Stick (line segments) percolation - graph theory?

asked 2013-08-23 11:37:20 -0600

mresimulator gravatar image

updated 2013-08-23 11:50:08 -0600

Hi experts!

I wrote an algorithm for study stick percolation (i.e.: networks between line segments that intersect between them). In my algorithm N sticks (line segments) are created inside a rectanglar box of sides 'b' and 'h' and then, one by one, the algorithm explores the intersection between all line segments. This is a Monte Carlo simulation, so the 'experiment' is executed many times (no less than 100 times). Writen like that, very much RAM is consumed:

array_x1=uniform.rvs(loc=-b/2, scale=b, size=N)  
array_y1=uniform.rvs(loc=-h/2, scale=h, size=N)
array_x2=uniform.rvs(loc=-b/2, scale=b, size=N)  
array_y2=uniform.rvs(loc=-h/2, scale=h, size=N)  

M = np.zeros([N,N])  

for u in xrange(100):  ----> This '100' is the number of experiments.
    for j in xrange(N):
        if j>0:
            x_A1B1 = array_x2[j]-array_x1[j]
            y_A1B1 = array_y2[j]-array_y1[j]
            x_A1A2 = array_x1[0:j]-array_x1[j]
            y_A1A2 = array_y1[0:j]-array_y1[j]      
            x_A2A1 = -1*x_A1A2
            y_A2A1 = -1*y_A1A2
            x_A2B2 = array_x2[0:j]-array_x1[0:j]
            y_A2B2 = array_y2[0:j]-array_y1[0:j]
            x_A1B2 = array_x2[0:j]-array_x1[j]
            y_A1B2 = array_y2[0:j]-array_y1[j]
            x_A2B1 = array_x2[j]-array_x1[0:j]
            y_A2B1 = array_y2[j]-array_y1[0:j]

            p1 = x_A1B1*y_A1A2 - y_A1B1*x_A1A2
            p2 = x_A1B1*y_A1B2 - y_A1B1*x_A1B2
            p3 = x_A2B2*y_A2B1 - y_A2B2*x_A2B1
            p4 = x_A2B2*y_A2A1 - y_A2B2*x_A2A1

            condition_1=p1*p2
            condition_2=p3*p4                         

            for k in xrange (j):
                if condicion_1[k]<=0 and condicion_2[k]<=0:
                    M[j,k]=1

        if j+1<N+4:
            x_A1B1 = array_x2[j]-array_x1[j]
            y_A1B1 = array_y2[j]-array_y1[j]
            x_A1A2 = array_x1[j+1:]-array_x1[j]
            y_A1A2 = array_y1[j+1:]-array_y1[j]     
            x_A2A1 = -1*x_A1A2
            y_A2A1 = -1*y_A1A2
            x_A2B2 = array_x2[j+1:]-array_x1[j+1:]
            y_A2B2 = array_y2[j+1:]-array_y1[j+1:]
            x_A1B2 = array_x2[j+1:]-array_x1[j]
            y_A1B2 = array_y2[j+1:]-array_y1[j]
            x_A2B1 = array_x2[j]-array_x1[j+1:]
            y_A2B1 = array_y2[j]-array_y1[j+1:]

            p1 = x_A1B1*y_A1A2 - y_A1B1*x_A1A2
            p2 = x_A1B1*y_A1B2 - y_A1B1*x_A1B2
            p3 = x_A2B2*y_A2B1 - y_A2B2*x_A2B1
            p4 = x_A2B2*y_A2A1 - y_A2B2*x_A2A1

            condicion_1=p1*p2
            condicion_2=p3*p4                         

            for k in xrange (N-j-1):
                if condicion_1[k]<=0 and condicion_2[k]<=0:
                    M[j,k+j+1]=1

Here, the element Mij=1 if stick i intersect stick j and Mij=0 if not.

How can i optimize my algorithm? Graph theory is usefull in this case?

Waiting for your answers.

Thanks a lot!

Best regards

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