I think this maybe will work out. I might have to just go with the
generalized form as you suggest
and forget about the random aspect.
In a message dated 12/6/2008 10:05:16 A.M. Central Standard Time,
[EMAIL PROTECTED] writes:
Please use the reply-all button when responding, so that your message gets
sent to the list as well.
If that's the sort of equation you're after, than the easiest way would
probably to decide on a generalised form:
y=(2x-1)*4x
y = 4*x**2 - 4x
y=2+5(x-1)
y = 5*x - 3
y=(2x+5)+(5x-25)
y = 10*x**2 + 75*x - 125
y=((x+13)/((x-18))*(2x-1)
y = (2*x**2 - 19*x -13) / (x - 18)
Except for the last equation, they are all of the "general form" ax^2 +bx +
c.
These can be generated using tools from the random module:
(pseudo python)
equation = randint(minimum, maximum) * x ** 2 + randint(minimum,maximum) * x
+ randint(minimum,maximum)
if you want to generate equations in the form of the last one you mentioned,
it will be a bit more difficult.
You could add a random number of terms with a random power, but actually
impliementing it might be a bit harder:
import random
def generate_terms(minimum, maximum):
"generate a list of random terms for an equation of the form (a*x)**b +
... "
return [(random.randint(minimum, maximum), random.randint(-1,1)) for x
in xrange(random.randint(1, 10))]
class Line(object):
epsilon = 1e-15
def __init__(self, equation_terms):
self._equation_terms = equation_terms
def is_on_line(self, (x,y)):
calulated_y = sum((a * x) ** b for a,b in self._equation_terms)
return abs(y - calculated_y) <= self.epsilon #see message from Paul
Then, instead of picking two points, you can do:
line = Line(generate_terms(-25, 25))
then proceed as with my previous message.
getting a nice string representation won't be as easy... unless you're happy
with seeing x**-1's dotted around.
You'll need to tweak the values within the generate_terms function to get
exactly what you want.
Alternatively (and I'm probably going to get shouted at for suggesting it),
you could write something that generates random python equations, and use
some variety of eval() to get a value out of it...
Does that help?
On 5 Dec 2008, at 13:52, [EMAIL PROTECTED]
(mailto:[EMAIL PROTECTED]) wrote:
Thanks for the response. This will help me passing the points and
compairing the results.
I however still need to find something that will generate the actual linear
equations or similar equations in a
random fashion. For instance lets say the program would first generate the
actual equations.
y=(2x-1)*4x
y=2+5(x-1)
y=(2x+5)+(5x-25)
y=((x+13)/((x-18))*(2x-1)
Then I could use your program to pass through the values.
Frank Hopkins
Houston, Tx
In a message dated 12/5/2008 7:29:42 A.M. Central Standard Time,
[EMAIL PROTECTED] (mailto:[EMAIL PROTECTED]) writes:
When you say linear, I'm assuming fitting y=mx+c, and passing through
points?
The line through points (x1, y1) and (x2,y2) is
y - y1 = (y2-y1) / (x2-x1) * (x-x1)
That multiplies out to:
y = (y2-y1)/(x2-x1) * x - (y2-y1)/(x2-x1) + y1
That gives m = (y2-y1)/(x2-x1) and c = y1 - (y2-y1)/(x2-x1)
you can then create a class to represent the line:
class Line(object):
def __init__(self, (x1,y1), (x2,y2)):
"create a line passing through points (x1,y1) and (x2,y2) (inputted
as tuples)"
self.m = (y2-y1)/(x2-x1)
self.c = y1 - self.m
def is_on_line(self,(x,y)):
'Test if point represtented by an (x,y) tuple is on the line"
if self. m * x + self.c == y:
return True
else:
return False
def __str__(self):
"returns the equation of the line in the form y=mx+c. Might be
quite long if floats are involved."
print "y=%dx + %d" % (self.m, self.c)
Then all you have to do is choose a pair of points, then iterate over the
list, testing each point in turn, wash, rinse and repeat.
Does that help?
On 4 Dec 2008, at 20:28, [EMAIL PROTECTED]
(mailto:[EMAIL PROTECTED]) wrote:
I am starting out with 7 fixed reference points. From there I want a
program that can randomly
generate linear equations. After the equations are generated I would then
like to randomly insert
the 7 fixed reference points into the equations and calculate the results.
I currently have several
programs that can generate random string of words from a file that contains
a list of word but is not
much help creating random equations.
Do you know if there is such a program that can do what I am trying to
get accomplished??
Thanks
Frank Hopkins
Houston, Tx
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