mathmatical expressions evaluation

[Tonino]

Hi,

I have a task of evaluating a complex series (sorta) of mathematical
expressions and getting an answer ...

I have looked at the numarray (not really suited??) and pythonica (too
simple??) and even tried using eval() ... but wondered if there were
other packages/modules that would enable me to to this a bit easier...

The formula/equations are for investment calculations (Swap Yields).
Is there a module/method that anyone can suggest ??

Many thanks
Tonino

[beliavsky@aol.com]

Re: mathmatical expressions evaluation

There is QuantLib at http://quantlib.org/ . The site says "QuantLib is
written in C++ with a clean object model, and is then exported to
different languages such as Python, Ruby, and Scheme." I have not tried
it -- if it is easily usable from Python please write back to c.l.p.

There is a Python Finance email list at
http://www.reportlab.co.uk/mailman/l...python-finance .

In calculations involving bonds one needs arrays to store payment dates
and amounts etc., for which numarray should be used instead of Python
lists, for efficiency.

[aaronwmail-usenet@yahoo.com]

Re: mathmatical expressions evaluation

> have a task of evaluating a complex series (sorta) of mathematical[color=blue]
> expressions and getting an answer ...[/color]

If we assume that you are looking for functionality and speed is
secondary,
please have a look at the technique in

http://cvs.sourceforge.net/viewcvs.py/xsdb/xsdbXML/xsdbXMLpy/functions.py?view=markup

which uses the python parser to generate a parse tree for an arbitrary
expression and then imposes its own semantics on the tree. In fact
take
a look at xsdb use guide under "Computing other derived values"

http://xsdb.sourceforge.net/guide.html

since xsdbXML implements general computations over xml inputs.
Let me know if you have any comments/questions/suggestions.
-- Aaron Watters

===
Later on we'll perspire, as we stare at the fire
And face so afraid, the bills left unpaid
Walking in a winter wonderland. --stolen from "for better or worse"

[Paul McGuire]

Re: mathmatical expressions evaluation

"Tonino" <tonino.greco@g mail.com> wrote in message
news:1103719856 .106409.190100@ z14g2000cwz.goo glegroups.com.. .[color=blue]
> Hi,
>
> I have a task of evaluating a complex series (sorta) of mathematical
> expressions and getting an answer ...
>
> I have looked at the numarray (not really suited??) and pythonica (too
> simple??) and even tried using eval() ... but wondered if there were
> other packages/modules that would enable me to to this a bit easier...
>
> The formula/equations are for investment calculations (Swap Yields).
> Is there a module/method that anyone can suggest ??
>
> Many thanks
> Tonino
>[/color]
Is it a financial analysis library you are looking for, or an expression
parser?

You will find a basic expression parser included in the examples with the
pyparsing. This parser can be easily extended to add built-in functions,
additional operators, etc. (You can download pyparsing at
http://pyparsing.sourceforge.net.)

What does one of these complex mathematical functions look like, anyway?

And I wouldn't necessarily agree with beliavsky's assertion that numarray
arrays are needed to represent payment dates and amounts, unless you were
going to implement a major banking financial system in Python. You can
easily implement payment schedules using lists, or even generators. Here's
a simple loan amortization schedule generator:

def amortizationSch edule( principal, term, rate ):
pmt = ( principal * rate * ( 1 + rate)**term ) / (( 1 + rate)**term - 1)
pmt = round(pmt,2) # people rarely pay in fractional pennies
remainingPrinci pal = principal
for pd in range(1,term+1) :
if pd < term:
pdInterest = rate * remainingPrinci pal
pdInterest = round(pdInteres t,2)
pdPmt = pmt
else:
pdInterest = 0
pdPmt = remainingPrinci pal
pdPrincipal = pdPmt - pdInterest
remainingPrinci pal -= pdPrincipal
yield pd, pdPmt, pdInterest, pdPrincipal, remainingPrinci pal

# print amortization schedule for $10,000 loan for 3 years at 6% annual
P = 10000
Y = 3
R = 6.00
for (i, pmt, int, princ, remaining) in amortizationSch edule(P, Y*12,
R/100.0/12.0):
print i, pmt, int, princ, remaining

print

def aprToEffectiveA pr(apr):
apr /= 1200.0
return round(((1+apr)* *12-1) * 100, 2)

APR = R
print "Nominal APR of %.2f%% is an effective APR of %.2f%%" % (APR,
aprToEffectiveA pr(APR) )

prints out (rather quickly, I might add):
1 304.22 50.0 254.22 9745.78
2 304.22 48.73 255.49 9490.29
3 304.22 47.45 256.77 9233.52
4 304.22 46.17 258.05 8975.47
5 304.22 44.88 259.34 8716.13
6 304.22 43.58 260.64 8455.49
7 304.22 42.28 261.94 8193.55
8 304.22 40.97 263.25 7930.3
9 304.22 39.65 264.57 7665.73
10 304.22 38.33 265.89 7399.84
11 304.22 37.0 267.22 7132.62
12 304.22 35.66 268.56 6864.06
13 304.22 34.32 269.9 6594.16
14 304.22 32.97 271.25 6322.91
15 304.22 31.61 272.61 6050.3
16 304.22 30.25 273.97 5776.33
17 304.22 28.88 275.34 5500.99
18 304.22 27.5 276.72 5224.27
19 304.22 26.12 278.1 4946.17
20 304.22 24.73 279.49 4666.68
21 304.22 23.33 280.89 4385.79
22 304.22 21.93 282.29 4103.5
23 304.22 20.52 283.7 3819.8
24 304.22 19.1 285.12 3534.68
25 304.22 17.67 286.55 3248.13
26 304.22 16.24 287.98 2960.15
27 304.22 14.8 289.42 2670.73
28 304.22 13.35 290.87 2379.86
29 304.22 11.9 292.32 2087.54
30 304.22 10.44 293.78 1793.76
31 304.22 8.97 295.25 1498.51
32 304.22 7.49 296.73 1201.78
33 304.22 6.01 298.21 903.57
34 304.22 4.52 299.7 603.87
35 304.22 3.02 301.2 302.67
36 302.67 0 302.67 0.0

Nominal APR of 6.00% is an effective APR of 6.17%


-- Paul

[John Machin]

Re: mathmatical expressions evaluation


Paul McGuire wrote:[color=blue]
> Here's
> a simple loan amortization schedule generator:
>
> def amortizationSch edule( principal, term, rate ):
> pmt = ( principal * rate * ( 1 + rate)**term ) / (( 1 +[/color]
rate)**term - 1)

Simpliciter:
pmt = principal * rate / (1 - (1 + rate)**(-term))
[color=blue]
> pmt = round(pmt,2) # people rarely pay in fractional pennies
> remainingPrinci pal = principal
> for pd in range(1,term+1) :
> if pd < term:
> pdInterest = rate * remainingPrinci pal
> pdInterest = round(pdInteres t,2)
> pdPmt = pmt
> else:[/color]

Huh? You don't charge interest in the last period? I'd like to apply
for a loan of $1B for a term of one month with monthly repayments.
[color=blue]
> pdInterest = 0
> pdPmt = remainingPrinci pal
> pdPrincipal = pdPmt - pdInterest
> remainingPrinci pal -= pdPrincipal
> yield pd, pdPmt, pdInterest, pdPrincipal, remainingPrinci pal
>[/color]

[beliavsky@aol.com]

Re: mathmatical expressions evaluation

Paul McGuire wrote:[color=blue]
>And I wouldn't necessarily agree with beliavsky's assertion that[/color]
numarray[color=blue]
>arrays are needed to represent payment dates and amounts, unless you[/color]
were[color=blue]
>going to implement a major banking financial system in Python.[/color]

Maybe arrays are not "needed", but especially for vectors of floating
point numbers, I prefer to use a Numeric array rather than a list
because

(1) array operations like sum and exp are possible, and I want z = x +
y to perform an element-wise sum rather than a concatenation of lists.
Given arrays containing a set of times, coupon amounts, and interest
rates, the value of a bond could be a calculated with a single
expression, without loops.

(2) A TypeError is raised if I do something illogical like

x = zeros(3,Float)
x[0] = "dog"

(3) Higher-dimensional arrays are better represented with Numeric or
Numarray arrays than with lists.

[Tonino]

Re: mathmatical expressions evaluation

thanks all for the info - and yes - speed is not really an issue and no
- it is not an implementation of a complete financial system - but
rather a small subset of a investment portfolio management system
developed by "another company" ...

What I am trying to achieve is to parse a formula(s) and generate a
result ...

I will look into the pyparsing suggested and maybe even leave out
numarrays for now - as it seems a bit overkill ...

The formula are a bit complex and maybe even difficult to write out
Thanks all - I will post my progress ;)

[Kent Johnson]

Re: mathmatical expressions evaluation

Tonino wrote:[color=blue]
> thanks all for the info - and yes - speed is not really an issue and no
> - it is not an implementation of a complete financial system - but
> rather a small subset of a investment portfolio management system
> developed by "another company" ...
>
> What I am trying to achieve is to parse a formula(s) and generate a
> result ...[/color]

Why do you need to parse the formulas at runtime? It sounds like they are known in advance and you
could just write functions to implement the calculations.

Kent
[color=blue]
>
> I will look into the pyparsing suggested and maybe even leave out
> numarrays for now - as it seems a bit overkill ...
>
> The formula are a bit complex and maybe even difficult to write out
> Thanks all - I will post my progress ;)
>[/color]

[Tonino]

Re: mathmatical expressions evaluation

yes - this is what I have been doing - created a set of functions to
handle the formula and they all calculate a section of the formula.
Thanks for all the help ;)
Tonino