Checking if minimum of a matrix occurs on the diagonal

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KAE 2018-10-4

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编辑： KAE 2018-10-4

For a matrix, I would like to check if the minimum value of each row is found on the diagonal. The minimum value can occur more than once within a row. Since the min command returns the index of the first occurrence of the minimum, min can miss later occurrences on the diagonal, as follows:

testMatrix = [     1     3     5     1
     2     0     4     6
     3     9     2     7
    -2     9     4    -2];
[~, iMin] = min(a)
iMin =
   4     2     3     4

How can I check if the row minimum is found on the diagonal? I am working with a very large matrix in reality, so I would like to avoid looping down the rows.

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Adam 2018-10-4

编辑：Adam 2018-10-4

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Can you not do something like

diag( testMatrix ) == min( testMatrix )

?

I haven't put a whole lot of thought into it so there may be perfectly good reasons why you can't!

KAE 2018-10-4

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This does not seem to check the diagonals, or maybe I am misunderstanding,

ans =

    4×4 logical array
 0   0   0
 1   0   0
 0   1   0
 0   0   1

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Answer 1

Julian Hapke 2018-10-4

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with a slight modification of Adams comment:

diag(testMatrix) == min(testMatrix , [], 2)

min accepts the dimension in which you want the minimum, in this case you want the minimum of each row, so in direction 2 and check against the diagonal of the matrix

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KAE 2018-10-4

编辑：KAE 2018-10-4

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Works and returns a vector saying whether it is on the diagonal or not, which I realized is what I was looking for when I saw the output. Thanks!

Here it shows it returns zero for rows when the minimum is not on the diagonal.

testMatrixOneWrong = ...
[     1     3     5    -2
     2     0     4     6
     3     9     2     7
    -2     9     4    -2]
diag(testMatrixOneWrong) == min(testMatrixOneWrong, [], 2)
ans =
    4×1 logical array
     0
     1
     1
     1