-by-3-by-1 grid at a second time point. If I concatenate these sets of data together along the time dimension I get a 3-by-3-by-1-by-2 matrix. The third dimension is singleton because I only sampled at one z value.
So, in the example c=cat(4,a,b), we are concatenating two matrices along the fourth dimension. The two matrices are 3-by-3, with the third dimension implicitly assumed to be singleton. However, when concatenating along the fourth dimension we end up having to explicitly show that the third dimension is still there by listing its size as 1.
I tried to update some part of a matrix, I got the following error message:
??? Assignment has fewer non-singleton rhs dimensions than non-singleton subscripts
My code tries to update some values of a matrix that represent a binary image. My code is as follows:
outImage(3:5,2:4,1) = max(imBinary(3:5,2:4,1));
When I delete last parameter (1), this time I get the same error. I guess there is a mismatch between dimensions but I could not get it. outImage is a new object that is created at that time (I tried to create it before, but nothing changed). What may be wrong?
You mention in one of your comments on another answer that you are trying to create your own dilation algorithm, and therefore want to take the maximum value in a 3-by-3-by-1 submatrix and replace the values in that submatrix with the maximum value. The function MAX will by default operate along the columns of your submatrix, which will give you a 1-by-3 matrix (i.e. the maximum values of the columns of your 3-by-3-by-1 matrix). The error results because MATLAB can't assign a 1-by-3 matrix to a 3-by-3-by-1 matrix.
One solution is to call MAX again on your 1-by-3 matrix to get a scalar value, which you can then assign to each element of your 3-by-3-by-1 submatrix without error:
outImage(3:5,2:4,1) = max(max(imBinary(3:5,2:4,1)));
On the rhs of your equation you take the max of a 3x3x1 sub-matrix, which returns a 1x3 vector. You then try to assign this to a 3x3x1 sub-matrix. A singleton subscript is one with the value 1. So the rhs has 1 non-singleton subscript, and the lhs has 2. Matlab can't figure out how to expand a 1x3 matrix to fill a 3x3x1 space.
I'm not entirely sure what you want to do, so I won't guess a solution. Do you want to make 3 copies of the rhs and put one into each row of the sub-matrix on the lhs ? Or are you trying to construct a 3x3x1 matrix on the rhs ?
Do you want to fill all indexed elements in outImage by maximum value for each column of rhs expression? You can expand the row you get on rhs with REPMAT:
outImage(3:5,2:4,1) = repmat(max(imBinary(3:5,2:4,1)),3,1)
outImage(3:5,2:4) works as well.
I got the same error before, and what I have done was defining the left hand matrix before. I don't know if you have the same case but you can try the following:
outImage=Zeros(M,N,K);
M, N, and K are the dimensions that you have. Then just type:
outImage(3:5,2:4,1) = max(max(imBinary(3:5,2:4,1)));