Info Catalog octave: Creating Diagonal Matrices octave: Basic Usage octave: Explicit and Implicit Conversions

octave: Creating Permutation Matrices

 
 21.1.2 Creating Permutation Matrices
 ------------------------------------
 
 For creating permutation matrices, Octave does not introduce a new
 function, but rather overrides an existing syntax: permutation matrices
 can be conveniently created by indexing an identity matrix by
 permutation vectors.  That is, if Q is a permutation vector of length N,
 the expression
 
        P = eye (n) (:, q);
 
 will create a permutation matrix - a special matrix object.
 
      eye (n) (q, :)
 
 will also work (and create a row permutation matrix), as well as
 
      eye (n) (q1, q2).
 
    For example:
 
        eye (4) ([1,3,2,4],:)
      ⇒
      Permutation Matrix
 
         1   0   0   0
         0   0   1   0
         0   1   0   0
         0   0   0   1
 
        eye (4) (:,[1,3,2,4])
      ⇒
      Permutation Matrix
 
         1   0   0   0
         0   0   1   0
         0   1   0   0
         0   0   0   1
 
    Mathematically, an identity matrix is both diagonal and permutation
 matrix.  In Octave, ‘eye (n)’ returns a diagonal matrix, because a
 matrix can only have one class.  You can convert this diagonal matrix to
 a permutation matrix by indexing it by an identity permutation, as shown
 below.  This is a special property of the identity matrix; indexing
 other diagonal matrices generally produces a full matrix.
 
        eye (3)
      ⇒
      Diagonal Matrix
 
         1   0   0
         0   1   0
         0   0   1
 
        eye(3)(1:3,:)
      ⇒
      Permutation Matrix
 
         1   0   0
         0   1   0
         0   0   1
 
    Some other built-in functions can also return permutation matrices.
 Examples include “inv” or “lu”.
 

Info Catalog octave: Creating Diagonal Matrices octave: Basic Usage octave: Explicit and Implicit Conversions