How to generate lower triangle in a matrix where elements are the inverse of the upper traingle and diagonal is one

I want to generate a matrix where lower triangle elements are the inverse of upper triangle elements and diagonal elements are one.

where user inputs the upper triangle elements and lower triangle elements are generated automatically. I have attached the required matrix as an example. Thanks!

Answer 1

[James Tursa]

E.g.,

>> M = [0 7 9 8;
        0 0 8 6;
        0 0 0 4;
        0 0 0 0]
M =
     0     7     9     8
     0     0     8     6
     0     0     0     4
     0     0     0     0
>> MT = (1./M)'
MT =
       Inf       Inf       Inf       Inf
    0.1429       Inf       Inf       Inf
    0.1111    0.1250       Inf       Inf
    0.1250    0.1667    0.2500       Inf
>> x = logical(tril(ones(size(M)),-1))
x =
     0     0     0     0
     1     0     0     0
     1     1     0     0
     1     1     1     0
>> M(x) = MT(x)
M =
         0    7.0000    9.0000    8.0000
    0.1429         0    8.0000    6.0000
    0.1111    0.1250         0    4.0000
    0.1250    0.1667    0.2500         0
>> M(1:size(M,1)+1:end) = 1
M =
    1.0000    7.0000    9.0000    8.0000
    0.1429    1.0000    8.0000    6.0000
    0.1111    0.1250    1.0000    4.0000
    0.1250    0.1667    0.2500    1.0000

[Sanjeev Goyal]

Hi Thank you very much Tursa, Can I take input from the user through inputdlg for specific elements of a matrix, like just the upper triangle elements.

[James Tursa]

You could take the input as a vector, and then map the elements into the appropriate upper triangle spots. Is that what you mean?

[Sanjeev Goyal]

Yes! I mean exactly this, but how to map the input into matrix as the order of the matrix will also be decided by the user

[James Tursa]

E.g., here is some rough code that will do it for row order entry:

k = 1:10000;
k = (k.*(k+1))/2;
while( true )
    disp('Enter the following vector inside of square brackets [ ]');
    v = input('Input upper triangular (super-diagonal) elements in row order: ');
    m = numel(v);
    [a b] = ismember(m,k);
    if( a )
        break;
    end
    disp('*** Invalid number of elements to fill out a square matrix ***');
end
n = b + 1;
M = zeros(n,n);
x = logical(tril(ones(size(M)),-1));
M(x) = v;
M = M.';
MT = (1./M).';
M(x) = MT(x);
M(1:size(M,1)+1:end) = 1;

For other orders you can ask for more inputs and vary the mapping accordingly. E.g., entering the lower triangle part, or entering the numbers in column order.

[Sanjeev Goyal]

Awesome! its working. Thank you very much. I have a last question- can graphical user input be made like a 4X4 matrix where user only inputs the upper triangle elements and the order of the matrix be decided by the user.Thanks once again