I have two tables x and y in Matlab that contain one column each of equal length. I just want to compute the RMSE between the two columns, but somehow I cannot do this simple operation.
rmse = sqrt(sum((x(:)-(y)(:)).^2)/1000)
It gives me an invalid array indexing error. What am I doing wrong? Thanks.
In MATLAB you can only index variables, but not expressions. But that's exactly what you try to do with
(y)(:)
as (y) is an expression. Instead use
y(:)
Related
I am trying to minimize sum((A-r*B).^2) in Matlab where A and B are matrices and r is the scalar I am manipulating. I tried the following code:
f = #(r) sum((A-r*B).^2);
Answer = fminbnd(f,lowrange,highrange);
But I get an error.
If A and B are matrices, then sum((A - r*B).^2) will not give you a single value. This will give you an array of values. If the input to sum is a matrix, the output of sum will give you an array where each element is the sum along the rows for each column in your matrix.
The function you are specifying to fminbnd must evaluate to a single value. I'm assuming you want to determine the sum of squared differences in your function, and so you need to wrap your sum with another sum. As such, try this instead:
f = #(r) sum(sum((A-r*B).^2));
Answer = fminbnd(f,lowrange,highrange);
The function f will now find the difference between matrices A and B which is weighted by r, square these differences and then add up all of these differences together.
Try that and see if it works.
If you don't need to impose limits on the possible values of the optimized scalar r, then you should be able to solve this equation directly without searching for the minimum. If A and B are vectors, use:
ropt=(B'*B)^(-1)*B'*A;
If A and B are arrays and you want to minimize the sum of squared residuals of all elements of the arrays then I believe the following will work (same formula, but convert A and B to vectors).
ropt=(B(:)'*B(:))^(-1)*B(:)'*A(:);
Examples:
b=[1;2;3]
a=2*b;
ropt=(b'*b)^(-1)*b'*a
returns ropt=2.0000, as desired
Similarly, for a matrix:
b=magic(3);
a=2*b;
ropt=(b(:)'*b(:))^(-1)*b(:)'*a(:)
also returns ropt=2.0000. This should work fine even if there isn't a perfect solution, as there is in the examples above.
Please see the following issue:
P=rand(4,4);
for i=1:size(P,2)
for j=1:size(P,2)
[r,p]=corr(P(:,i),P(:,j))
end
end
Clearly, the loop will cause the number of correlations to be doubled (i.e., corr(P(:,1),P(:,4)) and corr(P(:,4),P(:,1)). Does anyone have a suggestion on how to avoid this? Perhaps not using a loop?
Thanks!
I have four suggestions for you, depending on what exactly you are doing to compute your matrices. I'm assuming the example you gave is a simplified version of what needs to be done.
First Method - Adjusting the inner loop index
One thing you can do is change your j loop index so that it only goes from 1 up to i. This way, you get a lower triangular matrix and just concentrate on the values within the lower triangular half of your matrix. The upper half would essentially be all set to zero. In other words:
for i = 1 : size(P,2)
for j = 1 : i
%// Your code here
end
end
Second Method - Leave it unchanged, but then use unique
You can go ahead and use the same matrix like you did before with the full two for loops, but you can then filter the duplicates by using unique. In other words, you can do this:
[Y,indices] = unique(P);
Y will give you a list of unique values within the matrix P and indices will give you the locations of where these occurred within P. Note that these are column major indices, and so if you wanted to find the row and column locations of where these locations occur, you can do:
[rows,cols] = ind2sub(size(P), indices);
Third Method - Use pdist and squareform
Since you're looking for a solution that requires no loops, take a look at the pdist function. Given a M x N matrix, pdist will find distances between each pair of rows in a matrix. squareform will then transform these distances into a matrix like what you have seen above. In other words, do this:
dists = pdist(P.', 'correlation');
distMatrix = squareform(dists);
Fourth Method - Use the corr method straight out of the box
You can just use corr in the following way:
[rho, pvals] = corr(P);
corr in this case will produce a m x m matrix that contains the correlation coefficient between each pair of columns an n x m matrix stored in P.
Hopefully one of these will work!
this works ?
for i=1:size(P,2)
for j=1:i
Since you are just correlating each column with the other, then why not just use (straight from the documentation)
[Rho,Pval] = corr(P);
I don't have the Statistics Toolbox, but according to http://www.mathworks.com/help/stats/corr.html,
corr(X) returns a p-by-p matrix containing the pairwise linear correlation coefficient between each pair of columns in the n-by-p matrix X.
I have the following Matlab code snippet that I'm having to translate to VBScript. However, I'm not understanding why the last line is even necessary.
clear i
for i = 1:numb_days
doy(i) = floor(dt_daily(i) - datenum(2012,12,31,0,0,0));
end
doy = doy';
Looking over the rest of the code, this happens in a lot of other places where there are single dimension arrays (?) being transposed in place. I'm a newbie when it comes to both these languages, as well as posting a question on Stack, as I'm a sleuth when it comes to finding answers, just not in this case. Thanks in advance.
All "arrays" in MATLAB have at least two dimensions, and can be treated as having any number of dimensions you wish. The transpose operator here is converting between a row (size [1 N] array) and a column (size [N 1] array). This can be significant when it comes to either concatenating the arrays, or performing other operations.
Conceptually, the dimension vector of a MATLAB array has as many trailing 1s as is required to perform an operation. This means that you can index any MATLAB array with any number of subscripts, providing you don't exceed the bounds, like so:
x = magic(4); % 4-by-4 square matrix
x(2,3,1,1,1) % pick an element
One final note: the ' operator is the complex-conjugate transpose CTRANSPOSE. The .' operator is the ordinary TRANSPOSE operator.
Inside a MATLAB function I have built a matrix A, whose dimensions M and N are set as parameters of the function. I would like to plot all the columns of this matrix, given a vector of indices B with length M. Hence, I use these lines:
figure
plot(B,A)
I specified figure as the MATLAB function returns more different plots.
My problem is that the program plots just two columns of the matrix with different colours (blue and violet). Where is my mistake?
Thank you for your attention.
go for
plot(repmat(B,1,N),A);
or
plot(repmat(B,N,1),A);
(depending on your rows/columns). You need to have same size matrices in plot.
Moreover, if B are just consecutive indexes, you may want to consider Plot(A) (or Plot(A')).
I noticed that there was an error which caused the overlap of the different curves, so the way which I used to plot the colums of a matrix is valid. However, the method proposed by Acorbe is a possibility, too.
I am trying to take a matrix and normalize the values in each cell around the average for that column. By normalize I mean subtract the value in each cell from the mean value in that column i.e. subtract the mean for Column1 from the values in Column1...subtract mean for ColumnN from the values in ColumnN. I am looking for script in Matlab. Thanks!
You could use the function mean to get the mean of each column, then the function bsxfun to subtract that from each column:
M = bsxfun(#minus, M, mean(M, 1));
Additionally, starting in version R2016b, you can take advantage of the fact that MATLAB will perform implicit expansion of operands to the correct size for the arithmetic operation. This means you can simply do this:
M = M-mean(M, 1);
Try the mean function for starters. Passing a matrix to it will result in all the columns being averaged and returns a row vector.
Next, you need to subtract off the mean. To do that, the matrices must be the same size, so use repmat on your mean row vector.
a=rand(10);
abar=mean(a);
abar=repmat(abar,size(a,1),1);
anorm=a-abar;
or the one-liner:
anorm=a-repmat(mean(a),size(a,1),1);
% Assuming your matrix is in A
m = mean(A);
A_norm = A - repmat(m,size(A,1),1)
As has been pointed out, you'll want the mean function, which when called without any additional arguments gives the mean of each column in the input. A slight complication then comes up because you can't simply subtract the mean -- its dimensions are different from the original matrix.
So try this:
a = magic(4)
b = a - repmat(mean(a),[size(a,1) 1]) % subtract columnwise mean from elements in a
repmat replicates the mean to match the data dimensions.