# [SciPy-User] [SciPy-user] How to find the intersections between two lines

alexander baker baker.alexander@gmail....
Fri Apr 9 06:15:08 CDT 2010

```bit rushed but seems to do the trick!

Alex

import numpy as np
from scipy import interpolate
from scipy import optimize
import pylab

x = np.linspace(0,10,20)
y = np.random.random(20)*10
f = interpolate.interp1d(x,y,kind=5)
xx = np.linspace(0,10,100)
pylab.plot(xx,f(xx),'r-',x,x,'b-')

g = [(s,f(s)-s) for s in xx]
h = np.array([(i,k,l) for i, (k,l) in enumerate(g)])
for i,j in enumerate(h):
if i < 98:
if (h[i][2] > 0 and h[i+1][2] < 0) or (h[i][2] < 0 and
h[i+1][2] > 0):
print optimize.brentq(lambda x: f(x)-x, h[i][1],
h[i+1][1])

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--
All science is either physics or stamp collecting.

On 9 April 2010 08:23, seasoul <bioseasoul@gmail.com> wrote:

>
> A nice idea. Thank you Charles. I will give it a try.
>
> Charles R Harris wrote:
> >
> > On Thu, Apr 8, 2010 at 10:15 PM, seasoul <bioseasoul@gmail.com> wrote:
> >
> >>
> >> This is my first post in the mailing list.
> >> I want to find the intersections between two lines. One line is an
> >> arbitrary straight line, the other is a fitting line created by a
> >> interpolation procedure.
> >> Below is a simple code:
> >>
> >>
> >> x = linspace(0,10,20)
> >> y = rand(20)*10
> >> plt.plot(x,y,'o')
> >> f = interpolate.interp1d(x,y,kind=5)
> >> xx = linspace(0,10,100)
> >> yy = f(xx)
> >> plt.plot(xx,yy,'r-')
> >> y2 = x
> >> plt.plot(x,y2,'b-')
> >> def func(x):
> >>    out = [x[1]-x[0]]
> >>    out.append(x[1]-f(x[0]))
> >>    return out
> >> fsolve(func,[1,1])
> >>
> >> The fitting line is a polynomial curve, the straight line is y=x. This
> >> function can only find one of the intersection points,not all.
> >>
> >>
> >
> > This is spline interpolation, not polynomial. So I think you are stuck
> > with
> > sampling the difference of the two curves on a grid, finding adjacent
> > pairs
> > of sample points at which the function has opposite sign, and then
> calling
> > one of the 1d zero finders, brentq for instance.
> >
> > Chuck
> >
> > _______________________________________________
> > SciPy-User mailing list
> > SciPy-User@scipy.org
> > http://mail.scipy.org/mailman/listinfo/scipy-user
> >
> >
>
> --
> View this message in context:
> http://old.nabble.com/How-to-find-the-intersections-between-two-lines-tp28187442p28188548.html
> Sent from the Scipy-User mailing list archive at Nabble.com.
>
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