def iterate(self,
fullt,
steps,
autogen_fname=None,
localdefs=None,
autogen='autogen'):
"""
Iterates over the system of equations
"""
if autogen_fname is not None:
autogen = autogen_fname
del autogen_fname
util.warn(
"parameter 'autogen_fname' is deprecated. Use 'autogen' instead."
)
# setting up the timesteps
dt = fullt / float(steps)
self.t = [dt * i for i in range(steps)]
# generates the initializator and adds the timestep
self.init_text = self.generate_init(localdefs=localdefs)
self.init_text += '\ndt = %s' % dt
#print init_text
# generates the derivatives
self.func_text = self.generate_function()
#print func_text
self.dynamic_code = self.init_text + '\n' + self.func_text
try:
fp = open('%s.py' % autogen, 'wt')
fp.write('%s\n' % self.init_text)
fp.write('%s\n' % self.func_text)
fp.close()
autogen_mod = __import__(autogen)
try:
os.remove('%s.pyc' % autogen)
except OSError:
pass # must be a read only filesystem
imp.reload(autogen_mod)
except Exception as exc:
msg = "'%s' in:\n%s\n*** dynamic code error ***\n%s" % (
exc, self.dynamic_code, exc)
util.error(msg)
# x0 has been auto generated in the initialization
self.alldata = rk4(autogen_mod.derivs, autogen_mod.x0, self.t)
for index, node in enumerate(self.nodes):
self.lazy_data[node] = [row[index] for row in self.alldata]
def iterate( self, fullt, steps, autogen_fname=None, localdefs=None, autogen='autogen' ):
"""
Iterates over the system of equations
"""
if autogen_fname is not None:
autogen = autogen_fname
del autogen_fname
util.warn("parameter 'autogen_fname' is deprecated. Use 'autogen' instead." )
# setting up the timesteps
dt = fullt/float(steps)
self.t = [ dt * i for i in range(steps) ]
# generates the initializator and adds the timestep
self.init_text = self.generate_init( localdefs=localdefs )
self.init_text += '\ndt = %s' % dt
#print init_text
# generates the derivatives
self.func_text = self.generate_function()
#print func_text
self.dynamic_code = self.init_text + '\n' + self.func_text
try:
fp = open( '%s.py' % autogen, 'wt')
fp.write( '%s\n' % self.init_text )
fp.write( '%s\n' % self.func_text )
fp.close()
autogen_mod = __import__( autogen )
try:
os.remove( '%s.pyc' % autogen )
except OSError:
pass # must be a read only filesystem
imp.reload( autogen_mod )
except Exception as exc:
msg = "'%s' in:\n%s\n*** dynamic code error ***\n%s" % ( exc, self.dynamic_code, exc )
util.error(msg)
# x0 has been auto generated in the initialization
self.alldata = rk4(autogen_mod.derivs, autogen_mod.x0, self.t)
for index, node in enumerate( self.nodes ):
self.lazy_data[node] = [ row[index] for row in self.alldata ]
def df_dt(x, t):
a = 0.1
b = 0.02
c = 0.3
d = 0.01
"""Funcion del sistema en forma canonica"""
dx = a * x[0] - b * x[0] * x[1]
dy = -c * x[1] + d * x[0] * x[1]
return np.array([dx, dy])
# initial conditions for the system
x0 = 40
y0 = 9
# vector of times
t = np.linspace(0, 200, 800)
result = py.rk4(df_dt, [x0, y0], t)
print result
plt.plot(t, result)
plt.xlabel('Tiempo')
plt.ylabel('Tamano de la poblecion')
plt.legend(('presa', 'depredador'))
plt.title('Modelo Lotka-Volterra')
plt.show()
class PldeModel( BoolModel ):
"""
This class generates python code that will be executed inside
the Runge-Kutta integrator.
"""
def __init__(self, text, mode='plde'):
# run the regular boolen engine for one step to detect syntax errors
model = BoolModel(text=text, mode='sync')
model.initialize( missing=util.randbool )
model.iterate( steps=1 )
# onto the main initialization
self.INIT_LINE = helper.init_line
self.OVERRIDE = default_override
self.DEFAULT_EQUATION = default_equation
self.EXTRA_INIT = ''
# setting up this engine
BoolModel.__init__(self, text=text, mode=mode)
self.dynamic_code = '*** not yet generated ***'
self.lazy_data = {}
@property
def data(self):
"For compatibility with the async engine"
return self.lazy_data
def initialize(self, missing=None, defaults={} ):
"Custom initializer"
BoolModel.initialize( self, missing=missing, defaults=defaults )
# will also maintain the order of insertion
self.mapper = odict.odict()
self.indexer = {}
# this will maintain the order of nodes
self.nodes = list(self.nodes)
self.nodes.sort()
for index, node in enumerate(self.nodes):
triplet = self.first[node]
self.mapper [node] = ( index, node, triplet )
self.indexer[node] = index
# a sanity check
assert self.nodes == self.mapper.keys()
def generate_init( self, localdefs ):
"""
Generates the initialization lines
"""
init = [ ]
init.extend( self.EXTRA_INIT.splitlines() )
init.append( '# dynamically generated code' )
init.append( '# abbreviations: c=concentration, d=decay, t=threshold, n=newvalue' )
init.append( '# %s' % self.mapper.values() )
for index, node, triplet in self.mapper.values():
conc, decay, tresh = boolmapper(triplet)
#assert decay > 0, 'Decay for node %s must be larger than 0 -> %s' % (node, str(triplet))
store = dict( index=index, conc=conc, decay=decay, tresh=tresh, node=node)
line = self.INIT_LINE( store )
init.append( line )
if localdefs:
init.extend( [ '# custom imports', 'import %s' % localdefs, 'reload(%s)' % localdefs, 'from %s import *' % localdefs ] )
init_text = '\n'.join( init )
return init_text
def create_equation( self, tokens ):
"""
Creates a python equation from a list of tokens.
"""
original = '#' + tokenizer.tok2line(tokens)
node = tokens[1].value
lines = [ '', original ]
line = self.OVERRIDE(node, indexer=self.indexer, tokens=tokens)
if line is None:
line = self.DEFAULT_EQUATION( tokens=tokens, indexer=self.indexer )
if isinstance(line, str):
line = [ line ]
lines.extend( [ x.strip() for x in line ] )
return lines
def generate_function(self ):
"""
Generates the function that will be used to integrate
"""
sep = ' ' * 4
indices = [ x[0] for x in self.mapper.values() ]
assign = [ 'c%d' % i for i in indices ]
retvals = [ 'n%d' % i for i in indices ]
zeros = map(lambda x: '0.0', indices )
assign = ', '.join(assign)
retvals = ', '.join(retvals)
zeros = ', '.join( zeros )
body = []
body.append( 'x0 = %s' % assign )
body.append( 'def derivs( x, t):' )
body.append( ' %s = x' % assign )
body.append( ' %s = %s' % (retvals, zeros) )
for tokens in self.update_tokens:
equation = self.create_equation( tokens )
equation = [ sep + e for e in equation ]
body.append( '\n'.join( equation) )
body.append( '' )
body.append( " return ( %s ) " % retvals )
text = '\n'.join( body )
return text
def iterate( self, fullt, steps, autogen_fname=None, localdefs=None, autogen='autogen' ):
"""
Iterates over the system of equations
"""
if autogen_fname is not None:
autogen = autogen_fname
del autogen_fname
util.warn("parameter 'autogen_fname' is deprecated. Use 'autogen' instead." )
# setting up the timesteps
dt = fullt/float(steps)
self.t = [ dt * i for i in range(steps) ]
# generates the initializator and adds the timestep
self.init_text = self.generate_init( localdefs=localdefs )
self.init_text += '\ndt = %s' % dt
#print init_text
# generates the derivatives
self.func_text = self.generate_function()
#print func_text
self.dynamic_code = self.init_text + '\n' + self.func_text
try:
fp = open( '%s.py' % autogen, 'wt')
fp.write( '%s\n' % self.init_text )
fp.write( '%s\n' % self.func_text )
fp.close()
autogen_mod = __import__( autogen )
try:
os.remove( '%s.pyc' % autogen )
except OSError:
pass # must be a read only filesystem
reload( autogen_mod )
except Exception, exc:
msg = "'%s' in:\n%s\n*** dynamic code error ***\n%s" % ( exc, self.dynamic_code, exc )
util.error(msg)
# x0 has been auto generated in the initialization
self.alldata = rk4(autogen_mod.derivs, autogen_mod.x0, self.t)
for index, node in enumerate( self.nodes ):
self.lazy_data[node] = [ row[index] for row in self.alldata ]
timeSeries = np.arange(0, 20, timeStep)
X = (10.0, 1.0)
#Ranges of a and b to test over
a_range = np.arange(0.001, 0.05, 0.001).tolist()
b_range = np.arange(0.01, 1.0, 0.01).tolist()
#Default values of a and b
a = 0.0025
b = 0.1
#Record the values of X1 and X2 at t=20 for each value in a_range
a_sens = []
for i in a_range:
a = i
Xout = pylab.rk4(simulate, X, timeSeries)
t20_values = Xout[19].tolist()
#third column will be a value. b remains default throughout
t20_values.append(i)
a_sens.append(t20_values)
a_sens = np.array(a_sens)
#Reset a to default to test sensitivity to b
a = 0.0025
b_sens = []
for i in b_range:
b = i
Xout = pylab.rk4(simulate, X, timeSeries)
#dx=px
dx=v[2]
#dx=py
dy=v[3]
return(dx, dy, dpx, dpy)
#Values to go into the rk4 function
dt=0.01
fintime=500.0
tim=np.arange(0.0, fintime, dt)
# (x,y,px,py) <- intial values
Xout1=pylab.rk4(system1, (0.02, 0.2, 0.001, 0.2), tim)
Xout2=pylab.rk4(system1, (0.01, 0.3, 0.002, 0.1), tim)
fig=plt.figure()
ax = fig.gca(projection='3d')
#Graphs taken from http://matplotlib.org/examples/mplot3d/lorenz_attractor.html
#This system has 4 dimmensions but just looking at 3 still shows different patterns between the two starting conditions.
#Oringal initial values in red, slight change in them in blue.
ax.plot(Xout1[:,0], Xout1[:,1], Xout1[:,2], '-r')
ax.plot(Xout2[:,0], Xout2[:,1], Xout2[:,2], '-b')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.set_title('System 1')
ax.legend()
#dx=px
dx = v[2]
#dx=py
dy = v[3]
return (dx, dy, dpx, dpy)
#Values to go into the rk4 function
dt = 0.01
fintime = 500.0
tim = np.arange(0.0, fintime, dt)
# (x,y,px,py) <- intial values
Xout1 = pylab.rk4(system1, (0.02, 0.2, 0.001, 0.2), tim)
Xout2 = pylab.rk4(system1, (0.01, 0.3, 0.002, 0.1), tim)
fig = plt.figure()
ax = fig.gca(projection='3d')
#Graphs taken from http://matplotlib.org/examples/mplot3d/lorenz_attractor.html
#This system has 4 dimmensions but just looking at 3 still shows different patterns between the two starting conditions.
#Oringal initial values in red, slight change in them in blue.
ax.plot(Xout1[:, 0], Xout1[:, 1], Xout1[:, 2], '-r')
ax.plot(Xout2[:, 0], Xout2[:, 1], Xout2[:, 2], '-b')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.set_title('System 1')
ax.legend()
timeSeries=np.arange(0,20, timeStep)
X = (10.0, 1.0)
#Ranges of a and b to test over
a_range=np.arange(0.001, 0.05, 0.001).tolist()
b_range=np.arange(0.01, 1.0, 0.01).tolist()
#Default values of a and b
a=0.0025
b=0.1
#Record the values of X1 and X2 at t=20 for each value in a_range
a_sens=[]
for i in a_range:
a=i
Xout=pylab.rk4(simulate, X, timeSeries)
t20_values=Xout[19].tolist()
#third column will be a value. b remains default throughout
t20_values.append(i)
a_sens.append(t20_values)
a_sens=np.array(a_sens)
#Reset a to default to test sensitivity to b
a=0.0025
b_sens=[]
for i in b_range:
b=i
