Convert values upper triangular matrix into vector

Hi all,

Imagine a matrix of the following form:

     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
    

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

[Fathima Bareeda]

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]

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

Answer 1

[Jan]

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);

[Andrei Bobrov]

out = nonzeros(A.');

[Jos (10584)]

@Andrei. nonzeros does not work when the underlying vector has 0's

[Lucas Bezerra]

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

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

[Jan]

@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] .

Answer 2

[gb]

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;]

A = 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

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

v = 15×1

1 2 3 4 5 4 6 8 10 9

[Jan]

Why do you repeat this part of my answer?

Answer 3

[Witold Waldman]

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

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% 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

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