Determining if two column adjacent values in a matrix cross over any values in a vector

Hi there,

I have a matrix (attached as ExampleMatrix.mat), where I want to find where two adjacent column values "cross over" values of a separate vector.

Simpler example with only two columns:

TestMatrix = [...
    0,0.533459574621213;
    18.5334595746212,18;
    36,36.5334595746212;
    54,54.5334595746212;
    72,72.5334595746212;
    90,90.5334595746212;
    108,108.533459574621;
    126,126.533459574621;
    144,144.533459574621;
    162,162.533459574621;
    180,180.533459574621;
    198,198.533459574621;
    216,216.533459574621;
    234,234.533459574621;
    252,252.533459574621;
    270,270.533459574621;
    288,288.533459574621;
    306,306.533459574621;
    324,324.533459574621;
    342,342.533459574621...
    ];

TestTarget = [18.25; 306.25];

So far I've been looping over pairs of columns over the values of TestTarget like so:

% Find the difference between two adjacent columns
DifferenceVector = diff(TestMatrix, 1, 2);

% Find + differences
pV_ = sign(DifferenceVector) == 1;

% Find - differences
nV_ = sign(DifferenceVector) == -1;

for i = size(TestTarget, 1);
% For + differences, see if target value is crossed over
passingFromLeft(pV_) = TestMatrix(pV_, 1) + DifferenceVector(pV_) > TestTarget(i);
passingFromRight(pV_) = TestMatrix(pV_, 2) - DifferenceVector(pV_) <= TestTarget(i);

% For - differences, see if target value is crossed over
passingFromLeft(nV_) = TestMatrix(nV_, 1) + DifferenceVector(nV_) < TestTarget(i);
passingFromRight(nV_) = TestMatrix(nV_, 2) - DifferenceVector(nV_) >= TestTarget(i);

passingFromLeft & passingFromRight
end

ans =
  20×1 logical array
   0
   1
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   
ans =
  20×1 logical array
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   0
   1
   0
   0

Is there a more efficient method to do this without looping over the values of TestTarget, for multiple columns?

Answer 1

[Adam Danz]

After sorting the matrix so that minimum values of each row are on the left, you just need one line to find the intervals that 'skip over' the targets.

% Sort matrix so min val is always on left
TMsort = sort(TestMatrix,2); 
result = (TMsort(:,1) < TestTarget.') & (TMsort(:,2) > TestTarget.'); 

• * TestTarget in your example is a column vector. It must be a row vector in the line above which is why it's transposed.
• * Column 'n' of the 'result' matrix corresponds to TestTarget(n).

Results:

result =
  20×2 logical array
   0   0
   1   0
   0   0
   0   0
   0   0
   0   0
   0   0
   0   0
   0   0
   0   0
   0   0
   0   0
   0   0
   0   0
   0   0
   0   0
   0   0
   0   1
   0   0
   0   0

However, the data you attached in the mat file contains 101 columns so I'm not sure what needs adapted from this 2-column solution. In other words, are you just conserned with the first and last column (assuming they are sorted)?

[Terence Ng]

Hi Adam,

Sorry, I forgot to mention that the attached data has an extra column at the start for indexing data (row 1 tracks position of something, row 2 tracks position of another, etc...).

I'm not concerned with only the first and last column, as it's possible that the position crosses over the values in TestTarget multiple times, but maybe that should be for another question.

I had two loops going over pairs of columns and then each value in target, so simplifying it down to a single loop (for the pairs of columns) is in-line with what I was looking for.

[Adam Danz]

OK, I couldn't understand if there was a follow-up question or not. If I understand you correctly, you'll need to apply my method to the relevant portion of your matrix by removing it from the irrelevant columns. After you sort by row, if you're just interested in whether the target is skipped over within that row, you just need to look at the first and last (sorted) column within each row.

Let me know if can help more on this matter.