lower triangular semidefinite matrix

Question

Albert Stirling 2020-5-4

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/522852-lower-triangular-semidefinite-matrix

评论： Albert Stirling 2020-5-4

how can i build a sparse matrix in this form for a given semidefinite matrix? i only need the sparse lower triangular of semidefinite matrix

for example a semidefinite matrix as Q0:

2 0 -1

Q0 = 0 0.2 0

-1 0 2

is written as:

i = [1 2 3 3 ];

j = [1 2 3 1 ];

c = [2 0.2 2 -1 ];

where i shows number of row

j shows number of column

and c is the elemnt that belong to (i,j) that is not zero and belong to lower triangular of semidefinite matrix

2 个评论
显示无隐藏无

Guillaume 2020-5-4

I'm not sure I understand the problem, sparse(i, j, c) would create your sparse matrix.

Guillaume 2020-5-4

Albert Stirling's comment mistakenly posted as an Answer moved here:

I need a simple algorithm that select the non-zero values in shown lower triangular part of this symmetric matrix and return it as below:

i = [1 2 3 3 ];

j = [1 2 3 1 ];

c = [2 0.2 2 -1 ];

i need the algorithm to be flexible so i can give it any desired symmetric matrix and have an answer like the one mentioned.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Guillaume 2020-5-4

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/522852-lower-triangular-semidefinite-matrix#answer_430138

在 MATLAB Online 中打开

[i, j, c] = find(tril(yourmatrix))

seems to be what you're after.

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Albert Stirling 2020-5-4

在 MATLAB Online 中打开

thank you so much that was a quick way to handle this problam.

however i found a long one myself as below:

Q0=[-2 0 0.2;
    0 -2 0;
    0.2 0 -0.2]
[, c]=size(Q0);
for i=1:c
    
   for j=1:3-i
       
    Q0(i,i+j)=0;
   
   end
  
    
end
Q1=sparse(Q0);
[i,j,s] = find(Q1);
f=[i,j,s]'

请先登录，再进行评论。

Answer 2

John D'Errico 2020-5-4

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/522852-lower-triangular-semidefinite-matrix#answer_430140

编辑：John D'Errico 2020-5-4

在 MATLAB Online 中打开

You just want the lower triangle elements. semi-definite-ness is irrelevant to what you asked for at the end.

A = sprand(5,5,.3);
>> full(A)
ans =
      0.46421      0.83266            0     0.022104      0.18026
      0.26627            0            0            0            0
            0            0            0            0            0
            0            0            0      0.92865            0
            0            0      0.37763      0.42783            0
>> [Rind,Cind,val] = find(tril(A))
Rind =
     1
     2
     5
     4
     5
Cind =
     1
     1
     3
     4
     4
val =
      0.46421
      0.26627
      0.37763
      0.92865
      0.42783

That is how you would EXTRACT the lower triangle into a set of row and column indices, and the non-zero elements in those positions. Which on the face of it, seems to be your question. However, my guess is that you really want to build the sparse matrix from those values? Or, perhaps you just don't understand that sparse matrices already exist in MATLAB and can be used as such? It is not at all clear what is the real problem.

Regardless, if you wanted to build the matrix as a sparse one, then just call sparse using those vectors.

Atril = sparse(Rind,Cind,val,5,5)
Atril =
   (1,1)         0.46421
   (2,1)         0.26627
   (5,3)         0.37763
   (4,4)         0.92865
   (5,4)         0.42783
>> full(Atril)
ans =
      0.46421            0            0            0            0
      0.26627            0            0            0            0
            0            0            0            0            0
            0            0            0      0.92865            0
            0            0      0.37763      0.42783            0