How to get diagonal elements of non-square matrix?

13 次查看（过去 30 天）
turningpoint
turningpoint 2017-3-26
评论： Christopher Gordon 2021-2-20
Hi, guys!
I am working with rectangular matrixes and I want to extract the values that go from the upper left corner to lower right (diagonal). I have tried to write some codes, but they don't give me good results (it actually gets worst as the matrix gets "more rectangular"). Does anyone have an ideia?
Thank you,
Carolina Magalhães
  2 个评论
Jan
Jan 2017-3-26
What is the wanted output for a rectangular matrix? Do you mean the diagnonal from the [1,1] element to the [n,n] element, when the n is: min(size(X))? Or do you mean the "diagonal" from the element [1,1] to [m,n], when m and n are the dimensions of the matrix? In the latter case, what is the wanted result? The nearest element or a bilinear interpolation?
turningpoint
turningpoint 2017-3-26
Thanks for the fast response! I want the "diagonal" from (1,1) to (m,n). Bilinear interpolation would give me the most correct result.

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Guillaume
Guillaume 2017-3-26
What you want effectively is the values on the line going from one corner to the other.
If you have the image processing toolbox, you could use improfile for that:
m = rand(20, 10); %demo matrix;
[colfrom, rowfrom, values] = improfile(m, [1, size(m, 2)], [1, size(m, 1)]);
If you do not have the toolbox, you can implement your own line drawing algorithm. Bresenham's and Wu's are both very easy to implement.
  2 个评论
turningpoint
turningpoint 2017-3-26
Thanks a lot! I did not know that function, but it worked!
Jan
Jan 2017-3-26
improfile replies a [19 x 1] vector. This might be useful:
[s1, s2] = size(m);
values = improfile(m, [1, s2], [1, s1], max(s1, s2), 'bilinear')

请先登录，再进行评论。

更多回答（2 个）

Image Analyst
Image Analyst 2017-3-26
Try this:
m = randi(9, 5, 12) % Sample data
[rows, columns] = size(m)
for k = 1 : min([rows, columns])
output(k) = m(k,k);
end
output % Echo to command window
  2 个评论
turningpoint
turningpoint 2017-3-26
I wanna go from (1,1) to (m,n) and this only goes from (1,1) to (min(m,n),min(m,n)), which leaves most of the numbers out as my matrix gets more rectangular.
Image Analyst
Image Analyst 2017-3-27
I thought you wanted to go down the exact diagonal at 45 degrees. If you go from corner to corner without going down a 45 degree diagonal, then you'll have to interpolate values. I didn't know you wanted to interpolate - I thought you wanted to extract existing values. If you want to interpolate then improfile() is the way to go.

请先登录，再进行评论。

Jan
Jan 2017-3-26
编辑：Jan 2017-3-26
You can create your own interpolation method:
function D = Diagonal(M, n)
% Inputs: M: Matrix
% n: Number of points, default: length(M)
% Outputs: D: Interpolated values of diagonal with n elements
% Author: Jan Simon, License: CC BY-SA 3.0
[s1, s2] = size(M);
if nargin == 1
n = max(s1, s2); % Number of wanted points, can be defined freely
end
x = linspace(1, s2, n); % n steps along rows
xN = floor(x);
xN(n) = s2 - 1; % care about last step
xS = x - xN;
y = linspace(1, s1, n); % n steps along columns
yN = floor(y);
yN(n) = s1 - 1; % care about last step
yS = y - yN;
Index = sub2ind([s1, s2], yN, xN); % Get linear index
D = (M(Index) .* (1 - xS) + M(Index + s1) .* xS) .* (1 - yS) + ...
(M(Index + 1) .* (1 - xS) + M(Index + s1 + 1) .* xS) .* yS;
end
  2 个评论
turningpoint
turningpoint 2017-3-26
I have found a simpler way with the improfile tool. Thank you for your answer!
Christopher Gordon
Christopher Gordon 2021-2-20
Jan,
I'd like to try your method, but I keep ending up with a vector instead of the expanded array. My starting matrix is 30 columns (spectra) where each column is 1024 rows (pixels) long (1024 x 30 overall). Those spectra were taken at various points along my detectors 1024 pixel chip at randome points. The first is at pixel 13 and the last one is at pixel 1010, with 28 other pixels in between. What I would like to do is diagonally interpolate/extrapolate to see what the spectrum would be at each of the 1024 pixels. Is this possible with your function?

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Linear Algebra 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by