diff doc/interpreter/diagperm.txi @ 19630:0e1f5a750d00

maint: Periodic merge of gui-release to default.
author John W. Eaton <jwe@octave.org>
date Tue, 20 Jan 2015 10:24:46 -0500
parents 9e5b64b3c1fe 446c46af4b42
children 4197fc428c7d
line wrap: on
line diff
--- a/doc/interpreter/diagperm.txi	Tue Jan 20 09:55:41 2015 -0500
+++ b/doc/interpreter/diagperm.txi	Tue Jan 20 10:24:46 2015 -0500
@@ -6,12 +6,12 @@
 @c under the terms of the GNU General Public License as published by the
 @c Free Software Foundation; either version 3 of the License, or (at
 @c your option) any later version.
-@c 
+@c
 @c Octave is distributed in the hope that it will be useful, but WITHOUT
 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 @c FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 @c for more details.
-@c 
+@c
 @c You should have received a copy of the GNU General Public License
 @c along with Octave; see the file COPYING.  If not, see
 @c <http://www.gnu.org/licenses/>.
@@ -33,7 +33,7 @@
 @section Creating and Manipulating Diagonal/Permutation Matrices
 
 A diagonal matrix is defined as a matrix that has zero entries outside the main
-diagonal; that is, 
+diagonal; that is,
 @tex
 $D_{ij} = 0$ if $i \neq j$
 @end tex
@@ -46,14 +46,14 @@
 
 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) 
+is, there exists a permutation (vector)
 @tex
 $p$ such that $P_{ij}=1$ if $j = p_i$ and
-$P_{ij}=0$ otherwise.  
+$P_{ij}=0$ otherwise.
 @end tex
 @ifnottex
-@code{p} such that @code{P(i,j) == 1} if @code{j == p(i)} and 
-@code{P(i,j) == 0} otherwise.  
+@code{p} such that @code{P(i,j) == 1} if @code{j == p(i)} and
+@code{P(i,j) == 0} otherwise.
 @end ifnottex
 
 Octave provides special treatment of real and complex rectangular diagonal
@@ -124,7 +124,7 @@
    0   0   3
    0   0   0
    0   0   0
-@end example  
+@end example
 
 @node Creating Permutation Matrices
 @subsection Creating Permutation Matrices
@@ -142,11 +142,11 @@
 will create a permutation matrix - a special matrix object.
 
 @example
-eye (n) (q, :) 
+eye (n) (q, :)
 @end example
 
 @noindent
-will also work (and create a row permutation matrix), as well as 
+will also work (and create a row permutation matrix), as well as
 
 @example
 eye (n) (q1, q2).
@@ -250,7 +250,7 @@
 Assume @var{D} is a diagonal matrix.  If @var{M} is a full matrix,
 then @code{D*M} will scale the rows of @var{M}.  That means,
 if @code{S = D*M}, then for each pair of indices
-i,j it holds 
+i,j it holds
 @tex
 $$S_{ij} = D_{ii} M_{ij}$$
 @end tex
@@ -271,8 +271,8 @@
 @end example
 
 @noindent
-i.e., trailing @code{n-m} rows of @var{M} are ignored.  If @code{m > n}, 
-then @code{D*M} is equivalent to 
+i.e., trailing @code{n-m} rows of @var{M} are ignored.  If @code{m > n},
+then @code{D*M} is equivalent to
 
 @example
 [D(1:n,n) * M; zeros(m-n, columns (M))],
@@ -290,7 +290,7 @@
 a rectangular diagonal matrix is again a rectangular diagonal matrix
 with swapped dimensions, where each nonzero diagonal element is replaced
 by its reciprocal.
-The matrix division algorithms do, in fact, use division rather than 
+The matrix division algorithms do, in fact, use division rather than
 multiplication by reciprocals for better numerical accuracy; otherwise, they
 honor the above definition.  Note that a diagonal matrix is never truncated due
 to ill-conditioning; otherwise, it would not be of much use for scaling.  This
@@ -309,9 +309,9 @@
 @example
 @group
 D1 + D2
-D1 - D2 
-D1 * D2 
-D1 / D2 
+D1 - D2
+D1 * D2
+D1 / D2
 D1 \ D2
 @end group
 @end example
@@ -323,7 +323,7 @@
 
 Also, a diagonal matrix @var{D} can be multiplied or divided by a scalar, or
 raised to a scalar power if it is square, producing diagonal matrix result in
-all cases. 
+all cases.
 
 A diagonal matrix can also be transposed or conjugate-transposed, giving the
 expected result.  Extracting a leading submatrix of a diagonal matrix, i.e.,
@@ -351,7 +351,7 @@
 
 If @var{P} is a permutation matrix and @var{M} a matrix, the expression
 @code{P*M} will permute the rows of @var{M}.  Similarly, @code{M*P} will
-yield a column permutation. 
+yield a column permutation.
 Matrix division @code{P\M} and @code{M/P} can be used to do inverse permutation.
 
 The previously described syntax for creating permutation matrices can actually
@@ -414,7 +414,7 @@
 when given a diagonal matrix, as well as @dfn{cond}.
 The following mapper functions can be applied to a diagonal matrix
 without converting it to a full one:
-@dfn{abs}, @dfn{real}, @dfn{imag}, @dfn{conj}, @dfn{sqrt}. 
+@dfn{abs}, @dfn{real}, @dfn{imag}, @dfn{conj}, @dfn{sqrt}.
 A diagonal matrix can also be returned from the @dfn{balance}
 and @dfn{svd} functions.
 The @dfn{sparse} function will convert a diagonal matrix efficiently to a
@@ -522,7 +522,7 @@
 (diagonal, triangular) or a sparsity pattern; its value is usually not stored
 explicitly anywhere, but is implied by the underlying data structure.
 
-The primary distinction is that an assumed zero, when multiplied 
+The primary distinction is that an assumed zero, when multiplied
 by any number, or divided by any nonzero number,
 yields *always* a zero, even when, e.g., multiplied by @code{Inf}
 or divided by @code{NaN}.