Mercurial > hg > octave-lyh
diff scripts/general/del2.m @ 9165:8c71a86c4bf4
Update section 17.5 (Utility Functions) of arith.txi
author | Rik <rdrider0-list@yahoo.com> |
---|---|
date | Fri, 01 May 2009 10:06:16 -0700 |
parents | c1fff751b5a8 |
children | 1231b1762a9a |
line wrap: on
line diff
--- a/scripts/general/del2.m +++ b/scripts/general/del2.m @@ -22,14 +22,18 @@ ## @deftypefnx {Function File} {@var{d} =} del2 (@var{m}, @var{h}) ## @deftypefnx {Function File} {@var{d} =} del2 (@var{m}, @var{dx}, @var{dy}, @dots{}) ## -## Calculate the discrete Laplace operator. If @var{m} is a matrix this is -## defined as +## Calculate the discrete Laplace +## @tex +## operator $( \nabla^2 )$. +## @end tex +## @ifnottex +## operator. +## @end ifnottex +## For a 2-dimensional matrix @var{m} this is defined as ## -## @iftex ## @tex ## $$d = {1 \over 4} \left( {d^2 \over dx^2} M(x,y) + {d^2 \over dy^2} M(x,y) \right)$$ ## @end tex -## @end iftex ## @ifnottex ## @example ## @group @@ -40,15 +44,14 @@ ## @end example ## @end ifnottex ## -## The above to continued to N-dimensional arrays calculating the second -## derivative over the higher dimensions. +## For N-dimensional arrays the sum in parentheses is expanded to include second derivatives +## over the additional higher dimensions. ## ## The spacing between evaluation points may be defined by @var{h}, which is a ## scalar defining the equidistant spacing in all dimensions. Alternatively, -## the spacing -## in each dimension may be defined separately by @var{dx}, @var{dy}, etc. -## Scalar spacing values give equidistant spacing, whereas vector spacing -## values can be used to specify variable spacing. The length of the vectors +## the spacing in each dimension may be defined separately by @var{dx}, @var{dy}, +## etc. A scalar spacing argument defines equidistant spacing, whereas a vector +## argument can be used to specify variable spacing. The length of the spacing vectors ## must match the respective dimension of @var{m}. The default spacing value ## is 1. ##