Mercurial > octave-nkf
diff scripts/general/quadgk.m @ 9051:1bf0ce0930be
Grammar check TexInfo in all .m files
Cleanup documentation sources to follow a few consistent rules.
Spellcheck was NOT done. (but will be in another changeset)
author | Rik <rdrider0-list@yahoo.com> |
---|---|
date | Fri, 27 Mar 2009 22:31:03 -0700 |
parents | eb63fbe60fab |
children | 8970b4b10e9f |
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--- a/scripts/general/quadgk.m Thu Mar 26 11:47:34 2009 -0700 +++ b/scripts/general/quadgk.m Fri Mar 27 22:31:03 2009 -0700 @@ -22,10 +22,10 @@ ## @deftypefnx {Function File} {[@var{q}, @var{err}] =} quadgk (@dots{}) ## Numerically evaluate integral using adaptive Guass-Konrod quadrature. ## The formulation is based on a proposal by L.F. Shampine, -## @cite{"Vectorized adaptive quadrature in MATLAB", Journal of +## @cite{"Vectorized adaptive quadrature in @sc{matlab}", Journal of ## Computational and Applied Mathematics, pp131-140, Vol 211, Issue 2, ## Feb 2008} where all function evalutions at an iteration are -## calculated with a single call to @var{f}. Therefore the function +## calculated with a single call to @var{f}. Therefore the function ## @var{f} must be of the form @code{@var{f} (@var{x})} and accept ## vector values of @var{x} and return a vector of the same length ## representing the function evalutaions at the given values of @var{x}. @@ -33,9 +33,9 @@ ## inline function or string. ## ## The bounds of the quadrature @code{[@var{a}, @var{b}]} can be finite -## or infinite and contain weak end singularities. Variable +## or infinite and contain weak end singularities. Variable ## transformation will be used to treat infinite intervals and weaken -## the singularities. For example +## the singularities. For example ## ## @example ## quadgk(@@(x) 1 ./ (sqrt (x) .* (x + 1)), 0, Inf) @@ -47,35 +47,35 @@ ## @code{quadgk} should do the same. ## ## The absolute tolerance can be passed as a fourth argument in a manner -## compatible with @code{quadv}. Equally the user can request that +## compatible with @code{quadv}. Equally the user can request that ## information on the convergence can be printed is the fifth argument ## is logicallly true. ## ## Alternatively, certain properties of @code{quadgk} can be passed as -## pairs @code{@var{prop}, @var{val}}. Valid properties are +## pairs @code{@var{prop}, @var{val}}. Valid properties are ## ## @table @code ## @item AbsTol -## Defines the absolute error tolerance for the quadrature. The default +## Defines the absolute error tolerance for the quadrature. The default ## absolute tolerance is 1e-10. ## ## @item RelTol -## Defines the relative error tolerance for the quadrature. The default +## Defines the relative error tolerance for the quadrature. The default ## relative tolerance is 1e-5. ## ## @item MaxIntervalCount ## @code{quadgk} initially subdivides the interval on which to perform -## the quadrature into 10 intervals. Sub-intervals that have an -## unacceptable error are sub-divided and re-evaluated. If the number of +## the quadrature into 10 intervals. Sub-intervals that have an +## unacceptable error are sub-divided and re-evaluated. If the number of ## sub-intervals exceeds at any point 650 sub-intervals then a poor ## convergence is signaled and the current estimate of the integral is -## returned. The property 'MaxIntervalCount' can be used to alter the +## returned. The property 'MaxIntervalCount' can be used to alter the ## number of sub-intervals that can exist before exiting. ## ## @item WayPoints ## If there exists discontinuities in the first derivative of the ## function to integrate, then these can be flagged with the -## @code{"WayPoints"} property. This forces the ends of a sub-interval +## @code{"WayPoints"} property. This forces the ends of a sub-interval ## to fall on the breakpoints of the function and can result in ## significantly improved estimated of the error in the integral, faster ## computation or both. For example, @@ -94,12 +94,14 @@ ## ## If any of @var{a}, @var{b} or @var{waypoints} is complex, then the ## quadrature is treated as a contour integral along a piecewise -## continuous path defined by the above. In this case the integral is -## assuemd to have no edge singularities. For example +## continuous path defined by the above. In this case the integral is +## assuemd to have no edge singularities. For example ## ## @example +## @group ## quadgk (@@(z) log (z), 1+1i, 1+1i, "WayPoints", ## [1-1i, -1,-1i, -1+1i]) +## @end group ## @end example ## ## @noindent