Say I have a matrix A
A =
0 1 2
2 1 1
3 1 2
and another matrix B
B =
0 42
1 24
2 32
3 12
I want to replace each value in A by the one associated to it in B.
I would obtain
A =
42 24 32
32 24 24
12 24 32
How can I do that without loops?
There are several ways to accomplish this, but here is an short one:
[~,ind]=ismember(A,B(:,1));
Anew = reshape(B(ind,2),size(A))
If you can assume that the first column of B is always 0:size(B,1)-1, then it is easier, becoming just reshape(B(A+1,2),size(A)).
arrayfun(#(x)(B(find((x)==B(:,1)),2)),A)
Related
I am trying to implement a moving rank function, taking parameters of n, the number of items, and m, the column name. Here is how I implement it:
mwindow: k){[y;x]$[y>0;x#(!#x)+\:!y;x#(!#x)+\:(!-y)+y+1]};
mrank: {[n;x] sum each x > prev mwindow[neg n;x]};
But this seems to take quite some time if n is moderately large, say 100.
I figure it is because it has to calculate from scratch, unlike msum, which keeps a running variable and only calculate the difference between the newly added and the dropped.
There's a number of general sliding window functions here that you can use to generate rolling lists on which to apply your rank: https://code.kx.com/q/kb/programming-idioms/#how-do-i-apply-a-function-to-a-sequence-sliding-window
Those approaches seem to fill the lists out with zeros/nulls however which I think won't really suit your use of rank. Here's another possible approach which might be more suitable to rank (though I haven't tested this for performance on the large scale):
q)mwin:{x each (),/:{neg[x]sublist y,z}[y]\[z]}
q)update r:mwin[rank;4;c] from ([]c:10?100)
c r
----------
84 ,0
25 1 0
31 2 0 1
0 3 1 2 0
51 1 2 0 3
29 2 0 3 1
25 0 3 2 1
73 2 1 0 3
0 2 1 3 0
6 2 3 0 1
q)update r:last each mwin[rank;4;c] from ([]c:10?100)
c r
----
38 0
72 1
13 0
77 3
64 1
9 0
37 1
79 3
97 3
63 1
q)
I'd like to obtain all unique products for a given vector.
For example, given a:
a = [4,10,12,3,6]
I want to obtain a matrix that contains the results of:
4*10
4*12
4*3
4*6
10*12
10*3
10*6
12*3
12*6
3*6
Is there a short and/or quick way of doing this in MATLAB?
EDIT: a may contain duplicate numbers, giving duplicate products - and these must be kept.
Given:
a =
4 10 12 3 6
Construct the matrix of all pairwise products:
>> all_products = a .* a.'
all_products =
16 40 48 12 24
40 100 120 30 60
48 120 144 36 72
12 30 36 9 18
24 60 72 18 36
Now, construct a mask to keep only those values below the main diagonal:
>> mask = tril(true(size(all_products)), -1)
mask =
0 0 0 0 0
1 0 0 0 0
1 1 0 0 0
1 1 1 0 0
1 1 1 1 0
and apply the mask to the product matrix:
>> unique_products = all_products(mask)
unique_products =
40
48
12
24
120
30
60
36
72
18
If you have the Statistics Toolbox, you can abuse pdist, which considers only one of the two possible orders for each pair:
result = pdist(a(:), #times);
One option involves nchoosek, which returns all combinations of k elements out of a vector, each row is one combination. prod computes the product of rows or columns:
a = [4,10,12,3,6];
b = nchoosek(a,2);
b = prod(b,2); % 2 indicates rows
Try starting with this. Have the unique function filter out the result of multiplying a by itself.
b = unique(a*a')
I have a matrix of 2d lets assume the values of the matrix
a =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
17 24 1 8 15
11 18 25 2 9
This matrix is going to be divided into three different matrices randomly let say
b =
17 24 1 8 15
23 5 7 14 16
c =
4 6 13 20 22
11 18 25 2 9
d =
10 12 19 21 3
17 24 1 8 15
How can i know the index of the vectors in matrix d for example in the original matrix a,note that the values of the matrix can be duplicated.
for example if i want to know the index of {10 12 19 21 3} in matrix a?
or the index of {17 24 1 8 15} in matrix a,but for this one should return only on index value?
I would appreciate it so much if you can help me with this. Thank you in advance
You can use ismember with the 'rows' option. For example:
tf = ismember(a, c, 'rows')
Should produce:
tf =
0
0
1
0
0
1
To get the indices of the rows, you can apply find on the result of ismember (note that it's redundant if you're planning to use this vector for matrix indexing). Here find(tf) return the vector [3; 6].
If you want to know the number of the row in matrix a that matches a single vector, you either use the method explained and apply find, or use the second output parameter of ismember. For example:
[tf, loc] = ismember(a, [10 12 19 21 3], 'rows')
returns loc = 4 for your example. Note that here a is the second parameter, so that the output variable loc would hold a meaningful result.
Handling floating-point numbers
If your data contains floating point numbers, The ismember approach is going to fail because floating-point comparisons are inaccurate. Here's a shorter variant of Amro's solution:
x = reshape(c', size(c, 2), 1, []);
tf = any(all(abs(bsxfun(#minus, a', x)) < eps), 3)';
Essentially this is a one-liner, but I've split it into two commands for clarity:
x is the target rows to be searched, concatenated along the third dimension.
bsxfun subtracts each row in turn from all rows of a, and the magnitude of the result is compared to some small threshold value (e.g eps). If all elements in a row fall below it, mark this row as "1".
It depends on how you build those divided matrices. For example:
a = magic(5);
d = a([2 1 2 3],:);
then the matching rows are obviously: 2 1 2 3
EDIT:
Let me expand on the idea of using ismember shown by #EitanT to handle floating-point comparisons:
tf = any(cell2mat(arrayfun(#(i) all(abs(bsxfun(#minus, a, d(i,:)))<1e-9,2), ...
1:size(d,1), 'UniformOutput',false)), 2)
not pretty but works :) This would be necessary for comparisons such as: 0.1*3 == 0.3
(basically it compares each row of d against all rows of a using an absolute difference)
Well I do not know if I used the exact term. I tried to find an answer on the net.
Here is what i need:
I have a matix
a = 1 4 7
2 5 8
3 6 9
If I do a(4) the value is 4. So it is reading first column top to buttom then continuing to next .... I don't know why. However,
What I need is to call it using two indices. As row and column:
a(1,2)= 4
or even better if i can call it in the following way:
a{1}(2)=4
What is this process really called (want to learn) and how to perform in matlab.
I thought of a loop. Is there a built in function
Thanks a lot
Check this:
a =
18 18 16 18 18 18 16 0 0 0
16 16 18 0 18 16 0 18 18 16
18 0 18 18 0 16 0 0 0 18
18 0 18 18 16 0 16 0 18 18
>> a(4)
ans =
18
>> a(5)
ans =
18
>> a(10)
ans =
18
I tried reshape. it is reshaping not converting into 2 indeces
If you've already got a matrix, you already can access it with two indices:
if you've got
a = 1 4 7
2 5 8
3 6 9
you can access it as
a(3,2) = 6
However, the indexing goes from the top left, row first then column. If you want to get at the "4" in the matrix then do:
a(1,2)
To reshape a vector/matrix/array, use reshape().
Or you could leave it as a one dimensional array and just use
((Column - 1) * 3) + Row - 1) as the index. 3 because there are three columns.
NB a(4) = 4 because of the way you've arranged columns and rows in the one dimensional array, yours is "loaded" as
R1C1,R2C1,R3C1, R1C2 etc wher R is row and C is column
If that's inconvenient then you just need to get whatever fills the array row then column so the above mapping would be
((Row - 1) * 3) + Column - 1)
Don't do Matlab so above code assumes array starts at 0, if not just add 1 to it.
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