def condassign(b, c, d):
"""
Returns the result of (b>0)? c : d
Use instead of if statements to force taping both c and d
expressions. Uses type(b) to decide if ad.condexp_gt() should be
called, so make sure this an ad type if you are generating a tape.
"""
if type(b) == ad.cppad_.a_float:
try:
return ad.condexp_gt(b, ad.ad(0.), c, d)
except:
# Had to catch all because could not find exception name
if type(c) != ad.cppad_.a_float:
c = ad.ad(c)
if type(d) != ad.cppad_.a_float:
d = ad.ad(d)
return ad.condexp_gt(b, ad.ad(0.), c, d)
else:
if b > 0.:
#print('a',end='')
return c
else:
#print('b',end='')
return d
def condassign(b, c, d):
"""
Returns the result of (b>0)? c : d
Use instead of if statements to force taping both c and d
expressions. Uses type(b) to decide if ad.condexp_gt() should be
called, so make sure this an ad type if you are generating a tape.
"""
if type(b) == ad.cppad_.a_float:
try:
return ad.condexp_gt(b, ad.ad(0.), c, d)
except:
# Had to catch all because could not find exception name
if type(c) != ad.cppad_.a_float:
c = ad.ad(c)
if type(d) != ad.cppad_.a_float:
d = ad.ad(d)
return ad.condexp_gt(b, ad.ad(0.), c, d)
else:
if b > 0.:
#print('a',end='')
return c
else:
#print('b',end='')
return d
def ode_function(num_step, age_local, all_local, scipy=False):
global age, incidence, remission, excess, all_cause
global susceptible, condition
if scipy == False:
N = len(age_local)
age = age_local
all_cause = all_local
susceptible = pycppad.ad(numpy.zeros(N))
condition = pycppad.ad(numpy.zeros(N))
incidence = .00 * numpy.ones(N)
remission = .00 * numpy.ones(N)
excess = .00 * numpy.ones(N)
s0 = 0.
c0 = 0.
x = numpy.hstack((incidence, remission, excess, s0, c0))
x = pycppad.independent(x)
incidence = x[(0 * N):(1 * N)]
remission = x[(1 * N):(2 * N)]
excess = x[(2 * N):(3 * N)]
s0 = x[3 * N]
c0 = x[3 * N + 1]
ode_integrate(N, num_step, s0, c0)
y = numpy.hstack((susceptible, condition))
fun = pycppad.adfun(x, y)
return fun
if scipy == True:
res = integrate.solve_ivp(fun=odefun,
t_span=(age[0], age[-1]),
y0=[s0, c0],
method='RK45',
t_eval=age)
print(res.message)
s = res.y[0, :]
c = res.y[1, :]
return s, c
def safe_exp(x):
"""
Same as exp() except when x is greater than threshold. It has
continuous derivatives.
"""
threshold = 50.
c = np.exp(x)
d = np.exp(threshold) * (x - threshold + 1.)
if type(x) == ad.cppad_.a_float:
return ad.condexp_lt(x, ad.ad(threshold), c, d)
else:
if x < threshold:
return c
else:
return d
def safe_exp(x):
"""
Same as exp() except when x is greater than threshold. It has
continuous derivatives.
"""
threshold = 50.
c = np.exp(x)
d = np.exp(threshold) * (x - threshold + 1.)
if type(x) == ad.cppad_.a_float:
return ad.condexp_lt(x, ad.ad(threshold), c, d)
else:
if x < threshold:
return c
else:
return d
def ode_function(num_step, age_local, all_local):
global age, incidence, remission, excess, all_cause
global susceptible, condition
N = len(age_local)
age = age_local
all_cause = all_local
susceptible = pycppad.ad(numpy.zeros(N))
condition = pycppad.ad(numpy.zeros(N))
incidence = .00 * numpy.ones(N)
remission = .00 * numpy.ones(N)
excess = .00 * numpy.ones(N)
s0 = 0.
c0 = 0.
x = numpy.hstack((incidence, remission, excess, s0, c0))
x = pycppad.independent(x)
incidence = x[(0 * N):(1 * N)]
remission = x[(1 * N):(2 * N)]
excess = x[(2 * N):(3 * N)]
s0 = x[3 * N]
c0 = x[3 * N + 1]
ode_integrate(N, num_step, s0, c0)
y = numpy.hstack((susceptible, condition))
fun = pycppad.adfun(x, y)
return fun
def ode_function(num_step, age_local, all_local) : global age, incidence, remission, excess, all_cause global susceptible, condition N = len( age_local ) age = age_local all_cause = all_local susceptible = pycppad.ad( numpy.zeros(N) ) condition = pycppad.ad( numpy.zeros(N) ) incidence = .00 * numpy.ones(N) remission = .00 * numpy.ones(N) excess = .00 * numpy.ones(N) s0 = 0. c0 = 0. x = numpy.hstack( (incidence, remission, excess, s0, c0) ) x = pycppad.independent( x ) incidence = x[(0*N):(1*N)] remission = x[(1*N):(2*N)] excess = x[(2*N):(3*N)] s0 = x[3*N] c0 = x[3*N+1] ode_integrate(N, num_step, s0, c0) y = numpy.hstack( (susceptible, condition) ) fun = pycppad.adfun(x, y) return fun
def oscillator(self, x):
'''
The actual van der pol oscillator differential equations
'''
lx = x.size
l = lx/2
res = pcad.ad(np.zeros(np.shape(x)))
'''position calc \dot{x} = y '''
res[l:] = x[:l]
xa = np.tile(x[l:],(l,1))
dx = xa - xa.transpose()
'''velocity calc \dot{y} = m*(1-x^2)*y-w^2*x+A.dx'''
res[:l] = (self.mu*(1-x[l:]*x[l:])*x[:l]-self.w*self.w*x[l:] +
np.dot(self.A,dx.T).diagonal())
return res
