How do you put in a range of values into a variable of a matrix?

 I have a simple question. How do you put in a range of values into a variable of a matrix? I tried doing this code below:

 ho2 = linspace(5,50,51);

 A2 = [-35 30 0 0 0; 30 -30.32 .32 0 0; 0 .32 -2.82 2.5 0; 0 0 2.5 -16.5 14; 0 0 0 14 (14+ho2)]

The error I keep receiving is:

Error using vertcat Dimensions of matrices being concatenated are not consistent.

Error in Untitled3 (line 3) A2 = [-35 30 0 0 0; 30 -30.32 .32 0 0; 0 .32 -2.82 2.5 0; 0 0 2.5 -16.5 14; 0 0 0 14 (14+ho2)]

Answer 1

[Stephen23]

The matrix A2 has size 5x5 (excluding the last element), into one element of which you are trying to place the variable ho2, which has size 1x51. In MATLAB, an element of a numeric array is a single scalar value. But is this instance, you are trying to place 51 values into it...

Thus the error is telling you this: "You cannot put something with multiple values into a space that can only fit one value!"

By the looks of your code, you need to reconsider what you are trying to define as the last element of A2. If you replace the last element with a simple scalar numeric, then it works fine without any error.

[Yianni]

I understand what the problem is, but I just want to know how I can fix this so that I can start with 5 for ho2 and then move on to 6 and so on. Could I use a loop or the meshgrid command? What do you think?

[Stephen23]

How to "fix it" depends on you. I can't tell you whether you need to use a loop or arrayfun or some other solution. You mention meshgrid, but not how you want to use this data: is it going to be plotted, or saved in an array, or have some function applied to it?

Probably the easiest solution is to use a for loop over each element of the vector ho2:

for x = linspace(5,50,51)
    A2 = [-35,30,0,0,0;30,-30.32,0.32,0,0;0,0.32,-2.82,2.5,0;0,0,2.5,-16.5,14;0,0,0,14,(14+x)];
    ... other calculations here
end

[Stephen23]

If this answers your question, clicking "accept" would be appreciated. If this does not answer your question, please write the size of the resulting array that you wish to have.

[Yianni]

hi = 5;
Tin = 20;
ho2 = 5:1:50; Nho2 = length(ho2);

for i = 1:Nho2

A2 = [-35 30 0 0 0; 30 -30.32 .32 0 0; 0 .32 -2.82 2.5 0; 0 0 2.5 -16.5...
    14; 0 0 0 14 (14+ho2(i))];

B2 = [-100; 0; 0; 0; 10*ho2(i)];

%Temperature in different parts of the four-layer wall in C
TT = A2\B2;

%Heat loss per unit area of wall in W/m^2
Q2 = hi*(Tin -TT(1,:));

end

plot(ho2,Q2)

[Yianni]

I figured it out. This works how I want it to, but the graph is not coming out right. I want to plot ho2 vs. Q2, but I keep coming up with a straight line. I think it has to do with something being a scalar and not a vector with the dot arithmetic. I haven't had any luck. Any suggestions?

[Stephen23]

Answering questions is a little challenging when the actual purpose is not explained at the beginning. Now I see that you wish to plot some data, and that the values in ho2 are your independent variable.

Firstly: do NOT use i as the loop variable, as this is the name of the inbuilt imaginary unit . Shadowing inbuilt functions causes problems that you really don't want to get into...

Secondly: Every time your loop runs, the value of Q2 is completely redefined as a scalar value. Have a look at Q2 in your workspace: what size does it have? If you wished to accumulate the value from each loop iteration, then you need to use some array indexing, like this:

hi = 5;
Tin = 20;
ho2 = 5:1:50; Nho2 = length(ho2);
Q2 = ho2;
for k = 1:Nho2
    A2 = [-35 30 0 0 0; 30 -30.32 .32 0 0; 0 .32 -2.82 2.5 0; 0 0 2.5 -16.5...
        14; 0 0 0 14 (14+ho2(k))];
    B2 = [-100; 0; 0; 0; 10*ho2(k)];
    %Temperature in different parts of the four-layer wall in C
    TT = A2\B2;
    %Heat loss per unit area of wall in W/m^2
    Q2(k) = hi*(Tin -TT(1,:));
end
plot(ho2,Q2)

[Stephen23]

TT is the least-squares fit of the data A2 and B2, and it is a 5x1 array. But with the code TT(1,:) you only use the very first element from this array. Is this intentional?

[Yianni]

I apologize, I am still learning this program. But thank you for your help. I really appreciate it.

[Stephen23]

No need to apologize. Me asking questions helps make certain that we are using the same terminology, and that your code's purpose is being fulfilled.

I would suggest that you check your code again, and read the MATLAB documentation very carefully to make sure that it is doing the calculation that you think it is. Pay particular attention to matrix vs. array operations, indexing, and even the mldivide that you use.

[Yianni]

To answer your question, yes it was intentional because I am only using one value in the matrix to solve for Q2. Out of curiosity, is the line below needed?

Q2 = ho2;

I removed it and got the same output in the plot and for the values of each variable.

[Stephen23]

The line Q2 = ho2; performs array preallocation. MATLAB dynamically allocates memory as arrays grow bigger, which is very convenient, but this process can slow down code if the arrays grow many times or in large steps. Every time it grows, MATLAB has to check if it fits the current memory space allocated, and if not, it copies it to a new area of memory. It can be faster to preallocate an array to the size that it will need to be, before starting to work with it, which is what I did here by defining the output array to be the same size as one of the input arrays (otherwise it would grow fifty times in the for-loop).

http://blogs.mathworks.com/loren/2012/11/29/understanding-array-preallocation/

http://www.mathworks.com/matlabcentral/answers/99124-how-do-i-pre-allocate-memory-when-using-matlab