How do I solve an equation using two 1D matrices of different sizes and ranges as inputs?

This is seemingly basic, but for whatever reason I am unable to find the solution on my own or on the forums. I am attempting to solve for x, where y and z are 1D matrices, using any combination of 2 numbers, 1 number from each. For the sake of simplicity I think the same solution could be found assuming x=y*z+z, where y=1:3 and z=1:3. Note the addition of 'z' after multiplication does not allow for simply multiplying matrices, but requires selecting the individual values and applying them to the given equation for all possible combinations. I know there is a combination function, which my be required for this solution, but I am unaware of how to apply it here.

Answer 1

[EssJaySeeJr.]

This.

T1= evalin('base','T1');
T3= evalin('base','T3');
[x,sT1]=size(T1);
[y,sT3]=size(T3);
r1=1;
r2=1;
r3=1;
cT1=1;
cT2=1;
cT3=1;
T13=0;
while cT1<sT1+1
    T13a=0;
    iter=1;
 for iter=1:sT3
    T13a(iter)=T1(1,cT1);
    T13(r1,1)=T13a(iter)';
    T13(r1,2)=T3(r3,cT3);
    r1=(r1)+1;
    cT3=(cT3)+1;
 end
cT3=1;
cT1=(cT1)+1; 
end
[sT2,z]=size(T13);
T2=0;
while cT2<sT2+1
T2(cT2,r2)=(((L1*T13(cT2,1))/L2)+T13(cT2,2))/(1+(L1/L2));
cT2=(cT2)+1;
end

I know this can use cleaning up, but obviously I am not very proficient with MATLAB. Either way, this does what I need it to do, how I need it to do it, regardless of the two input matrices sizes or ranges. Now if this should be or can be a function, that's another story. Right now I am content with just running the script as is. I will also probably find a way to combine T13 and T2 and plot in 3D. Not sure how to do this at the moment, but I already got this far...

Answer 2

[Star Strider]

I’m not sure what you want.

One of these will likely work:

y=1:3;
z=1:3;

x1 = y * z.';
x2 = y.' * z;
x3 = bsxfun(@times, y, z);

[EssJaySeeJr.]

I will try to elaborate using the same equation. Essentially, I'm looking for an output similar to:

x= 1 2 3 2 4 6 3 6 9

That means it calculated when y=1, z=1; y=1, z=2; y=1, z=3; y=2, z=1; and so forth. Ideally, these would be linked to the input values so I could plot in 3d, but this is unnecessary, I'm just looking for outliers which I can run another line to automate without visualization. Although, your example taught me something new (bsxfun) I can't find a way to apply that to my problem.

[Star Strider]

Just convert ‘x2’ to a vector and then transpose it to get what you want:

Out = x2(:)'

[EssJaySeeJr.]

Thank you for the help, but can you take a look at the other comment where I try to elaborate a bit more? This is still essentially only multiplying matrices, which isn't the ultimate goal. I want to use the values that are stored in the matrices and multiply those different combinations. If that is possible, it would allow the solution to also be applied to the equation x=y*z+z and essentially any other higher order equation. The solution you provide doesn't allow for this to be applied to any problem other than matrix multiplication, again not really the goal.

[EssJaySeeJr.]

I added the lines:

y=1:3;

z=1:3;

comb=nchoosek([y z],2);

y= comb(:,1);

z= comb(:,2);

While this is definitely a step in the right direction, I'm still not sure how to now use this to do the arithmetic below. I know it is because the matrices don't agree, but I'm only try to do the calculation one point at a time and ultimately create a 1D matrix output.

x=y*z+z

Secondly, it seems if the ranges of 'z' and 'y' do not overlap, 'y' will end with values that were previously only associated with 'z' and vice-versa. This can be seen if ran as follows:

y=1:3;

z=4:6;

comb=nchoosek([y z],2);

y= comb(:,1);

z= comb(:,2);

[Star Strider]

Ambiguity begets ambiguity.

Give an exact problem statement with exact input arguments and the exact result you want from them, even if you have to do the calculations by hand.

[EssJaySeeJr.]

Here it is:

T1=223:253;
T3=273:303;
L1=.045;
L2=.01905;  
T2=(((L1*T3)/L2)+T1)/(1+(L1/L2));

Yeah, I am not able to hand calculate all the potential outputs...

If the size of T1 does not agree with T3 (it does in the case provided, but it won't in all cases), this equation is not valid, and this also only calculates T2=f(T1(1,1),T3(1,1)) and doesn't allow for any combination of the two. This I found the nchoosek to sort of work, but again, if those ranges aren't the same (they aren't here),then it will pick a value designated for T3 and give it to T1 if you use the script provided in my previous comment. I'm not sure how providing this really helps other than make it look more complicated than it really is. If the script actually does what I am asking of it, not just mimicking the operation as the solutions have up to now, it can be applied to x=y*z+z, and eventually applied to the case presented (along with others). Maybe it can't be done. I choose not to believe this though as I know I am getting close.

Using the x=y*z+z example, where y=1:3 and z=4:5, the results should be as follows.

x=f(y,z)

x=f(1,4)=8

x=f(1,5)=10

x=f(2,4)=12

x=f(2,5)=15

x=f(3,4)=16

x=f(3,5)=20

[Star Strider]

That’s a bit easier to understand if I let the Symbolic Math Toolbox simplify it:

T2 = (L2*T1 + L1*T3)/(L1 + L2);

Looking at it from this perspective, ‘T1’ and ‘T3’ must always both be the same sizes or it will simply not work. It is not possible to add matrices or vectors of different sizes.

This code will give you the result you want, but ‘T2V’ will only as long as the shortest vector, so it’s something of a compromise. It essentially trims the longest vector to the length of the shortest. However it does calculate all the values for both vectors in ‘T2M’, so I will leave you to consider how you might want to get the other values:

FT2 = @(T1,T3) (L2*T1 + L1*T3)/(L1 + L2);
[T1M,T3M] = meshgrid(T1, T3);
T2M = FT2(T1M, T3M);
T2V = diag(T2M);

[EssJaySeeJr.]

Yeah, you are still only trying to mimic the desired operation. I know it can't be done using just matrix arithmetic. Again, I know how to do this, and know its limitations, I took math... This is why I asked to stop attempting to manipulate the arrays and find a way to combine the values.

After sleeping on it, I know what needs to be done. I will attempt it with my limited script knowledge. Initially, I will need to determine the size of T1 and T3, then run a loop to match all values of T1 with T3 and create an array from that. The size of the initial T1 and T3 array, relative to each other, is irrelevant. I can then run this new array to run my calculation. I will post this once I complete it. Also, I will post it for the x=y*z+z as it is a simple example that can be easily applied to all cases where this is needed.

[Star Strider]

What you want to do is what the meshgrid approach does. It performs the calculation on all combinations of all the elements in your vectors in the resulting matrix. You simply have to define the results you want in your vector. The diagonal of the resulting matrix will reproduce the vector your function creates.

Take a look at the resulting matrix of my most recent Comment before this one. You likely won’t need a loop, just an addressing scheme to get the elements you want.

[EssJaySeeJr.]

I answered my own question :D If you look, you will understand exactly what I was looking for. I think some things were getting lost in my lack of translation. Thanks, your input did ultimately help.

Answer 3

[Torsten]

y=[1 2 3];
z=[1 2 3];
x=y'*z;

Best wishes

Torsten.

[EssJaySeeJr.]

This actually does provide the same values in the output, but not in the format requested. Essentially, this can't be applied to my case because of it. I am not trying to multiply the matrices (I know how to do this). I am trying to multiply combinations of the values within it. Maybe if I make the equation more complex it may help. I don't want someone to solve my problem for me (others might not find it useful in the future), which is why I haven't posted my actual equation. I feel like the same solution could eventually be reached using these examples. x=y*z+z

[Torsten]

Use

x=reshape(x',1,9)

at the end, and you will get the x-vector you want.

Best wishes

Torsten.

[EssJaySeeJr.]

This solution can't be applied to anything other than matrix arithmetic. Please note the update to the question. I apologize for not properly conveying my problem initially. Thank you for your time.