diff options
Diffstat (limited to 'src/algebra')
| -rw-r--r-- | src/algebra/Makefile.in | 16 | ||||
| -rw-r--r-- | src/algebra/axtimer.as.pamphlet | 191 | ||||
| -rw-r--r-- | src/algebra/ffrac.as.pamphlet | 204 | ||||
| -rw-r--r-- | src/algebra/herm.as.pamphlet | 369 | ||||
| -rw-r--r-- | src/algebra/interval.as.pamphlet | 564 | ||||
| -rw-r--r-- | src/algebra/invnode.as.pamphlet | 340 | ||||
| -rw-r--r-- | src/algebra/invrender.as.pamphlet | 172 | ||||
| -rw-r--r-- | src/algebra/invtypes.as.pamphlet | 302 | ||||
| -rw-r--r-- | src/algebra/invutils.as.pamphlet | 172 | ||||
| -rw-r--r-- | src/algebra/iviews.as.pamphlet | 330 | ||||
| -rw-r--r-- | src/algebra/ndftip.as.pamphlet | 1174 | ||||
| -rw-r--r-- | src/algebra/nepip.as.pamphlet | 626 | ||||
| -rw-r--r-- | src/algebra/noptip.as.pamphlet | 241 | ||||
| -rw-r--r-- | src/algebra/nqip.as.pamphlet | 231 | ||||
| -rw-r--r-- | src/algebra/nrc.as.pamphlet | 132 | ||||
| -rw-r--r-- | src/algebra/nsfip.as.pamphlet | 1223 |
16 files changed, 0 insertions, 6287 deletions
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index 54243dc8..dd588899 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -726,22 +726,6 @@ SPADFILES= \ ${OUTSRC}/zerodim.spad -ALDORFILES= \ - axtimer.as \ - ffrac.as \ - herm.as \ - interval.as \ - invnode.as \ - invrender.as \ - invtypes.as \ - invutils.as \ - iviews.as \ - ndftip.as \ - nepip.as \ - noptip.as nqip.as \ - nrc.as nsfip.as - - TESTS=${INPUT}/INTHEORY.input ${INPUT}/VIEW2D.input ${INPUT}/TESTFR.input diff --git a/src/algebra/axtimer.as.pamphlet b/src/algebra/axtimer.as.pamphlet deleted file mode 100644 index 76fefd66..00000000 --- a/src/algebra/axtimer.as.pamphlet +++ /dev/null @@ -1,191 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra axtimer.as} -\author{The Axiom Team} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\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>> - --------------------------------------------------------------------------------- --- --- BasicMath: timer.as --- Objects for tracking time --- --------------------------------------------------------------------------------- --- - --- ToDo: Write so that start!(x) ; start!(x) ; stop!(x); stop!(x) works. - -#include "axiom.as" - -Z ==> Integer; - -Duration ==> Record(hours: Z, mins: Z, seconds: Z, milliseconds: Z); - -+++ Timer -+++ History: 22/5/94 Original version by MB. -+++ 9/4/97 [Peter Broadbery] incorporated into Basicmath. -+++ 7/8/97 [PAB] Hacked into axiom. -+++ Timer is a type whose elements are stopwatch timers, which can be used -+++ to time precisely various sections of code. -+++ The precision can be up to 1 millisecond but depends on the operating system. -+++ The times returned are CPU times used by the process that created the timer. - -Timer: BasicType with { - HMS: Z -> Duration; - ++ Returns (h, m, s, u) where n milliseconds is equal - ++ to h hours, m minutes, s seconds and u milliseconds. - read: % -> Z; - ++ Reads the timer t without stopping it. - ++ Returns the total accumulated time in milliseconds by all - ++ the start/stop cycles since t was created or last reset. - ++ If t is running, the time since the last start is added in, - ++ and t is not stopped or affected. - reset!: % -> %; - ++ Resets the timer t to 0 and stops it if it is running. - ++Returns the timer t after it is reset. - start!: % -> Z; - ++ Starts or restarts t, without resetting it to 0, - ++ It has no effect on t if it is already running. - ++ Returns 0 if t was already running, the absolute time at which - ++ the start/restart was done otherwise. - stop!: % -> Z; - ++ Stops t without resetting it to 0. - ++ It has no effect on t if it is not running. - ++ Returns the elapsed time in milliseconds since the last time t - ++ was restarted, 0 if t was not running. - timer: () -> %; - ++ Creates a timer, set to 0 and stopped. - ++ Returns the timer that has been created. - - coerce: % -> OutputForm; -#if 0 - gcTimer: () -> %; - ++ Returns the system garbage collection timer. - ++ Do not use for other purposes! -#endif -} == add { - -- time = total accumulated time since created or reset - -- start = absolute time of last start - -- running? = true if currently running, false if currently stopped - Rep ==> Record(time:Z, start:Z, running?:Boolean); - import { - BOOT_:_:GET_-INTERNAL_-RUN_-TIME: () -> Integer; - } from Foreign Lisp; - cpuTime(): Integer == BOOT_:_:GET_-INTERNAL_-RUN_-TIME(); - - import from Rep, Z, Boolean; - - timer():% == per [0, 0, false]; - - read(t:%):Z == { - rec := rep t; - ans := rec.time; - if rec.running? then ans := ans + cpuTime() - rec.start; - ans - } - - stop!(t:%):Z == { - local ans:Z; - rec := rep t; - if rec.running? then { - ans := cpuTime() - rec.start; - rec.time := rec.time + ans; - rec.running? := false - } - else ans := 0; - ans - } - - start!(t:%):Z == { - local ans:Z; - rec := rep t; - if not(rec.running?) then { - rec.start := ans := cpuTime(); - rec.running? := true; - } - else ans := 0; - ans - } - - reset!(t:%):% == { - rec := rep t; - rec.time := rec.start := 0; - rec.running? := false; - t - } - - HMS(m:Z): Duration == { - import from Record(quotient: Integer, remainder: Integer); - (h, m) := explode divide(m, 3600000); - (m, s) := explode divide(m, 60000); - (s, l) := explode divide(s, 1000); - [h, m, s, l] - } - -#if 0 - import { - gcTimer: () -> Pointer; - } from Foreign C; - - gcTimer(): % == (gcTimer())@Pointer pretend %; -#endif - coerce(x: %): OutputForm == { - import from List OutputForm; - assign(name: String, val: OutputForm): OutputForm == { - import from Symbol; - blankSeparate [outputForm(name::Symbol), outputForm("="::Symbol), val]; - } - state: Symbol := coerce(if rep(x).running? then "on" else "off"); - bracket [outputForm("Timer:"::Symbol), - commaSeparate [assign("state", outputForm state), - assign("value", (read x)::OutputForm)]]; - } - - (a: %) = (b: %): Boolean == error "No equality for Timers"; -} - -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/ffrac.as.pamphlet b/src/algebra/ffrac.as.pamphlet deleted file mode 100644 index d038a101..00000000 --- a/src/algebra/ffrac.as.pamphlet +++ /dev/null @@ -1,204 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra ffrac.as} -\author{Michael Richardson} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\begin{verbatim} - --- FormalFraction - --- N.B. ndftip.as inlines this, must be recompiled if this is. - --- To test: --- sed '1,/^#if NeverAssertThis/d;/#endif/d' < ffrac.as > ffrac.input --- axiom --- )set nag host <some machine running nagd> --- )r ffrac.input - -\end{verbatim} -\section{FormalFraction} -<<FormalFraction>>= - -#include "axiom.as" - -FFRAC ==> FormalFraction ; - -OF ==> OutputForm ; -SC ==> SetCategory ; -FRAC ==> Fraction ; -ID ==> IntegralDomain ; - -+++ Author: M.G. Richardson -+++ Date Created: 1996 Jan. 23 -+++ Date Last Updated: -+++ Basic Functions: -+++ Related Constructors: Fraction -+++ Also See: -+++ AMS Classifications: -+++ Keywords: -+++ References: -+++ Description: -+++ This type represents formal fractions - that is, pairs displayed as -+++ fractions with no simplification. -+++ -+++ If the elements of the pair have a type X which is an integral -+++ domain, a FFRAC X can be coerced to a FRAC X, provided that this -+++ is a valid type. A FRAC X can always be coerced to a FFRAC X. -+++ If the type of the elements is a Field, a FFRAC X can be coerced -+++ to X. -+++ -+++ Formal fractions are used to return results from numerical methods -+++ which determine numerator and denominator separately, to enable -+++ users to inspect these components and recognise, for example, -+++ ratios of very small numbers as potentially indeterminate. - -FormalFraction(X : SC) : SC with { - --- Could generalise further to allow numerator and denominator to be of --- different types, X and Y, both SCs. "Left as an exercise." - - / : (X,X) -> % ; -++ / forms the formal quotient of two items. - - numer : % -> X ; -++ numer returns the numerator of a FormalFraction. - - denom : % -> X ; -++ denom returns the denominator of a FormalFraction. - - if X has ID then { - - coerce : % -> FRAC(X pretend ID) ; -++ coerce x converts a FormalFraction over an IntegralDomain to a -++ Fraction over that IntegralDomain. - - coerce : FRAC(X pretend ID) -> % ; -++ coerce converts a Fraction to a FormalFraction. - - } - - if X has Field then coerce : % -> (X pretend Field) ; - -} == add { - - import from Record(num : X, den : X) ; - - Rep == Record(num : X, den : X) ; -- representation - - ((x : %) = (y : %)) : Boolean == - ((rep(x).num = rep(y).num) and (rep(x).den = rep(y).den)) ; - - ((n : X)/(d : X)) : % == per(record(n,d)) ; - - coerce(r : %) : OF == (rep(r).num :: OF) / (rep(r).den :: OF) ; - - numer(r : %) : X == rep(r).num ; - - denom(r : %) : X == rep(r).den ; - - if X has ID then { - - coerce(r : %) : FRAC(X pretend ID) - == ((rep(r).num)/(rep(r).den)) @ (FRAC(X pretend ID)) ; - - coerce(x : FRAC(X pretend ID)) : % == x pretend % ; - - } - - if X has Field then coerce(r : %) : (X pretend Field) - == ((rep(r).num)/(rep(r).den)) $ (X pretend Field) ; - -} - -#if NeverAssertThis - -)lib ffrac - -f1 : FormalFraction Integer -f1 := 6/3 - --- 6 --- - --- 3 - -f2 := (3.6/2.4)$FormalFraction Float - --- 3.6 --- --- --- 2.4 - -numer f1 - --- 6 - -denom f2 - --- 2.4 - -f1 :: FRAC INT - --- 2 - -% :: FormalFraction Integer - --- 2 --- - --- 1 - -f2 :: Float - --- 1.5 - -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>> - -<<FormalFraction>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/herm.as.pamphlet b/src/algebra/herm.as.pamphlet deleted file mode 100644 index fb44b00f..00000000 --- a/src/algebra/herm.as.pamphlet +++ /dev/null @@ -1,369 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra herm.as} -\author{Michael Richardson} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\begin{verbatim} --- N.B. ndftip.as inlines this, must be recompiled if this is. - --- To test: --- sed -ne '1,/^#if NeverAssertThis/d;/#endif/d;p' < herm.as > herm.input --- axiom --- )set nag host <some machine running nagd> --- )r herm.input -\end{verbatim} -\section{PackedHermitianSequence} -<<PackedHermitianSequence>>= -#include "axiom.as" - -INT ==> Integer ; -NNI ==> NonNegativeInteger ; -PHS ==> PackedHermitianSequence ; - -+++ Author: M.G. Richardson -+++ Date Created: 1995 Nov. 24 -+++ Date Last Updated: -+++ Basic Functions: -+++ Related Constructors: Vector -+++ Also See: -+++ AMS Classifications: -+++ Keywords: -+++ References: -+++ Description: -+++ This type represents packed Hermitian sequences - that is, complex -+++ sequences s, whose tails ("rest s", in Axiom terms) are conjugate to -+++ themselves reversed - by real sequences, in the "standard" manner; -+++ in this, the real parts of the elements of the first "half" of the -+++ tail are stored there and the imaginary parts are stored in reverse -+++ order in the second "half" of the tail. -+++ (If the tail has an odd number of elements, its middle element is -+++ real and is stored unchanged. The "halves" mentioned above then -+++ refer to the elements before and after the middle, respectively.) - -PackedHermitianSequence(R : CommutativeRing) : LinearAggregate(R) with{ - - pHS : List R -> % ; -++ pHS(l) converts the list l to a packedHermitianSequence. - - expand : % -> Vector Complex R ; -++ expand(h) converts the packedHermitianSequence h to a Hermitian -++ sequence (a complex vector). - - packHS : Vector Complex R -> % ; -++ packHS(v) checks that the complex vector v represents a Hermitian -++ sequences and, if so, converts it to a packedHermitianSequence; -++ otherwise an error message is printed. - - conjHerm : % -> % ; -++ conjHerm(h) returns the packedHermitianSequence which represents the -++ Hermitian sequence conjugate to that represented by h. - - coerce : % -> OutputForm -- shouldn't need this, should be inherited - -- from Vector. - -} == Vector(R) add { - Rep ==> Vector R; - import from Rep; - import from INT ; - import from R ; - import from Vector R ; - import from Complex R ; - import from Vector Complex R ; - import from ErrorFunctions ; - import from String ; - import from List String ; - - local (..)(a:INT,b:INT):Generator INT == { - generate { - t := a ; - while (t <= b) repeat { - yield t ; - t := t + 1 ; - } - } - } - - pHS(l : List R) : % == (vector l) pretend PHS R ; - - expand(h : %) : Vector Complex R == { - - local len : NNI ; - local nvals, npairs, n1, n2 : INT ; - local fullh : Vector Complex R ; - - { - len := # h ; - nvals := len pretend INT ; -- pretend since :: fails - npairs := (nvals - 1) quo 2 ; - fullh := new(len, 0) ; - (nvals = 0) => () ; - fullh.1 := complex(h.1,0) ; - (nvals = 1) => () ; - fullh.(npairs+2) := complex(h.(npairs+2),0) ; -- need if even length - -- (not worth testing) - for j in 1 .. npairs repeat { - n1 := j + 1 ; - n2 := nvals - j + 1 ; - fullh.n1 := complex(h.n1, h.n2) ; - fullh.n2 := complex(h.n1, -(h.n2)) ; - } - - } - - fullh - - } - - packHS(v : Vector Complex R) : % == { - - local len : NNI ; - local nonhs : String == "The argument of packHS is not Hermitian" ; - local nvals, testprs, n1, n2 : INT ; - local hpacked : Vector R ; - local v1, v2 : Complex R ; - local r1, i1, r2, i2 : R ; - - { - len := # v ; - nvals := len pretend INT ; -- pretend since :: fails - testprs := nvals quo 2 ; - hpacked := new(len, 0) ; - (nvals = 0) => () ; - if imag(v.1) ~= 0 - then error [nonhs, " - the first element must be real."] - else { - hpacked.1 := real(v.1) ; - (nvals = 1) => () ; - for j in 1 .. testprs repeat { - n1 := j + 1 ; - n2 := nvals - j + 1 ; - v1 := v.n1 ; - v2 := v.n2 ; - r1 := real v1 ; - i1 := imag v1 ; - r2 := real v2 ; - i2 := imag v2 ; - if r1 ~= r2 or i1 ~= -i2 - then if n1 = n2 - then error [nonhs, - " - element ", - string(n1), - " must be real to be self-conjugate."] - else error [nonhs, - " - elements ", - string(n1), - " and ", - string(n2), - " are not conjugate."] - else { - hpacked.n2 := i1 ; -- This order means that when the tail of v - hpacked.n1 := r1 ; -- has odd length, the (real part) of its - -- middle element ends up in that position. - } - } - } - } - - hpacked pretend % - - } - - local set!(x: %, i: INT, v: R): () == { - (rep x).i := v; - } - conjHerm(h : %) : % == { - - local len : NNI ; - local nvals, npairs : INT ; - local ch : % ; - - ch := copy h ; - len := # h ; - (len < 3) => ch ; -- these Hermitian sequences are self-conjugate. - nvals := len pretend INT ; -- pretend since :: fails - npairs := (nvals - 1) quo 2 ; - for j in (nvals - npairs + 1) .. nvals repeat ch.j := - h.j ; - ch - - } - - import from List OutputForm ; - - coerce(h : %) : OutputForm == - bracket commaSeparate [ - qelt(h, k) :: OutputForm for k in minIndex h .. maxIndex h] - -} - -#if NeverAssertThis - -)lib herm - -h0 := pHS([] :: List INT) - --- [] - -h1 := pHS [1] - --- [1] - -h2 := pHS [1,2] - --- [1,2] - -h3 := pHS [1,2,3] - --- [1,2,3] - -h4 := pHS [1,2,3,4] - --- [1,2,3,4] - -h5 := pHS [1,2,3,4,5] - --- [1,2,3,4,5] - - -f0 := expand h0 - --- [] - -f1 := expand h1 - --- [1] - -f2 := expand h2 - --- [1,2] - -f3 := expand h3 - --- [1,2 + 3%i,2 - 3%i] - -f4 := expand h4 - --- [1,2 + 4%i,3,2 - 4%i] - -f5 := expand h5 - --- [1,2 + 5%i,3 + 4%i,3 - 4%i,2 - 5%i] - -packHS f0 - --- [] - -packHS f1 - --- [1] - -packHS f2 - --- [1,2] - -packHS f3 - --- [1,2,3] - -packHS f4 - --- [1,2,3,4] - -packHS f5 - --- [1,2,3,4,5] - -packHS vector[%i,3,3,3] - --- Error signalled from user code: --- The argument of packHS is not Hermitian - the first element must --- be real. - -packHS vector [1, 3, 5, 7] - --- Error signalled from user code: --- The argument of packHS is not Hermitian - elements 2 and 4 are --- not conjugate. - -packHS [1, 3, %i, 3] - --- Error signalled from user code: --- The argument of packHS is not Hermitian - element 3 must be real --- to be self-conjugate. - -conjHerm h0 - --- [] - -conjHerm h1 - --- [1] - -conjHerm h2 - --- [1,2] - -conjHerm h3 - --- [1,2,- 3] - -conjHerm h4 - --- [1,2,3,- 4] - -conjHerm h5 - --- [1,2,3,- 4,- 5] - -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>> - -<<PackedHermitianSequence>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/interval.as.pamphlet b/src/algebra/interval.as.pamphlet deleted file mode 100644 index 123f1d97..00000000 --- a/src/algebra/interval.as.pamphlet +++ /dev/null @@ -1,564 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra interval.as} -\author{Mike Dewar} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{IntervalCategory} -<<IntervalCategory>>= -#include "axiom.as" - -+++ Author: Mike Dewar -+++ Date Created: November 1996 -+++ Date Last Updated: -+++ Basic Functions: -+++ Related Constructors: -+++ Also See: -+++ AMS Classifications: -+++ Keywords: -+++ References: -+++ Description: -+++ This category is an implementation of interval arithmetic and transcendental -+++ functions over intervals. - -FUNCAT ==> Join(FloatingPointSystem,TranscendentalFunctionCategory); - -define IntervalCategory(R:FUNCAT): Category == - Join(GcdDomain, OrderedSet, TranscendentalFunctionCategory, RadicalCategory, - RetractableTo(Integer)) - with { - approximate; - interval : (R,R) -> %; - ++ interval(inf,sup) creates a new interval, either \axiom{[inf,sup]} if - ++ \axiom{inf <= sup} or \axiom{[sup,in]} otherwise. - qinterval : (R,R) -> %; - ++ qinterval(inf,sup) creates a new interval \axiom{[inf,sup]}, without - ++ checking the ordering on the elements. - interval : R -> %; - ++ interval(f) creates a new interval around f. - interval : Fraction Integer -> %; - ++ interval(f) creates a new interval around f. - inf : % -> R; - ++ inf(u) returns the infinum of \axiom{u}. - sup : % -> R; - ++ sup(u) returns the supremum of \axiom{u}. - width : % -> R; - ++ width(u) returns \axiom{sup(u) - inf(u)}. - positive? : % -> Boolean; - ++ positive?(u) returns \axiom{true} if every element of u is positive, - ++ \axiom{false} otherwise. - negative? : % -> Boolean; - ++ negative?(u) returns \axiom{true} if every element of u is negative, - ++ \axiom{false} otherwise. - contains? : (%,R) -> Boolean; - ++ contains?(i,f) returns true if \axiom{f} is contained within the interval - ++ \axiom{i}, false otherwise. -} - -@ -\section{Interval} -<<Interval>>= -+++ Author: Mike Dewar -+++ Date Created: November 1996 -+++ Date Last Updated: -+++ Basic Functions: -+++ Related Constructors: -+++ Also See: -+++ AMS Classifications: -+++ Keywords: -+++ References: -+++ Description: -+++ This domain is an implementation of interval arithmetic and transcendental -+++ functions over intervals. - -Interval(R:FUNCAT): IntervalCategory(R) == add { - - import from Integer; - import from R; - - Rep ==> Record(Inf:R, Sup:R); - - import from Rep; - - local roundDown(u:R):R == - if zero?(u) then float(-1,-(bits() pretend Integer)); - else float(mantissa(u) - 1,exponent(u)); - - local roundUp(u:R):R == - if zero?(u) then float(1, -(bits()) pretend Integer); - else float(mantissa(u) + 1,exponent(u)); - - -- Sometimes the float representation does not use all the bits (e.g. when - -- representing an integer in software using arbitrary-length Integers as - -- your mantissa it is convenient to keep them exact). This function - -- normalises things so that rounding etc. works as expected. It is only - -- called when creating new intervals. - local normaliseFloat(u:R):R == - if zero? u then u else { - m : Integer := mantissa u; - b : Integer := bits() pretend Integer; - l : Integer := length(m); - if (l < b) then { - BASE : Integer := base()$R pretend Integer; - float(m*BASE**((b-l) pretend PositiveInteger),exponent(u)-b+l); - } - else - u; - } - - interval(i:R,s:R):% == { - i > s => per [roundDown normaliseFloat s,roundUp normaliseFloat i]; - per [roundDown normaliseFloat i,roundUp normaliseFloat s]; - } - - interval(f:R):% == { - zero?(f) => 0; - one?(f) => 1; - -- This next part is necessary to allow e.g. mapping between Expressions: - -- AXIOM assumes that Integers stay as Integers! - import from Union(value1:Integer,failed:'failed'); - fnew : R := normaliseFloat f; - retractIfCan(f)@Union(value1:Integer,failed:'failed') case value1 => - per [fnew,fnew]; - per [roundDown fnew, roundUp fnew]; - } - - qinterval(i:R,s:R):% == - per [roundDown normaliseFloat i,roundUp normaliseFloat s]; - - local exactInterval(i:R,s:R):% == per [i,s]; - local exactSupInterval(i:R,s:R):% == per [roundDown i,s]; - local exactInfInterval(i:R,s:R):% == per [i,roundUp s]; - - inf(u:%):R == (rep u).Inf; - sup(u:%):R == (rep u).Sup; - width(u:%):R == (rep u).Sup - (rep u).Inf; - - contains?(u:%,f:R):Boolean == (f > inf(u)) and (f < sup(u)); - - positive?(u:%):Boolean == inf(u) > 0; - negative?(u:%):Boolean == sup(u) < 0; - - (<)(a:%,b:%):Boolean == - if inf(a) < inf(b) then - true - else if inf(a) > inf(b) then - false - else - sup(a) < sup(b); - - (+)(a:%,b:%):% == { - -- A couple of blatent hacks to preserve the Ring Axioms! - if zero?(a) then return(b) else if zero?(b) then return(a); - if a=b then return qinterval(2*inf(a),2*sup(a)); - qinterval(inf(a) + inf(b), sup(a) + sup(b)); - } - - (-)(a:%,b:%):% == { - if zero?(a) then return(-b) else if zero?(b) then return(a); - if a=b then 0 else qinterval(inf(a) - sup(b), sup(a) - inf(b)); - } - - (*)(a:%,b:%):% == { - -- A couple of blatent hacks to preserve the Ring Axioms! - if one?(a) then return(b) else if one?(b) then return(a); - if zero?(a) then return(0) else if zero?(b) then return(0); - prods : List R := sort [inf(a)*inf(b),sup(a)*sup(b), - inf(a)*sup(b),sup(a)*inf(b)]; - qinterval(first prods, last prods); - } - - (*)(a:Integer,b:%):% == { - if (a > 0) then - qinterval(a*inf(b),a*sup(b)); - else if (a < 0) then - qinterval(a*sup(b),a*inf(b)); - else - 0; - } - - (*)(a:PositiveInteger,b:%):% == qinterval(a*inf(b),a*sup(b)); - - (**)(a:%,n:PositiveInteger):% == { - contains?(a,0) and zero?((n pretend Integer) rem 2) => - interval(0,max(inf(a)**n,sup(a)**n)); - interval(inf(a)**n,sup(a)**n); - } - - (^) (a:%,n:PositiveInteger):% == { - contains?(a,0) and zero?((n pretend Integer) rem 2) => - interval(0,max(inf(a)**n,sup(a)**n)); - interval(inf(a)**n,sup(a)**n); - } - - (-)(a:%):% == exactInterval(-sup(a),-inf(a)); - - (=)(a:%,b:%):Boolean == (inf(a)=inf(b)) and (sup(a)=sup(b)); - (~=)(a:%,b:%):Boolean == (inf(a)~=inf(b)) or (sup(a)~=sup(b)); - - 1:% == {one : R := normaliseFloat 1; per([one,one])}; - 0:% == per([0,0]); - - recip(u:%):Union(value1:%,failed:'failed') == { - contains?(u,0) => [failed]; - vals:List R := sort[1/inf(u),1/sup(u)]; - [qinterval(first vals, last vals)]; - } - - unit?(u:%):Boolean == contains?(u,0); - - exquo(u:%,v:%):Union(value1:%,failed:'failed') == { - contains?(v,0) => [failed]; - one?(v) => [u]; - u=v => [1]; - u=-v => [-1]; - vals:List R := sort[inf(u)/inf(v),inf(u)/sup(v),sup(u)/inf(v),sup(u)/sup(v)]; - [qinterval(first vals, last vals)]; - } - - gcd(u:%,v:%):% == 1; - - coerce(u:Integer):% == { - ur := normaliseFloat(u::R); - exactInterval(ur,ur); - } - - interval(u:Fraction Integer):% == { - import { log2 : % -> %; - coerce : Integer -> %; - retractIfCan : % -> Union(value1:Integer,failed:'failed');} - from Float; - flt := u::R; - - -- Test if the representation in R is exact - --den := denom(u)::Float; - local bin : Union(value1:Integer,failed:'failed'); - bin := retractIfCan(log2(denom(u)::Float)); - bin case value1 and length(numer u)$Integer < (bits() pretend Integer) => { - flt := normaliseFloat flt; - exactInterval(flt,flt); - } - - qinterval(flt,flt); - } - - retractIfCan(u:%):Union(value1:Integer,failed:'failed') == { - not zero? width(u) => [failed]; - retractIfCan inf u; - } - - retract(u:%):Integer == { - not zero? width(u) => - error "attempt to retract a non-Integer interval to an Integer"; - retract inf u; - } - - coerce(u:%):OutputForm == - bracket([coerce inf(u), coerce sup(u)]$List(OutputForm)); - - characteristic:NonNegativeInteger == 0; - - - -- Explicit export from TranscendentalFunctionCategory - pi():% == qinterval(pi(),pi()); - - -- From ElementaryFunctionCategory - log(u:%):% == { - positive?(u) => qinterval(log inf u, log sup u); - error "negative logs in interval"; - } - - exp(u:%):% == qinterval(exp inf u, exp sup u); - - (**)(u:%,v:%):% == { - zero?(v) => if zero?(u) then error "0**0 is undefined" else 1; - one?(u) => 1; - expts : List R := sort [inf(u)**inf(v),sup(u)**sup(v), - inf(u)**sup(v),sup(u)**inf(v)]; - qinterval(first expts, last expts); - } - - -- From TrigonometricFunctionCategory - - -- This function checks whether an interval contains a value of the form - -- `offset + 2 n pi'. - local hasTwoPiMultiple(offset:R,Pi:R,i:%):Boolean == { - import from Integer; - next : Integer := retract ceiling( (inf(i) - offset)/(2*Pi) ); - contains?(i,offset+2*next*Pi); - } - - -- This function checks whether an interval contains a value of the form - -- `offset + n pi'. - local hasPiMultiple(offset:R,Pi:R,i:%):Boolean == { - import from Integer; - next : Integer := retract ceiling( (inf(i) - offset)/Pi ); - contains?(i,offset+next*Pi); - } - - sin(u:%):% == { - import from Integer; - Pi : R := pi(); - hasOne? : Boolean := hasTwoPiMultiple(Pi/(2::R),Pi,u); - hasMinusOne? : Boolean := hasTwoPiMultiple(3*Pi/(2::R),Pi,u); - - if hasOne? and hasMinusOne? then - exactInterval(-1,1); - else { - vals : List R := sort [sin inf u, sin sup u]; - if hasOne? then - exactSupInterval(first vals, 1); - else if hasMinusOne? then - exactInfInterval(-1,last vals); - else - qinterval(first vals, last vals); - } - } - - cos(u:%):% == { - Pi : R := pi(); - hasOne? : Boolean := hasTwoPiMultiple(0,Pi,u); - hasMinusOne? : Boolean := hasTwoPiMultiple(Pi,Pi,u); - - if hasOne? and hasMinusOne? then - exactInterval(-1,1); - else { - vals : List R := sort [cos inf u, cos sup u]; - if hasOne? then - exactSupInterval(first vals, 1); - else if hasMinusOne? then - exactInfInterval(-1,last vals); - else - qinterval(first vals, last vals); - } - } - - tan(u:%):% == { - Pi : R := pi(); - if width(u) > Pi then - error "Interval contains a singularity" - else { - -- Since we know the interval is less than pi wide, monotonicity implies - -- that there is no singularity. If there is a singularity on a endpoint - -- of the interval the user will see the error generated by R. - lo : R := tan inf u; - hi : R := tan sup u; - - lo > hi => error "Interval contains a singularity"; - qinterval(lo,hi); - } - } - - csc(u:%):% == { - Pi : R := pi(); - if width(u) > Pi then - error "Interval contains a singularity" - else { - import from Integer; - -- singularities are at multiples of Pi - if hasPiMultiple(0,Pi,u) then error "Interval contains a singularity"; - vals : List R := sort [csc inf u, csc sup u]; - if hasTwoPiMultiple(Pi/(2::R),Pi,u) then - exactInfInterval(1,last vals); - else if hasTwoPiMultiple(3*Pi/(2::R),Pi,u) then - exactSupInterval(first vals,-1); - else - qinterval(first vals, last vals); - } - } - - sec(u:%):% == { - Pi : R := pi(); - if width(u) > Pi then - error "Interval contains a singularity" - else { - import from Integer; - -- singularities are at Pi/2 + n Pi - if hasPiMultiple(Pi/(2::R),Pi,u) then - error "Interval contains a singularity"; - vals : List R := sort [sec inf u, sec sup u]; - if hasTwoPiMultiple(0,Pi,u) then - exactInfInterval(1,last vals); - else if hasTwoPiMultiple(Pi,Pi,u) then - exactSupInterval(first vals,-1); - else - qinterval(first vals, last vals); - } - } - - - cot(u:%):% == { - Pi : R := pi(); - if width(u) > Pi then - error "Interval contains a singularity" - else { - -- Since we know the interval is less than pi wide, monotonicity implies - -- that there is no singularity. If there is a singularity on a endpoint - -- of the interval the user will see the error generated by R. - hi : R := cot inf u; - lo : R := cot sup u; - - lo > hi => error "Interval contains a singularity"; - qinterval(lo,hi); - } - } - - -- From ArcTrigonometricFunctionCategory - - asin(u:%):% == { - lo : R := inf(u); - hi : R := sup(u); - if (lo < -1) or (hi > 1) then error "asin only defined on the region -1..1"; - qinterval(asin lo,asin hi); - } - - acos(u:%):% == { - lo : R := inf(u); - hi : R := sup(u); - if (lo < -1) or (hi > 1) then error "acos only defined on the region -1..1"; - qinterval(acos hi,acos lo); - } - - atan(u:%):% == qinterval(atan inf u, atan sup u); - - acot(u:%):% == qinterval(acot sup u, acot inf u); - - acsc(u:%):% == { - lo : R := inf(u); - hi : R := sup(u); - if ((lo <= -1) and (hi >= -1)) or ((lo <= 1) and (hi >= 1)) then - error "acsc not defined on the region -1..1"; - qinterval(acsc hi, acsc lo); - } - - asec(u:%):% == { - lo : R := inf(u); - hi : R := sup(u); - if ((lo < -1) and (hi > -1)) or ((lo < 1) and (hi > 1)) then - error "asec not defined on the region -1..1"; - qinterval(asec lo, asec hi); - } - - -- From HyperbolicFunctionCategory - - tanh(u:%):% == qinterval(tanh inf u, tanh sup u); - - sinh(u:%):% == qinterval(sinh inf u, sinh sup u); - - sech(u:%):% == { - negative? u => qinterval(sech inf u, sech sup u); - positive? u => qinterval(sech sup u, sech inf u); - vals : List R := sort [sech inf u, sech sup u]; - exactSupInterval(first vals,1); - } - - cosh(u:%):% == { - negative? u => qinterval(cosh sup u, cosh inf u); - positive? u => qinterval(cosh inf u, cosh sup u); - vals : List R := sort [cosh inf u, cosh sup u]; - exactInfInterval(1,last vals); - } - - csch(u:%):% == { - contains?(u,0) => error "csch: singularity at zero"; - qinterval(csch sup u, csch inf u); - } - - coth(u:%):% == { - contains?(u,0) => error "coth: singularity at zero"; - qinterval(coth sup u, coth inf u); - } - - -- From ArcHyperbolicFunctionCategory - - acosh(u:%):% == { - inf(u)<1 => error "invalid argument: acosh only defined on the region 1.."; - qinterval(acosh inf u, acosh sup u); - } - - acoth(u:%):% == { - lo : R := inf(u); - hi : R := sup(u); - if ((lo <= -1) and (hi >= -1)) or ((lo <= 1) and (hi >= 1)) then - error "acoth not defined on the region -1..1"; - qinterval(acoth hi, acoth lo); - } - - acsch(u:%):% == { - contains?(u,0) => error "acsch: singularity at zero"; - qinterval(acsch sup u, acsch inf u); - } - - asech(u:%):% == { - lo : R := inf(u); - hi : R := sup(u); - if (lo <= 0) or (hi > 1) then - error "asech only defined on the region 0 < x <= 1"; - qinterval(asech hi, asech lo); - } - - asinh(u:%):% == qinterval(asinh inf u, asinh sup u); - - atanh(u:%):% == { - lo : R := inf(u); - hi : R := sup(u); - if (lo <= -1) or (hi >= 1) then - error "atanh only defined on the region -1 < x < 1"; - qinterval(atanh lo, atanh hi); - } - - -- From RadicalCategory - (**)(u:%,n:Fraction Integer):% == interval(inf(u)**n,sup(u)**n); - -} - -@ -\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>> - -<<IntervalCategory>> -<<Interval>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/invnode.as.pamphlet b/src/algebra/invnode.as.pamphlet deleted file mode 100644 index 3d0958c2..00000000 --- a/src/algebra/invnode.as.pamphlet +++ /dev/null @@ -1,340 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra invnode.as} -\author{The Axiom Team} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{IVNodeCategory} -<<IVNodeCategory>>= -#include "axiom" - -POINT ==> Point DoubleFloat; - -local DF2S; -DF2S(u:DoubleFloat):String == { - STRINGIMAGE ==> VMLISP_:_:STRINGIMAGE; - import { STRINGIMAGE : DoubleFloat -> String} from Foreign Lisp; - STRINGIMAGE(u); -} - -+++ Category of all open inventor node types -+++ Uses IVObject as a 'generic' value. -define IVNodeCategory: Category == SetCategory with { - quickWrite: (TextFile, %) -> (); - ++ Quick version. Not guaranteed to terminate - children: % -> List IVNodeObject; - addChild!: (%, IVNodeObject) -> (); - fields: % -> List IVField; - className: % -> String; - coerce: % -> IVNodeObject; - default { - import from Symbol; - quickWrite(out: TextFile, node: %): () == { - write!(out, className(node)); - write!(out, " {"); - writeLine!(out); - import from List IVField; - import from IVValue; - for field in fields node repeat { - write!(out, string name field); - write!(out, " "); - invWrite(out, value field); - } - writeLine!(out, "}"); - } - coerce(x: %): IVNodeObject == - make(% pretend IVNodeCategory, x); - - coerce(x: %): OutputForm == { - import from String; - coerce className x; - } - } -} - -@ -\section{IVLeafNodeCategory} -<<IVLeafNodeCategory>>= -+++ Category for leaves --- just adds a few defaults to make life -+++ easy. -define IVLeafNodeCategory: Category == IVNodeCategory with { - default { - children(v: %): List IVNodeObject == []; - addChild!(v: %, new: IVNodeObject): () == - error "can't add child to a leaf"; - } -} - -@ -\section{IVNodeObject} -<<IVNodeObject>>= --- virtual functions for fun and profit... -IVNodeObject: IVNodeCategory with { - make: (T: IVNodeCategory, T) -> %; - coerce: (T: IVNodeCategory, %) -> T; - uniqueID: % -> Integer; -} == add { - Rep ==> Record(NT: IVNodeCategory, val: NT, idx: Integer); - import from Rep; - default z: Integer; - - local iCount: Integer := 0; - local explode: (o: %) -> (NodeType: IVNodeCategory, NodeType); - - uniqueID(o: %): Integer == rep(o).idx; - - explode(o: %): (NodeType: IVNodeCategory, v: NodeType) == { - (NT, val, id) == explode rep o; - (NT, val); - } - - make(T: IVNodeCategory, val: T): % == { - free iCount := iCount + 1; - per [T, val, iCount]; - } - coerce(T: IVNodeCategory, val: %): T == { - (type, v, id) == explode rep val; - v pretend T; - } - - -- The '0' functions are needed to turn non-constants - -- (eg. fn return values) -- into constants. - children(v: %): List IVNodeObject == { - children0(NodeType: IVNodeCategory, val: NodeType): - List IVNodeObject == - children val; - children0 explode v; - } - - fields(v: %): List IVField == { - fields0(NodeType: IVNodeCategory, val: NodeType): List IVField == - fields val; - fields0 explode v; - } - - className(v: %): String == { - name0(NodeType: IVNodeCategory, val: NodeType): String == - className(val)$NodeType; - name0 explode v; - } - - addChild!(v: %, child: %): () == { - addChild0!(NodeType: IVNodeCategory, val: NodeType): () == - addChild!(val, child); - addChild0! explode v; - } - - -- BasicType stuff - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality on ivobject"; -} - -@ -\section{IVNodeConnection} -<<IVNodeConnection>>= -IVNodeConnection: with { - bracket: (IVNodeObject, Symbol) -> %; - field: % -> Symbol; - node: % -> IVNodeObject; -} == add { - Rep ==> Record(o: IVNodeObject, f: Symbol); - import from Rep; - - [o: IVNodeObject, f: Symbol]: % == per [o,f]; - field(c: %): Symbol == rep(c).f; - node(c: %): IVNodeObject == rep(c).o; -} - -@ -\section{IVValue} -<<IVValue>>= -IVValue: BasicType with { - DECL(T, fld, flg) ==> { - coerce: % -> T; - flg: % -> Boolean; - fld: T -> %; - } - DECL(DoubleFloat, float, float?); - DECL(IVNodeObject, node, node?); - DECL(Boolean, bool, bool?); - DECL(SingleInteger, int, int?); - DECL(String, string, string?); - DECL(Symbol, symbol, symbol?); - DECL(POINT, point, point?); - DECL(List DoubleFloat, floatlist, floatlist?); - DECL(List SingleInteger, intlist, intlist?); - DECL(List POINT, pointlist, pointlist?); - DECL(IVNodeConnection, connect, connect?); - - invWrite: (TextFile, %) -> (); -} == add { - Rep ==> Union( float: DoubleFloat, - node: IVNodeObject, - bool: Boolean, - int: SingleInteger, - string: String, - symbol: Symbol, - point: POINT, - intlist: List SingleInteger, - floatlist: List DoubleFloat, - pointlist: List POINT, - connect: IVNodeConnection - ); - import from Rep; - - Accessor(T, fld, flg) ==> { - coerce(x: %): T == rep(x).fld; - flg(x: %): Boolean == rep(x) case fld; - fld(x: T): % == per [x, fld]; - } - Accessor(DoubleFloat, float, float?); - Accessor(IVNodeObject, node, node?); - Accessor(Boolean, bool, bool?); - Accessor(SingleInteger, int, int?); - Accessor(String, string, string?); - Accessor(Symbol, symbol, symbol?); - Accessor(POINT, point, point?); - Accessor(List DoubleFloat, floatlist, floatlist?); - Accessor(List SingleInteger, intlist, intlist?); - Accessor(List POINT, pointlist, pointlist?); - Accessor(IVNodeConnection, connect, connect?); - - local ppoint(out: TextFile, val: POINT, dim: Integer): () == { - for i in 1..dim repeat { - write!(out, DF2S(val.(i::Integer))); - write!(out, " "); - } - } - invWrite(out: TextFile, val: %): () == { - import from Float, Integer; - float? val => { - writeLine!(out, - convert(convert(val::DoubleFloat)$Float)); - } - node? val or connect? val => { - error "Sorry, can't write a node here"; - --writeLine!(out, val::IVNodeObject); - } - bool? val => { - writeLine!(out, - if val::Boolean then "true" else "false"); - } - int? val => { - writeLine!(out, - convert(convert(val::SingleInteger)@Integer)); - } - string? val => { - writeLine!(out, val::String); - } - symbol? val => { - writeLine!(out, string(val::Symbol)); - } - point? val => { - ppoint(out, rep(val).point, 3); - writeLine!(out, ""); - } - floatlist? val => { - write!(out, "[ "); - for fl in val::List DoubleFloat repeat { - write!(out,convert(convert(fl)$Float)); - write!(out, ", "); - } - writeLine!(out, "]"); - } - intlist? val => { - write!(out, "[ "); - for i in val::List SingleInteger repeat { - write!(out,convert(convert(i)@Integer)); - write!(out, ", "); - } - writeLine!(out, "]"); - } - pointlist? val => { - write!(out, "[ "); - for p in val::List POINT repeat { - ppoint(out, p, 3); - writeLine!(out, ","); - } - writeLine!(out, "]"); - } - never - } - -- - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality for values"; -} - -@ -\section{IVField} -<<IVField>>= -IVField: BasicType with { - new: (Symbol,IVValue) -> %; - name: % -> Symbol; - value: % -> IVValue; -} == add { - Rep ==> Record(name: Symbol, v: IVValue); - import from Rep; - - new(name: Symbol, val: IVValue): % == per [name, val]; - name(f: %): Symbol == rep(f).name; - value(f: %): IVValue == rep(f).v; - - -- - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality for values"; -} - -@ -\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>> - -<<IVNodeCategory>> -<<IVLeafNodeCategory>> -<<IVNodeObject>> -<<IVNodeConnection>> -<<IVValue>> -<<IVField>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/invrender.as.pamphlet b/src/algebra/invrender.as.pamphlet deleted file mode 100644 index 924d1a39..00000000 --- a/src/algebra/invrender.as.pamphlet +++ /dev/null @@ -1,172 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra invrender.as} -\author{The Axiom Team} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{RenderTools} -<<RenderTools>>= -#include "axiom" - -POINT ==> Point DoubleFloat; -NNI ==> NonNegativeInteger; -SI ==> SingleInteger; - -RenderTools: with { - renderToFile!: (FileName, ThreeSpace DoubleFloat) -> (); - makeSceneGraph: (ThreeSpace DoubleFloat) -> IVNodeObject; -} == add { - import from IVUtilities; - - renderToFile!(f: FileName, space: ThreeSpace DoubleFloat): () == { - root := makeSceneGraph(space); - write!(f, root); - } - - local makePts: (lpts: List POINT, - indicies: List List List NonNegativeInteger) -> - (List POINT, List DoubleFloat); - - local makePts(lp: List POINT, indicies: List List List NonNegativeInteger): - (List POINT, List DoubleFloat) == { - local colorIdx: Integer; - indexList := concat concat indicies; - coordpts := lp; - if (# first lp = 4) then colorIdx := 4 else colorIdx := 3; - colors := [pt.colorIdx for pt in lp]; - (coordpts, colors) - } - - local makeBaseColor(l: List DoubleFloat): IVBaseColor == { - -- This works by interpolating between blue and green (via cyan). - -- There may well be better ways... - import from POINT; - import from List POINT; - import from DoubleFloat; - import from List DoubleFloat; - low := 10000.0; - high := -10000.0; - for df in l repeat { - if low > df then low := df; - if high < df then high := df; - } - if (high = low) then high := high + 1.0; - new [ point([0, (df - low)/(high - low), (high - df)/(high - low)]) - for df in l] - } - makeSceneGraph(space: ThreeSpace DoubleFloat): IVNodeObject == { - import from List ThreeSpace DoubleFloat; - import from List List List NNI; - import from Integer; - import from Symbol; - import from IVValue; - check(space); - lpts := lp(space); - indicies := lllip(space); - root: IVSeparator := new(); - (coordpts, colorvalues) := makePts(lpts, indicies); - coords: IVCoordinate3 := new coordpts; - colors: IVBaseColor := makeBaseColor(colorvalues); - addChild!(root, coerce coords); - addChild!(root, coerce colors); - binding: IVBasicNode := make "MaterialBinding"; - addField!(binding, "value", symbol "PER__VERTEX"); - addChild!(root, coerce binding); - offset: NNI := 0; - for ss in components space - for index in indicies repeat { - local coordIndex: List NNI; - default i: Integer; - closedCurve? ss => { - n: Integer := (#(index.1))::Integer; - coordIndex := - [offset+coerce(i) for i in 0..n::Integer]; - -- Close the curve - setlast!(coordIndex,offset); - curve : IVIndexedLineSet := new coordIndex; - addChild!(root, coerce curve); - offset := offset+n::NNI; - } - curve? ss => { - n := (#(index.1))::Integer; - coordIndex := - [offset+coerce(i) for i in 0..(n-1)]; - curve : IVIndexedLineSet := new coordIndex; - addChild!(root, coerce curve); - offset := offset+n::NNI; - } - polygon? ss => { - vertices := #(index.1) + #(index.2); - face : IVFaceSet := new(vertices::SI,offset::SI); - addChild!(root, coerce face); - offset := offset+vertices; - } - mesh? ss => { - xStep: SingleInteger := (#index)::SingleInteger; - yStep: SingleInteger := (#(first index))::SingleInteger; - quadMesh : IVQuadMesh := - new(xStep,yStep,offset::SingleInteger); - addChild!(root, coerce quadMesh); - offset := offset+coerce(xStep*yStep); - } - point? ss => { - pt : IVPointSet := new(offset::SingleInteger, - 1$SingleInteger); - addChild!(root, coerce pt); - offset := offset+1; - } - error "Unrecognised SubSpace component"; - } - coerce root; - } -} - -@ -\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>> - -<<RenderTools>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/invtypes.as.pamphlet b/src/algebra/invtypes.as.pamphlet deleted file mode 100644 index 002a544d..00000000 --- a/src/algebra/invtypes.as.pamphlet +++ /dev/null @@ -1,302 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra invtypes.as} -\author{The Axiom Team} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{IVSimpleInnerNode} -<<IVSimpleInnerNode>>= -#include "axiom" - -import from IVValue, Symbol; - -POINT ==> Point DoubleFloat; -NNI ==> NonNegativeInteger; - -IVSimpleInnerNode: with { - new: () -> %; - addChild!: (%, IVNodeObject) -> (); - children: % -> List IVNodeObject; - fields: % -> List IVField; - - =: (%, %) -> Boolean; - -} == add { - Rep ==> Record(lst: List IVNodeObject); - import from Rep; - - new(): % == per [[]]; - addChild!(v: %, new: IVNodeObject): () == { - rep(v).lst := concat!(rep(v).lst, new); - } - - children(v: %): List IVNodeObject == rep(v).lst; - - fields(node: %): List IVField == []; - - -- - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality on IVInnerNodes"; -} - -@ -\section{IVSeparator} -<<IVSeparator>>= -IVSeparator: IVNodeCategory with { - new: () -> %; -} == IVSimpleInnerNode add { - className(v: %): String == "Separator"; -} - -@ -\section{IVGroup} -<<IVGroup>>= -IVGroup: IVNodeCategory with { - new: () -> %; -} == IVSimpleInnerNode add { - className(v: %): String == "Group"; -} - -@ -\section{IVCoordinate3} -<<IVCoordinate3>>= -IVCoordinate3: IVLeafNodeCategory with { - new: List POINT -> %; -} == add { - Rep ==> List POINT; - className(x: %): String == "Coordinate3"; - - new(l: List POINT): % == per l; - fields(v: %): List IVField == [ new("point", pointlist rep v)]; - - -- - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality on IVCoord3"; -} - -@ -\section{IVCoordinate4} -<<IVCoordinate4>>= -IVCoordinate4: IVLeafNodeCategory with { - new: List POINT -> %; -} == add { - Rep ==> List POINT; - import from Rep; - - className(x: %): String == "Coordinate4"; - - new(l: List POINT): % == per l; - fields(v: %): List IVField == [ new("point", pointlist rep v)]; - - -- - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality on IVCoord4"; -} - -@ -\section{IVQuadMesh} -<<IVQuadMesh>>= -IVQuadMesh: IVLeafNodeCategory with { - new: (SingleInteger, SingleInteger, SingleInteger) -> %; -} == add { - Rep ==> Record( rowc: SingleInteger, - colc: SingleInteger, - start: SingleInteger); - import from Rep; - - className(x: %): String == "QuadMesh"; - - new(rc: SingleInteger, cc: SingleInteger, start: SingleInteger): % == - per [rc, cc, start]; - - fields(v: %): List IVField == [ - new("verticesPerColumn", int rep(v).colc), - new("verticesPerRow", int rep(v).rowc), - new("startIndex", int rep(v).start) - ]; - - -- - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality on IVQuadMesh"; -} - -@ -\section{IVBaseColor} -<<IVBaseColor>>= -IVBaseColor: IVLeafNodeCategory with { - new: List POINT -> %; -} == add { - Rep ==> List POINT; - import from Rep; - - className(x: %): String == "BaseColor"; - - new(l: List POINT): % == per l; - fields(v: %): List IVField == [ new("rgb", pointlist rep v) ]; - - -- - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality on IVBaseColor"; -} - -@ -\section{IVIndexedLineSet} -<<IVIndexedLineSet>>= -IVIndexedLineSet: IVLeafNodeCategory with { - new: List NNI -> %; - new: List SingleInteger -> %; -} == add { - Rep ==> List SingleInteger; - import from Rep; - - className(x: %): String == "IndexedLineSet"; - - new(l: List SingleInteger): % == per l; - new(l: List NNI): % == new [ coerce n for n in l]; - - fields(v: %): List IVField == [ new("points", intlist rep v) ]; - - -- - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality on IVBaseColor"; -} - -@ -\section{IVFaceSet} -<<IVFaceSet>>= -IVFaceSet: IVLeafNodeCategory with { - new: (SingleInteger, SingleInteger) -> %; -} == add { - Rep ==> Record(startIndex: SingleInteger, numVertices: SingleInteger); - import from Rep; - - className(x: %): String == "FaceSet"; - - new(x: SingleInteger, y: SingleInteger): % == per [x,y]; - fields(v: %): List IVField == [ - new("numVertices", int rep(v).numVertices), - new("startIndex", int rep(v).startIndex) - ]; - - -- - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality on IVFaceSet"; -} - -@ -\section{IVPointSet} -<<IVPointSet>>= -IVPointSet: IVLeafNodeCategory with { - new: (SingleInteger, SingleInteger) -> %; -} == add { - Rep ==> Record(startIndex: SingleInteger, numPoints: SingleInteger); - import from Rep; - - className(x: %): String == "PointSet"; - - new(x: SingleInteger, y: SingleInteger): % == per [x,y]; - - fields(v: %): List IVField == [ - new("numPoints", int rep(v).numPoints), - new("startIndex", int rep(v).startIndex) - ]; - - -- - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality on IVFaceSet"; -} - -@ -\section{IVBasicNode} -<<IVBasicNode>>= -IVBasicNode: IVNodeCategory with { - make: String -> %; - addField!: (%, IVField) -> (); - addField!: (%, Symbol, IVValue) -> (); -} == add { - Rep ==> Record(class: String, - kids: List IVNodeObject, - fields: List IVField); - import from Rep, IVField; - - make(name: String): % == per [name, [], []]; - - className(node: %): String == rep(node).class; - children(node: %): List IVNodeObject == rep(node).kids; - fields(node: %): List IVField == rep(node).fields; - - addField!(node: %, fld: IVField): () == { - rep(node).fields := cons(fld, rep(node).fields); - } - - addChild!(node: %, kid: IVNodeObject): () == { - rep(node).kids := cons(kid, rep(node).kids); - } - - addField!(node: %, sym: Symbol, val: IVValue): () == - addField!(node, new(sym, val)); - - -- - sample: % == % pretend %; - (=)(a: %, b: %): Boolean == error "no equality on IVBasicNode"; -} - -@ -\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>> - -<<IVSimpleInnerNode>> -<<IVSeparator>> -<<IVGroup>> -<<IVCoordinate3>> -<<IVCoordinate4>> -<<IVQuadMesh>> -<<IVBaseColor>> -<<IVIndexedLineSet>> -<<IVFaceSet>> -<<IVPointSet>> -<<IVBasicNode>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/invutils.as.pamphlet b/src/algebra/invutils.as.pamphlet deleted file mode 100644 index c20261da..00000000 --- a/src/algebra/invutils.as.pamphlet +++ /dev/null @@ -1,172 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra invutils.as} -\author{The Axiom Team} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{IVUtilities} -<<IVUtilities>>= -#include "axiom" - -IVUtilities: with { - walkTree: ((IVNodeObject, Boolean) -> Boolean, - (IVNodeObject, Boolean) -> Boolean, - IVNodeObject, Boolean) -> (); - write!: (TextFile, IVNodeObject) -> (); - write!: (FileName, IVNodeObject) -> (); -} == add { - -- walk a tree from 'root', and call f on each node. - -- nodesOnly will stop the recursion finding subnodes within - -- fields. - -- preFn is a function that takes a node, a flag indicating if the - -- node has already been traversed. It returns a flag - -- indicating if the traversal should descend the node. - walkTree(preFn: (IVNodeObject, Boolean) -> Boolean, - postFn: (IVNodeObject, Boolean) -> Boolean, - root: IVNodeObject, - nodesOnly: Boolean): () == { - tab: Table(Integer, IVNodeObject) := table(); - innerWalk(node: IVNodeObject): () == { - import from List IVNodeObject; - import from List IVField; - import from IVValue; - present := key?(uniqueID node, tab); - not preFn(node, present) => return; - tab.(uniqueID node) := node; - for child in children node repeat - innerWalk(child); - if not nodesOnly then { - for fld in fields node repeat { - import from IVNodeConnection; - connect? value fld => - innerWalk(node coerce value fld); - node? value fld => - innerWalk(coerce value fld); - } - } - postFn(node, false); - } - innerWalk(root); - } - - write!(out: TextFile, root: IVNodeObject): () == { - import from Boolean; - names: Table(Integer, IVNodeObject) := table(); - - getName(node: IVNodeObject): String == { - import from Integer; - convert uniqueID node; - } - - doNamingVisit(node: IVNodeObject, flag: Boolean): Boolean == { - if flag then names.(uniqueID node) := node; - flag - } - writeNodeHeader(node: IVNodeObject): () == { - present := key?(uniqueID node, names); - if present then { - write!(out, "DEF "); - write!(out, getName node); - } - } - doPrintingVisit(node: IVNodeObject, - flag: Boolean): Boolean == { - if flag then { - write!(out, "USE "); - write!(out, getName node); - return false; - } - write!(out, className(node)); - writeLine!(out, " {"); - import from List IVField, Symbol; - for field in fields node repeat { - import from IVNodeConnection; - val: IVValue := value field; - write!(out, string name field); - write!(out, " "); - node? val => { - walkTree(doPrintingVisit, - doFinalPrint, - coerce val, false); - } - connect? val => { - walkTree(doPrintingVisit, - doFinalPrint, - node coerce val, false); - write!(out, "."); - writeLine!(out, - string field coerce val); - } - -- simple case: - invWrite(out, value field); - } - return true; - } - - doFinalPrint(node: IVNodeObject, x: Boolean): Boolean == { - writeLine!(out, "}"); - true; - } - doNothing(node: IVNodeObject, x: Boolean): Boolean == x; - - writeLine!(out, "#Inventor V2.0 ascii"); - walkTree(doNamingVisit, doNothing, root, true); - walkTree(doPrintingVisit, doFinalPrint, root, false); - } - - write!(file: FileName, root:IVNodeObject): () == { - out: TextFile := open(file, "output"); - write!(out, root); - close!(out); - } -} - -@ -\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>> - -<<IVUtilities>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/iviews.as.pamphlet b/src/algebra/iviews.as.pamphlet deleted file mode 100644 index 2937713e..00000000 --- a/src/algebra/iviews.as.pamphlet +++ /dev/null @@ -1,330 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra iviews.as} -\author{The Axiom Team} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{InventorDataSink} -<<InventorDataSink>>= -#include "axiom" -#assert Real - -NNI ==> NonNegativeInteger; -SI ==> SingleInteger; -DF ==> DoubleFloat; -POINT ==> Point DF; -SPACE3 ==> ThreeSpace DoubleFloat; - -DefaultSize ==> 65530; - -Value ==> Symbol; - -InventorDataSink: with { - CoercibleTo OutputForm; - new: () -> %; - dispose!: % -> (); - - put!: (%, SI) -> (); - put!: (%, DF) -> (); - put!: (%, String) -> (); - - vstart!: (%, 'int,float', SI) -> (); - vput!: (%, SI) -> (); - vput!: (%, DF) -> (); - - lstart!: % -> (); - lend!: % -> (); - export from 'int,float' -} == add { -#if Real - -- No rep (we cheat!) - import from SI; - valOf(x) ==> x pretend Value; - default sink: %; - import { - LISP_:_:GR_-GET_-MEM_-AREA: SI -> %; - LISP_:_:GR_-KILL_-MEM_-AREA: % -> (); - LISP_:_:GR_-PUT_-ITEM: (%, Value) -> (); - LISP_:_:GR_-PUT_-LSTART: % -> (); - LISP_:_:GR_-PUT_-LEND: % -> (); - LISP_:_:GR_-INIT_-VECTOR: (%, Value, Value) -> %; - LISP_:_:GR_-ADD_-TO_-VECTOR: (%, Value) -> %; - } from Foreign Lisp; - - new(): % == LISP_:_:GR_-GET_-MEM_-AREA(DefaultSize); - dispose!(sink): () == LISP_:_:GR_-KILL_-MEM_-AREA(sink); - - put!(sink, si: SI): () == LISP_:_:GR_-PUT_-ITEM(sink, valOf(si)); - put!(sink, st: String): () == LISP_:_:GR_-PUT_-ITEM(sink, valOf(st)); - put!(sink, fl: DF): () == LISP_:_:GR_-PUT_-ITEM(sink, valOf(fl)); - - vstart!(sink, type: 'int,float', sz: SI): () == { - local sym: Symbol; - if type = int then - sym := coerce("integer"); - else - sym := coerce("float"); - LISP_:_:GR_-INIT_-VECTOR(sink, valOf(sym), valOf(sz)); - } - - vput!(sink, si: SI): () == - LISP_:_:GR_-ADD_-TO_-VECTOR(sink, valOf(si)); - vput!(sink, df: DF): () == - LISP_:_:GR_-ADD_-TO_-VECTOR(sink, valOf(df)); - - lstart!(sink): () == LISP_:_:GR_-PUT_-LSTART sink; - lend!(sink): () == LISP_:_:GR_-PUT_-LEND sink; - - coerce(sink): OutputForm == { - [outputForm "aSink"] - } -#else - Rep ==> Record(count: NonNegativeInteger); - import from Rep, NNI; - default sink: %; - coerce(sink): OutputForm == { - import from List OutputForm; - bracket [outputForm "Sink: ", - outputForm coerce rep(sink).count]; - } - - local addn!(sink, n: NNI): () == - rep(sink).count := rep(sink).count + n; - new(): % == per [0]; - dispose!(sink): () == dispose! rep sink; - - put!(sink, n: SI): () == addn!(sink, 1 + 4); - put!(sink, f: DF): () == addn!(sink, 1 + 4); - put!(sink, s: String): () == { - addn!(sink, #s + 1 + 1); - } - - vstart!(sink, type: 'int, float', n: SI): () == { - addn!(sink, 1 + n::NNI*4); - } - - vput!(sink, n: SI): () == {}; - vput!(sink, n: DF): () == {}; - - lstart!(sink): () == addn!(sink, 1); - lend!(sink): () == addn!(sink, 1); - -#endif -} - -@ -\section{InventorViewPort} -<<InventorViewPort>>= -InventorViewPort: with { - new: () -> %; - new: ThreeSpace DoubleFloat -> %; - addData!: (%, InventorDataSink) -> %; - addData!: (%, ThreeSpace DoubleFloat) -> %; -} == add { -#if Real - import { - LISP_:_:GR_-MAKE_-VIEW: (SI) -> %; - LISP_:_:GR_-SET_-DATA: (%, InventorDataSink) -> (); - } from Foreign Lisp; - import from SingleInteger; - - new(): % == LISP_:_:GR_-MAKE_-VIEW(0); - - new(space: ThreeSpace DoubleFloat): % == { - import from InventorDataSink; - import from InventorRenderPackage; - view: % := new(); - addData!(view, space); - view - } - - addData!(view: %, data: InventorDataSink): % == { - LISP_:_:GR_-SET_-DATA(view, data); - view; - } - - addData!(view: %, space: ThreeSpace DoubleFloat): % == { - import from InventorRenderPackage; - sink: InventorDataSink := new(); - render(sink, space, cartesian$CoordinateSystems(DoubleFloat)); - addData!(view, sink); - view - } - -#else - Rep ==> SingleInteger; - import from Rep; - new(): % == per 1; - new(x: ThreeSpace DoubleFloat): % == per 2; - addData!(view: %, data: InventorDataSink): % == view; -#endif - -} - -@ -\section{InventorRenderPackage} -<<InventorRenderPackage>>= -InventorRenderPackage: with { - render: (InventorDataSink, ThreeSpace DoubleFloat, POINT->POINT) -> (); -} == add { - default sink: InventorDataSink; - default space: ThreeSpace DoubleFloat; - default transform: POINT->POINT; - import from SI; - - local put!(sink, dims: UniversalSegment SI, - lp: List Point DoubleFloat, - f: Point DoubleFloat -> Point DoubleFloat): () == { - import from NNI, Integer; - i : SI := 0; - for x in dims repeat i:= i+1; - vstart!(sink, float, i*(coerce #lp)); - for p in lp repeat { - p1 := f(p); - for idx in dims repeat - vput!(sink, p1.(idx::Integer)); - } - } - - local put!(sink, lp: List SI): () == { - import from NNI; - vstart!(sink, int, coerce #lp); - for p in lp repeat { - vput!(sink, p); - } - } - - local putPoints!(sink, transform, - lpts: List POINT, indexList: List NNI): () == { - import from Integer; - if not sorted? indexList - then { - -- not nice! - lst: List POINT := []; - for idx in indexList repeat - lst := cons(lpts.(coerce idx), lst); - lpts := reverse! lst; - } - put!(sink, 1..3, lpts, transform); - if (# first lpts) = 4 - then { - put!(sink, "Colours"); - put!(sink, 4..4, lpts, transform); - } - } - render(sink, space, transform): () == { - default ss: SPACE3; - default i: NNI; - import from List POINT; - import from List List List NNI; - import from List List NNI; - import from List SPACE3; - import from SingleInteger; - put!(sink, "ThreeDScene"); - -- Get the point data - check(space); - indices := lllip(space); - lpts := lp(space); - indexList := concat concat indices; - put!(sink, "Points"); - putPoints!(sink, transform, lpts, indexList); - offset : SI := 0; - lstart!(sink); - for ss in components(space) for index in indices repeat { - closedCurve? ss => { - put!(sink, "closedCurve"); - n: SI := coerce #(first index); - put!(sink, offset); - put!(sink, n); - offset := offset + n; - } - curve? ss=> { - put!(sink, "curve"); - n: SI := coerce #(first index); - put!(sink, offset); - put!(sink, n); - offset := offset + n; - } - polygon? ss => { - local vertices: SI; - put!(sink, "polygon"); - vertices := coerce(#(first index) - + #(first rest index)); - put!(sink, offset); - put!(sink, vertices); - offset := offset+vertices; - } - mesh? ss=> { - local xStep, yStep: SI; - put!(sink, "mesh"); - xStep := coerce #index; - yStep := coerce #(first index); - put!(sink, offset); - put!(sink, xStep); - put!(sink, yStep); - offset := offset+xStep*yStep; - } - point? ss => { - put!(sink, "points"); - put!(sink, offset); - put!(sink, 1); - offset := offset+1; - } - error "Unrecognised SubSpace component"; - } - lend!(sink); - } - -} - -@ -\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>> - -<<InventorDataSink>> -<<InventorViewPort>> -<<InventorRenderPackage>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/ndftip.as.pamphlet b/src/algebra/ndftip.as.pamphlet deleted file mode 100644 index 4c186a67..00000000 --- a/src/algebra/ndftip.as.pamphlet +++ /dev/null @@ -1,1174 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra ndftip.as} -\author{Michael Richardson} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{NagDiscreteFourierTransformInterfacePackage} -<<NagDiscreteFourierTransformInterfacePackage>>= -+++ Author: M.G. Richardson -+++ Date Created: 1995 Dec. 08 -+++ Date Last Updated: -+++ Basic Functions: -+++ Related Constructors: -+++ Also See: -+++ AMS Classifications: -+++ Keywords: -+++ References: -+++ Description: -+++ This package provides Axiom-like interfaces to the NAG -+++ Finite Fourier Transform routines in the NAGlink. - -NagDiscreteFourierTransformInterfacePackage: with { - - nagDFT : VDF -> VCDF ; -- test 1 - -++ nagDFT(seq) calculates the discrete Fourier transform of a sequence -++ of real data values -#if saturn -++ $x_{1} \ldots x_{n}$ -#else -++ \spad{x[1] .. x[n]} -#endif -++ supplied in the vector seq. -++ Note that the definition used for the discrete Fourier transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} x_{j} e^{-i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(x[j]*%e^(-i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06EAF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06eaf. - - nagDFT : VCDF -> VCDF ; -- test 3 - -++ nagDFT(seq) calculates the discrete Fourier transform of a sequence -++ of complex data values -#if saturn -++ $z_{1} \ldots z_{n}$ -#else -++ \spad{z[1] .. z[n]} -#endif -++ supplied in the vector seq. -++ Note that the definition used for the discrete Fourier transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} z_{j} e^{-i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(z[j]*%e^(-i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06ECF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06ecf. - - nagDFT : PHSDF -> VDF ; -- test 7 - -++ nagDFT(seq) calculates the discrete Fourier transform of a Hermitian -++ sequence of complex data values, -#if saturn -++ $z_{1} \ldots z_{n}$ -#else -++ \spad{z[1] .. z[n]} -#endif -++ supplied in the PackedHermitianSequence seq. -++ Note that the definition used for the discrete Fourier transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} z_{j} e^{-i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(z[j]*%e^(-i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06EBF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06ebf. - - nagDFT : LVDF -> LVCDF ; -- test 10, 19 - -++ nagDFT(seqs) calculates the discrete Fourier transform of each of a -++ list of sequences of real data values -#if saturn -++ $x_{1} \ldots x_{n}$ -#else -++ \spad{x[1] .. x[n]} -#endif -++ supplied in the list of vectors, seqs. -++ Note that the definition used for the discrete Fourier transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} x_{j} e^{-i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(x[j]*%e^(-i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06FPF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06fpf. - - nagDFT : LVCDF -> LVCDF ; -- test 16 - -++ nagDFT(seqs) calculates the discrete Fourier transform of each of a -++ list of sequences of complex data values -#if saturn -++ $z_{1} \ldots z_{n}$ -#else -++ \spad{z[1] .. z[n]} -#endif -++ supplied in the list of vectors, seqs. -++ Note that the definition used for the discrete Fourier transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} z_{j} e^{-i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(z[j]*%e^(-i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06FRF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06frf. - - nagDFT : LPHSDF -> LVDF ; -- test 12, 21 - -++ nagDFT(seq) calculates the discrete Fourier transform of a each of a -++ list of Hermitian sequences of complex data values, -#if saturn -++ $z_{1} \ldots z_{n}$ -#else -++ \spad{z[1] .. z[n]} -#endif -++ supplied in the List PackedHermitianSequence, seq. -++ Note that the definition used for the discrete Fourier transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} z_{j} e^{-i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(z[j]*%e^(-i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06FQF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06fqf. - - nagInverseDFT : VDF -> VCDF ; -- test 8 - -++ nagInverseDFT(seq) calculates the inverse discrete Fourier -++ transform of a sequence of real data values -#if saturn -++ $x_{1} \ldots x_{n}$ -#else -++ \spad{x[1] .. x[n]} -#endif -++ supplied in the vector seq. -++ Note that the definition used for the inverse discrete Fourier -++ transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} x_{j} e^{i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(x[j]*%e^(i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06EAF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06eaf. - - nagInverseDFT : VCDF -> VCDF ; -- test 2, 4 - -++ nagInverseDFT(seq) calculates the inverse discrete Fourier -++ transform of a sequence of complex data values -#if saturn -++ $z_{1} \ldots z_{n}$ -#else -++ \spad{z[1] .. z[n]} -#endif -++ supplied in the vector seq. -++ Note that the definition used for the inverse discrete Fourier -++ transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} z_{j} e^{i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(z[j]*%e^(i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06ECF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06ecf. - - nagInverseDFT : PHSDF -> VDF ; -- test 6 - -++ nagInverseDFT(seq) calculates the inverse discrete Fourier transform -++ of a Hermitian sequence of complex data values -#if saturn -++ $z_{1} \ldots z_{n}$ -#else -++ \spad{z[1] .. z[n]} -#endif -++ supplied in the PackedHermitianSequence seq. -++ Note that the definition used for the inverse discrete Fourier -++ transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} z_{j} e^{i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(z[j]*%e^(i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06EBF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06ebf. - - nagInverseDFT : LVDF -> LVCDF ; -- test 13 - -++ nagInverseDFT(seqs) calculates the inverse discrete Fourier -++ transform of each of a list of sequences of real data values -#if saturn -++ $x_{1} \ldots x_{n}$ -#else -++ \spad{x[1] .. x[n]} -#endif -++ supplied in the list of vectors, seqs. -++ Note that the definition used for the inverse discrete Fourier -++ transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} x_{j} e^{i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(x[j]*%e^(i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06FPF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06fpf. - - nagInverseDFT : LVCDF -> LVCDF ; -- test 11, 17 - -++ nagInverseDFT(seqs) calculates the inverse discrete Fourier -++ transform of each of a list of sequences of complex data values -#if saturn -++ $z_{1} \ldots z_{n}$ -#else -++ \spad{z[1] .. z[n]} -#endif -++ supplied in the list of vectors, seqs. -++ Note that the definition used for the inverse discrete Fourier -++ transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} z_{j} e^{i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(z[j]*%e^(i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06FRF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06frf. - - nagInverseDFT : LPHSDF -> LVDF ; -- test 15 - -++ nagInverseDFT(seqs) calculates the inverse discrete Fourier transform -++ of each of a list of Hermitian sequences of complex data values -#if saturn -++ $z_{1} \ldots z_{n}$ -#else -++ \spad{z[1] .. z[n]} -#endif -++ supplied in the List PackedHermitianSequence, seqs. -++ Note that the definition used for the inverse discrete Fourier -++ transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} z_{j} e^{i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(z[j]*%e^(i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06FQF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06fqf. - - nagHermitianDFT : VDF -> PHSDF ; -- test 5 - -++ nagHermitianDFT(seq) calculates the discrete Fourier transform, in -++ packed Hermitian form, of a sequence of real data values -#if saturn -++ $x_{1} \ldots x_{n}$ -#else -++ \spad{x[1] .. x[n]} -#endif -++ supplied in the vector seq. -++ Note that the definition used for the discrete Fourier transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} x_{j} e^{-i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(x[j]*%e^(-i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06EAF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06eaf. - - nagHermitianDFT : LVDF -> LPHSDF ; -- test 14, 20 - -++ nagHermitianDFT(seqs) calculates the discrete Fourier transform, in -++ packed Hermitian form, of each of a list of sequences of real data -++ values -#if saturn -++ $x_{1} \ldots x_{n}$ -#else -++ \spad{x[1] .. x[n]} -#endif -++ supplied in the list of vectors, seqs. -++ Note that the definition used for the discrete Fourier transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} x_{j} e^{-i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(x[j]*%e^(-i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06FPF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06fpf. - - nagHermitianInverseDFT : VDF -> PHSDF ; -- test 9 - -++ nagHermitianInverseDFT(seq) calculates the inverse discrete Fourier -++ transform, in packed Hermitian form, of a sequence of real data -++ values -#if saturn -++ $x_{1} \ldots x_{n}$ -#else -++ \spad{x[1] .. x[n]} -#endif -++ supplied in the vector seq. -++ Note that the definition used for the inverse discrete Fourier -++ transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} x_{j} e^{i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(x[j]*%e^(i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06EAF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06eaf. - - nagHermitianInverseDFT : LVDF -> LPHSDF ; -- test 18 - -++ nagHermitianInverseDFT(seqs) calculates the inverse discrete Fourier -++ transform, in packed Hermitian form, of each of a list of sequences -++ of real data values -#if saturn -++ $x_{1} \ldots x_{n}$ -#else -++ \spad{x[1] .. x[n]} -#endif -++ supplied in the list of vectors, seqs. -++ Note that the definition used for the inverse discrete Fourier -++ transform is -#if saturn -++ \[ \frac{1}{\sqrt{n} \sum_{j=0}^{n-1} x_{j} e^{i \frac{2 \pi j k}{n} -++ \qquad k = 0 \ldots n - 1 \] -#else -++ \spad{1/sqrt(n)*sum(x[j]*%e^(i*2*%pi*j*k/n), j=0..(n-1))} for -++ \spad{k=0..(n-1)}. -#endif -++ The numerical calculation is performed by the NAG routine C06FPF. -++ -++ For more detailed information, please consult the NAG -++ manual via the Browser page for the operation c06fpf. - -} == add { - - import from AnyFunctions1 MDF ; - import from CDF; - import from ErrorFunctions ; - import from LLDF ; - import from MCDF ; - import from MDF ; - import from NagResultChecks ; - import from NagSeriesSummationPackage ; - import from PHSDF; - import from STRG ; - import from List STRG ; - import from Symbol ; - import from VDF ; - - local (..)(a:INT,b:INT):Generator INT == { - generate { - t := a ; - while (t <= b) repeat { - yield t ; - t := t + 1 ; - } - } - } - - local ipIfail : INT := -1 ; - --- First, the functions corresponding to single NAGlink calls of C06E --- routines (single vector transforms): - --- c06eaf: - - nagHermitianDFT(seq : VDF) : PHSDF ; == { - local lseq : INT ; - - lseq := ((# seq)@NNI) pretend INT ; -- @ to eliminate SI possibility - row(checkMxDF(c06eaf(lseq,matrix [members seq],ipIfail), - "x", - "C06EAF"), - 1) - pretend PHSDF - } - --- c06ebf: - - nagDFT(seq : PHSDF) : VDF == { - local lseq : INT ; - - lseq := ((# seq)@NNI) pretend INT ; -- @ to eliminate SI possibility - row(checkMxDF(c06ebf(lseq,matrix [members seq],ipIfail), - "x", - "C06EBF"), - 1) - } - --- c06ecf: - - nagDFT(seq : VCDF) : VCDF == { - local nseq : NNI ; - local lseq : INT ; - local rvec, ivec : VDF ; - local cvec : VCDF ; - local c06ecfResult : RSLT ; - - nseq := # seq ; - lseq := nseq pretend INT ; - rvec := new(nseq,0) ; - ivec := new(nseq,0) ; - for i in 1..lseq repeat { - rvec(i) := real seq(i) ; - ivec(i) := imag seq(i) ; - } - c06ecfResult := c06ecf(lseq, - matrix [members rvec], - matrix [members ivec], - ipIfail) ; - rvec := row(checkMxDF(c06ecfResult,"x","C06ECF"),1) ; - ivec := row((retract(c06ecfResult."y") @ MDF),1) ; - cvec := new(nseq,0) ; - for i in 1..lseq repeat cvec(i) := complex(rvec(i),ivec(i)) ; - cvec - } - --- inverse transforms, in terms of these and functions from PHS: - - nagInverseDFT(seq : PHSDF) : VDF == nagDFT conjHerm seq ; - - nagHermitianInverseDFT(seq : VDF) : PHSDF - == conjHerm nagHermitianDFT seq ; - - nagInverseDFT(seq : VCDF) : VCDF == { - local nseq : NNI ; - local lseq : INT ; - local rvec, ivec : VDF ; - local cvec : VCDF ; - local c06ecfResult : RSLT ; - - nseq := # seq ; - lseq := nseq pretend INT ; - rvec := new(nseq,0) ; - ivec := new(nseq,0) ; - for i in 1..lseq repeat { - rvec(i) := real seq(i) ; - ivec(i) := - imag seq(i) ; - } - c06ecfResult := c06ecf(lseq, - matrix [members rvec], - matrix [members ivec], - ipIfail) ; - rvec := row(checkMxDF(c06ecfResult,"x","C06ECF"),1) ; - ivec := row((retract(c06ecfResult."y") @ MDF),1) ; - cvec := new(nseq,0) ; - for i in 1..lseq repeat cvec(i) := complex(rvec(i), - ivec(i)) ; - cvec - } - --- "Full form" equivalents of c06eaf and inverse: - - nagDFT(seq : VDF) : VCDF == expand nagHermitianDFT seq ; - - nagInverseDFT(seq : VDF) : VCDF == expand nagHermitianInverseDFT seq ; - - --- Next, the functions corresponding to single NAGlink calls of C06F --- routines (multiple vector transforms): - --- basic routines: - --- c06fpf - - nagHermitianDFT(seqs : LVDF) : LPHSDF ; == { - - local nr, nc : NNI ; - local inr, inc : INT ; - local seqMat, trig, result : MDF ; - local nextSeq : PHSDF ; - local hermDFTs : LPHSDF ; - - nr := # seqs ; - inr := nr pretend INT ; - nc := # (seqs.1) ; - inc := nc pretend INT ; - seqMat := new(nr,nc,0) ; - for j in 1 .. inc repeat seqMat(1,j) := (seqs.1).j ; - for i in 2 .. inr repeat - if (# seqs.i) ~= nc - then error ["The data sequences in nagHermitianDFT must all", - " have the same length. ", - "The length of sequence 1 is ", - string(inc), - "that of sequence ", - string(i pretend INT), - " is ", - string((# seqs.i)@NNI pretend INT), -- @ avoids SI - "."] - else for j in 1 .. inc repeat seqMat(i,j) := (seqs.i).j ; - trig := new(1@NNI,2*nc,0) ; - result := - checkMxDF(c06fpf(inr,inc,"i",seqMat,trig,ipIfail),"x","C06FPF") ; - hermDFTs := [] ; - for i in inr .. 1 by -1 repeat { - nextSeq := new(nc,0) ; - for j in 1 .. inc repeat nextSeq(j) := result(1,(j-1)*inr + i) ; - hermDFTs := cons(nextSeq,hermDFTs) ; - } - hermDFTs - } - --- c06fqf - - nagDFT(seqs : LPHSDF) : LVDF == { - - local nr, nc : NNI ; - local inr, inc : INT ; - local seqMat, trig, result : MDF ; - local nextSeq : VDF ; - local dfts : LVDF ; - - nr := # seqs ; - inr := nr pretend INT ; - nc := # (seqs.1) ; - inc := nc pretend INT ; - seqMat := new(nr,nc,0) ; - for j in 1 .. inc repeat seqMat(1,j) := (seqs.1).j ; - for i in 2 .. inr repeat - if (# seqs.i) ~= nc - then error ["The data sequences in nagDFT must all", - " have the same length. ", - "The length of sequence 1 is ", - string(inc), - "that of sequence ", - string(i pretend INT), - " is ", - string((# seqs.i)@NNI pretend INT), -- @ avoids SI - "."] - else for j in 1 .. inc repeat seqMat(i,j) := (seqs.i).j ; - trig := new(1@NNI,2*nc,0) ; - result := - checkMxDF(c06fqf(inr,inc,"i",seqMat,trig,ipIfail),"x","C06FQF") ; - dfts := [] ; - for i in inr .. 1 by -1 repeat { - nextSeq := new(nc,0) ; - for j in 1 .. inc repeat nextSeq(j) := result(1,(j-1)*inr + i) ; - dfts := cons(nextSeq,dfts) ; - } - dfts - } - --- c06frf - - nagDFT(seqs : LVCDF) : LVCDF == { - - local nr, nc : NNI ; - local inr, inc : INT ; - local trig, rMat, iMat : MDF ; - local result : RSLT ; - local nextSeq : VCDF ; - local dfts : LVCDF ; - - nr := # seqs ; - inr := nr pretend INT ; - nc := # (seqs.1) ; - inc := nc pretend INT ; - rMat := new(nr,nc,0) ; - iMat := new(nr,nc,0) ; - for j in 1 .. inc repeat { - rMat(1,j) := real((seqs.1).j) ; - iMat(1,j) := imag((seqs.1).j) ; - } - for i in 2 .. inr repeat { - if (# seqs.i) ~= nc - then error ["The data sequences in nagDFT must all", - " have the same length. ", - "The length of sequence 1 is ", - string(inc), - "that of sequence ", - string(i pretend INT), - " is ", - string((# seqs.i)@NNI pretend INT), -- @ avoids SI - "."] - else for j in 1 .. inc repeat { - rMat(i,j) := real((seqs.i).j) ; - iMat(i,j) := imag((seqs.i).j) ; - } - } - trig := new(1@NNI,2*nc,0) ; - result := c06frf(inr,inc,"i",rMat,iMat,trig,ipIfail) ; - rMat := checkMxDF(result, "x", "C06FRF") ; - iMat := retract(result."y") @ MDF ; - dfts := [] ; - for i in inr .. 1 by -1 repeat { - nextSeq := new(nc,0) ; - for j in 1 .. inc repeat - nextSeq(j) := complex(rMat(1,(j-1)*inr+i),iMat(1,(j-1)*inr+i)) ; - dfts := cons(nextSeq,dfts) ; - } - dfts - } - --- inverse transforms, in terms of these and functions from PHS: - - nagInverseDFT(seqs : LVCDF) : LVCDF == { - - local nr, nc : NNI ; - local inr, inc : INT ; - local conjSeq : VCDF ; - local temp, invdfts : LVCDF ; - - nr := # seqs ; - inr := nr pretend INT ; - temp := [] ; - for i in inr .. 1 by -1 repeat { - nc := #(seqs.i) ; - inc := nc pretend INT ; - conjSeq := new(nc,0) ; - for j in 1 .. inc repeat - conjSeq(j) := conjugate((seqs.i).j) ; - temp := cons(conjSeq,temp) ; - } - temp := nagDFT temp ; - invdfts := [] ; - for i in inr .. 1 by -1 repeat { - conjSeq := new(nc,0) ; - for j in 1 .. inc repeat -- know inc is constant after nagDFT call - conjSeq(j) := conjugate((temp.i).j) ; - invdfts := cons(conjSeq,invdfts) ; - } - invdfts - } - - nagInverseDFT(seqs : LPHSDF) : LVDF == { - local nr : NNI ; - local inr : INT ; - local conjSeqs : LPHSDF ; - - nr := # seqs ; - inr := nr pretend INT ; - conjSeqs := [] ; - for i in inr .. 1 by -1 repeat - conjSeqs := cons(conjHerm(seqs.i),conjSeqs) ; - nagDFT conjSeqs ; - } - - nagHermitianInverseDFT(seqs : LVDF) : LPHSDF == { - local nr : NNI ; - local inr : INT ; - local conjSeqs, invSeqs : LPHSDF ; - - nr := # seqs ; - inr := nr pretend INT ; - conjSeqs := nagHermitianDFT seqs ; - invSeqs := [] ; - for i in inr .. 1 by -1 repeat - invSeqs := cons(conjHerm(conjSeqs.i),invSeqs) ; - invSeqs - } - --- "Full form" equivalents of c06fpf and inverse: - - nagDFT(seqs : LVDF) : LVCDF == { - - local nr : NNI ; - local inr : INT ; - local hermdfts : LPHSDF ; - local dfts : LVCDF ; - - nr := # seqs ; - inr := nr pretend INT ; - hermdfts := nagHermitianDFT seqs ; - dfts := [] ; - for i in inr .. 1 by -1 repeat - dfts := cons(expand(hermdfts.i),dfts) ; - dfts - } - - nagInverseDFT(seqs : LVDF) : LVCDF == { - local nr : NNI ; - local inr : INT ; - local hermdfts : LPHSDF ; - local invdfts : LVCDF ; - - nr := # seqs ; - inr := nr pretend INT ; - hermdfts := nagHermitianDFT seqs ; - invdfts := [] ; - for i in inr .. 1 by -1 repeat - invdfts := cons(expand conjHerm(hermdfts.i),invdfts) ; - invdfts - } - -} - -#if NeverAssertThis - --- Note that the conversions of results from DoubleFloat to Float --- will become unnecessary if outputGeneral is extended to apply to --- DoubleFloat quantities. Those results not converted will, of --- course, then be displayed to 6 s.f. - -)lib nrc -)lib herm -)lib ndftip - -outputGeneral 6 - -seqA := [0.34907,0.54890,0.74776,0.94459,1.1385,1.3285,1.5137]; - -seqB := [0.34907 - 0.37168*%i, _ - 0.54890 - 0.35669*%i, _ - 0.74776 - 0.31175*%i, _ - 0.94459 - 0.23702*%i, _ - 1.13850 - 0.13274*%i, _ - 1.32850 + 0.00074*%i, _ - 1.51370 + 0.16298*%i]; - -hseqC : PackedHermitianSequence DoubleFloat -hseqC := packHS [0.34907, _ - 0.54890 + %i*1.51370, _ - 0.74776 + %i*1.32850, _ - 0.94459 + %i*1.13850, _ - 0.94459 - %i*1.13850, _ - 0.74776 - %i*1.32850, _ - 0.54890 - %i*1.51370]; - -seqsD : List Vector DoubleFloat; -seqsD := [vector [0.3854, 0.6772, 0.1138, 0.6751, 0.6362, 0.1424], _ - vector [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _ - vector [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]]; - -seqsE : List PackedHermitianSequence DoubleFloat; -seqsE := [pHS [0.3854, 0.6772, 0.1138, 0.6751, 0.6362, 0.1424], _ - pHS [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _ - pHS [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]]; - -seqsF : List Vector Complex DoubleFloat -seqsF := [vector [0.3854 + 0.5417*%i, 0.6772 + 0.2983*%i, _ - 0.1138 + 0.1181*%i, 0.6751 + 0.7255*%i, _ - 0.6362 + 0.8638*%i, 0.1424 + 0.8723*%i], _ - vector [0.9172 + 0.9089*%i, 0.0644 + 0.3118*%i, _ - 0.6037 + 0.3465*%i, 0.6430 + 0.6198*%i, _ - 0.0428 + 0.2668*%i, 0.4815 + 0.1614*%i], _ - vector [0.1156 + 0.6214*%i, 0.0685 + 0.8681*%i, _ - 0.2060 + 0.7060*%i, 0.8630 + 0.8652*%i, _ - 0.6967 + 0.9190*%i, 0.2792 + 0.3355*%i]]; - --- test 1 - -dftA := nagDFT seqA; -dftA :: Vector Complex Float :: Matrix Complex Float - -- Matrix to force display as a column, - -- Float to allow outputGeneral to work. - --- + 2.48361 + --- | | --- |- 0.265985 + 0.530898 %i | --- | | --- |- 0.257682 + 0.202979 %i | --- | | --- |- 0.256363 + 0.0580623 %i| --- | | --- |- 0.256363 - 0.0580623 %i| --- | | --- |- 0.257682 - 0.202979 %i | --- | | --- +- 0.265985 - 0.530898 %i + - --- test 2 - -nagInverseDFT dftA :: Vector Float - --- [0.34907,0.5489,0.74776,0.94459,1.1385,1.3285,1.5137] - --- test 3 - -dftB := nagDFT seqB; -dftB :: Vector Complex Float :: Matrix Complex Float - --- + 2.48361 - 0.471004 %i + --- | | --- | - 0.5518 + 0.496841 %i | --- | | --- |- 0.367113 + 0.0975621 %i| --- | | --- |- 0.287669 - 0.0586476 %i| --- | | --- |- 0.225057 - 0.174772 %i | --- | | --- |- 0.148251 - 0.308396 %i | --- | | --- + 0.0198297 - 0.564956 %i + - --- test 4 - -(nagInverseDFT dftB) :: Vector Complex Float :: Matrix Complex Float - --- +0.34907 - 0.37168 %i+ --- | | --- |0.5489 - 0.35669 %i | --- | | --- |0.74776 - 0.31175 %i| --- | | --- |0.94459 - 0.23702 %i| --- | | --- |1.1385 - 0.13274 %i | --- | | --- |1.3285 + 0.00074 %i | --- | | --- +1.5137 + 0.16298 %i + - --- test 5 - -hdftA := nagHermitianDFT seqA; -(expand hdftA) :: Vector Complex Float :: Matrix Complex Float - --- + 2.48361 + --- | | --- |- 0.265985 + 0.530898 %i | --- | | --- |- 0.257682 + 0.202979 %i | --- | | --- |- 0.256363 + 0.0580623 %i| --- | | --- |- 0.256363 - 0.0580623 %i| --- | | --- |- 0.257682 - 0.202979 %i | --- | | --- +- 0.265985 - 0.530898 %i + - --- test 6 - -(nagInverseDFT hdftA) :: Vector Float - --- [0.34907,0.5489,0.74776,0.94459,1.1385,1.3285,1.5137] - --- test 7 - -dftC := nagDFT hseqC; -dftC :: Vector Float - --- [1.82616,1.86862,- 0.017503,0.502001,- 0.598725,- 0.0314404,- 2.62557] - --- test 8 - -(nagInverseDFT dftC) :: Vector Complex Float - --- [0.34907, 0.5489 + 1.5137 %i, 0.74776 + 1.3285 %i, 0.94459 + 1.1385 %i, --- 0.94459 - 1.1385 %i, 0.74776 - 1.3285 %i, 0.5489 - 1.5137 %i] - --- test 9 - -nagHermitianInverseDFT dftC - --- [0.34907000000000005, 0.54889999999999983, 0.74775999999999987, --- 0.94459000000000004, 1.1385000000000003, 1.3284999999999998, --- 1.5136999999999998] - --- test 10: - -dftsD := nagDFT seqsD; - -dftsD :: List Vector Complex Float - --- [ --- [1.07373, - 0.104062 - 0.00438406 %i, 0.112554 - 0.373777 %i, - 0.146684, --- 0.112554 + 0.373777 %i, - 0.104062 + 0.00438406 %i] --- , - --- [1.39609, - 0.0365178 + 0.466584 %i, 0.077955 - 0.0607051 %i, - 0.152072, --- 0.077955 + 0.0607051 %i, - 0.0365178 - 0.466584 %i] --- , - --- [1.12374, 0.0914068 - 0.050841 %i, 0.393551 + 0.345775 %i, 0.153011, --- 0.393551 - 0.345775 %i, 0.0914068 + 0.050841 %i] --- ] - --- test 11: - -invdftsD := nagInverseDFT dftsD ; -invdftsD :: List Vector Complex Float - --- [[0.3854,0.6772,0.1138,0.6751,0.6362,0.1424], --- [0.5417,0.2983,0.1181,0.7255,0.8638,0.8723], --- [0.9172,0.0644,0.6037,0.643,0.0428,0.4815]] - --- test 12: - -dftsE := nagDFT seqsE; -dftsE :: List Vector Float - --- [[1.0788,0.662291,- 0.239146,- 0.578284,0.459192,- 0.438816], --- [0.857321,1.22614,0.353348,- 0.222169,0.341327,- 1.22908], --- [1.18245,0.262509,0.674406,0.552278,0.0539906,- 0.478963]] - --- test 13: - -invdftsE := nagInverseDFT dftsE; -invdftsE :: List Vector Complex Float - --- [ --- [0.3854, 0.6772 + 0.1424 %i, 0.1138 + 0.6362 %i, 0.6751, --- 0.1138 - 0.6362 %i, 0.6772 - 0.1424 %i] --- , - --- [0.5417, 0.2983 + 0.8723 %i, 0.1181 + 0.8638 %i, 0.7255, --- 0.1181 - 0.8638 %i, 0.2983 - 0.8723 %i] --- , - --- [0.9172, 0.0644 + 0.4815 %i, 0.6037 + 0.0428 %i, 0.643, --- 0.6037 - 0.0428 %i, 0.0644 - 0.4815 %i] --- ] - --- test 14: - -hdftsD := nagHermitianDFT seqsD; -map(expand,hdftsD) :: List Vector Complex Float - --- [ --- [1.07373, - 0.104062 - 0.00438406 %i, 0.112554 - 0.373777 %i, - 0.146684, --- 0.112554 + 0.373777 %i, - 0.104062 + 0.00438406 %i] --- , - --- [1.39609, - 0.0365178 + 0.466584 %i, 0.077955 - 0.0607051 %i, - 0.152072, --- 0.077955 + 0.0607051 %i, - 0.0365178 - 0.466584 %i] --- , - --- [1.12374, 0.0914068 - 0.050841 %i, 0.393551 + 0.345775 %i, 0.153011, --- 0.393551 - 0.345775 %i, 0.0914068 + 0.050841 %i] --- ] - --- test 15: - -(nagInverseDFT hdftsD) :: List Vector Float - --- [[0.3854,0.6772,0.1138,0.6751,0.6362,0.1424], --- [0.5417,0.2983,0.1181,0.7255,0.8638,0.8723], --- [0.9172,0.0644,0.6037,0.643,0.0428,0.4815]] - --- test 16: - -dftsF := nagDFT seqsF; -dftsF :: List Vector Complex Float - --- [ --- [1.07373 + 1.39609 %i, - 0.570647 - 0.0409019 %i, 0.173259 - 0.295822 %i, --- - 0.146684 - 0.152072 %i, 0.0518489 + 0.451732 %i, --- 0.362522 - 0.0321337 %i] --- , - --- [1.12374 + 1.06765 %i, 0.172759 + 0.0385858 %i, 0.418548 + 0.748083 %i, --- 0.153011 + 0.17522 %i, 0.368555 + 0.0565331 %i, 0.0100542 + 0.140268 %i] --- , - --- [0.909985 + 1.76167 %i, - 0.305418 + 0.0624335 %i, --- 0.407884 - 0.0694786 %i, - 0.078547 + 0.0725049 %i, --- - 0.119334 + 0.128511 %i, - 0.531409 - 0.433531 %i] --- ] - --- test 17: - -invdftsF := nagInverseDFT dftsF ; -invdftsF :: List Vector Complex Float - --- [ --- [0.3854 + 0.5417 %i, 0.6772 + 0.2983 %i, 0.1138 + 0.1181 %i, --- 0.6751 + 0.7255 %i, 0.6362 + 0.8638 %i, 0.1424 + 0.8723 %i] --- , - --- [0.9172 + 0.9089 %i, 0.0644 + 0.3118 %i, 0.6037 + 0.3465 %i, --- 0.643 + 0.6198 %i, 0.0428 + 0.2668 %i, 0.4815 + 0.1614 %i] --- , - --- [0.1156 + 0.6214 %i, 0.0685 + 0.8681 %i, 0.206 + 0.706 %i, --- 0.863 + 0.8652 %i, 0.6967 + 0.919 %i, 0.2792 + 0.3355 %i] --- ] - --- test 18: - -nagHermitianInverseDFT dftsE - --- [ --- [0.38540000000000013, 0.67720000000000025, 0.11380000000000001, --- 0.67510000000000014, 0.63620000000000021, 0.14240000000000003] --- , - --- [0.54170000000000018, 0.29830000000000012, 0.1181, 0.72550000000000014, --- 0.86380000000000023, 0.87230000000000019] --- , - --- [0.91720000000000035, 0.064399999999999999, 0.60370000000000024, --- 0.64300000000000013, 0.042799999999999991, 0.48150000000000015] --- ] - --- error tests: - --- test 19: - -nagDFT [vector [0.3854 + 0.5417*%i, 0.6772 + 0.2983*%i, _ - 0.1138 + 0.1181*%i, 0.6751 + 0.7255*%i, _ - 0.6362 + 0.8638*%i, 0.1424 + 0.8723*%i], _ - vector [0.1156 + 0.6214*%i, 0.0685 + 0.8681*%i, _ - 0.6967 + 0.9190*%i, 0.2792 + 0.3355*%i]] - --- Error signalled from user code: --- The data sequences in nagDFT must all have the same length. The --- length of sequence 1 is 6 that of sequence 2 is 4. - --- test 20: - -nagHermitianDFT [vector [0.3854, 0.6751, 0.6362, 0.1424], _ - vector [0.5417, 0.7255, 0.8638, 0.8723], _ - vector [0.9172, 0.0428, 0.4815]] - --- Error signalled from user code: --- The data sequences in nagHermitianDFT must all have the same --- length. The length of sequence 1 is 4 that of sequence 3 is 3. - --- test 21: - -badSeqs : List PackedHermitianSequence DoubleFloat -badSeqs := [pHS [0.3854, 0.1138, 0.6751, 0.6362, 0.1424], _ - pHS [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _ - pHS [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]]; - -nagDFT badSeqs - --- Error signalled from user code: --- The data sequences in nagDFT must all have the same length. The --- length of sequence 1 is 5 that of sequence 2 is 6. - -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>> - --- To test: --- sed -ne '1,/^#if NeverAssertThis/d;/#endif/d;p' < ndftip.as > ndftip.input --- axiom --- )set nag host <some machine running nagd> --- )r ndftip.input - -#unassert saturn - -#include "axiom.as" - -DF ==> DoubleFloat ; -CDF ==> Complex DoubleFloat ; -LDF ==> List DoubleFloat ; -LLDF ==> List LDF ; -VDF ==> Vector DoubleFloat ; -LVDF ==> List VDF ; -VCDF ==> Vector Complex DoubleFloat ; -LVCDF ==> List VCDF ; -MDF ==> Matrix DoubleFloat ; -MCDF ==> Matrix Complex DoubleFloat ; -INT ==> Integer ; -NNI ==> NonNegativeInteger ; -RSLT ==> Result ; -STRG ==> String ; -PHSDF ==> PackedHermitianSequence DF; -LPHSDF ==> List PackedHermitianSequence DF; - -<<NagDiscreteFourierTransformInterfacePackage>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/nepip.as.pamphlet b/src/algebra/nepip.as.pamphlet deleted file mode 100644 index 4bfb2b5a..00000000 --- a/src/algebra/nepip.as.pamphlet +++ /dev/null @@ -1,626 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra nepip.as} -\author{Michael Richardson} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{NagEigenInterfacePackage} -<<NagEigenInterfacePackage>>= -+++ Author: M.G. Richardson -+++ Date Created: 1996 January 12 -+++ Date Last Updated: -+++ Basic Functions: -+++ Related Constructors: -+++ Also See: -+++ AMS Classifications: -+++ Keywords: -+++ References: -+++ Description: -+++ This package provides Axiom-like interfaces to the NAG generalised -+++ eigenvalue and eigenvector routines in the NAGlink. - -DF ==> DoubleFloat ; -CDF ==> Complex DoubleFloat ; -FFCDF ==> FormalFraction Complex DoubleFloat ; -LFFCDF ==> List FormalFraction Complex DoubleFloat ; -LDF ==> List DoubleFloat ; -LCDF ==> List Complex DoubleFloat ; -LLDF ==> List LDF ; -VDF ==> Vector DoubleFloat ; -LVDF ==> List VDF ; -VCDF ==> Vector Complex DoubleFloat ; -LVCDF ==> List VCDF ; -MDF ==> Matrix DoubleFloat ; -MCDF ==> Matrix Complex DoubleFloat ; -INT ==> Integer ; -NNI ==> NonNegativeInteger ; -RCD ==> Record ; -RSLT ==> Result ; -STRG ==> String ; -UNNRES ==> Union(a:LDF,b:LFFCDF) ; -- a & b are dummy tags -RURSLV ==> RCD(eigenvalues : UNNRES, eigenvectors : LVCDF) ; - -NagEigenInterfacePackage: with { - - nagEigenvalues : (MDF,MDF,DF) -> UNNRES ; - -++ nagEigenvalues(A,B,eps) returns a list of the eigenvalues -#if saturn -++ $ \lambda $ -#else -++ \spad{l} -#endif -++ of the system -#if saturn -++ $ A x = \lambda B x $ -#else -++ \spad{A*x = l*B*x} -#endif -++ -++ The numerical calculation is performed by one of the NAG routines -++ F02ADF and F02BJF, depending on the the form of \spad{A} and B. -++ The result is of type Union(List DoubleFloat, List FormalFraction -++ Complex DoubleFloat), the first branch resulting from F02ADF and -++ the second from F02BJF. Note that in the latter case values should -++ be inspected for numerically small numerators and denominators, -++ ratios of which may be in effect indeterminate, before the result is -++ converted to List Complex DoubleFloat. -++ -++ The parameter eps, if positive, defines a tolerance to be used in -++ recognising negligable matrix elements when F02BJF is called; setting -++ this may result in faster execution with less accuracy. -++ -++ For more detailed information, please consult the NAG manual -++ via the Browser pages for the operations f02adf and f02bjf. - - nagEigenvalues : (MDF,MDF) -> UNNRES ; - -++ nagEigenvalues(A,B) returns a list of the eigenvalues -#if saturn -++ $ \lambda $ -#else -++ \spad{l} -#endif -++ of the system -#if saturn -++ $ A x = \lambda B x $ -#else -++ \spad{A*x = l*B*x} -#endif -++ -++ The numerical calculation is performed by one of the NAG routines -++ F02ADF and F02BJF, depending on the the form of \spad{A} and B. -++ The result is of type Union(List DoubleFloat, List FormalFraction -++ Complex DoubleFloat), the first branch resulting from F02ADF and -++ the second from F02BJF. Note that in the latter case values should -++ be inspected for numerically small numerators and denominators, -++ ratios of which may be in effect indeterminate, before the result is -++ converted to List Complex DoubleFloat. -++ -++ For more detailed information, please consult the NAG manual -++ via the Browser pages for the operations f02adf and f02bjf. - - nagEigenvectors : (MDF,MDF,DF) -> RURSLV ; - -++ nagEigenvectors(A,B,eps) returns a record consisting of a list of the -++ eigenvalues -#if saturn -++ $ \lambda $ -#else -++ \spad{l} -#endif -++ and a list of the corresponding eigenvectors of the system -#if saturn -++ $ A x = \lambda B x $ -#else -++ \spad{A*x = l*B*x} -#endif -++ where -#if saturn -++ $A$ and $B$ -#else -++ \spad{A} and B -#endif - -#if saturn -++ $B$ -#else -++ B -#endif -++ is positive-definite. -++ -++ The numerical calculation is performed by one of the NAG routines -++ F02AEF and F02BJF, depending on the the form of \spad{A} and B. -++ The first component of the result, \spad{eigenvalues}, -++ is of type Union(List DoubleFloat, List FormalFraction -++ Complex DoubleFloat), the first branch resulting from F02AEF and -++ the second from F02BJF. Note that in the latter case values should -++ be inspected for numerically small numerators and denominators, -++ ratios of which may be in effect indeterminate, before the result is -++ converted to List Complex DoubleFloat. -++ -++ The parameter eps, if positive, defines a tolerance to be used in -++ recognising negligable matrix elements when F02BJF is called; setting -++ this may result in faster execution with less accuracy. -++ -++ For more detailed information, please consult the NAG manual -++ via the Browser pages for the operations f02aef and f02bjf. - - nagEigenvectors : (MDF,MDF) -> RURSLV ; - -++ nagEigenvectors(A,B) returns a record consisting of a list of the -++ eigenvalues -#if saturn -++ $ \lambda $ -#else -++ \spad{l} -#endif -++ and a list of the corresponding eigenvectors of the system -#if saturn -++ $ A x = \lambda B x $ -#else -++ \spad{A*x = l*B*x} -#endif -++ where -#if saturn -++ $A$ and $B$ -#else -++ \spad{A} and B -#endif - -#if saturn -++ $B$ -#else -++ B -#endif -++ is positive-definite. -++ -++ The numerical calculation is performed by one of the NAG routines -++ F02AEF and F02BJF, depending on the the form of \spad{A} and B. -++ The first component of the result, \spad{eigenvalues}, -++ is of type Union(List DoubleFloat, List FormalFraction -++ Complex DoubleFloat), the first branch resulting from F02AEF and -++ the second from F02BJF. Note that in the latter case values should -++ be inspected for numerically small numerators and denominators, -++ ratios of which may be in effect indeterminate, before the result is -++ converted to List Complex DoubleFloat. -++ -++ For more detailed information, please consult the NAG manual -++ via the Browser pages for the operations f02aef and f02bjf. - -} == add { - - import from AnyFunctions1 INT ; - import from AnyFunctions1 MDF ; - import from CDF; - import from ErrorFunctions ; - import from MDF ; - import from NagResultChecks ; - import from NagEigenPackage ; - import from List STRG ; - import from Symbol ; - import from VDF ; - import from Boolean ; - import from Result ; - - local (..)(a:INT,b:INT):Generator INT == { - generate { - t := a ; - while (t <= b) repeat { - yield t ; - t := t + 1 ; - } - } - } - - local ipIfail : INT := -1 ; - - -- First, some local functions: - - f02bjfEigVals(A : MDF, B : MDF, orderAB : INT, eps : DF) : LFFCDF == { - - -- orderAB is the common order of the square matrices A and B. - - local f02bjfResult : RSLT ; - local numR, numI, den : LDF ; - - f02bjfResult := f02bjf(orderAB,orderAB,orderAB,eps, - false,orderAB,A,B,ipIfail) ; - den := entries(row(checkMxDF(f02bjfResult, "beta", "F02BJF"), 1)) ; - numR := entries(row(retract(f02bjfResult."alfr") @ MDF, 1)) ; - numI := entries(row(retract(f02bjfResult."alfi") @ MDF, 1)) ; - - [ (complex(r,i)/complex(d,0@DF))$FFCDF for r in numR - for i in numI - for d in den ] - - } - - - f02bjfEigVecs(A : MDF, B : MDF, orderAB : INT, eps : DF) : RURSLV == { - - -- orderAB is the common order of the square matrices A and B. - - local size : NNI ; - local f02bjfResult : RSLT ; - local numR, numI, den : LDF ; - local eVals : UNNRES ; - local vecMat : MDF ; - local eVecs : LVCDF ; - local j : INT ; - local thisVec, leftVec : VCDF ; - - size := orderAB pretend NNI ; - - f02bjfResult := f02bjf(orderAB,orderAB,orderAB,eps, - true,orderAB,A,B,ipIfail) ; - - den := entries(row(checkMxDF(f02bjfResult, "beta", "F02BJF"), 1)) ; - numR := entries(row(retract(f02bjfResult."alfr") @ MDF, 1)) ; - numI := entries(row(retract(f02bjfResult."alfi") @ MDF, 1)) ; - vecMat := retract(f02bjfResult."v") @ MDF ; - - -- outer [] for union type: - eVals := [[(complex(r,i)/complex(d,0@DF))$FFCDF for r in numR - for i in numI - for d in den]] ; - - eVecs := [] ; - j := orderAB ; - while j > 0 repeat { - if numI.j ~= 0$DF then { - if j = 1 or numI.(j-1) = 0$DF then - error("nagEigenvectors", - "Inconsistent results returned from NAG routine F02BJF") ; - thisVec := new(size,0) ; - leftVec := new(size,0) ; - for i in 1 .. orderAB repeat { - thisVec.i := complex(vecMat(i,j-1),-vecMat(i,j)) ; - leftVec.i := complex(vecMat(i,j-1),vecMat(i,j)) ; - } - eVecs := cons(leftVec,cons(thisVec,eVecs)) ; - j := j - 2; - } - else { - thisVec := new(size,0) ; - for i in 1 .. orderAB repeat - thisVec.i := complex(vecMat(i,j),0@DF) ; - eVecs := cons(thisVec,eVecs) ; - j := j - 1 ; - } - } - - [eVals,eVecs] - - } - - - nagError(routine : STRG, opIfail : INT) : Exit == - error ["An error was detected when calling the NAG Library routine ", - routine, - ". The error number (IFAIL value) is ", - string(opIfail), - ", please consult the NAG manual via the Browser for", - " diagnostic information."] ; - - -- Then the exported functions: - - nagEigenvalues(A : MDF, B : MDF, eps : DF) : UNNRES == { - - -- Strategy: if either matrix is asymmetric, use F02BJF, otherwise - -- try F02ADF in case B is positive-definite. - -- If F02ADF gives IFAIL=1 (should happen quickly if at all), - -- not positive-definite, use less efficient F02BJF. - - local rA, rB, cA, cB : NNI ; - local orderAB, opIfail: INT ; - local vals : UNNRES ; - - rA := nrows A ; - rB := nrows B ; - - if rA ~= rB - then error("nagEigenvalues", - "the two matrices supplied are of different sizes.") ; - orderAB := rA pretend INT ; - - if symmetric?(A) and symmetric?(B) then { - f02adfResult := f02adf(orderAB,orderAB,orderAB,A,B,ipIfail) ; - opIfail := retract(f02adfResult."ifail") @ INT ; - if zero? opIfail then -- using [] to give union type: - vals := [entries(row(retract(f02adfResult."r") @ MDF,1))] ; - else if opIfail = 1 then - vals := [f02bjfEigVals(A,B,orderAB,eps)] - else - nagError("F02BJF",opIfail) ; - } - else { - cA := ncols A ; - if cA ~= rA then - error("nagEigenvalues", - "the first matrix supplied is not square") ; - cB := ncols B ; - if cB ~= rB then - error("nagEigenvalues", - "the second matrix supplied is not square") ; - vals := [f02bjfEigVals(A,B,orderAB,eps)] ; - } - - vals - - } - - - nagEigenvalues(A : MDF, B : MDF) : UNNRES - == nagEigenvalues(A,B,0@DF) ; - - - nagEigenvectors(A : MDF, B : MDF, eps : DF) : RURSLV == { - - -- Strategy: if either matrix is asymmetric, use F02BJF, otherwise - -- try F02AEF in case B is positive-definite. - -- If F02AEF gives IFAIL=1 (should happen quickly if at all), - -- not positive-definite, use less efficient F02BJF. - - local rA, rB, cA, cB : NNI ; - local orderAB, opIfail, j : INT ; - local eVals : UNNRES ; - local eVecs : LVCDF ; - local vecMat : MDF ; - local thisVec : VCDF ; - local f02aefResult : RSLT ; - local result : RURSLV ; - - rA := nrows A ; - rB := nrows B ; - - if rA ~= rB - then error("nagEigenvectors", - "the two matrices supplied are of different sizes.") ; - orderAB := rA pretend INT ; - - if symmetric?(A) and symmetric?(B) then { - f02aefResult := f02aef(orderAB,orderAB,orderAB, - orderAB,A,B,ipIfail) ; - opIfail := retract(f02aefResult."ifail") @ INT ; - if zero? opIfail then { - -- using [] to give union type: - eVals := [entries(row(retract(f02aefResult."r") @ MDF,1))] ; - vecMat := retract(f02aefResult."v") @ MDF ; - eVecs := [] ; - j := orderAB ; - while j > 0 repeat { - thisVec := new(rA,0) ; - for i in 1 .. orderAB repeat - thisVec.i := complex(vecMat(i,j),0@DF) ; - eVecs := cons(thisVec,eVecs) ; - j := j - 1 ; - } - result := [eVals,eVecs] - } - else if opIfail = 1 then - result := f02bjfEigVecs(A,B,orderAB,eps) - else - nagError("F02BJF",opIfail) ; - } - else { - cA := ncols A ; - if cA ~= rA then - error("nagEigenvectors", - "the first matrix supplied is not square") ; - cB := ncols B ; - if cB ~= rB then - error("nagEigenvectors", - "the second matrix supplied is not square") ; - result := f02bjfEigVecs(A,B,orderAB,eps) ; - } - - result - - } - - - nagEigenvectors(A : MDF, B : MDF) : RURSLV - == nagEigenvectors(A,B,0@DF) ; - -} - -#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 ffrac -)lib nepip - -outputGeneral 5 - -mA1 := matrix [[ 0.5 , 1.5 , 6.6 , 4.8], _ - [ 1.5 , 6.5 , 16.2 , 8.6], _ - [ 6.6 , 16.2 , 37.6 , 9.8], _ - [ 4.8 , 8.6 , 9.8 , -17.1]]; - -mB1 := matrix[[ 1 , 3 , 4 , 1], _ - [ 3 , 13 , 16 , 11], _ - [ 4 , 16 , 24 , 18], _ - [ 1 , 11 , 18 , 27]]; - -mA2 := matrix [[ 3.9 , 12.5 , -34.5 , -0.5], _ - [ 4.3 , 21.5 , -47.5 , 7.5], _ - [ 4.3 , 21.5 , -43.5 , 3.5], _ - [ 4.4 , 26.0 , -46.0 , 6.0]]; - -mB2 := matrix[[ 1 , 2 , -3 , 1], _ - [ 1 , 3 , -5 , 4], _ - [ 1 , 3 , -4 , 3], _ - [ 1 , 3 , -4 , 4]]; - -nagEigenvalues(mA1,mB1) :: List Float - --- [- 3.0,- 1.0,2.0,4.0] - -vv1 := nagEigenvectors(mA1,mB1); -(vv1.eigenvalues) :: List Float - --- [- 3.0,- 1.0,2.0,4.0] - -(vv1.eigenvectors) :: List Vector Complex Float - --- [[- 4.35,0.05,1.0,- 0.5], [- 2.05,0.15,0.5,- 0.5], [- 3.95,0.85,0.5,- 0.5], --- [2.65,0.05,- 1.0,0.5]] - -nagEigenvalues(mA2,mB2) - --- all components are O(1) or more so: - -% :: List Complex Float - --- [2.0,3.0 + 4.0 %i,3.0 - 4.0 %i,4.0] - -vv2 := nagEigenvectors(mA2,mB2); -vv2.eigenvalues - --- all components are O(1) or more so: - -% :: List Complex Float - --- [2.0,3.0 + 4.0 %i,3.0 - 4.0 %i,4.0] - -vv2.eigenvectors :: List Vector Complex Float - --- [[0.99606,0.0056917,0.062609,0.062609], --- --- [0.94491, 0.18898 + 0.26077 E -14 %i, 0.11339 - 0.15119 %i, --- 0.11339 - 0.15119 %i] --- , --- --- [0.94491, 0.18898 - 0.26077 E -14 %i, 0.11339 + 0.15119 %i, --- 0.11339 + 0.15119 %i] --- , --- [0.98752,0.010972,- 0.032917,0.15361]] - --- The same call with eps=0.0001: - -vv2a := nagEigenvectors(mA2,mB2,0.0001); -vv2a.eigenvalues :: List Complex Float - --- [1.9989,3.0003 + 3.9994 %i,3.0003 - 3.9994 %i,4.0] - -vv2a.eigenvectors :: List Vector Complex Float - --- [[0.99605,0.0057355,0.062656,0.062656], --- --- [0.94491, 0.18899 - 0.000048882 %i, 0.11336 - 0.15119 %i, --- 0.11336 - 0.15119 %i] --- , --- --- [0.94491, 0.18899 + 0.000048882 %i, 0.11336 + 0.15119 %i, --- 0.11336 + 0.15119 %i] --- , --- [0.98751,0.011031,- 0.032912,0.15367]] - -mB1(1,1) := -1; - --- The next test should fail on F02ADF then call F02BJF: - -nagEigenvalues(mA1,mB1) - --- all components are O(1) or more so: - -% :: List Complex Float - --- [3.5016,- 1.5471,0.041212 + 0.21738 %i,0.041212 - 0.21738 %i] - --- Similarly, this should fail on F02AEF then call F02BJF: - -vv3 := nagEigenvectors(mA1,mB1); -vv3.eigenvalues - --- all components are O(1) or more so: - -% :: List Complex Float - --- [3.5016,- 1.5471,0.041212 + 0.21738 %i,0.041212 - 0.21738 %i] - -vv3.eigenvectors :: List Vector Complex Float - --- [[- 0.034577,0.63045,- 0.75202,0.1892], --- [0.17876,- 0.73845,0.047413,0.64845], --- --- [0.80838, - 0.00095133 + 0.47557 %i, - 0.20354 - 0.21737 %i, --- 0.15404 + 0.089179 %i] --- , --- --- [0.80838, - 0.00095133 - 0.47557 %i, - 0.20354 + 0.21737 %i, --- 0.15404 - 0.089179 %i] --- ] - -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>> - --- NagEigenProblemInterfacePackage - --- To test: --- sed '1,/^#if NeverAssertThis/d;/#endif/d' < nepip.as > nepip.input --- axiom --- )set nag host <some machine running nagd> --- )r nepip.input - -#unassert saturn - -#include "axiom.as" - -<<NagEigenInterfacePackage>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/noptip.as.pamphlet b/src/algebra/noptip.as.pamphlet deleted file mode 100644 index 10e20ce3..00000000 --- a/src/algebra/noptip.as.pamphlet +++ /dev/null @@ -1,241 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra noptip.as} -\author{Michael Richardson} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{NagOptimisationInterfacePackage} -<<NagOptimisationInterfacePackage>>= -+++ Author: M.G. Richardson -+++ Date Created: 1996 Feb. 01 -+++ 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 -+++ optimisation routines in the NAGlink. - -NagOptimisationInterfacePackage: with { - - nagMin : (EDF,LEQPDF) -> LEQPDF ; - -} == add { - - import from MINT ; - import from BOOL ; - import from LLDF ; - import from VDF ; - import from PDF ; - import from LEQEDF ; - import from MDF ; - import from EDF ; - import from FL ; - import from SMBL ; - import from A49 ; - import from A55 ; - import from U49 ; - import from U55 ; - import from NagOptimisationPackage ; - import from OF ; - import from LOF ; - import from LLOF ; - import from ListFunctions2(INT,OF) ; - import from NagResultChecks ; - import from EF2DFFL ; - - local (..)(a:INT,b:INT):Generator INT == { - generate { - t := a ; - while (t <= b) repeat { - yield t ; - t := t + 1 ; - } - } - } - - -- to avoid unrecognised versions of U49 type for e04dgf: - e04dgflocal := e04dgf$NagOptimisationPackage pretend - ((INT,DF,DF,INT,DF,BOOL, DF,DF,INT,INT,INT,INT,MDF,INT, U49)->RSLT) ; - - nagMin(objective:EDF,startList:LEQPDF) : LEQPDF == { - - -- Note that, as objective is an EDF, subst and eval - -- for this have as 2nd parameters LEQEDFs. - - local nv : INT ; - local substList : LEQEDF ; - local indxOb : EF ; - local startVals : LDF ; - local startListXDF : LEQEDF ; - local startFVal : DF ; - local e04dgfResult : RSLT ; - local location : LDF ; - - - nv := ((# startList)@NNI pretend INT) ; -- @ avoids SI - - substList := [lhs(startList.i)::EDF - = (script("x"::SMBL,[[i::OF]]@LLOF))::EDF - for i in 1..nv] ; - -- [x=x[1], y=x[2], etc.] - - indxOb := map(convert$Float,subst(objective,substList)) ; - -- objective function as an EF with x[i]'s, as required by A49 - - startVals := [retract(rhs(startList.i))@DF for i in 1..nv] ; - - startListXDF := [lhs(startList.i)::EDF = rhs(startList.i)::EDF - for i in 1..nv] ; - startFVal := ground(eval(objective,startListXDF))::DF ; - startFVal := startFVal * 1.015625 ; - --- Note that there appears to be a problem running the standard NAG --- example on Suns with an exact value for startFVal. It looks as if --- this causes too large a stepsize, perhaps due to exception code --- being obeyed in the Fortran. Until this is fixed, using the above --- slightly perturbed value (adding 1/64) seems to avoid the problem. - - e04dgfResult := e04dgflocal( - nv, -- No.vbls. - -- - -- "optional" params next: - -- - startFVal, -- es(timated obj've fn val) - -1.0, -- fun: - -1, -- it: - -1.0, -- lin: - false, -- list: - -1.0, -- ma: - -2.0, -- opt: made < fun for safety - 0, -- pr: - -1, -- sta: - -1, -- sto: - -1, -- ve: - -- - matrix [startVals], -- initial position estimate - -1, -- IFAIL - [retract(indxOb)@A49]@U49 -- objective function - ) ; - - location := entries(row(checkMxDF(e04dgfResult,"x","E04DGF"),1)) ; - - [ ((retract(lhs(startList.i))@SMBL)::PDF - = (location.i)::PDF)@EQPDF for i in 1..nv ] - - } - -} - -#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 - -outputGeneral 5 - -f := %e^x*(4*x^2 + 2*y^2 + 4*x*y + 2*y + 1); -start := [x=-1.0, y=1.0]; -nagMin(f,start) :: List Equation Polynomial Float - --- [x= 0.5,y= - 1.0] - -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>> - --- To test: --- sed '1,/^#if NeverAssertThis/d;/#endif/d' < noptip.as > noptip.input --- axiom --- )set nag host <some machine running nagd> --- )r noptip.input - -#unassert saturn - -#include "axiom.as" - -INT ==> Integer ; -NNI ==> NonNegativeInteger ; -MINT ==> Matrix INT ; -DF ==> DoubleFloat ; -EDF ==> Expression DF ; -EQEDF ==> Equation EDF ; -LEQEDF ==> List EQEDF ; -LDF ==> List DF ; -LLDF ==> List LDF ; -VDF ==> Vector DF ; -MDF ==> Matrix DF ; -PDF ==> Polynomial DF ; -EQPDF ==> Equation PDF ; -LEQPDF ==> List EQPDF ; -FL ==> Float ; -EF ==> Expression FL ; -BOOL ==> Boolean ; -A49 ==> Asp49("OBJFUN") ; -A55 ==> Asp55("CONFUN") ; -U49 ==> Union(fn: FileName, fp: A49) ; -U55 ==> Union(fn: FileName, fp: A55) ; -SMBL ==> Symbol ; -RSLT ==> Result ; -OF ==> OutputForm ; -LOF ==> List OF ; -LLOF ==> List LOF ; -EF2DFFL ==> ExpressionFunctions2(DF,FL) ; - -<<NagOptimisationInterfacePackage>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} 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} diff --git a/src/algebra/nrc.as.pamphlet b/src/algebra/nrc.as.pamphlet deleted file mode 100644 index 70dd6222..00000000 --- a/src/algebra/nrc.as.pamphlet +++ /dev/null @@ -1,132 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra nrc.as} -\author{Michael Richardson} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{NagResultChecks} -<<NagResultChecks>>= -+++ Author: M.G. Richardson -+++ Date Created: 1995 Dec. 06 -+++ Date Last Updated: -+++ Basic Functions: -+++ Related Constructors: -+++ Also See: -+++ AMS Classifications: -+++ Keywords: -+++ References: -+++ Description: - -NagResultChecks: with { - - checkResult : (RSLT, STRG, STRG) -> DF ; - checkCxResult : (RSLT, STRG, STRG) -> CDF ; - checkMxCDF : (RSLT, STRG, STRG) -> MCDF ; - checkMxDF : (RSLT, STRG, STRG) -> MDF ; - -} == add { - - import from DF ; - import from SMBL ; - import from INT ; - import from AnyFunctions1 INT ; - import from AnyFunctions1 DF ; - import from AnyFunctions1 CDF ; - import from AnyFunctions1 MDF ; - import from AnyFunctions1 MCDF ; - import from ErrorFunctions ; - import from STRG ; - import from List STRG ; - - checkResult(returnValue : RSLT, returnKey : STRG, routine : STRG) : DF == - if not zero?(retract(returnValue."ifail") @ INT) - then nagError(routine, retract(returnValue."ifail") @ INT) - else retract(returnValue.(returnKey::SMBL)) @ DF ; - - checkCxResult(returnValue : RSLT, returnKey : STRG, routine : STRG) : CDF == - if not zero?(retract(returnValue."ifail") @ INT) - then nagError(routine, retract(returnValue."ifail") @ INT) - else retract(returnValue.(returnKey::SMBL)) @ CDF ; - - checkMxDF(returnValue : RSLT, returnKey : STRG, routine : STRG) : MDF == - if not zero?(retract(returnValue."ifail") @ INT) - then nagError(routine, retract(returnValue."ifail") @ INT) - else retract(returnValue.(returnKey::SMBL)) @ MDF ; - - checkMxCDF(returnValue : RSLT, returnKey : STRG, routine : STRG) : MCDF == - if not zero?(retract(returnValue."ifail") @ INT) - then nagError(routine, retract(returnValue."ifail") @ INT) - else retract(returnValue.(returnKey::SMBL)) @ MCDF ; - - nagError(routine : STRG, opIfail : INT) : Exit == - error ["An error was detected when calling the NAG Library routine ", - routine, - ". The error number (IFAIL value) is ", - string(opIfail), - ", please consult the NAG manual via the Browser for", - " diagnostic information."] ; -} - -@ -\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>> - --- N.B. ndftip.as, nqip.as and nsfip.as inline from nrc --- and must be recompiled if this is. - -#include "axiom.as" - -DF ==> DoubleFloat ; -CDF ==> Complex DoubleFloat ; -MDF ==> Matrix DoubleFloat ; -MCDF ==> Matrix Complex DoubleFloat ; -INT ==> Integer ; -RSLT ==> Result ; -SMBL ==> Symbol ; -STRG ==> String ; - -<<NagResultChecks>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/nsfip.as.pamphlet b/src/algebra/nsfip.as.pamphlet deleted file mode 100644 index a0ceb8cd..00000000 --- a/src/algebra/nsfip.as.pamphlet +++ /dev/null @@ -1,1223 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra nsfip.as} -\author{Michael Richardson} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{NagSpecialFunctionsInterfacePackage} -<<NagSpecialFunctionsInterfacePackage>>= -+++ Author: M.G. Richardson -+++ Date Created: 1995 Nov. 27 -+++ Date Last Updated: -+++ Basic Functions: -+++ Related Constructors: -+++ Also See: -+++ AMS Classifications: -+++ Keywords: -+++ References: -+++ Description: -+++ This package provides Axiom-like interfaces to those of the NAG -+++ special functions in the NAGlink for which no equivalent -+++ functionality is transparently present in Axiom. - -NagSpecialFunctionsInterfacePackage: with { - - nagExpInt : DF -> DF ; - - ++ nagExpInt calculates an approximation to the exponential integral, - ++ \spad{E1}, defined by -#if saturn - ++ \[E_{1}(x) = \int_{x}^{\infty }\frac{e^{-u}}{u}\,du\] -#else - ++ \spad{E1(x) = integrate(1/u*%e^u, u=x..%infinity)} -#endif - ++ using the NAG routine S13AAF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s13aaf. - - nagSinInt : DF -> DF ; - - ++ nagSinInt calculates an approximation to the sine integral, - ++ \spad{Si}, defined by -#if saturn - ++ \[{\rm Si} (x) = \int_{0}^{x}\frac{\sin u}{u}\,du\] -#else - ++ \spad{Si(x) = integrate(1/u*sin(u), u=0..x)} -#endif - ++ using the NAG routine S13ADF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s13adf. - - nagCosInt : DF -> DF ; - - ++ nagCosInt calculates an approximation to the cosine integral, - ++ \spad{Ci}, defined by -#if saturn - ++ \[{\rm Ci} (x) = - ++ \gamma + \ln x+ \int_{0}^{x}\frac{\cos u- 1}{u}\,du\] -#else - ++ \spad{Ci(x) = gamma + log x + integrate(1/u*cos(u), u=0..x)} - ++ where \spad{gamma} is Euler's constant, -#endif - ++ using the NAG routine S13ACF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s13acf. - - nagIncompleteGammaP : (DF, DF) -> DF ; -- to machine precision - - ++ nagIncompleteGammaP evaluates the incomplete gamma function - ++ \spad{P}, defined by -#if saturn - ++ \[P(a,x) & = & \frac{1}{\Gamma(a)}\int_{0}^{x}t^{a-1}e^{-t}\,dt\] -#else - ++ \spad{P(a,x) = 1/Gamma(a)*integrate(t^(a-1)%e^(-t),t=0..x)} -#endif - ++ to machine precision, using the NAG routine S14BAF. - - nagIncompleteGammaP : (DF, DF, DF) -> DF ; - - ++ nagIncompleteGammaP(a,x,tol) evaluates the incomplete gamma - ++ function \spad{P}, defined by -#if saturn - ++ \[P(a,x) & = & \frac{1}{\Gamma(a)}\int_{0}^{x}t^{a-1}e^{-t}\,dt\] -#else - ++ \spad{P(a,x) = 1/Gamma(a)*integrate(t^(a-1)%e^(-t),t=0..x)} -#endif - ++ to a relative accuracy \spad{tol}, using the NAG routine S14BAF. - - nagIncompleteGammaQ : (DF, DF) -> DF ; - - ++ nagIncompleteGammaQ evaluates the incomplete gamma function - ++ \spad{Q}, defined by -#if saturn - ++ \[Q(a,x)&=&\frac{1}{\Gamma(a)}\int_{x}^{\infty}t^{a-1}e^{-t}\,dt\] -#else - ++ \spad{Q(a,x) = 1/Gamma(a)*integrate(t^(a-1)%e^(-t),t=x..%infinity)} -#endif - ++ to machine precision, using the NAG routine S14BAF. - - nagIncompleteGammaQ : (DF, DF, DF) -> DF ; - - ++ nagIncompleteGammaQ(a,x,tol) evaluates the incomplete gamma - ++ function \spad{Q}, defined by -#if saturn - ++ \[Q(a,x)&=&\frac{1}{\Gamma(a)}\int_{x}^{\infty}t^{a-1}e^{-t}\,dt\] -#else - ++ \spad{Q(a,x) = 1/Gamma(a)*integrate(t^(a-1)%e^(-t),t=x..%infinity)} -#endif - ++ to a relative accuracy \spad{tol}, using the NAG routine S14BAF. - - nagErf : DF -> DF ; - - ++ nagErf calculates an approximation to the error function, - ++ \spad{erf}, defined by -#if saturn - ++ \[{\rm erf}\, x = \frac{2}{\sqrt{\pi}}\int_{0}^{x}e^{-t^{2}}\,dt\] -#else - ++ \spad{erf(x) = 2/sqrt(\%pi)*integrate(\%e^(-t^2),t=0..x)} -#endif - ++ using the NAG routine S15AEF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s15aef. - - nagErfC : DF -> DF ; - - ++ nagErfC calculates an approximation to the complementary error - ++ function \spad{erfc}, defined by -#if saturn - ++ \[{\rm erfc}\,x = - ++ \frac{2} {\sqrt{\pi}}\int_{x}^{\infty}e^{-t^{2}}\,dt\] -#else - ++ \spad{erfc(x) = 2/sqrt(%pi)*integrate(%e^(-t^2),t=x..%infinity)} -#endif - ++ using the NAG routine S15ADF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s15adf. - - nagDAiryAi : DF -> DF ; - - ++ nagDAiryAi calculates an approximation to \spad{Ai'}, the - ++ derivative of the Airy function \spad{Ai}, using the NAG routine - ++ S17AJF. - - nagDAiryAi : CDF -> CDF ; - - ++ nagDAiryAi calculates an approximation to \spad{Ai'}, the - ++ derivative of the Airy function \spad{Ai}, using the NAG routine - ++ S17DGF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dgf. - - nagDAiryBi : DF -> DF ; - - ++ nagDAiryBi calculates an approximation to \spad{Bi'}, the - ++ derivative of the Airy function \spad{Bi}, using the NAG routine - ++ S17AKF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17akf. - - nagDAiryBi : CDF -> CDF ; - - ++ nagDAiryBi calculates an approximation to \spad{Bi'}, the - ++ derivative of the Airy function \spad{Bi}, using the NAG routine - ++ S17DHF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dhf. - - nagScaledDAiryAi : CDF -> CDF ; - - ++ nagDAiryAi(z) calculates an approximation to \spad{Ai'(z)}, the - ++ derivative of the Airy function \spad{Ai(z)}, with the result - ++ scaled by a factor -#if saturn - ++ $e^{2z\sqrt{z}/ 3}$ -#else - ++ \spad{%e^(2*z*sqrt(z)/3)} -#endif - ++ using the NAG routine S17DGF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dgf. - - nagScaledDAiryBi : CDF -> CDF ; - - ++ nagDAiryBi(z) calculates an approximation to \spad{Bi'(z)}, the - ++ derivative of the Airy function \spad{Bi(z)}, with the result - ++ scaled by a factor -#if saturn - ++ $e^{2z\sqrt{z}/ 3}$ -#else - ++ \spad{%e^(2*z*sqrt(z)/3)} -#endif - ++ using the NAG routine S17DHF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dhf. - - nagHankelH1 : (DF, CDF, INT) -> MCDF ; - - ++ nagHankelH1(nu,z,n) calculates an approximation to a sequence of n - ++ values of the Hankel function -#if saturn - ++ $H_{\nu + k}^{(1)}(z)$ -#else - ++ \spad{H1(nu + k, z)} -#endif - ++ for non-negative nu and \spad{k = 0,1 ... n-1}, using the NAG - ++ routine S17DLF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dlf. - - nagHankelH2 : (DF, CDF, INT) -> MCDF ; - - ++ nagHankelH2(nu,z,n) calculates an approximation to a sequence of n - ++ values of the Hankel function -#if saturn - ++ $H_{\nu + k}^{(2)}(z)$ -#else - ++ \spad{H2(nu + k, z)} -#endif - ++ for non-negative nu and \spad{k = 0,1 ... n-1}, using the NAG - ++ routine S17DLF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dlf. - - nagScaledHankelH1 : (DF, CDF, INT) -> MCDF ; - - ++ nagHankelH1(nu,z,n) calculates an approximation to a sequence of n - ++ values of the Hankel function -#if saturn - ++ $H_{\nu + k}^{(1)}(z)$ -#else - ++ \spad{H1(nu + k, z)} -#endif - ++ for non-negative nu and \spad{k = 0,1 ... n-1}, with the result - ++ scaled by a factor -#if saturn - ++ $e^{-iz} -#else - ++ \spad{%e^(-%i*z)} -#endif - ++ using the NAG routine S17DLF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dlf. - - nagScaledHankelH2 : (DF, CDF, INT) -> MCDF ; - - ++ nagHankelH2(nu,z,n) calculates an approximation to a sequence of n - ++ values of the Hankel function -#if saturn - ++ $H_{\nu + k}^{(2)}(z)$ -#else - ++ \spad{H2(nu + k, z)} -#endif - ++ for non-negative nu and \spad{k = 0,1 ... n-1}, with the result - ++ scaled by a factor -#if saturn - ++ $e^{iz} -#else - ++ \spad{%e^(%i*z)} -#endif - ++ using the NAG routine S17DLF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dlf. - - nagKelvinBer : DF -> DF ; - - ++ nagKelvinBer calculates an approximation to the Kelvin function - ++ \spad{ber}, using the NAG routine S19AAF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s19aaf. - - nagKelvinBei : DF -> DF ; - - ++ nagKelvinBei calculates an approximation to the Kelvin function - ++ \spad{bei}, using the NAG routine S19ABF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s19abf. - - nagKelvinKer : DF -> DF ; - - ++ nagKelvinKer calculates an approximation to the Kelvin function - ++ \spad{ker}, using the NAG routine S19ACF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s19acf. - - nagKelvinKei : DF -> DF ; - - ++ nagKelvinKei calculates an approximation to the Kelvin function - ++ \spad{kei}, using the NAG routine S19ADF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s19adf. - - nagFresnelS : DF -> DF ; - - ++ nagFresnelS calculates an approximation to the Fresnel integral - ++ \spad{S}, defined by -#if saturn - ++ \[S(x) = \int_{0}^{x}\sin\left(\frac{\pi}{2}t^{2}\right)\,dt\] -#else - ++ \spad{S(x) = integrate(sin(%pi/2*t^2),t=0..x)} -#endif - ++ using the NAG routine S20ACF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s20acf. - - nagFresnelC : DF -> DF ; - - ++ nagFresnelC calculates an approximation to the Fresnel integral - ++ \spad{C}, defined by -#if saturn - ++ \[C(x) = \int_{0}^{x}\cos\left(\frac{\pi}{2}t^{2}\right)\,dt\] -#else - ++ \spad{C(x) = integrate(cos(%pi/2*t^2),t=0..x)} -#endif - ++ using the NAG routine S20ADF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s20adf. - - nagEllipticIntegralRC : (DF, DF) -> DF ; - - ++ nagEllipticIntegralRC(x,y) calculates an approximation to the - ++ elementary (degenerate symmetrised elliptic) integral -#if saturn - ++ \[R_{C}(x,y) = - ++ \frac{1}{2}\int_{0}^{\infty}\frac{dt}{\sqrt{t+x}(t+y)}\] -#else - ++ \spad{RC(x,y) = 1/2*integrate(1/(sqrt(t+x)*(t+y)),t=0..\infinity)} -#endif - ++ using the NAG routine S21BAF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s21baf. - - nagEllipticIntegralRF : (DF, DF, DF) -> DF ; - - ++ nagEllipticIntegralRF(x,y,z) calculates an approximation to the - ++ symmetrised elliptic integral of the first kind, -#if saturn - ++ \[R_{F}(x, y, z) = - ++ \frac{1}{2}\int_{0}^{\infty}\frac{dt}{\sqrt{(t+x)(t+y)(t+z)}}\] -#else - ++ \spad{RF(x,y,z) = - ++ 1/2*integrate(1/sqrt((t+x)*(t+y)*(t+z)),t=0..\infinity)} -#endif - ++ using the NAG routine S21BBF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s21bbf. - - nagEllipticIntegralRD : (DF, DF, DF) -> DF ; - - ++ nagEllipticIntegralRD(x,y,z) calculates an approximation to the - ++ symmetrised elliptic integral of the second kind, -#if saturn - ++ \[R_{D}(x, y, z) = - ++ \frac{3}{2}\int_{0}^{\infty}\frac{dt}{\sqrt{(t+x)(t+y)(t+z)^{3}}}\] -#else - ++ \spad{RD(x,y,z) = - ++ 1/2*integrate(1/sqrt((t+x)*(t+y)*(t+z)^3),t=0..\infinity)} -#endif - ++ using the NAG routine S21BCF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s21bcf. - - nagEllipticIntegralRJ : (DF, DF, DF, DF) -> DF ; - - ++ nagEllipticIntegralRJ(x,y,z,rho) calculates an approximation to - ++ the symmetrised elliptic integral of the third kind, -#if saturn - ++ \[R_{J}(x, y, z, \rho ) = - ++ \frac{3}{2}\int_{0}^{\infty} - ++ \frac{dt}{(t+\rho)\sqrt{(t+x)(t+y)(t+z)}}\] -#else - ++ \spad{RJ(x,y,z,rho) = - ++ 3/2*integrate(1/((t+rho)*sqrt((t+x)*(t+y)*(t+z))),t=0..\infinity))u} -#endif - ++ using the NAG routine S21BDF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s21bdf. - -} == add { - - import from NagSpecialFunctionsPackage ; - import from NagResultChecks ; - - local ipIfail : Integer := -1 ; - - nagExpInt(x : DF) : DF == - checkResult(s13aaf(x,ipIfail), "s13aafResult", "S13AAF") ; - - nagCosInt(x : DF) : DF == - checkResult(s13acf(x,ipIfail), "s13acfResult", "S13ACF") ; - - nagSinInt(x : DF) : DF == - checkResult(s13adf(x,ipIfail), "s13adfResult", "S13ADF") ; - - nagIncompleteGammaP(a : DF, x : DF) : DF == - checkResult(s14baf(a,x,0.0,ipIfail), "p", "S14BAF") ; - - nagIncompleteGammaP(a : DF, x : DF, tol : DF) : DF == - checkResult(s14baf(a,x,tol,ipIfail), "p", "S14BAF") ; - - nagIncompleteGammaQ(a : DF, x : DF) : DF == - checkResult(s14baf(a,x,0.0,ipIfail), "q", "S14BAF") ; - - nagIncompleteGammaQ(a : DF, x : DF, tol : DF) : DF == - checkResult(s14baf(a,x,tol,ipIfail), "q", "S14BAF") ; - - nagErfC(x : DF) : DF == - checkResult(s15adf(x,ipIfail), "s15adfResult", "S15ADF") ; - - nagErf(x : DF) : DF == - checkResult(s15aef(x,ipIfail), "s15aefResult", "S15AEF") ; - - nagDAiryAi(x : DF) : DF == - checkResult(s17ajf(x,ipIfail), "s17ajfResult", "S17AJF") ; - - nagDAiryAi(z : CDF) : CDF == - checkCxResult(s17dgf("d",z,"u",ipIfail), "ai", "S17DGF") ; - - nagDAiryBi(x : DF) : DF == - checkResult(s17akf(x,ipIfail), "s17akfResult", "S17AKF") ; - - nagDAiryBi(z : CDF) : CDF == - checkCxResult(s17dhf("d",z,"u",ipIfail), "bi", "S17DHF") ; - - nagScaledDAiryAi(z : CDF) : CDF == - checkCxResult(s17dgf("d",z,"s",ipIfail), "ai", "S17DGF") ; - - nagScaledDAiryBi(z : CDF) : CDF == - checkCxResult(s17dhf("d",z,"s",ipIfail), "bi", "S17DHF") ; - - nagHankelH1(order : DF, z : CDF, n : INT) : Matrix CDF == - checkMxCDF(s17dlf(1,order,z,n,"u",ipIfail), "cy", "S17DLF") ; - - nagHankelH2(order : DF, z : CDF, n : INT) : Matrix CDF == - checkMxCDF(s17dlf(2,order,z,n,"u",ipIfail), "cy", "S17DLF") ; - - nagScaledHankelH1(order : DF, z : CDF, n : INT) : Matrix CDF == - checkMxCDF(s17dlf(1,order,z,n,"s",ipIfail), "cy", "S17DLF") ; - - nagScaledHankelH2(order : DF, z : CDF, n : INT) : Matrix CDF == - checkMxCDF(s17dlf(2,order,z,n,"s",ipIfail), "cy", "S17DLF") ; - - nagKelvinBer(x : DF) : DF == - checkResult(s19aaf(x,ipIfail), "s19aafResult", "S19AAF") ; - - nagKelvinBei(x : DF) : DF == - checkResult(s19abf(x,ipIfail), "s19abfResult", "S19ABF") ; - - nagKelvinKer(x : DF) : DF == - checkResult(s19acf(x,ipIfail), "s19acfResult", "S19ACF") ; - - nagKelvinKei(x : DF) : DF == - checkResult(s19adf(x,ipIfail), "s19adfResult", "S19ADF") ; - - nagFresnelS(x : DF) : DF == - checkResult(s20acf(x,ipIfail), "s20acfResult", "S20ACF") ; - - nagFresnelC(x : DF) : DF == - checkResult(s20adf(x,ipIfail), "s20adfResult", "S20ADF") ; - - nagEllipticIntegralRC(x : DF, y : DF) : DF == - checkResult(s21baf(x,y,ipIfail), "s21bafResult", "S21BAF") ; - - nagEllipticIntegralRF(x : DF, y : DF, z : DF) : DF == - checkResult(s21bbf(x,y,z,ipIfail), "s21bbfResult", "S21BBF") ; - - nagEllipticIntegralRD(x : DF, y : DF, z : DF) : DF == - checkResult(s21bcf(x,y,z,ipIfail), "s21bcfResult", "S21BCF") ; - - nagEllipticIntegralRJ(x : DF, y : DF, z : DF, rho : DF) : DF == - checkResult(s21bdf(x,y,z,rho,ipIfail), "s21bdfResult", "S21BDF") ; -} - -#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 nsfip - -outputGeneral 4 - --- DF here means DoubleFloat. --- Results converted to Float as outputGeneral not working on DF. - --- nagExpInt : DF -> DF ; - -nagExpInt(2) :: Float - --- 0.0489 - -nagExpInt(-1) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S13AAF: IFAIL = 1 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S13AAF. The error number (IFAIL value) is 1, please consult the --- NAG manual via the Browser for diagnostic information. - --- nagSinInt : DF -> DF ; - -nagSinInt(0) :: Float - --- 0.0 - -nagSinInt(0.2) :: Float - --- 0.1996 - -nagSinInt(0.4) :: Float - --- 0.3965 - -nagSinInt(0.6) :: Float - --- 0.5881 - -nagSinInt(0.8) :: Float - --- 0.7721 - -nagSinInt(1) :: Float - --- 0.9461 - --- nagCosInt : DF -> DF ; - -nagCosInt(0.2) :: Float - --- - 1.042 - -nagCosInt(0.4) :: Float - --- - 0.3788 - -nagCosInt(0.6) :: Float - --- - 0.02227 - -nagCosInt(0.8) :: Float - --- 0.1983 - -nagCosInt(1) :: Float - --- 0.3374 - --- nagIncompleteGammaP : (DF, DF) -> DF ; (to machine precision) - -nagIncompleteGammaP(2,3) :: Float - --- 0.8009 - -nagIncompleteGammaP(7,1) :: Float - --- 0.00008324 - -nagIncompleteGammaP(0.5,99) :: Float - --- 1.0 - -nagIncompleteGammaP(20,21) :: Float - --- 0.6157 - -nagIncompleteGammaP(21,20) :: Float - --- 0.4409 - --- nagIncompleteGammaP : (DF, DF, DF) -> DF ; (to specified precision) - -nagIncompleteGammaP(7,1,0.1) :: Float - --- 0.00008313 - --- nagIncompleteGammaQ : (DF, DF) -> DF ; (to machine precision) - -nagIncompleteGammaQ(2,3) :: Float - --- 0.1991 - -nagIncompleteGammaQ(7,1) :: Float - --- 0.9999 - -nagIncompleteGammaQ(0.5,99) :: Float - --- 0.5705 E -44 - -nagIncompleteGammaQ(20,21) :: Float - --- 0.3843 - -nagIncompleteGammaQ(21,20) :: Float - --- 0.5591 - -nagIncompleteGammaQ(25,14) :: Float - --- 0.995 - --- nagIncompleteGammaQ : (DF, DF, DF) -> DF ; (to specified precision) - -nagIncompleteGammaQ(25,14,0.1) :: Float - --- 0.9953 - --- nagErf : DF -> DF ; - -nagErf(-6) :: Float - --- - 1.0 - -nagErf(-4.5) :: Float - --- - 1.0 - -nagErf(-1) :: Float - --- - 0.8427 - -nagErf(1) :: Float - --- 0.8427 - -nagErf(4.5) :: Float - --- 1.0 - -nagErf(6) :: Float - --- 1.0 - --- nagErfC : DF -> DF ; - -nagErfC(-10) :: Float - --- 2.0 - -nagErfC(-1) :: Float - --- 1.843 - -nagErfC(0) :: Float - --- 1.0 - -nagErfC(1) :: Float - --- 0.1573 - -nagErfC(15) :: Float - --- 0.7213 E -99 - --- nagDAiryAi : DF -> DF ; - -nagDAiryAi(-10) :: Float - --- 0.9963 - -nagDAiryAi(-1) :: Float - --- - 0.01016 - -nagDAiryAi(0) :: Float - --- - 0.2588 - -nagDAiryAi(1) :: Float - --- - 0.1591 - -nagDAiryAi(5) :: Float - --- - 0.0002474 - -nagDAiryAi(10) :: Float - --- - 0.3521 E -9 - -nagDAiryAi(20) :: Float - --- - 0.7586 E -26 - --- nagDAiryAi : CDF -> CDF ; - -nagDAiryAi(0.3+0.4*%i) :: Complex Float - --- - 0.2612 + 0.03848 %i - --- nagDAiryBi : DF -> DF ; - -nagDAiryBi(-10) :: Float - --- 0.1194 - -nagDAiryBi(-1) :: Float - --- 0.5924 - -nagDAiryBi(0) :: Float - --- 0.4483 - -nagDAiryBi(1) :: Float - --- 0.9324 - -nagDAiryBi(5) :: Float - --- 1436.0 - -nagDAiryBi(10) :: Float - --- 0.1429 E 10 - -nagDAiryBi(20) :: Float - --- 0.9382 E 26 - --- nagDAiryBi : CDF -> CDF ; - -nagDAiryBi(0.3+0.4*%i) :: Complex Float - --- 0.4093 + 0.07966 %i - --- nagScaledDAiryAi : CDF -> CDF ; - -nagScaledDAiryAi(0.3+0.4*%i) :: Complex Float - --- - 0.2744 - 0.02356 %i - --- nagScaledDAiryBi : CDF -> CDF ; - -nagScaledDAiryBi(0.3+0.4*%i) :: Complex Float - --- 0.3924 + 0.07638 %i - --- nagHankelH1 : (DF, CDF, Int) -> List CDF ; - -nagHankelH1(0,0.3+0.4*%i,2) :: Matrix Complex Float - --- [0.3466 - 0.5588 %i - 0.7912 - 0.8178 %i] - -nagHankelH1(2.3,2,2) :: Matrix Complex Float - --- [0.2721 - 0.7398 %i 0.08902 - 1.412 %i] - -nagHankelH1(2.12,-1,2) :: Matrix Complex Float - --- [- 0.7722 - 1.693 %i 2.601 + 6.527 %i] - --- nagHankelH2 : (DF, CDF, Int) -> List CDF ; - -nagHankelH2(6,3.1-1.6*%i,2) :: Matrix Complex Float - --- [- 1.371 - 1.28 %i - 1.491 - 5.993 %i] - --- nagScaledHankelH1 : (DF, CDF, Int) -> List CDF ; - -nagScaledHankelH1(0,0.3+0.4*%i,2) :: Matrix Complex Float - --- [0.2477 - 0.9492 %i - 1.488 - 0.8166 %i] - --- nagScaledHankelH2 : (DF, CDF, Int) -> List CDF ; - -nagScaledHankelH2(6,3.1-1.6*%i,2) :: Matrix Complex Float - --- [7.05 + 6.052 %i 8.614 + 29.35 %i] - --- nagKelvinBer : DF -> DF ; - -nagKelvinBer(0.1) :: Float - --- 1.0 - -nagKelvinBer(1) :: Float - --- 0.9844 - -nagKelvinBer(2.5) :: Float - --- 0.4 - -nagKelvinBer(5) :: Float - --- - 6.23 - -nagKelvinBer(10) :: Float - --- 138.8 - -nagKelvinBer(15) :: Float - --- - 2967.0 - -nagKelvinBer(60) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19AAF: IFAIL = 1 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19AAF. The error number (IFAIL value) is 1, please consult the --- NAG manual via the Browser for diagnostic information. - -nagKelvinBer(-1) :: Float - --- 0.9844 - --- nagKelvinBei : DF -> DF ; - -nagKelvinBei(0.1) :: Float - --- 0.0025 - -nagKelvinBei(1) :: Float - --- 0.2496 - -nagKelvinBei(2.5) :: Float - --- 1.457 - -nagKelvinBei(5) :: Float - --- 0.116 - -nagKelvinBei(10) :: Float - --- 56.37 - -nagKelvinBei(15) :: Float - --- - 2953.0 - -nagKelvinBei(60) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ABF: IFAIL = 1 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ABF. The error number (IFAIL value) is 1, please consult the --- NAG manual via the Browser for diagnostic information. - -nagKelvinBei(-1) :: Float - --- 0.2496 - --- nagKelvinKer : DF -> DF ; - -nagKelvinKer(0) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL = 2 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ACF. The error number (IFAIL value) is 2, please consult the --- NAG manual via the Browser for diagnostic information. - -nagKelvinKer(0.1) :: Float - --- 2.42 - -nagKelvinKer(1) :: Float - --- 0.2867 - -nagKelvinKer(2.5) :: Float - --- - 0.06969 - -nagKelvinKer(5) :: Float - --- - 0.01151 - -nagKelvinKer(10) :: Float - --- 0.0001295 - -nagKelvinKer(15) :: Float - --- - 0.1514 E -7 - -nagKelvinKer(1100) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL = 1 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ACF. The error number (IFAIL value) is 1, please consult the --- NAG manual via the Browser for diagnostic information. - -nagKelvinKer(-1) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL = 2 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ACF. The error number (IFAIL value) is 2, please consult the --- NAG manual via the Browser for diagnostic information. - --- nagKelvinKei : DF -> DF ; - -nagKelvinKei(0) :: Float - --- - 0.7854 - -nagKelvinKei(0.1) :: Float - --- - 0.7769 - -nagKelvinKei(1) :: Float - --- - 0.495 - -nagKelvinKei(2.5) :: Float - --- - 0.1107 - -nagKelvinKei(5) :: Float - --- 0.01119 - -nagKelvinKei(10) :: Float - --- - 0.0003075 - -nagKelvinKei(15) :: Float - --- 0.000007963 - -nagKelvinKei(1100) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ADF: IFAIL = 1 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ADF. The error number (IFAIL value) is 1, please consult the --- NAG manual via the Browser for diagnostic information. - -nagKelvinKei(-1) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ADF: IFAIL = 2 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ADF. The error number (IFAIL value) is 2, please consult the --- NAG manual via the Browser for diagnostic information. - - --- nagFresnelS : DF -> DF ; - -nagFresnelS(0) :: Float - --- 0.0 - -nagFresnelS(0.5) :: Float - --- 0.06473 - -nagFresnelS(1) :: Float - --- 0.4383 - -nagFresnelS(2) :: Float - --- 0.3434 - -nagFresnelS(4) :: Float - --- 0.4205 - -nagFresnelS(5) :: Float - --- 0.4992 - -nagFresnelS(6) :: Float - --- 0.447 - -nagFresnelS(8) :: Float - --- 0.4602 - -nagFresnelS(10) :: Float - --- 0.4682 - -nagFresnelS(-1) :: Float - --- - 0.4383 - -nagFresnelS(1000) :: Float - --- 0.4997 - --- nagFresnelC : DF -> DF ; - -nagFresnelC(0) :: Float - --- 0.0 - -nagFresnelC(0.5) :: Float - --- 0.4923 - -nagFresnelC(1) :: Float - --- 0.7799 - -nagFresnelC(2) :: Float - --- 0.4883 - -nagFresnelC(4) :: Float - --- 0.4984 - -nagFresnelC(5) :: Float - --- 0.5636 - -nagFresnelC(6) :: Float - --- 0.4995 - -nagFresnelC(8) :: Float - --- 0.4998 - -nagFresnelC(10) :: Float - --- 0.4999 - -nagFresnelC(-1) :: Float - --- - 0.7799 - -nagFresnelC(1000) :: Float - --- 0.5 - --- nagEllipticIntegralRC : (DF, DF) -> DF ; - -nagEllipticIntegralRC(0.5,1) :: Float - --- 1.111 - -nagEllipticIntegralRC(1,1) :: Float - --- 1.0 - -nagEllipticIntegralRC(1.5,1) :: Float - --- 0.9312 - --- nagEllipticIntegralRD : (DF, DF, DF) -> DF ; - -nagEllipticIntegralRD(0.5,0.5,1) :: Float - --- 1.479 - -nagEllipticIntegralRD(0.5,1,1) :: Float - --- 1.211 - -nagEllipticIntegralRD(0.5,1.5,1) :: Float - --- 1.061 - -nagEllipticIntegralRD(1,1,1) :: Float - --- 1.0 - -nagEllipticIntegralRD(1,1.5,1) :: Float - --- 0.8805 - -nagEllipticIntegralRD(1.5,1.5,1) :: Float - --- 0.7775 - --- nagEllipticIntegralRF : (DF, DF, DF) -> DF ; - -nagEllipticIntegralRF(0.5,1,1.5) :: Float - --- 1.028 - -nagEllipticIntegralRF(1,1.5,2) :: Float - --- 0.826 - -nagEllipticIntegralRF(1.5,2,2.5) :: Float - --- 0.7116 - --- nagEllipticIntegralRJ : (DF, DF, DF, DF) -> DF ; - -nagEllipticIntegralRJ(0.5,0.5,0.5,2) :: Float - --- 1.118 - -nagEllipticIntegralRJ(0.5,0.5,1,2) :: Float - --- 0.9221 - -nagEllipticIntegralRJ(0.5,0.5,1.5,2) :: Float - --- 0.8115 - -nagEllipticIntegralRJ(0.5,1,1,2) :: Float - --- 0.7671 - -nagEllipticIntegralRJ(0.5,1,1.5,2) :: Float - --- 0.6784 - -nagEllipticIntegralRJ(0.5,1.5,1.5,2) :: Float - --- 0.6017 - -nagEllipticIntegralRJ(1,1,1,2) :: Float - --- 0.6438 - -nagEllipticIntegralRJ(1,1,1.5,2) :: Float - --- 0.5722 - -nagEllipticIntegralRJ(1,1.5,1.5,2) :: Float - --- 0.5101 - -nagEllipticIntegralRJ(1.5,1.5,1.5,2) :: Float - --- 0.4561 - -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>> - --- NagSpecialFunctionsInterfacePackage - --- To test: --- sed -ne '1,/^#if NeverAssertThis/d;/#endif/d;p' < nsfip.as > nsfip.input --- axiom --- )set nag host <some machine running nagd> --- )r nsfip.input - -#unassert saturn - -#include "axiom.as" - -DF ==> DoubleFloat ; -CDF ==> Complex DoubleFloat ; -MCDF ==> Matrix Complex DoubleFloat ; -INT ==> Integer ; -RSLT ==> Result ; -SMBL ==> Symbol ; -STRG ==> String ; - -<<NagSpecialFunctionsInterfacePackage>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} |