Mercurial > hg > octave-max
changeset 9067:8970b4b10e9f
Cleanup documentation for quad.texi and diffeq.texi
Grammarcheck input .txi files
Spellcheck .texi files
author | Rik <rdrider0-list@yahoo.com> |
---|---|
date | Sat, 28 Mar 2009 22:18:51 -0700 |
parents | be150a172010 |
children | 5d3059e2a34c |
files | doc/interpreter/diffeq.txi doc/interpreter/quad.txi liboctave/DASPK-opts.in liboctave/DASRT-opts.in liboctave/DASSL-opts.in liboctave/LSODE-opts.in scripts/general/quadgk.m src/DLD-FUNCTIONS/daspk.cc src/DLD-FUNCTIONS/dasrt.cc src/DLD-FUNCTIONS/dassl.cc src/DLD-FUNCTIONS/lsode.cc |
diffstat | 11 files changed, 35 insertions(+), 17 deletions(-) [+] |
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--- a/doc/interpreter/diffeq.txi +++ b/doc/interpreter/diffeq.txi @@ -46,9 +46,11 @@ @ifinfo @example +@group dx -- = f (x, t) dt +@end group @end example @end ifinfo @@ -136,7 +138,7 @@ @ifnottex @math{x-dot} @end ifnottex -is the derivative of @math{x}. The equation is solved using Petzold's +is the derivative of @math{x}. The equation is solved using Petzold's DAE solver @sc{Daspk}. @DOCSTRING(daspk)
--- a/doc/interpreter/quad.txi +++ b/doc/interpreter/quad.txi @@ -51,7 +51,7 @@ Numerical integration using an adaptive Lobatto rule. @item quadgk -Numerical integration using an adaptive Guass-Konrod rule. +Numerical integration using an adaptive Gauss-Konrod rule. @item quadv Numerical integration using an adaptive vectorized Simpson's rule. @@ -176,8 +176,10 @@ Then the solution at the roots @var{r} is @example +@group u = [ 0; (at - alpha * bt) \ rhs; 1] @result{} [ 0.00; 0.004; 0.01 0.00; 0.12; 0.62; 1.00 ] +@end group @end example @node Functions of Multiple Variables @@ -213,6 +215,7 @@ the following code does. @example +@group function I = g(y) I = ones(1, length(y)); for i = 1:length(y) @@ -223,15 +226,18 @@ I = quadl("g", 0, 1) @result{} 0.30022 +@end group @end example The above process can be simplified with the @code{dblquad} and @code{triplequad} functions for integrals over two and three -variables. For example +variables. For example @example +@group I = dblquad (@@(x, y) sin(pi.*x.*y).*sqrt(x.*y), 0, 1, 0, 1) @result{} 0.30022 +@end group @end example @DOCSTRING(dblquad) @@ -255,15 +261,17 @@ the sum over @code{i=1:n} and @code{j=1:n} of @code{q(i)*q(j)*f(r(i),r(j))}, @end ifnottex where @math{q} and @math{r} is as returned by @code{colloc(n)}. The -generalisation to more than two variables is straight forward. The +generalization to more than two variables is straight forward. The following code computes the studied integral using @math{n=7} points. @example +@group f = @@(x,y) sin(pi*x*y').*sqrt(x*y'); n = 7; [t, A, B, q] = colloc(n); I = q'*f(t,t)*q; @result{} 0.30022 +@end group @end example @noindent
--- a/liboctave/DASPK-opts.in +++ b/liboctave/DASPK-opts.in @@ -56,8 +56,10 @@ The local error test applied at each integration step is @example +@group abs (local error in x(i)) <= rtol(i) * abs (Y(i)) + atol(i) +@end group @end example END_DOC_ITEM TYPE = "Array<double>" @@ -94,7 +96,7 @@ In either case, initial values for the given components are input, and initial guesses for the unknown components must also be provided as input. Set this option to 1 to solve the first problem, or 2 to solve -the second (the default default is 0, so you must provide a set of +the second (the default is 0, so you must provide a set of initial conditions that are consistent). If this option is set to a nonzero value, you must also set the @@ -148,7 +150,7 @@ Jacobian. For convergence, the weighted RMS norm of this vector (scaled by the error weights) must be less than @code{EPINIT*EPCON}, where @code{EPCON} = 0.33 is the analogous test constant used in the -time steps. The default is @code{EPINIT} = 0.01. +time steps. The default is @code{EPINIT} = 0.01. @end table END_DOC_ITEM TYPE = "Array<double>"
--- a/liboctave/DASRT-opts.in +++ b/liboctave/DASRT-opts.in @@ -55,8 +55,10 @@ The local error test applied at each integration step is @example +@group abs (local error in x(i)) <= ... rtol(i) * abs (Y(i)) + atol(i) +@end group @end example END_DOC_ITEM TYPE = "Array<double>"
--- a/liboctave/DASSL-opts.in +++ b/liboctave/DASSL-opts.in @@ -56,8 +56,10 @@ The local error test applied at each integration step is @example +@group abs (local error in x(i)) <= rtol(i) * abs (Y(i)) + atol(i) +@end group @end example END_DOC_ITEM TYPE = "Array<double>"
--- a/liboctave/LSODE-opts.in +++ b/liboctave/LSODE-opts.in @@ -54,8 +54,10 @@ The local error test applied at each integration step is @example +@group abs (local error in x(i)) <= ... rtol * abs (y(i)) + atol(i) +@end group @end example END_DOC_ITEM TYPE = "double"
--- a/scripts/general/quadgk.m +++ b/scripts/general/quadgk.m @@ -20,15 +20,15 @@ ## @deftypefn {Function File} {} quadgk (@var{f}, @var{a}, @var{b}, @var{abstol}, @var{trace}) ## @deftypefnx {Function File} {} quadgk (@var{f}, @var{a}, @var{b}, @var{prop}, @var{val}, @dots{}) ## @deftypefnx {Function File} {[@var{q}, @var{err}] =} quadgk (@dots{}) -## Numerically evaluate integral using adaptive Guass-Konrod quadrature. +## Numerically evaluate integral using adaptive Gauss-Konrod quadrature. ## The formulation is based on a proposal by L.F. Shampine, ## @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 +## Feb 2008} where all function evaluations at an iteration are ## 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}. +## representing the function evaluations at the given values of @var{x}. ## The function @var{f} can be defined in terms of a function handle, ## inline function or string. ## @@ -49,7 +49,7 @@ ## The absolute tolerance can be passed as a fourth argument in a manner ## compatible with @code{quadv}. Equally the user can request that ## information on the convergence can be printed is the fifth argument -## is logicallly true. +## is logically true. ## ## Alternatively, certain properties of @code{quadgk} can be passed as ## pairs @code{@var{prop}, @var{val}}. Valid properties are @@ -95,7 +95,7 @@ ## 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 +## assumed to have no edge singularities. For example ## ## @example ## @group @@ -277,7 +277,7 @@ endif ## Split interval into at least 10 sub-interval with a 15 point - ## Guass-Kronrod rule giving a minimum of 150 function evaluations + ## Gauss-Kronrod rule giving a minimum of 150 function evaluations while (length (subs) < 11) subs = [subs' ; subs(1:end-1)' + diff(subs') ./ 2, NaN](:)(1 : end - 1); endwhile @@ -380,7 +380,7 @@ endfunction function [q, err] = __quadgk_eval__ (f, subs) - ## A (15,7) point pair of Guass-Konrod quadrature rules. The abscissa + ## A (15,7) point pair of Gauss-Konrod quadrature rules. The abscissa ## and weights are copied directly from dqk15w.f from quadpack persistent abscissa = [-0.9914553711208126e+00, -0.9491079123427585e+00, ...
--- a/src/DLD-FUNCTIONS/daspk.cc +++ b/src/DLD-FUNCTIONS/daspk.cc @@ -219,7 +219,7 @@ scalar.\n\ \n\ If @var{fcn} is a two-element string array or a two-element cell array\n\ -of strings, inlines, or function handles, the first element names\n\ +of strings, inline functions, or function handles, the first element names\n\ the function @math{f} described above, and the second element names a\n\ function to compute the modified Jacobian\n\ @tex\n\
--- a/src/DLD-FUNCTIONS/dasrt.cc +++ b/src/DLD-FUNCTIONS/dasrt.cc @@ -262,7 +262,7 @@ scalar.\n\ \n\ If @var{fcn} is a two-element string array or a two-element cell array\n\ -of strings, inlines, or function handles, the first element names\n\ +of strings, inline functions, or function handles, the first element names\n\ the function @math{f} described above, and the second element names a\n\ function to compute the modified Jacobian\n\ \n\
--- a/src/DLD-FUNCTIONS/dassl.cc +++ b/src/DLD-FUNCTIONS/dassl.cc @@ -222,7 +222,7 @@ scalar.\n\ \n\ If @var{fcn} is a two-element string array or a two-element cell array\n\ -of strings, inlines, or function handles, the first element names\n\ +of strings, inline functions, or function handles, the first element names\n\ the function @math{f} described above, and the second element names a\n\ function to compute the modified Jacobian\n\ \n\
--- a/src/DLD-FUNCTIONS/lsode.cc +++ b/src/DLD-FUNCTIONS/lsode.cc @@ -206,7 +206,7 @@ in which @var{xdot} and @var{x} are vectors and @var{t} is a scalar.\n\ \n\ If @var{fcn} is a two-element string array or a two-element cell array\n\ -of strings, inlines, or function handles, the first element names\n\ +of strings, inline functions, or function handles, the first element names\n\ the function @math{f} described above, and the second element names a\n\ function to compute the Jacobian of @math{f}. The Jacobian function\n\ must have the form\n\