Permanent A for any txt matrix

I am new to matlab and would like to know how we can find the number of 0-1 matrices in a given t x t matrix with permanent greater or equal to 1. I have function that find the permanent of any given matrix but I am not sure how to use that to have my desired results. Any help would be highly appreciated.

[Oleg Komarov]

What's a permanent?

[Walter Roberson]

Determinant I _suspect_

Answer 1

[John D'Errico]

Actaually, probably NOT the determinant.

The matrix permanent is sadly more computationally intensive than the determinant, which can be computed using an O(n^3) algorithm based on an LU factorization of the matrix.

Below is some code I wrote a few years ago to compute the matrix permanent. Of course, that is not the real question, I think. I think you were looking for the number of submatrices of A, such that the permanent of those submatrices is greater than 1?

Anyway, far too late for my response. Sorry for missing your question long ago.

function P = permanent(A)
  % permanent - compute the matrix permanent of A. A need not be square
  % usage: P = permanent(A)
  %
  %  https://en.wikipedia.org/wiki/Computing_the_permanent
  %
  %  Think of the permanent as something like a determinant, but the
  %  terms are not added and subtracted as in the determinant.
  %
  % arguments: (input)
  %  A - matrix (usually squares) but it need not be so.
  %      Because the computations of the permanent are extremely
  %      intensive, this code will be terribly slow for large
  %      matrices. Large here is roughly larger than 10x10. This
  %      is true even though a non-recursive algorithm is employed.
  %
  %      In the case of a non-square matrix A, all terms are summed.
  %
  % arguments: (output)
  %  P - permanent of the matrix A.
  %
  % Example:
  %   A = magic(3);
  %   permanent(A)
  %   ans =
  %     900
  %
  % Example:
  %  A = ones(5);
  %  permanent(A)
  %  ans =
  %     120
  %
  % Example:
  %  A = tril(ones(5),1);
  %  permanent(A)
  %  ans =
  %      16
  %  
  % Example:
  %  A = reshape(1:6,2,3)
  %  permanent(A)
  %  ans =
  %      64
  %
  % Author: John D'Errico
  % E-mail: [e-mail]
  % Date: 6/19/2017
  
  if isempty(A)
    P = [];
    return
  end
  
  % A shape
  [N,M] = size(A);
  
  % The simple case is where A is square. But if A is non-square, 
  % make sure it has more columns than rows. transpose won't impact the
  % permanent.
  if N > M
    A = A.';
    [N,M] = deal(M,N);
  end
  
  % special case, N == 1
  if N == 1
    P = sum(A);
    return
  end
   
  % if we drop through to here, then A is at least 2x2. That is,
  % we know that A now has more columns than rows. And since we
  % know that A has more than 2 rows, at least 2x2 is a given.
  
  % assume the non-square case. But if A is square, the computation
  % will be simple enough. While not a recursive method, all combinations
  % are explicitly generated using perms. This will be memory intensive
  % for N larger than 10.
  if N == M
    cols = 1:N;
  else
    cols = nchoosek(1:M,N);
  end
  cN = perms(1:N);
  
  P = 0;
  for i = 1:size(cols,1)
    P_i = A(cN(:,1),cols(i,1));
    
    for j = 2:N
      P_i = P_i .* A(cN(:,j),cols(i,j));
    end
    
    P = P + sum(P_i);
  end