diff options
Diffstat (limited to 'src/algebra/nqip.as.pamphlet')
| -rw-r--r-- | src/algebra/nqip.as.pamphlet | 231 |
1 files changed, 0 insertions, 231 deletions
diff --git a/src/algebra/nqip.as.pamphlet b/src/algebra/nqip.as.pamphlet deleted file mode 100644 index a7092fd5..00000000 --- a/src/algebra/nqip.as.pamphlet +++ /dev/null @@ -1,231 +0,0 @@ -\documentclass{article} -\usepackage{open-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} |