I want to create a matrix like
A = [0 0 0 0 1;
0 0 0 1 1;
0 0 0 1 1;
0 0 0 1 1;
0 0 1 1 1;
0 1 1 1 1]
based on a vector indicating how many '0's should precede '1's on each row:
B = [4 3 3 3 2 1]
Is there a loopless way to do this ?
You don't mention in your question how the horizontal size of the array should be defined (the number of ones).
For predefined width you can use this code:
width = 5;
A = cell2mat(arrayfun(#(x) [ zeros(1,x), ones(1,width-x) ], B, 'UniformOutput', false)');
If you want that A has minimal width, but still at least one 1 in every row:
A = cell2mat(arrayfun(#(x) [ zeros(1,x), ones(1,max(B)+1-x) ], B, 'UniformOutput', false)');
A shorter “old-school” way to achieve this without a loop would be as follows:
A = repmat(B',1,max(B)+1)<repmat([1:max(B)+1],size(B,2),1)
If you want to have a minimum number of ones
min_ones=1; %or whatever
A = repmat(B',1,max(B)+min_ones)<repmat([1:max(B)+min_ones],size(B,2),1)
I don’t know how this compares speedwise to #nrz’s approach (I’ve only got Octave to hand right now), but to me it's more intuitive as it’s simply comparing a max(B) + min_ones * column tiling of B:
4 4 4 4 4
3 3 3 3 3
3 3 3 3 3
3 3 3 3 3
2 2 2 2 2
1 1 1 1 1
with a row tiling of [1 : max(B) + min_ones]
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
To generate:
A =
0 0 0 0 1
0 0 0 1 1
0 0 0 1 1
0 0 0 1 1
0 0 1 1 1
0 1 1 1 1
This requires only one line, and seems to be faster than previous solutions based on repmat or arrayfun:
%// Example data
ncols = 5;
B = [4 3 3 3 2 1];
%// Generate A
A = bsxfun(#gt, 1:ncols, B(:));
Related
I am essentially trying to figure out how to generate code for basis vectors of different configurations of M objects into N different states (for example, if I had 2 snacks between 2 kids, I could have (2,0) (0,2) or (1,1), terrible example, but thats the idea)
I am struggling to figure out how to do this without going into many different loops (I want this to be automatic). The idea would be to create a Matrix where each row is a vector of length M. I would start with vec(1) = N then an if loop where if sum(vec) == N, Matrix(1,:)=vec; Then I could take vec(1)=N-i and do the same.
My only issue is I do not see how to use the if and forget it so that if I had maybe 2 objects in 5 locations, how would I do this to get (1 0 0 0 1).
I am not seeing how to do this.
You could use a recursive function:
function out = combos(M,N)
if N == 1
out = M;
else
out = [];
for i = 0:M
subout = combos(M-i,N-1);
subout(:,end+1) = i;
out = [out;subout];
end
end
I think this does what you want.
The key idea is to generate not the number of elements in each group, but the split points between groups. This can be done via combinations with repetition. Matlab's nchoosek generates combinations without repetition, but these are easily converted into what we need.
M = 5; % number of objects
N = 3; % number of groups
t = nchoosek(1:M+N-1, N-1); % combinations without repetition...
t = bsxfun(#minus, t, 1:N-1); % ...convert into combinations with repetition
t = diff([zeros(size(t,1), 1) t repmat(M, size(t,1), 1) ], [], 2); % the size of each
% group is the distance between split points
In this example, the result is
t =
0 0 5
0 1 4
0 2 3
0 3 2
0 4 1
0 5 0
1 0 4
1 1 3
1 2 2
1 3 1
1 4 0
2 0 3
2 1 2
2 2 1
2 3 0
3 0 2
3 1 1
3 2 0
4 0 1
4 1 0
5 0 0
This is a similar approach to Luis' without bsxfun. Because we don't like fun.
n = 5;
k = 3;
c = nchoosek(n+k-1, k-1);
result = diff([zeros(c, 1) nchoosek(1:(n+k-1), k-1) ones(c, 1)*(n+k)], [], 2) - 1;
This creates the partitions of the integer n with length k. Given an array of length n + (k-1), we find all combinations of (k-1) places to place partitions between the (unary) integers. For 5 items and 3 locations, we have 7 choices of where to put the partitions:
[ 0 0 0 0 0 0 0 ]
If our chosen combination is [2 4], we replace positions 2 and 4 with partitions to look like this:
[ 0 | 0 | 0 0 0 ]
The O's give the value in unary, so this combination is 1 1 3. To recover the values easily, we just augment the combinations with imaginary partitions at the next values to the left and right of the array (0 and n+k) and take the difference and subtract 1 (because the partitions themselves don't contribute to the value):
diff([0 2 4 8]) - 1
ans =
1 1 3
By sliding the partitions in to each possible combination of positions, we get all of the partitions of n.
Output:
result =
0 0 5
0 1 4
0 2 3
0 3 2
0 4 1
0 5 0
1 0 4
1 1 3
1 2 2
1 3 1
1 4 0
2 0 3
2 1 2
2 2 1
2 3 0
3 0 2
3 1 1
3 2 0
4 0 1
4 1 0
5 0 0
I want to stack each row of a matrix A in Matlab a different number of times according to what is reported in the vector count. To do that I use repmat in the following way:
counts=[524282; 524286; 524283; 524290];
A=randn(4,19);
f=#() cell2mat(arrayfun(#(x) repmat(A(x,:),counts(x),1), 1:size(counts,1), 'UniformOutput', 0)');
timeit(f)
The code takes approx 0.45 sec.
Would you be able to suggest anything faster?
You could use repelem to repeat each element in the initial matrix a particular number of times
result = reshape(repelem(A(:), repmat(counts(:), size(A, 2), 1)), [], size(A, 2));
Explanation
A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
counts = [1, 3, 2];
repelem (for vector inputs), repeats the ith element of the first input the number of times specified in the corresponding element of the second input.
repelem([1, 2, 3], [3, 4, 1])
% 1 1 1 2 2 2 2 3
Since repelem only supports vector inputs, we flatten A into a column vector using A(:). We also then need to craft the second input (the number of times to repeat each element of A) such that we repeat counts for each column of A.
nTimes = repmat(counts(:), size(A, 2), 1)
We then use repelem to perform the repetition
repeated = repelem(A(:), nTimes);
We then reshape the result to have the correct number of columns
reshape(repeated, [], size(A, 2))
A solution base on diff and cumsum:
co = size(A,2);
A_diff=diff([zeros(1,co);A]);
idx=cumsum([1;counts(1:end-1)]);
result=zeros(sum(counts),co);
result(idx,:)=A_diff;
result = cumsum(result)
The idea is using cumsum we can reconstruct a vector form the first difference of it.
a=[5 3 2 4];
d= diff([0 a]);
out = cumsum(d)
So out is equal to a.
We can make a matrix all of zeros of the desired size:
result=zeros(sum(count),co);
we should find indices of rows of each section
idx=cumsum([1;count(1:end-1)]);
set the first row of each section to first difference of the matrix A
A_diff=diff([zeros(1,co);A]);
result(idx,:)=A_diff;
so
A = randi(4,4,7);
count=[3 ;4 ;2 ;5];
A =
2 1 4 2 1 3 1
2 3 2 4 4 3 2
1 3 1 4 1 2 1
2 3 2 2 3 1 2
A_diff =
2 1 4 2 1 3 1
0 2 -2 2 3 0 1
-1 0 -1 0 -3 -1 -1
1 0 1 -2 2 -1 1
result =
2 1 4 2 1 3 1
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 2 -2 2 3 0 1
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
-1 0 -1 0 -3 -1 -1
0 0 0 0 0 0 0
1 0 1 -2 2 -1 1
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
apply cumsum to it to get the desired result
result = cumsum(result)
result =
2 1 4 2 1 3 1
2 1 4 2 1 3 1
2 1 4 2 1 3 1
2 3 2 4 4 3 2
2 3 2 4 4 3 2
2 3 2 4 4 3 2
2 3 2 4 4 3 2
1 3 1 4 1 2 1
1 3 1 4 1 2 1
2 3 2 2 3 1 2
2 3 2 2 3 1 2
2 3 2 2 3 1 2
2 3 2 2 3 1 2
2 3 2 2 3 1 2
I'm attempting to find a critical point in a matrix. The value at index (i,j) should be greater than or equal to all elements in its row, and less than or equal to all elements in its column.
Here is what I have (it's off but I'm close):
function C = critical(A)
[nrow ncol] = size(A);
C = [];
for i = 1:nrow
for j = 1:ncol
if (A(i,j) >= A(i,1:end)) && (A(i,j) <= A(1:end,j))
C = [C ; A(i,j)]
end
end
end
You can use logical indexing.
minI = min(A,[],1);
maxI = max(A,[],2);
[row,col] = find(((A.'==maxI.').' & A==minI) ==1)
Details
Remember that Matlab is column major. We therefore transpose A and maxI.
A = [
3 4 1 1 2
2 4 2 1 4
4 3 2 1 2
3 3 1 1 1
2 3 0 2 1];
A.'==maxI.'
ans =
0 0 1 1 0
1 1 0 1 1
0 0 0 0 0
0 0 0 0 0
0 1 0 0 0
Then do the minimum
A==minI
ans =
0 0 0 1 0
1 0 0 1 0
0 1 0 1 0
0 1 0 1 1
1 1 1 0 1
And then multiply the two
((A.'==maxI.').' & A==minI)
ans =
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 1 0 0 0
0 1 0 0 0
Then find the rows and cols
[row,col] = find(((A.'==maxI.').' & A==minI) ==1)
row =
4
5
col =
2
2
Try this vectorised solution using bsxfun
function [ r,c,criP ] = critical( A )
%// finding the min and max values of each col & row resptly
minI = min(A,[],1);
maxI = max(A,[],2);
%// matching all the values of min & max for each col and row resptly
%// getting the indexes of the elements satisfying both the conditions
idx = find(bsxfun(#eq,A,maxI) & bsxfun(#eq,A,minI));
%// getting the corresponding values from the indexes
criP = A(idx);
%// Also getting corresponding row and col sub
[r,c] = ind2sub(size(A),idx);
end
Sample Run:
r,c should be a vector of equal length which represents the row and column subs of each Critical point. While val is a vector of same length giving the value of the critical point itself
>> A
A =
3 4 1 1 2
2 4 2 1 4
4 3 2 1 2
3 3 1 1 1
2 3 0 2 1
>> [r,c,val] = critical(A)
r =
4
5
c =
2
2
val =
3
3
I think there is a simpler way with intersect:
>> [~, row, col] = intersect(max(A,[],2), min(A));
row =
4
col =
2
UPDATE:
With intersect, in case you have multiple critical points, it will only give you the first one. To have all the indicies, there is also another simple way:
>> B
B =
3 4 1 4 2 5
2 5 2 4 4 4
4 4 2 4 2 4
3 4 1 4 1 4
2 5 4 4 4 5
>> row = find(ismember(max(B,[],2),min(B)))
row =
3
4
>> col = find(ismember(min(B),max(B,[],2)))
col =
2 4 6
Note that the set of critical points now should be the combination of row and col, means you have total 6 critical points in this example: (3,2),(4,2),(3,4),(4,4),(3,6),(4,6).
Here you can find how to export such combination.
I have a matrix like the following (arbitrary cols/rows):
1 0 0 0 0
1 2 0 0 0
1 2 3 0 0
1 2 3 4 0
1 2 3 4 5
1 2 5 0 0
1 2 5 3 0
1 2 5 3 4
1 4 0 0 0
1 4 2 0 0
1 4 2 3 0
1 4 2 5 0
1 4 2 5 3
1 4 5 0 0
1 4 5 3 0
2 0 0 0 0
2 3 0 0 0
2 3 4 0 0
2 3 4 5 0
2 5 0 0 0
2 5 3 0 0
2 5 3 4 0
3 0 0 0 0
3 4 0 0 0
3 4 2 0 0
3 4 2 5 0
3 4 5 0 0
and now I want to get all rows where the first element is a certain value X and the last element (that is the last element != 0) is a certain value Y, OR turned around: the first is Y and the last is X.
Can't see any speedful code which does NOT use a for-loop :(
Thanks!
EDIT: To filter all rows with a certain first element is really easy, you don't need to help me here. So let's assume I only want to do the following: Filter all rows where the last element (i.e. the last element != 0 in each row) is either X or Y.
EDIT
Thanks a lot for your posts. I benchmarked the three possible solutions with a matrix of 473408*10 elements. Here's the benchmarkscript:
http://pastebin.com/9hEAWw9a
The results were:
t1 = 2.9425 Jonas
t2 = 0.0999 Brendan
t3 = 0.0951 Oli
So thanks a lot you guys, I'm sticking with Oli's solution and thus accept it. Thanks though for all the other solutions!
All you need to do is to find the linear indices of the last non-zero element of every row. The rest is easy:
[nRows,nCols] = size(A);
[u,v] = find(A); %# find all non-zero elements in A
%# for each row, find the highest column index with accumarray
%# and convert to linear index with sub2ind
lastIdx = sub2ind([nRows,nCols],(1:nRows)',accumarray(u,v,[nRows,1],#max,NaN));
To filter rows, you can then write
goodRows = A(:,1) == X & A(lastIdx) == Y
Here is a trick: Look for numbers with a 0 on the right, and sum them all:
H=[1 2 0 0 0;
2 3 1 0 0;
4 5 8 0 0;
8 5 4 2 2];
lastNumber=sum(H.*[H(:,2:end)==0 true(size(H,1),1)],2)
ans =
2
1
8
2
The rest is easy:
firstNumber=H(:,1);
find( (firstNumber==f) & (lastNumber==l) )
This works only if the numbers in each row are x number of non-zeros followed by a series of zeros. i.e. it will not work if the following is possible 1 0 3 4 0 0, I assume that isn't possible based on the sample input you gave ...
% 'a' is your array
[nx, ny] = size(a);
inds = [0:ny:ny*(nx-1)]' + sum(a ~= 0, 2);
% Needs to transpose so that the indexing reads left-to-right
aT = a';
valid1 = aT(inds) == Y;
valid2 = a(:,1) == X;
valid = valid1 & valid2;
valid_rows = a(valid,:);
This is messy I know ...
i'm trying to find local maxima of a vector of numbers using MATLAB. The built-in findpeaks function will work for a vector such as:
[0 1 2 3 2 1 1 2 3 2 1 0]
where the peaks (each of the 3's) only occupy one position in the vector, but if I have a vector like:
[0 1 2 3 3 2 1 1 2 3 2 1 0]
the first 'peak' occupies two positions in the vector and the findpeaks function won't pick it up.
Is there a nice way to write a maxima-finding function which will detect these sort of peaks?
You can use the REGIONALMAX function from the Image Processing Toolbox:
>> x = [0 1 2 3 3 2 1 1 2 3 2 1 0]
x =
0 1 2 3 3 2 1 1 2 3 2 1 0
>> idx = imregionalmax(x)
idx =
0 0 0 1 1 0 0 0 0 1 0 0 0
Something much easier:
a = [1 2 4 5 5 3 2];
b = find(a == max(a(:)));
output:
b = [4,5]
a = [ 0 1 2 3 3 2 1 2 3 2 1 ];
sizeA = length(a);
result = max(a);
for i=1:sizeA,
if a(i) == result(1)
result(length(result) + 1) = i;
end
end
result contains the max, followed by all the values locations that are equal to max.