(octave.info)Basic Usage

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Next: Matrix Algebra Up: Diagonal and Permutation Matrices

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21.1 Creating and Manipulating Diagonal/Permutation Matrices
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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.

     See also: Note: disable_range, Note:
     disable_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.

     See also: Note: disable_range, Note:
     disable_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

Creating Diagonal Matrices

Creating Permutation Matrices

Explicit and Implicit Conversions