fonction in python

[aliassaf]

Hello,

If we write = x^2 and if I give to the program the values of x, it will
going to calculate the values of y, and also for x.

But it is possible ? that is if I give to the program the values of X and Y,
it will indicate to me the relation between the two variables, in the other
hand if I look to the program x=2 y=4, x=3 y=9 ect... it is going to show me
that f (t)!!!

Thanks

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[Georg Brandl]

aliassaf wrote:

Hello,

If we write = x^2 and if I give to the program the values of x, it will
going to calculate the values of y, and also for x.

But it is possible ? that is if I give to the program the values of X and Y,
it will indicate to me the relation between the two variables, in the other
hand if I look to the program x=2 y=4, x=3 y=9 ect... it is going to show me
that f (t)!!!

That is not possible at all. There are too many possible functions mapping
2 to 4, 3 to 9 etc.

You can, however, create a list of candidate functions and check your input
pairs (x,y) against each of those functions to see if any of them matches.

Short, unoptimized example:

functions = [
lambda x: x,
lambda x: x+1,
lambda x: x*x,
lambda x: x**3,
]

input = [(1,1), (2,2)]

for function in functions:
for x,y in input:
if function(x) != y:
break
else:
print "function", function, "matches"

Georg

[Steven D'Aprano]

On Tue, 04 Jul 2006 03:06:37 -0700, aliassaf wrote:

>
Hello,

If we write = x^2 and if I give to the program the values of x, it will
going to calculate the values of y, and also for x.

But it is possible ? that is if I give to the program the values of X and Y,
it will indicate to me the relation between the two variables, in the other
hand if I look to the program x=2 y=4, x=3 y=9 ect... it is going to show me
that f (t)!!!

You are asking for curve-fitting. There is a HUGE amount of work on
curve-fitting in computer science and statistics.

Generally, you start with some data points (x, y). You generally have some
idea of what sort of function you expect -- is it a straight line? A
curve? What sort of curve? A polynomial, an exponential, a sine curve, a
cubic spline, a Bezier curve?

You might like to google on "least squares curve fitting" and "linear
regression". That's just two methods out of many.

Some curve-fitting methods also estimate the error between the predicted
curve and the data points; you could then try all of the methods and pick
the one with the least error.

--
Steven.

[Grant Edwards]

On 2006-07-04, aliassaf <as*****@ensiet a.frwrote:

But it is possible ? that is if I give to the program the values of X and Y,
it will indicate to me the relation between the two variables, in the other
hand if I look to the program x=2 y=4, x=3 y=9 ect... it is going to show me
that f (t)!!!

Sort of. There are a number of curve-fitting modules available
for Python as part of packages like ScyPy http://www.scipy.org/
and Scientific Python http://sourcesup.cru.fr/projects/scientific-py/

You generally have to provide the fitter with a function
"template" for which it can find the coefficients. For
example, you tell the fitter that you want a polynomial of the
form f(y) = Ax^2 + Bx + C, and the fitter will find the values
of A, B, C that best fit the data.

There are also commercial products that have lists of hundreds
of "templates" and will crunch through thme to find the ones
that provide the best fits.

--
Grant Edwards
gr****@visi.com

[mensanator]

aliassaf wrote:

Hello,

If we write = x^2 and if I give to the program the values of x, it will
going to calculate the values of y, and also for x.

But it is possible ? that is if I give to the program the values of X and Y,
it will indicate to me the relation between the two variables, in the other
hand if I look to the program x=2 y=4, x=3 y=9 ect... it is going to show me
that f (t)!!!

You can use the GMPY module to determine square & power relationships:

>>import gmpy
for n in range(20):

print n,
if gmpy.is_square( n):
print True,
else:
print False,
if gmpy.is_power(n ):
print True
else:
print False
0 True True
1 True True
2 False False
3 False False
4 True True
5 False False
6 False False
7 False False
8 False True
9 True True
10 False False
11 False False
12 False False
13 False False
14 False False
15 False False
16 True True
17 False False
18 False False
19 False False

9 is both a power and a square whereas 8 is a power but not a square.

>
Thanks

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[Duncan Smith]

Steven D'Aprano wrote:

On Tue, 04 Jul 2006 03:06:37 -0700, aliassaf wrote:

>>Hello,

If we write = x^2 and if I give to the program the values of x, it will
going to calculate the values of y, and also for x.

But it is possible ? that is if I give to the program the values of X and Y,
it will indicate to me the relation between the two variables, in the other
hand if I look to the program x=2 y=4, x=3 y=9 ect... it is going to show me
that f (t)!!!

You are asking for curve-fitting. There is a HUGE amount of work on
curve-fitting in computer science and statistics.

Generally, you start with some data points (x, y). You generally have some
idea of what sort of function you expect -- is it a straight line? A
curve? What sort of curve? A polynomial, an exponential, a sine curve, a
cubic spline, a Bezier curve?

You might like to google on "least squares curve fitting" and "linear
regression". That's just two methods out of many.

Some curve-fitting methods also estimate the error between the predicted
curve and the data points; you could then try all of the methods and pick
the one with the least error.

The problem being that complex enough models will fit the data
arbitrarily closely (i.e. over-fit). The OP should take into account
any prior expectations over the type of function (as you indicate) and
apply Occam's razor (find a relatively simple model that gives a
reasonable fit to the data).

Duncan

[John Machin]

On 4/07/2006 8:06 PM, aliassaf wrote:

Hello,

If we write = x^2 and if I give to the program the values of x, it will
going to calculate the values of y, and also for x.

But it is possible ? that is if I give to the program the values of X and Y,
it will indicate to me the relation between the two variables, in the other
hand if I look to the program x=2 y=4, x=3 y=9 ect... it is going to show me
that f (t)!!!

Please pardon me for introducing Python-related subject matter into a
thread devoted to curve-fitting :-)

Consider the following:

|>[x ^ 2 for x in range(10)]
[2, 3, 0, 1, 6, 7, 4, 5, 10, 11]

Not what you wanted? Try this:

|>[x ** 2 for x in range(10)]
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

Cheers,
John