I have a large number of entries arranged in three columns. Sample of the data is:
A=[1 3 2 3 5 4 1 5 ;
22 25 27 20 22 21 23 27;
17 15 15 17 12 19 11 18]'
I want the first column (hours) to control the entire matrix to create new matrix as follows:
Anew=[1 2 3 4 5 ; 22.5 27 22.5 21 24.5; 14 15 16 19 15]'
Where the 2nd column of Anew is the average value of each corresponding hour for example:
from matrix A:
at hour 1, we have 2 values in 2nd column correspond to hour 1
which are 22 and 23 so the average is 22.5
Also the 3rd column: at hour 1 we have 17 and 11 and the
average is 14 and this continues to the hour 5 I am using Matlab
You can use ACCUMARRAY for this:
Anew = [unique(A(:,1)),...
cell2mat(accumarray(A(:,1),1:size(A,1),[],#(x){mean(A(x,2:3),2)}))]
This uses the first column A(:,1) as indices (x) to pick the values in columns 2 and 3 for averaging (mean(A(x,2:3),1)). The curly brackets and the call to cell2mat allow you to work on both columns at once. Otherwise, you could do each column individually, like this
Anew = [unique(A(:,1)), ...
accumarray(A(:,1),A(:,2),[],#mean), ...
accumarray(A(:,1),A(:,3),[],#mean)]
which may actually be a bit more readable.
EDIT
The above assumes that there's no missing entry for any of the hours. It will result in an error otherwise. Thus, a more robust way to calculate Anew is to allow for missing values. For easy identification of the missing values, we use the fillval input argument to accumarray and set it to NaN.
Anew = [(1:max(A(:,1)))', ...
accumarray(A(:,1),A(:,2),[],#mean,NaN), ...
accumarray(A(:,1),A(:,3),[],#mean,NaN)]
You can use consolidator to do the work for you.
[Afinal(:,1),Afinal(:,2:3)] = consolidator(A(:,1),A(:,2:3),#mean);
Afinal
Afinal =
1 22.5 14
2 27 15
3 22.5 16
4 21 19
5 24.5 15
Related
Say I have a matrix A whose first column contains item IDs with repetition and second column contains their weights.
A= [1 40
3 33
2 12
4 22
2 10
3 6
1 15
6 29
4 10
1 2
5 18
5 11
2 8
6 25
1 14
2 11
4 28
3 38
5 35
3 9];
I now want to find the difference of each instance of A and its associated minimum weight. For that, I make a matrix B with its first column containing the unique IDs from column 1 of A, and its column 2 containing the associated minimum weight found from column 2 of A.
B=[1 2
2 8
3 6
4 10
5 11
6 25];
Then, I want to store in column 3 of A the difference of each entry and its associated minimum weight.
A= [1 40 38
3 33 27
2 12 4
4 22 12
2 10 2
3 6 0
1 15 13
6 29 4
4 10 0
1 2 0
5 18 7
5 11 0
2 8 0
6 25 0
1 14 12
2 11 3
4 28 18
3 38 32
5 35 24
3 9 3];
This is the code I wrote to do this:
for i=1:size(A,1)
A(i,3) = A(i,1) - B(B(:,1)==A(i,2),2);
end
But this code takes a long time to execute as it needs to loop through B every time it loops through A. That is, it has a complexity of size(A) x size(B). Is there a better way to do this without using loops, that would execute faster?
You can use accumarray to first compute the minimum value in the second column of A for each unique value in the first column of A. We can then index into the result using the first column of A and compare to the second column of A to create the third column.
% Compute the mins
min_per_group = accumarray(A(:,1), A(:,2), [], #min);
% Compute the difference between the second column and the minima
A(:,3) = A(:,2) - min_per_group(A(:,1));
I want to create a matrix which has distinct rows selected from another matrix.
For Example, I have a 10x3 matrix A
A =
1 2 3
4 5 6
7 8 9
10 11 12
13 14 15
16 17 18
19 20 21
22 23 24
25 26 27
28 29 30
Now I want to create a new matrix B of size 2 X 3 from A in a iterative process in such a way that the matrix B should consist different rows in each iteration (max iteration = 5)
My Pseudo-code:
for j=1:5
create matrix 'B' by selecting 2 rows randomly from 'A', which should be different
end
You could use randperm to mess up the rows randomly and then take two rows in each iteration successively in order.
iterations = 4;
permu = randperm(size(A,1));
out = A(permu(1:iterations*2),:);
for ii = 1:iterations
B = out(2*ii - 1:2*ii,:)
end
Results:
B =
22 23 24
25 26 27
B =
1 2 3
13 14 15
B =
19 20 21
16 17 18
B =
7 8 9
10 11 12
I have data of integers in x = 500 X 612 matrix. I need a new variable xx in a 500 X 612 matrix but I need to apply cumsum along each row (500) across 12 column steps and applying cumsum like this 51 times --> 500 X (12 X 51) matrix. Then I need a for loop to produce 51 plots of the 500 rows and 12 columns of the cumsum time series. thank you!
I will rephrase what the question is asking to benefit those who are reading.
The OP wishes to segment a matrix into chunks by splitting up the matrix into a bunch of columns. A cumsum is applied to each row individually for each column and are then concatenated together to build a final matrix. As such, given this source matrix:
x =
1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
Supposing that we wish to split up the matrix by columns 3, 6 and 9 and 12, we will have four chunks to work with. We do a cumsum on each of these blocks individually and piece the final result together. So the result would like the following:
xx =
1 3 6 4 9 15 7 15 24 10 21 33
13 27 42 16 33 51 19 39 60 22 45 69
First, you need to determine how many columns you want to break up the matrix into. In your case, we wish to segment the matrix into 4 chunks: Columns 1 - 3, columns 4 - 6, columns 7 - 9, and columns 10 - 12. As such, I'm going to reshape this matrix so that each column is an individual row from a chunk in this matrix. We then apply cumsum over this reshaped matrix and we then reshape it back to what you had originally.
Therefore, do this:
num_chunks = 4; %// Columns 3, 6, 9, 12
divide_point = size(x,2) / num_chunks; %// Determine how many elements are in a row for a cumsum
x_reshape = reshape(x.', divide_point, []); %// Get reshaped matrix
xy = cumsum(x_reshape); %// cumsum over all columns individually
xx = reshape(xy, size(x,2), size(x,1)).'; %// Reconstruct matrix
In the third line of code, x_reshape = reshape(x.', divide_point, []); may seem a bit daunting, but it's actually not that bad. I had to transpose the matrix first because you want to take each row of a chunk and place them into individual columns so we can perform a cumsum on each column. When you reshape something in MATLAB, it collects values column-wise and reshapes the input into an output of a specified size. Therefore, to collect the rows, we need to collect row-wise and so we must transpose this matrix. Next, divide_point tells you how many elements we have for a single row in one chunk. As such, we want to construct a matrix that is of size divide_point x N where divide_point tells you how many elements we have in a row of a chunk and N is the total number of rows over all chunks. Because I don't want to calculate how many there are (am rather lazy actually....), the [] syntax is to automatically infer this number so that we can get a reshaped matrix that respects the total number of elements in the original input. We then perform cumsum on each of these columns, and then we need to reshape this back into the original shape of the input. With this, we use reshape again on the cumsum result, but in order to get it back into the row-order that you want, we have to determine the transpose as reshape takes values in column-major order, then re-transpose that result.
We get:
xx =
1 3 6 4 9 15 7 15 24 10 21 33
13 27 42 16 33 51 19 39 60 22 45 69
In general, the total number of elements to sum over for a row needs to be evenly divisible by the total number of columns that your matrix contains. For example, given the above, if you were to try to segment this matrix into 5 chunks, you would certainly get an error as the number of rows to cumsum over is not symmetric.
As another example, let's say we wanted to break up the matrix into 6 chunks. Therefore, by setting num_chunks = 6, we get:
xx =
1 3 3 7 5 11 7 15 9 19 11 23
13 27 15 31 17 35 19 39 21 43 23 47
You can see that cumsum restarts at every second column, as we desired 6 chunks and to get 6 chunks with a matrix of 12 columns, a chunk is created at every second column.
I have a sparse matrix:
A=
(14,13) 0.5286
(15,14) 0.6781
(16,15) 0.5683
(17,16) 1.2773
(18,17) 1.0502
(19,18) 0.4966
(21,19) 0.9951
(21,20) 0.4522
(22,21) 0.8507
(23,22) 1.0727
(24,23) 0.8288
(25,24) 0.5811
(26,25) 0.8235
(28,26) 1.5128
(30,28) 0.7966
(30,29) 0.6363
(31,29) 0.8254
(32,31) 0.8573
(33,32) 1.0753
that is result of a minimum spanning tree. now I want to extract 13,14,15,...26,28,29,...33.
as seen 27 is not between numbers. so pred give: 13 14 15 16 17 18 19 21 22 23 24 25 26 28 29 30 31 32 that 20 and 33 is not.
how can I extract total of numbers that say in top?
[ii jj] = find(A);
answer = unique([ii(:); jj(:)]);
should do it.
Note that the find command with two outputs gives you the row and column index of all nonzero elements. Since you have a minimum spanning tree, each number you care about needs to occur at least once in the row or column (for example your matrix never has the number 29 in the first index, but it occurs in the second).
The unique function makes sure that each number that occurs is only represented once.
Suppose I have:
>> X = magic(5)
X =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
How do I get i'th element from the second column?
I already figured that indices in (some?) collections in Octave are one-based, but I'm not sure if that holds for matrices, too.
See the index expressions section of the manual. To get the i'th element from second column:
X(i,2) # element 'i' from column 2
X(1:end,2) # the whole 2nd column
X(:,2) # same thing but shorter
x(:, [2 3]) # whole 2nd and 3rd column
Note that Octave is a language where array elements are in column-major order.