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doc: Update all documentation for chapter on Numerical Integration * cumtrapz.m, dblquad.m, quadgk.m, quadl.m, quadv.m, trapz.m, triplequad.m, quad.cc, quadcc.cc: Improve docstrings. * Quad-opts.in: Keep code sample together on a single line. * mk-opts.pl: Update quad-options function description * octave.texi: Update order of detailmenu to match order in quad.texi. * quad.txi: Add language about when to use each quad function, add examples of using trapz. * aspell-octave.en.pws: Add new spelling words from quad.texi chapter
author Rik <octave@nomad.inbox5.com>
date Sun, 17 Apr 2011 19:57:07 -0700
parents c792872f8942
children f96b9b9f141b
line wrap: on
line diff
--- a/scripts/general/trapz.m
+++ b/scripts/general/trapz.m
@@ -17,15 +17,38 @@
 ## <http://www.gnu.org/licenses/>.
 
 ## -*- texinfo -*-
-## @deftypefn  {Function File} {@var{z} =} trapz (@var{y})
-## @deftypefnx {Function File} {@var{z} =} trapz (@var{x}, @var{y})
-## @deftypefnx {Function File} {@var{z} =} trapz (@dots{}, @var{dim})
+## @deftypefn  {Function File} {@var{q} =} trapz (@var{y})
+## @deftypefnx {Function File} {@var{q} =} trapz (@var{x}, @var{y})
+## @deftypefnx {Function File} {@var{q} =} trapz (@dots{}, @var{dim})
+##
+## Numerically evaluate the integral of points @var{y} using the trapezoidal
+## method.
+## @w{@code{trapz (@var{y})}} computes the integral of @var{y} along the first
+## non-singleton dimension.  When the argument @var{x} is omitted an
+## equally spaced @var{x} vector with unit spacing (1) is assumed.  
+## @code{trapz (@var{x}, @var{y})} evaluates the integral with respect
+## to the spacing in @var{x} and the values in @var{y}.  This is useful if
+## the points in @var{y} have been sampled unevenly.
+## If the optional @var{dim} argument is given, operate along this dimension.
 ##
-## Numerical integration using trapezoidal method.  @code{trapz
-## (@var{y})} computes the integral of the @var{y} along the first
-## non-singleton dimension.  If the argument @var{x} is omitted a
-## equally spaced vector is assumed.  @code{trapz (@var{x}, @var{y})}
-## evaluates the integral with respect to @var{x}.
+## If @var{x} is not specified then unit spacing will be used.  To scale
+## the integral to the correct value you must multiply by the actual spacing
+## value (deltaX).  As an example, the integral of @math{x^3} over the range
+## [0, 1] is @math{x^4/4} or 0.25.  The following code uses @code{trapz} to
+## calculate the integral in three different ways.
+##
+## @example
+## @group
+## x = 0:0.1:1;
+## y = x.^3;
+## q = trapz (y)
+##   @result{} q = 2.525   # No scaling
+## q * 0.1
+##   @result{} q = 0.2525  # Approximation to integral by scaling
+## trapz (x, y) 
+##   @result{} q = 0.2525  # Same result by specifying @var{x}
+## @end group
+## @end example
 ##
 ## @seealso{cumtrapz}
 ## @end deftypefn