"""
Illustration of a plot of solution paths
computed with the aid of phcpy.
"""
print 'we fix the seed for reproducibiliy ...'
from phcpy.phcpy2c import py2c_set_seed
py2c_set_seed(34234234)
print 'using the blackbox solver ...'
from phcpy.solver import solve
p = ['x^2 + y - 3;', 'x + 0.125*y^2 - 1.5;']
s = solve(p)
for sol in s:
   print sol
print 'now we redo the computation for one path ...'
print 'constructing a total degree start system ...'
from phcpy.solver import total_degree_start_system as tds
q, qsols = tds(p)
print 'number of start solutions :', len(qsols)
print 'tracking one path ...'
from phcpy.trackers import standard_double_track as track
ss = track(p,q,[qsols[0]])
print ss[0]
print 'deflate the singular solution at the end ...'
from phcpy.solver import deflate
ds = deflate(p,[ss[0]])
print ds[0]
from phcpy.trackers import initialize_standard_tracker
from phcpy.trackers import initialize_standard_solution
from phcpy.trackers import next_standard_solution
initialize_standard_tracker(p,q)
from phcpy.solutions import strsol2dict
import matplotlib.pyplot as plt
plt.ion()
fig = plt.figure()
for k in range(len(qsols)):
   if(k == 0):
      axs = fig.add_subplot(221)
   elif(k == 1):
      axs = fig.add_subplot(222)
   elif(k == 2):
      axs = fig.add_subplot(223)
   elif(k == 3):
      axs = fig.add_subplot(224)
   startsol = qsols[k]
   initialize_standard_solution(len(p),startsol)
   dictsol = strsol2dict(startsol)
   xpoints =  [dictsol['x']]
   ypoints =  [dictsol['y']]
   for k in range(30):
       ns = next_standard_solution()
       dictsol = strsol2dict(ns)
       xpoints.append(dictsol['x'])
       ypoints.append(dictsol['y'])
   xre = [point.real for point in xpoints]
   yre = [point.real for point in ypoints]
   axs.set_xlim(min(xre)-0.3, max(xre)+0.3)
   axs.set_ylim(min(yre)-0.3, max(yre)+0.3)
   dots, = axs.plot(xre,yre,'ro')
fig.canvas.draw()
ans = raw_input('hit return to exit')