Re: Matheval (was: Dos32Lib, Win32Lib)
On 2000-06-02 EUPHORIA at LISTSERV.MUOHIO.EDU said:
EU>By normal, I really mean mathematical notation as you would write
EU>it with paper and pencil. Of course, some things aren't really
EU>possible, especially in a text environment. Eventually, it may
EU>support some scripting to allow actual algorithms, but no Eu or C
EU>code or anything like that.
Sounds ... different.
EU>Yeah, Matheval was never really intended for speed/computation
EU>intensive applications. My real goal is the symbolic manipulation.
I'd say that you going to require a database for this .
EU>Unfortunately, the project has been shelved for a while...ran into
EU>a brick wall, where the only solution I see is a dramatic slash and
EU>burn and a new approach to my pattern recognition/substitution
EU>algorithms. Maybe I'll bring it back out and polish up the parts
EU>that do seem to work.
If I were to liken this to kayaking , I'd say that I go back to a
stream that can be navigated when the rapids appear to be too daunting.
Then return to the previous for yet another attempt ; if at all
possible.
EU>There are several quirks about the parser and naming
EU>conventions (eg, can't have a var begin with the same
EU>characters as an existing function), but it
eu> seems to work fast enough. You would only
EU>need to parse an expression once, and then you'd have the
EU>expression in matheval format, able to pass it directly to
EU>the evaluation routines.
EU>> Are right brackets automatically appended now , or are these
EU>>seen as being unnecessary clutter.
EU>I'm not sure what you mean here.
when I entered an expression into eval.e , it returned something like
this for the expression sin(x*(a*x+ , without the closing right
bracketts.
EU>> I'm a little unfamiliar with recursion , hence my tendency
EU>> to bury my
EU>> head in the sand , a bit more familarity might put me at ease
EU>>with this approach.
EU>Basically, I tried to take each operation, and make sure that it's
EU>function 'knows' how to handle any other data type (constant,
EU>matrix, etc) and return a proper value. If an argument for the
EU>operation is some other function (or a variable), the appropriate
EU>routine is simply called. I tend to visualize this as 'diving
EU>into' the nested sequences, and in effect, evaluating the most
EU>deeply nested sequences first, and passing the value 'up'. It
EU>allows pretty easy addition of new operations.
Getting into that 'mind set' , again , seems a little foreign to me ;
and certainly to most persons.
EU>> F(x1,x2,x3,....,xn) = type functions are readily
EU>> available with my
EU>> approach , is this true of yours also ?
EU>This is easy to do, however, it works a little differently.
EU>Actually, there are several ways to go about it. One would be to
EU>assign the function to variable F:
EU>F = Parse("x1+x2+x3+...+xn") -- we'd currently have to rename the
EU>x's without numbers
EU>SetVar("F", F )
EU>SetVar("x1",x1) -- where xi is either an atom or any matheval
EU>sequence SetVar("x2",x2)
EU>SetVar("x3",x3)
EU>..
EU>..
EU>SetVar("xn",xn)
EU>F = Evaluate(F)
EU>If you take a look at the regression example I posted with matheval,
EU>I take a slightly different approach, by defining constants which
EU>hold the functions. Granted, these aren't parsed, but written
EU>directly in matheval sequence format.
I'm having some difficulty locating matheval
EU>-- Begin code
EU>include matheval.e
EU>include G1.e -- your graphics include per parr1.txt -- u1.e ?
EU>sequence F, f
EU>F = Parse("x^2+X+1")
EU>for x = -5 to 5 by .5 -- change .5 to whatever interval you'd like
EU>SetVar("x",x)
EU>f = Evaluate( F )
EU>GraphPoint(x, f[2][1]) -- since f = {CONSTANT, {F(x)}, {} }
EU>-- or whatever your graphics routine might be...
EU>end for
EU>-- end code
EU>> By collapsing the token I assume you mean making a
EU>>corresponding sequence , to the equation , that can be more
EU>>quickly evaluated ; within
EU>> a loop ; perhaps even an assembly language loop. To date I
EU>>haven't bothered with this possibility as once the function has
EU>> been defined ,
EU>> within the editable include file I can generate an output
EU>> sequence of
EU>> values from an input sequence of values in the usual manner
EU>> with just
EU>> a few lines of euphoria code.
EU>More or less. Everything gets mapped to a sequence. The parser
EU>makes two passes (not counting recursive parentheses handling).
EU>The first pass identifies functions, variables and constants, and
EU>puts them into sequences, but most things require additional
EU>arguments. In order to properly parse things, I have to take into
EU>account the proper order of precendence (ie, + vs *). By
EU>collapsing, I'm really talking about shoving adjacent sequences
EU>into each other to fill out required arguments:
EU>"1+1" =>
EU>{ {CONSTANT, {1},{}}, {ADD,{},{}}, {CONSTANT,{1},{} } =>
EU>{ {ADD, {CONSTANT, {1},{}},{CONSTANT, {1},{}} } }
Sounds like sequences are useful in this aspect.
EU>> Hence , understandably , your reluctance to be overly
EU>> public with your
EU>> code.
EU>Actually, I'm fine with this stuff being public. I just don't get
EU>to work on it much, so there's not a lot of progress. And I'd be
EU>happy if someone else could make it better.
So where can I find the most recent version , I was unable to locate
this on d.cunys website , certainly not within the more recent versions of
dos32lib.* or win32lib.* .
EU>> With the type of
EU>> convoluted code
EU>> you might be involved with I'd be even more reluctant to
EU>> post. Parsers ,
EU>> especially small functional ones can appear to be real mind
EU>>benders. Some of the literature surrounding these , as you're
EU>> probably aware ,
EU>> is pretty daunting until you break through some unknown barrier
EU>>of comprehension. To some extent I managed this , though not
EU>> at the basic
EU>> level of understanding I'd prefer.
EU>I think the biggest reason I made my own was that I didn't really
EU>understand the other code/literature out there, so I came up with a
EU>solution that made sense to me. I'm just happy that this was one
EU>occasion where it actually worked. :)
Similarly here , though I'd very much prefer a clear and concise
text about this ; from somewhere . One that a developer might keep in
their library , alongside info' about assembly and C/C++ coding ,
standard graphics routines , unlimited precision etc .Written in , or
understandable in , any type of language.
EU>> The sequence that contains the, syntax corrected , expression
EU>> might be manipulated symbolically , I haven't really looked
EU>> into this , as
EU>> potentially , this involves more complexity than attempting
EU>> to parse the
EU>> sequence using the basic concepts.
EU>Definitely more complexity. :) But a really interesting problem.
EU>It does very simple things, so far, and if I can get the pattern
EU>match/substitution working, it should really improve the
EU>functionality (using things like trig id's and a table of
EU>integration). I can imagine using lot's of neat techniques, like
EU>completing the square, or the quadratic equation.
Polynomial roots , via newtons' method are possible , especially if
you have an equation/expression that has a few dominant roots.
EU>> Anyway , I should get some text , if I don't have an
EU>> unexpected brainwave first .
EU>> hint:
EU>> Associative sequences.
EU>This is basically the approach that I'm taking. As an aside, I use
EU>an associated sequence to keep track of variables.
They seem to be adding or improving upon the associative method ,
at the moment. Basic notions with diverse applications.
EU>> As this type of software might not exist , except for the
EU>>features available through euphoria , I don't mind discussing
EU>>this at all , probably I should make all of the code available .
EU>>A bit of scrutiny from more competent software developers, than
EU>>I, might lead off into new directions.
EU>> I suppose I could send , in plain text format , the code
EU>> to this list
EU>> server ; I think it's about 120k . I shall do this only if
EU>> requested.
EU>Sending to the list might not be a good idea, but I'd appreciate if
EU>you could send it to me:
EU>matthewlewis at hotmail.com
As you should be aware now , I uploaded this ; via email to you ; a few
days ago. I understand , you might have numerous other concerns at this
time , therefore you haven't evaluated this.
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