Help with the matrix creation pls ? if possible not a hardcoded solution but a function .

2015 9 14
3 个回答
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更新时间：2015 9 15
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0 个投票

Hi i need some help, i need to create a matrix that will have n columns (n is the only input) and the output would be a matrix of n x m in a way that every row has a sum of 1, where all the numbers are positive and have an increment of 0.1. For example i n = 3 the first couple of rows would look like this
0 0 1
0 0.1 0.9
0 0.2 0.8
....
1 0 0

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Steven Lord
Steven Lord 2015-9-15
Your example matrix does not satisfy your requirement "where all the numbers are positive" since it contains 0 values. I assume you meant "where all the numbers are nonnegative?"

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Stephen23
Stephen23 2015-9-15
编辑：Stephen23 2015-9-15

1 个投票

This is Roger Stafford's memory-efficient solution, proposed here http://de.mathworks.com/matlabcentral/newsreader/view_thread/143037. It runs about twice as fast a Jos' and my other solutions.
n = 3;
d = 10;
c = nchoosek(1:d+n-1,n-1);
m = size(c,1);
t = ones(m,d+n-1);
t(repmat((1:m).',1,n-1)+(c-1)*m) = 0;
u = [zeros(1,m);t.';zeros(1,m)];
v = cumsum(u,1);
x = diff(reshape(v(u==0),n+1,m),1).'/d;
Where the output array is:
>> x
x =
0.00000 0.00000 1.00000
0.00000 0.10000 0.90000
0.00000 0.20000 0.80000
0.00000 0.30000 0.70000
0.00000 0.40000 0.60000
0.00000 0.50000 0.50000
0.00000 0.60000 0.40000
0.00000 0.70000 0.30000
0.00000 0.80000 0.20000
0.00000 0.90000 0.10000
0.00000 1.00000 0.00000
0.10000 0.00000 0.90000
0.10000 0.10000 0.80000
0.10000 0.20000 0.70000
0.10000 0.30000 0.60000
0.10000 0.40000 0.50000
0.10000 0.50000 0.40000
0.10000 0.60000 0.30000
0.10000 0.70000 0.20000
0.10000 0.80000 0.10000
0.10000 0.90000 0.00000
0.20000 0.00000 0.80000
0.20000 0.10000 0.70000
0.20000 0.20000 0.60000
0.20000 0.30000 0.50000
0.20000 0.40000 0.40000
0.20000 0.50000 0.30000
0.20000 0.60000 0.20000
0.20000 0.70000 0.10000
0.20000 0.80000 0.00000
0.30000 0.00000 0.70000
0.30000 0.10000 0.60000
0.30000 0.20000 0.50000
0.30000 0.30000 0.40000
0.30000 0.40000 0.30000
0.30000 0.50000 0.20000
0.30000 0.60000 0.10000
0.30000 0.70000 0.00000
0.40000 0.00000 0.60000
0.40000 0.10000 0.50000
0.40000 0.20000 0.40000
0.40000 0.30000 0.30000
0.40000 0.40000 0.20000
0.40000 0.50000 0.10000
0.40000 0.60000 0.00000
0.50000 0.00000 0.50000
0.50000 0.10000 0.40000
0.50000 0.20000 0.30000
0.50000 0.30000 0.20000
0.50000 0.40000 0.10000
0.50000 0.50000 0.00000
0.60000 0.00000 0.40000
0.60000 0.10000 0.30000
0.60000 0.20000 0.20000
0.60000 0.30000 0.10000
0.60000 0.40000 0.00000
0.70000 0.00000 0.30000
0.70000 0.10000 0.20000
0.70000 0.20000 0.10000
0.70000 0.30000 0.00000
0.80000 0.00000 0.20000
0.80000 0.10000 0.10000
0.80000 0.20000 0.00000
0.90000 0.00000 0.10000
0.90000 0.10000 0.00000
1.00000 0.00000 0.00000

更多回答（2 个）

Jos (10584)
Jos (10584) 2015-9-15

1 个投票

% brute force
A = [] ;
for k=0:10
for j=0:10-k
A(end+1,:) = [k, j 10-k-j] ;
end
end
A = A ./ 10
Stephen23
Stephen23 2015-9-15
编辑：Stephen23 2015-9-15

0 个投票

This code generates permutations (with replacement) of the vector 0:0.1:1, and then selects only the rows that sum to one. I don't claim that this is an efficient use of memory, but it works. For the most efficient code see my other answer.
N = 3;
V = 0:0.1:1;
[Y{N:-1:1}] = ndgrid(1:numel(V));
X = reshape(cat(N+1,Y{:}),[],N);
B = V(X);
Z = sum(B,2);
B = B(0.99<Z&Z<1.01,:);
And the output matrix for N=3 (N=4 is below):
>> B
B =
0.00000 0.00000 1.00000
0.00000 0.10000 0.90000
0.00000 0.20000 0.80000
0.00000 0.30000 0.70000
0.00000 0.40000 0.60000
0.00000 0.50000 0.50000
0.00000 0.60000 0.40000
0.00000 0.70000 0.30000
0.00000 0.80000 0.20000
0.00000 0.90000 0.10000
0.00000 1.00000 0.00000
0.10000 0.00000 0.90000
0.10000 0.10000 0.80000
0.10000 0.20000 0.70000
0.10000 0.30000 0.60000
0.10000 0.40000 0.50000
0.10000 0.50000 0.40000
0.10000 0.60000 0.30000
0.10000 0.70000 0.20000
0.10000 0.80000 0.10000
0.10000 0.90000 0.00000
0.20000 0.00000 0.80000
0.20000 0.10000 0.70000
0.20000 0.20000 0.60000
0.20000 0.30000 0.50000
0.20000 0.40000 0.40000
0.20000 0.50000 0.30000
0.20000 0.60000 0.20000
0.20000 0.70000 0.10000
0.20000 0.80000 0.00000
0.30000 0.00000 0.70000
0.30000 0.10000 0.60000
0.30000 0.20000 0.50000
0.30000 0.30000 0.40000
0.30000 0.40000 0.30000
0.30000 0.50000 0.20000
0.30000 0.60000 0.10000
0.30000 0.70000 0.00000
0.40000 0.00000 0.60000
0.40000 0.10000 0.50000
0.40000 0.20000 0.40000
0.40000 0.30000 0.30000
0.40000 0.40000 0.20000
0.40000 0.50000 0.10000
0.40000 0.60000 0.00000
0.50000 0.00000 0.50000
0.50000 0.10000 0.40000
0.50000 0.20000 0.30000
0.50000 0.30000 0.20000
0.50000 0.40000 0.10000
0.50000 0.50000 0.00000
0.60000 0.00000 0.40000
0.60000 0.10000 0.30000
0.60000 0.20000 0.20000
0.60000 0.30000 0.10000
0.60000 0.40000 0.00000
0.70000 0.00000 0.30000
0.70000 0.10000 0.20000
0.70000 0.20000 0.10000
0.70000 0.30000 0.00000
0.80000 0.00000 0.20000
0.80000 0.10000 0.10000
0.80000 0.20000 0.00000
0.90000 0.00000 0.10000
0.90000 0.10000 0.00000
1.00000 0.00000 0.00000
And the output matrix for N=4:
>> B
B =
0.00000 0.00000 0.00000 1.00000
0.00000 0.00000 0.10000 0.90000
0.00000 0.00000 0.20000 0.80000
0.00000 0.00000 0.30000 0.70000
0.00000 0.00000 0.40000 0.60000
0.00000 0.00000 0.50000 0.50000
0.00000 0.00000 0.60000 0.40000
0.00000 0.00000 0.70000 0.30000
0.00000 0.00000 0.80000 0.20000
0.00000 0.00000 0.90000 0.10000
0.00000 0.00000 1.00000 0.00000
0.00000 0.10000 0.00000 0.90000
....
0.80000 0.00000 0.20000 0.00000
0.80000 0.10000 0.00000 0.10000
0.80000 0.10000 0.10000 0.00000
0.80000 0.20000 0.00000 0.00000
0.90000 0.00000 0.00000 0.10000
0.90000 0.00000 0.10000 0.00000
0.90000 0.10000 0.00000 0.00000
1.00000 0.00000 0.00000 0.00000

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