Info Catalog octave: Diagonal and Permutation Matrices octave: Matrix Algebra

octave: Basic Usage

 
 21.1 Creating and Manipulating Diagonal/Permutation Matrices
 ============================================================
 
 A diagonal matrix is defined as a matrix that has zero entries outside
 the main diagonal; that is, ‘D(i,j) == 0’ if ‘i != j’.  Most often,
 square diagonal matrices are considered; however, the definition can
 equally be applied to non-square matrices, in which case we usually
 speak of a rectangular diagonal matrix.
 
    A permutation matrix is defined as a square matrix that has a single
 element equal to unity in each row and each column; all other elements
 are zero.  That is, there exists a permutation (vector) ‘p’ such that
 ‘P(i,j) == 1’ if ‘j == p(i)’ and ‘P(i,j) == 0’ otherwise.
 
    Octave provides special treatment of real and complex rectangular
 diagonal matrices, as well as permutation matrices.  They are stored as
 special objects, using efficient storage and algorithms, facilitating
 writing both readable and efficient matrix algebra expressions in the
 Octave language.  The special treatment may be disabled by using the
 functions “disable_diagonal_matrix” and “disable_permutation_matrix”.
 
  -- : VAL = disable_diagonal_matrix ()
  -- : OLD_VAL = disable_diagonal_matrix (NEW_VAL)
  -- : disable_diagonal_matrix (NEW_VAL, "local")
      Query or set the internal variable that controls whether diagonal
      matrices are stored in a special space-efficient format.
 
      The default value is true.  If this option is disabled Octave will
      store diagonal matrices as full matrices.
 
      When called from inside a function with the "local" option, the
      variable is changed locally for the function and any subroutines it
      calls.  The original variable value is restored when exiting the
      function.
 
DONTPRINTYET       See also: disable_range XREFdisable_range, *noteDONTPRINTYET       See also: disable_range XREFdisable_range, 
      disable_permutation_matrix XREFdisable_permutation_matrix.
 
  -- : VAL = disable_permutation_matrix ()
  -- : OLD_VAL = disable_permutation_matrix (NEW_VAL)
  -- : disable_permutation_matrix (NEW_VAL, "local")
      Query or set the internal variable that controls whether
      permutation matrices are stored in a special space-efficient
      format.
 
      The default value is true.  If this option is disabled Octave will
      store permutation matrices as full matrices.
 
      When called from inside a function with the "local" option, the
      variable is changed locally for the function and any subroutines it
      calls.  The original variable value is restored when exiting the
      function.
 
DONTPRINTYET       See also: disable_range XREFdisable_range, *noteDONTPRINTYET       See also: disable_range XREFdisable_range, 
      disable_diagonal_matrix XREFdisable_diagonal_matrix.
 
    The space savings are significant as demonstrated by the following
 code.
 
      x = diag (rand (10, 1));
      xf = full (x);
      sizeof (x)
      ⇒ 80
      sizeof (xf)
      ⇒ 800
 

Menu

 
· Creating Diagonal Matrices
· Creating Permutation Matrices
· Explicit and Implicit Conversions
 

Info Catalog octave: Diagonal and Permutation Matrices octave: Matrix Algebra