# HG changeset patch
# User jwe
# Date 848450068 0
# Node ID 80a42c3fefc9468638c61103ece7a40514be238b
# Parent  c3d634d49ce4e63a455ebadcd02de8151cfdb317
[project @ 1996-11-20 00:34:27 by jwe]

diff --git a/doc/interpreter/arith.texi b/doc/interpreter/arith.texi
--- a/doc/interpreter/arith.texi
+++ b/doc/interpreter/arith.texi
@@ -155,6 +155,20 @@
 @end ifinfo
 @end deftypefn
 
+@deftypefn {Function File} {} nextpow2 (@var{x})
+If @var{x} is a scalar, returns the first integer @var{n} such that
+@iftex
+@tex
+ $2^n \ge |x|$.
+@end tex
+@end iftex
+@ifinfo
+ 2^n >= abs (x).
+@end ifinfo
+
+If @var{x} is a vector, return @code{nextpow2 (length (@var{x}))}.
+@end deftypefn
+
 @deftypefn {Mapping Function} {} sqrt (@var{x})
 Compute the square root of @var{x}.  To compute the matrix square root,
 see @ref{Linear Algebra}.
@@ -468,6 +482,124 @@
 Returns the natural logarithm of the gamma function.
 @end deftypefn
 
+@deftypefn {Function File} {} cross (@var{x}, @var{y})
+Computes the vector cross product of the two 3-dimensional vectors
+@var{x} and @var{y}.
+@end deftypefn
+
+@deftypefn {Function File} {} commutation_matrix (@var{m}, @var{n})
+Returns the commutation matrix
+@iftex
+ $K_{m,n}$
+@tex
+@end tex
+@end iftex
+@ifinfo
+ K(m,n)
+@end ifinfo
+ which is the unique
+@iftex
+@tex
+ $m n \times m n$
+@end tex
+@end iftex
+@ifinfo
+ @var{m}*@var{n} by @var{m}*@var{n}
+@end ifinfo
+ matrix such that
+@iftex
+@tex
+ $K_{m,n} * {\rm vec} (A) = {\rm vec} (A^T)$
+@end tex
+@end iftex
+@ifinfo
+ @var{K}(@var{m},@var{n}) * vec (@var{A}) = vec (@var{A}')
+@end ifinfo
+ for all
+@iftex
+@tex
+ $m\times n$
+@end tex
+@end iftex
+@ifinfo
+ @var{m} by @var{n}
+@end ifinfo
+ matrices
+@iftex
+@tex
+ $A$.
+@end tex
+@end iftex
+@ifinfo
+ @var{A}.
+@end ifinfo
+
+If only one argument @var{m} is given,
+@iftex
+@tex
+ $K_{m,m}$
+@end tex
+@end iftex
+@ifinfo
+ K(m,m)
+@end ifinfo
+ is returned.
+
+See Magnus and Neudecker (1988), Matrix differential calculus with
+applications in statistics and econometrics.
+@end deftypefn
+
+@deftypefn {Function File} {} duplication_matrix (@var{n})
+Returns the duplication matrix
+@iftex
+@tex
+ $D_n$
+@end tex
+@end iftex
+@ifinfo
+ @var{D}_@var{n}
+@end ifinfo
+ which is the unique
+@iftex
+@tex
+ $n^2 \times n(n+1)/2$
+@end tex
+@end iftex
+@ifinfo
+ @var{n}^2 by @var{n}*(@var{n}+1)/2
+@end ifinfo
+ matrix such that
+@iftex
+@tex
+ $D_n * {\rm vech} (A) = {\rm vec} (A)$
+@end tex
+@end iftex
+@ifinfo
+ @var{D}_@var{n} * vech (@var{A}) = vec (@var{A})
+@end ifinfo
+ for all symmetric
+@iftex
+@tex
+@end tex
+ $n \times n$
+@end iftex
+@ifinfo
+ @var{n} by @var{n}
+@end ifinfo
+ matrices
+@iftex
+@tex
+ $A$.
+@end tex
+@end iftex
+@ifinfo
+ @var{A}.
+@end ifinfo
+
+See Magnus and Neudecker (1988), Matrix differential calculus with
+applications in statistics and econometrics.
+@end deftypefn
+
 @node Mathematical Constants,  , Special Functions, Arithmetic
 @section Mathematical Constants
 
diff --git a/doc/interpreter/linalg.texi b/doc/interpreter/linalg.texi
--- a/doc/interpreter/linalg.texi
+++ b/doc/interpreter/linalg.texi
@@ -366,13 +366,12 @@
  is a unitary matrix
 @iftex
 @tex
-($U' U$
+($U^T U$ is identity)
 @end tex
 @end iftex
 @ifinfo
-(@code{u'* u}
+(@code{u'* u} is identity)
 @end ifinfo
- is identity)
 and
 @iftex
 @tex
diff --git a/doc/interpreter/matrix.texi b/doc/interpreter/matrix.texi
--- a/doc/interpreter/matrix.texi
+++ b/doc/interpreter/matrix.texi
@@ -75,6 +75,47 @@
 @code{while} statements) Octave treats the test as if you had typed
 @code{all (all (condition))}.
 
+@deftypefn {Function File} {[@var{errorcode}, @var{y_1}, ...] =} common_size (@var{x_1}, ...)
+Determine if all input arguments are either scalar or of common
+size.  If so, errorcode is zero, and @var{y_i} is a matrix of the
+common size with all entries equal to @var{x_i} if this is a scalar or
+@var{x_i} otherwise.  If the inputs cannot be brought to a common size,
+errorcode is 1, and @var{y_i} is @var{x_i}.  For example,
+
+@example
+@group
+[errorcode, a, b] = common_size ([1 2; 3 4], 5)
+     @result{} errorcode = 0
+     @result{} a = [1 2, 3 4]
+     @result{} b = [5 5; 5 5]
+@end group
+@end example
+
+@noindent
+This is useful for implementing functions where arguments can either
+be scalars or of common size.
+@end deftypefn
+
+@deftypefn {Function File} {} diff (@var{x}, @var{k})
+If @var{x} is a vector of length @var{n}, @code{diff (@var{x})} is the
+vector of first differences
+@iftex
+@tex
+ $x_2 - x_1, \ldots{}, x_n - x_{n-1}$.
+@end tex
+@end iftex
+@ifinfo
+ @var{x}(2) - @var{x}(1), @dots{}, @var{x}(n) - @var{x}(n-1).
+@end ifinfo
+
+If @var{x} is a matrix, @code{diff (@var{x})} is the matrix of column
+differences.
+
+The second argument is optional.  If supplied, @code{diff (@var{x},
+@var{k})}, where @var{k} is a nonnegative integer, returns the
+@var{k}-th differences.
+@end deftypefn
+
 @deftypefn {Mapping Function} {} isinf (@var{x})
 Return 1 for elements of @var{x} that are infinite and zero
 otherwise. For example,
@@ -250,6 +291,13 @@
 matrix must match the total number of elements in the new matrix.
 @end deftypefn
 
+@deftypefn {Function File} {} shift (@var{x}, @var{b})
+If @var{x} is a vector, perform a circular shift of length @var{b} of
+the elements of @var{x}.
+
+If @var{x} is a matrix, do the same for each column of @var{x}.
+@end deftypefn
+
 @deftypefn {Loadable Function} {[s, i] =} sort (@var{x})
 Returns a copy of @var{x} with the elements elements arranged in
 increasing order.  For matrices, @code{sort} orders the elements in each
@@ -352,3 +400,20 @@
 @end group
 @end example
 @end deftypefn
+
+@deftypefn {Function File} {} vec (@var{x})
+For a matrix @var{x}, returns the vector obtained by stacking the
+columns of @var{x} one above the other.
+
+See Magnus and Neudecker (1988), Matrix differential calculus with
+applications in statistics and econometrics.
+@end deftypefn
+
+@deftypefn {Function File} {} vech (@var{x})
+For a square matrix @var{x}, returns the vector obtained from @var{x}
+by eliminating all supradiagonal elements and stacking the result
+one column above the other.
+
+See Magnus and Neudecker (1988), Matrix differential calculus with
+applications in statistics and econometrics.
+@end deftypefn