Convert values upper triangular matrix into vector

Question

Tim Elbers 2019-5-14

1
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/461966-convert-values-upper-triangular-matrix-into-vector

编辑： Witold Waldman 2024-4-25，5:31

采纳的回答： Jan

在 MATLAB Online 中打开

Hi all,

Imagine a matrix of the following form:

   2     3     4     5
   4     6     8    10
   0     9    12    15
   0     0    16    20
   0     0     0    25
    

Now i do like to obtain a vector with only the values of the upper triangular matrix. in other words a vector of underneath form.

[1 2 3 4 5 4 6 8 10 9 12 15 16 20 25]

What is the best way to obtain this vector?

Thanks in advance

2 个评论
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Fathima Bareeda 2021-6-5

What is the best way to obtain vector in the form of diagonal elements first and then upper triangular elements..

For eg:[1 4 9 16 25 2 3 4 5 6 8 10 12 15 20]

Walter Roberson 2021-6-5

在 MATLAB Online 中打开

M = [     1     2     3     4     5
     0     4     6     8    10
     0     0     9    12    15
     0     0     0    16    20
     0     0     0     0    25
    ]
M = 5×5
     1     2     3     4     5
     0     4     6     8    10
     0     0     9    12    15
     0     0     0    16    20
     0     0     0     0    25
D = diag(M);
eg = [D.', squareform((M-diag(D)).')]
eg = 1×15
     1     4     9    16    25     2     3     4     5     6     8    10    12    15    20

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Answer 1

Jan 2019-5-14

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/461966-convert-values-upper-triangular-matrix-into-vector#answer_374919

编辑：Jan 2019-5-17

在 MATLAB Online 中打开

At = A.';
m  = tril(true(size(At)));
v  = At(m).'

Maybe this is faster (>=R2016b due to auto-expanding):

At = A.';
m  = (1:size(At,1)).' >= (1:size(At,2));
v  = At(m);

4 个评论
显示 2更早的评论隐藏 2更早的评论

Lucas Bezerra 2021-5-25

在 MATLAB Online 中打开

It becomes even simpler if you use the triu function instead:

m  = triu(true(size(A)));
v  = A(m)

Jan 2021-5-25

@Lucas Bezerra: The replies the elements in the wrong order [1 2 4 3 6 9 4 8 12 16 5 10 15 20 25].' instead of the wanted [1 2 3 4 5 4 6 8 10 9 12 15 16 20 25] .

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Answer 2

Witold Waldman 2024-4-25，5:29

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/461966-convert-values-upper-triangular-matrix-into-vector#answer_1447466

编辑：Witold Waldman 2024-4-25，5:31

在 MATLAB Online 中打开

A=[
    1     2     3     4     5
    0     4     6     8    10
    0     0     9    12    15
    0     0     0    16    20
    0     0     0     0    25
    ];
% The following previously submitted code creates two intermediate
% matrices, At and m, in addition to the solution array v.
tic
At = A.';
m  = tril(true(size(At)));
v  = At(m).';
toc
Elapsed time is 0.003788 seconds.
v
v = 1x15
     1     2     3     4     5     4     6     8    10     9    12    15    16    20    25
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
% The following code does not create any intermediate matrices.
% It might be preferred when dealing with very large matrices.
% In testing, this code was the slower of the two.
tic
nA = size(A,1);
ibeg = 1;
for n = 1:nA
    iend = ibeg+nA-n;
    v(ibeg:iend) = A(n,n:nA);
    ibeg = iend+1;
end
toc
Elapsed time is 0.002825 seconds.
v
v = 1x15
     1     2     3     4     5     4     6     8    10     9    12    15    16    20    25
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>