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diff --git a/src/algebra/nqip.as.pamphlet b/src/algebra/nqip.as.pamphlet new file mode 100644 index 00000000..e3e8d968 --- /dev/null +++ b/src/algebra/nqip.as.pamphlet @@ -0,0 +1,231 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/algebra nqip.as} +\author{Michael Richardson} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{NagQuadratureInterfacePackage} +<<NagQuadratureInterfacePackage>>= ++++ Author: M.G. Richardson ++++ Date Created: 1995 Dec. 07 ++++ Date Last Updated: ++++ Basic Functions: ++++ Related Constructors: ++++ Also See: ++++ AMS Classifications: ++++ Keywords: ++++ References: ++++ Description: ++++ This package provides Axiom-like interfaces to some of the NAG ++++ quadrature (numerical integration) routines in the NAGlink. + +NagQuadratureInterfacePackage: with { + + nagPolygonIntegrate : (LDF, LDF) -> + RCD(integral : DF, errorEstimate : DF) ; + + ++ nagPolygonIntegrate(xlist,ylist) evaluates the definite integral +#if saturn + ++ $\int_{x_{1}}^{x_{n}}y(x) \, dx$ +#else + ++ integrate(y(x), x=x[1]..x[n]) +#endif + ++ where the numerical value of the function \spad{y} is specified at + ++ the \spad{n} distinct points +#if saturn + ++ $x_{1}, x_{2}, \ldots , x_{n}$. +#else + ++ x[1], x[2] ... x[n]. +#endif + ++ The \spad{x} and \spad{y} values are specified in the lists + ++ \spad{xlist} and \spad{ylist}, respectively; the \spad{xlist} + ++ values must form a strictly monotonic sequence of four or more + ++ points. + ++ The calculation is performed by the NAG routine D01GAF. + ++ + ++ An estimate of the numerical error in the calculation is also + ++ returned; however, by choosing unrepresentative data points to + ++ approximate the function it is possible to achieve an arbitrarily + ++ large difference between the true integral and the value + ++ calculated. + ++ For more detailed information, please consult the NAG + ++ manual via the Browser page for the operation d01gaf. + + nagPolygonIntegrate : MDF -> RCD(integral : DF, errorEstimate : DF) ; + + +} == add { + + import from NagIntegrationPackage ; + import from NagResultChecks ; + import from AnyFunctions1 DF ; + import from STRG ; + import from List STRG ; + import from Symbol ; + import from LLDF ; + import from VDF ; + import from MDF ; + import from ErrorFunctions ; + + local ipIfail : INT := -1 ; + local d01gafError : DF := 0 ; + + nagPolygonIntegrate(xlist : LDF, ylist : LDF) + : RCD(integral : DF, errorEstimate : DF) == { + + local lx, ly : INT ; + local d01gafResult : RSLT ; + + lx := (# xlist) pretend INT ; + ly := (# ylist) pretend INT ; + if lx ~= ly + then error ["The lists supplied to nagPolygonIntegrate are of ", + "different lengths: ", + string(lx), + " and ", + string(ly), + "."] + else { + d01gafResult := d01gaf(matrix [xlist],matrix [ylist],lx,ipIfail) ; + [checkResult(d01gafResult,"ans","D01GAF"), + retract(d01gafResult."er") @ DF] + } + } + + nagPolygonIntegrate(coords : MDF) + : RCD(integral : DF, errorEstimate : DF) == + if (ncols(coords) pretend INT) ~= 2 + then error ["Please supply the coordinate matrix in ", + "nagPolygonIntegrate with each row consisting of ", + "a single x-y pair."] + else nagPolygonIntegrate(members column(coords,1), + members column(coords,2)) ; + +} + +#if NeverAssertThis + +-- Note that the conversions of results from DoubleFloat to Float +-- will become unnecessary if outputGeneral is extended to apply to +-- DoubleFloat quantities. + +)lib nrc +)lib nqip + +outputGeneral 5 + +xvals := [0.00,0.04,0.08,0.12,0.22,0.26,0.30,0.38,0.39,0.42,0.45, + 0.46,0.60,0.68,0.72,0.73,0.83,0.85,0.88,0.90,1.00]; + +yvals := [4.0000,3.9936,3.9746,3.9432,3.8135,3.7467,3.6697,3.4943, + 3.4719,3.4002,3.3264,3.3017,2.9412,2.7352,2.6344, + 2.6094,2.3684,2.3222,2.2543,2.2099,2.0000]; + +result := nagPolygonIntegrate(xvals,yvals); +result.integral :: Float + +-- 3.1414 + +result.errorEstimate :: Float + +-- - 0.000025627 + +coords := transpose matrix [xvals, yvals]; +result := nagPolygonIntegrate coords; +result.integral :: Float + +-- 3.1414 + +result.errorEstimate :: Float + +-- - 0.000025627 + +nagPolygonIntegrate([1,2,3],[1,2,3,4]) + +-- Error signalled from user code: +-- The lists supplied to nagPolygonIntegrate are of different +-- lengths: 3 and 4. + +nagPolygonIntegrate([[1,2,3],[4,5,6]]) + +-- Error signalled from user code: +-- Please supply the coordinate matrix in nagPolygonIntegrate with +-- each row consisting of single a x-y pair. + +outputGeneral() + +output "End of tests" + +#endif + +@ +\section{License} +<<license>>= +--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. +--All rights reserved. +-- +--Redistribution and use in source and binary forms, with or without +--modification, are permitted provided that the following conditions are +--met: +-- +-- - Redistributions of source code must retain the above copyright +-- notice, this list of conditions and the following disclaimer. +-- +-- - Redistributions in binary form must reproduce the above copyright +-- notice, this list of conditions and the following disclaimer in +-- the documentation and/or other materials provided with the +-- distribution. +-- +-- - Neither the name of The Numerical ALgorithms Group Ltd. nor the +-- names of its contributors may be used to endorse or promote products +-- derived from this software without specific prior written permission. +-- +--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS +--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A +--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER +--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF +--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING +--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +@ +<<*>>= +<<license>> + +-- NagQuadratureInterfacePackage + +-- To test: +-- sed -ne '1,/^#if NeverAssertThis/d;/#endif/d;p' < nqip.as > nqip.input +-- axiom +-- )set nag host <some machine running nagd> +-- )r nqip.input + +#unassert saturn + +#include "axiom.as" + +DF ==> DoubleFloat ; +LDF ==> List DoubleFloat ; +LLDF ==> List LDF ; +VDF ==> Vector DoubleFloat ; +MDF ==> Matrix DoubleFloat ; +INT ==> Integer ; +RCD ==> Record ; +RSLT ==> Result ; +STRG ==> String ; + +<<NagQuadratureInterfacePackage>> +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |