How to create matrix with fixed sum in rows and fixed increment in elements
显示 更早的评论
I would like to create a 231*3 matrix whose elements are all multiples of 0.05 and the sum of each row be equal to 1.
E.g.
0 0 1
0 0.05 0.95
0.05 0 0.95
0 0.1 0.90
0.1 0 0.90
0.05 0.05 0.90
......
采纳的回答
Straightforward exhaustive search which does not generate any superfluous rows:
V = 0:5:100;
Z = nan(0,3);
for n1 = V
for n2 = V
for n3 = V
if (n1+n2+n3)==100
Z(end+1,:) = [n1,n2,n3];
end
end
end
end
Z = Z/100;
This gives all 231 unique rows:
>> Z
Z =
0.00000 0.00000 1.00000
0.00000 0.05000 0.95000
0.00000 0.10000 0.90000
0.00000 0.15000 0.85000
0.00000 0.20000 0.80000
0.00000 0.25000 0.75000
0.00000 0.30000 0.70000
0.00000 0.35000 0.65000
0.00000 0.40000 0.60000
0.00000 0.45000 0.55000
0.00000 0.50000 0.50000
0.00000 0.55000 0.45000
0.00000 0.60000 0.40000
0.00000 0.65000 0.35000
0.00000 0.70000 0.30000
... lots of rows here
0.85000 0.05000 0.10000
0.85000 0.10000 0.05000
0.85000 0.15000 0.00000
0.90000 0.00000 0.10000
0.90000 0.05000 0.05000
0.90000 0.10000 0.00000
0.95000 0.00000 0.05000
0.95000 0.05000 0.00000
1.00000 0.00000 0.00000
>> size(Z)
ans =
231 3
>> size(unique(Z,'rows'))
ans =
231 3
4 个评论
Zijin Xu
2018-9-7
Rik
2018-9-7
As is often the case, it is a trade-off between memory and speed. My solution is slightly faster, but yours will consume less memory (especially for cases with smaller step sizes).
"My solution is slightly faster, but yours will consume less memory (especially for cases with smaller step sizes)."
The speed of my answer could be improved by preallocation and using a counter as the index:
Z = nan(231,3);
K = 0;
...
K = K+1;
Z(K,:) = [...];
...
I guess there is also some formula for getting "231", but it escapes me at this moment...
Bruno Luong
2018-9-7
The formula is 231=nchoosek(20+3-1,3-1), you can see my code to see why.
更多回答（1 个）
Bruno Luong
2018-9-7
编辑：Bruno Luong
2018-9-7
s = 0.05;
n = round(1/s);
m = 3;
r = nchoosek(1:n+m-1,m-1);
z = zeros(size(r,1),1);
r = (diff([z, r, n+m+z],1,2)-1)/n
4 个评论
Rik
2018-9-7
I don't know if it is relevant, but this method is not guaranteed to give unique rows.
Bruno Luong
2018-9-7
I miss understood whereas OP wants random or all combinations. Now I fix it since the number of combinations is just 231.
Zijin Xu
2018-9-7
Stephen23
2018-9-7
+1 Very nice.
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