def test_deepcopy_trust_input(self):
a = tt.dscalar() # the a is for 'anonymous' (un-named).
x, s = tt.dscalars("xs")
f = function(
[
x,
In(a, value=1.0, name="a"),
In(s, value=0.0, update=s + a * x, mutable=True),
],
s + a * x,
)
f.trust_input = True
try:
g = copy.deepcopy(f)
except NotImplementedError as e:
if e[0].startswith("DebugMode is not picklable"):
return
else:
raise
assert f.trust_input is g.trust_input
f(np.asarray(2.0))
with pytest.raises(
(ValueError, AttributeError, theano.compile.debugmode.InvalidValueError)
):
f(2.0)
g(np.asarray(2.0))
with pytest.raises(
(ValueError, AttributeError, theano.compile.debugmode.InvalidValueError)
):
g(2.0)
def test_scalars(self):
try:
import theano.tensor as T
from theano import function
except:
return
# Set up variables and function
vals = [1, 2, 3, 4, 5]
f = lambda a, b, c, d, e: a + (b * c) - d**e
# Set up our objects
Cs = [ch.Ch(v) for v in vals]
C_result = f(*Cs)
# Set up Theano's equivalents
Ts = T.dscalars('T1', 'T2', 'T3', 'T4', 'T5')
TF = f(*Ts)
T_result = function(Ts, TF)
# Make sure values and derivatives are equal
self.assertEqual(C_result.r, T_result(*vals))
for k in range(len(vals)):
theano_derivative = function(Ts, T.grad(TF, Ts[k]))(*vals)
#print(C_result.dr_wrt(Cs[k]))
our_derivative = C_result.dr_wrt(Cs[k])[0, 0]
#print(theano_derivative, our_derivative)
self.assertEqual(theano_derivative, our_derivative)
def sample_gradient():
print "微分"
x, y = T.dscalars("x", "y")
z = (x+2*y)**2
# dz/dx
gx = T.grad(z, x)
fgx = theano.function([x,y], gx)
print fgx(1.0, 1.0)
# dz/dy
gy = T.grad(z, y)
fgy = theano.function([x,y], gy)
print fgy(1.0, 1.0)
# d{sigmoid(x)}/dx
x = T.dscalar("x")
sig = sigmoid(x)
dsig = T.grad(sig, x)
f = theano.function([x], dsig)
print f(0.0)
print f(1.0)
# d{sigmoid(<x,w>)}/dx
w = T.dscalar("w")
sig = sigmoid(T.dot(x,w))
dsig = T.grad(sig, x)
f = theano.function([x, w], dsig)
print f(1.0, 2.0)
print f(3.0, 4.0)
print
def test_scalars(self):
try:
import theano.tensor as T
from theano import function
except:
return
# Set up variables and function
vals = [1, 2, 3, 4, 5]
f = lambda a, b, c, d, e : a + (b * c) - d ** e
# Set up our objects
Cs = [ch.Ch(v) for v in vals]
C_result = f(*Cs)
# Set up Theano's equivalents
Ts = T.dscalars('T1', 'T2', 'T3', 'T4', 'T5')
TF = f(*Ts)
T_result = function(Ts, TF)
# Make sure values and derivatives are equal
self.assertEqual(C_result.r, T_result(*vals))
for k in range(len(vals)):
theano_derivative = function(Ts, T.grad(TF, Ts[k]))(*vals)
#print C_result.dr_wrt(Cs[k])
our_derivative = C_result.dr_wrt(Cs[k])[0,0]
#print theano_derivative, our_derivative
self.assertEqual(theano_derivative, our_derivative)
def test_examples_6(self):
from theano import Param
x, y = T.dscalars('x', 'y')
z = x + y
f = function([x, Param(y, default=1)], z)
assert f(33) == array(34.0)
assert f(33, 2) == array(35.0)
def test_examples_6(self):
from theano import Param
x, y = T.dscalars('x', 'y')
z = x + y
f = function([x, Param(y, default=1)], z)
assert f(33) == array(34.0)
assert f(33, 2) == array(35.0)
def test_examples_7(self):
from theano import Param
x, y, w = T.dscalars('x', 'y', 'w')
z = (x + y) * w
f = function([x, Param(y, default=1), Param(w, default=2, name='w_by_name')], z)
assert f(33) == array(68.0)
assert f(33, 2) == array(70.0)
assert f(33, 0, 1) == array(33.0)
assert f(33, w_by_name=1) == array(34.0)
assert f(33, w_by_name=1, y=0) == array(33.0)
def defaultValue(*arg):
x, y, w = T.dscalars('x', 'y', 'w')
z = x + y + w
f = th.function([x, th.In(y, value=1), th.In(w, value=2, name='wName')], z)
if len(arg) == 3:
print(f(arg[0], wName = arg[1], y = arg[2]))
elif len(arg) == 2:
print(f(arg[0], arg[1]))
else:
print(f(arg[0]))
def test_examples_7(self):
from theano import Param
x, y, w = T.dscalars('x', 'y', 'w')
z = (x + y) * w
f = function([x, Param(y, default=1), Param(w, default=2, name='w_by_name')], z)
assert f(33) == array(68.0)
assert f(33, 2) == array(70.0)
assert f(33, 0, 1) == array(33.0)
assert f(33, w_by_name=1) == array(34.0)
assert f(33, w_by_name=1, y=0) == array(33.0)
def main():
x = T.dmatrix('x')
# T.exp
s = 1 / (1 + T.exp(-x))
logistic = function([x], s)
# 0 is 0.5, negative < 0.5...
print(logistic([[0, 1], [-1, -2]]))
# logistic function can be expressed with hyperbolic tan term
s2 = (1 + T.tanh(x / 2)) / 2
logistic2 = function([x], s2)
print(
np.allclose(logistic([[0, 1], [-1, -2]]), logistic2([[0, 1], [-1,
-2]])))
# do more things at a time
a, b = T.dmatrices('a', 'b')
diff = a - b
abs_diff = abs(diff)
diff_squared = diff**2
f = function([a, b], [diff, abs_diff, diff_squared])
print(f([[1, 1], [1, 1]], [[0, 1], [2, 3]]))
# default value
x, y = T.dscalars('x', 'y')
z = x + y
f = function([x, In(y, value=1)], z)
print(f(33))
print(f(33, 2))
# Inputs with default values must follow inputs without default
# values (like Python’s functions). There can be multiple inputs
# with default values. These parameters can be set positionally
# or by name, as in standard Python
x, y, w = T.dscalars('x', 'y', 'w')
z = (x + y) * w
f = function([x, In(y, value=1), In(w, value=2, name='w_by_name')], z)
print(f(33))
print(f(33, 2))
print(f(33, 0, 1))
print(f(33, w_by_name=1))
print(f(33, w_by_name=1, y=0))
def test_default_values(self):
# Check that default values are restored
# when an exception occurs in interactive mode.
a, b = T.dscalars('a', 'b')
c = a + b
func = theano.function([theano.In(a, name='first'), theano.In(b, value=1, name='second')], c)
x = func(first=1)
try:
func(second=2)
except TypeError:
assert(func(first=1) == x)
def test_default_values(self):
# Check that default values are restored
# when an exception occurs in interactive mode.
a, b = T.dscalars('a', 'b')
c = a + b
func = theano.function([theano.In(a, name='first'), theano.In(b, value=1, name='second')], c)
x = func(first=1)
try:
func(second=2)
except TypeError:
assert(func(first=1) == x)
def test_default_values(self):
# Check that default values are restored
# when an exception occurs in interactive mode.
a, b = tt.dscalars("a", "b")
c = a + b
func = theano.function(
[theano.In(a, name="first"), theano.In(b, value=1, name="second")], c
)
x = func(first=1)
try:
func(second=2)
except TypeError:
assert func(first=1) == x
def __init__(self, Q, D, layers, order, D_cum_sum, N, M, non_rec):
try:
print('Trying to load model...')
with open('model_SV1.save', 'rb') as file_handle:
self.f, self.g = pickle.load(file_handle)
print('Loaded!')
return
except:
print('Failed. Creating a new model...')
print('Setting up variables...')
hyp, SIGMA_S, U, b, MU_S = T.dmatrices('hyp', 'SIGMA_S', 'U', 'b','MU_S')
y, MEAN_MAP, sn, sf = T.dvectors('y','MEAN_MAP','sn','sf')
w = T.dscalars('w')
if Q > 1:
X = T.dmatrix('X')
else:
X = T.dvector('X')
if layers > 1:
MU, SIGMA = T.dmatrices('MU', 'SIGMA')
else:
MU, SIGMA = T.dvectors('MU', 'SIGMA')
SIGMA_trf, SIGMA_S_trf = T.log(1+T.exp(SIGMA))**2, T.log(1+T.exp(SIGMA_S))**2
sf_trf, sn_trf, lengthscale_trf, lengthscale_p_trf = T.log(1 + T.exp(sf))**2, T.log(1 + T.exp(sn))**2, T.log(1 + T.exp(hyp[:,0])), T.log(1 + T.exp(hyp[:,1]))
print('Setting up model...')
LL, KL = self.get_model(w, lengthscale_trf, lengthscale_p_trf, sn_trf, sf_trf, MU_S, SIGMA_S_trf, MU, SIGMA_trf, U, b, X, y, MEAN_MAP, Q, D, D_cum_sum, layers, order, non_rec, N, M)
print('Compiling model...')
inputs = {'X': X, 'MU': MU, 'SIGMA': SIGMA, 'MU_S': MU_S, 'SIGMA_S': SIGMA_S, 'U': U, 'b': b, 'hyp': hyp, 'y': y, 'MEAN_MAP': MEAN_MAP, 'sn': sn, 'sf': sf, 'w': w}
z = 0.0 * sum([T.sum(v) for v in inputs.values()]) # solve a bug with derivative wrt inputs not in the graph
f = {'LL': LL, 'KL': KL}
self.f = {fn: theano.function(list(inputs.values()), fv+z, name=fn, on_unused_input='ignore') for fn,fv in f.items()}
g = {'LL': LL, 'KL': KL}
wrt = {'MU': MU, 'SIGMA': SIGMA, 'MU_S': MU_S, 'SIGMA_S': SIGMA_S, 'U': U, 'b': b, 'hyp': hyp, 'MEAN_MAP': MEAN_MAP, 'sn': sn, 'sf': sf, 'w': w}
self.g = {vn: {gn: theano.function(list(inputs.values()), T.grad(gv+z, vv), name='d'+gn+'_d'+vn, on_unused_input='ignore') for gn,gv in g.items()} for vn, vv in wrt.items()}
with open('model_SV1.save', 'wb') as file_handle:
print('Saving model...')
sys.setrecursionlimit(100000)
pickle.dump([self.f, self.g], file_handle, protocol=pickle.HIGHEST_PROTOCOL)
def operation_bilinear(self):
# Declare variables
te_1, te_2, ne_1, ne_2, emis_11, emis_12, emis_21, emis_22, x_in, y_in = tt.dscalars(
10)
# Output function
out_bInterp = (emis_11 * (te_2 - x_in) * (ne_2 - y_in) + emis_21 *
(x_in - te_1) * (ne_2 - y_in) + emis_12 *
(te_2 - x_in) * (y_in - ne_1) + emis_22 *
(x_in - te_1) * (y_in - ne_1)) / ((te_2 - te_1) *
(ne_2 - ne_1))
# Compile function
self.tt_interp_array = function(inputs=[
te_1, te_2, ne_1, ne_2, emis_11, emis_12, emis_21, emis_22, x_in,
y_in
],
outputs=out_bInterp)
def test_deepcopy_trust_input(self):
a = T.dscalar() # the a is for 'anonymous' (un-named).
x, s = T.dscalars('xs')
f = function([x, In(a, value=1.0, name='a'),
In(s, value=0.0, update=s + a * x, mutable=True)],
s + a * x)
f.trust_input = True
try:
g = copy.deepcopy(f)
except NotImplementedError as e:
if e[0].startswith('DebugMode is not picklable'):
return
else:
raise
self.assertTrue(f.trust_input is g.trust_input)
f(np.asarray(2.))
self.assertRaises((ValueError, AttributeError), f, 2.)
g(np.asarray(2.))
self.assertRaises((ValueError, AttributeError), g, 2.)
def test_deepcopy_trust_input(self):
a = T.dscalar() # the a is for 'anonymous' (un-named).
x, s = T.dscalars('xs')
f = function([x, In(a, value=1.0, name='a'),
In(s, value=0.0, update=s + a * x, mutable=True)],
s + a * x)
f.trust_input = True
try:
g = copy.deepcopy(f)
except NotImplementedError as e:
if e[0].startswith('DebugMode is not picklable'):
return
else:
raise
self.assertTrue(f.trust_input is g.trust_input)
f(np.asarray(2.))
self.assertRaises((ValueError, AttributeError), f, 2.)
g(np.asarray(2.))
self.assertRaises((ValueError, AttributeError), g, 2.)
def __init__(self, label_list, ion_list):
# Inherit Emission flux model
print('\n- Compiling theano flux equations')
EmissionFluxModel.__init__(self, label_list, ion_list)
# Loop through all the observed lines and assign a flux equation
self.declare_emission_flux_functions(label_list, ion_list)
# Compile the theano functions for all the input emission lines
for label, func in self.emFluxEqDict.items():
func_params = tt.dscalars(self.emFluxParamDict[label])
self.emFluxEqDict[label] = function(inputs=func_params,
outputs=func(*func_params),
on_unused_input='ignore')
# Assign function dictionary with flexible arguments
self.assign_flux_eqtt()
print('-- done\n')
return
def test():
# multiple inputs, multiple outputs
a, b = T.dmatrices('a', 'b')
diff = a - b
abs_diff = T.abs_(diff)
sqr_diff = diff ** 2
f = function([a, b], [diff, abs_diff, sqr_diff])
h, i, j = f([[0, 1], [2, 3]], [[4, 5], [6, 7]])
# default value for function arguments
a, b = T.dscalars('a', 'b')
z = a + b
f = function([a, Param(b, default=1)], z)
print f(1, b=2)
print f(1)
print f(1, 2)
# shared variable
state = shared(0)
inc = T.lscalar('inc') # state is int64 by default
accumulator = function([inc], state, updates=[(state, state + inc)])
print accumulator(300)
print state.get_value()
def brachistochrone_functional():
# define all symbols
lx, ly = T.dscalars('lx', 'ly')
fseq = T.dvector('fseq')
N = fseq.size + 1
delta_x = lx / N
iseq = T.arange(N-1)
# functional term
functional_ithterm = lambda i: T.switch(T.eq(i, 0),
T.sqrt(0.5*(delta_x**2+(fseq[0]-ly)**2)/(ly-0.5*(fseq[0]+ly))),
T.sqrt(0.5*(delta_x**2+(fseq[i]-fseq[i-1])**2)/(ly-0.5*(fseq[i]+fseq[i-1])))
)
# defining the functions
functional_parts, _ = theano.map(fn=lambda k: functional_ithterm(k), sequences=[iseq])
functional = functional_parts.sum() + T.sqrt(0.5*(delta_x**2+(0-fseq[N-2])**2)/(ly-0.5*(0+fseq[N-2])))
gfunc = T.grad(functional, fseq)
# compile the functions
time_fcn = theano.function(inputs=[fseq, lx, ly], outputs=functional)
grad_time_fcn = theano.function(inputs=[fseq, lx, ly], outputs=gfunc)
return time_fcn, grad_time_fcn
from time import clock
from numpy import ones
from theano import Mode
from theano import function
from theano.tensor import dscalars
from theano.tensor import dmatrices
from theano.tensor import lt
from theano.tensor import mean
from theano.tensor import switch
from theano.ifelse import ifelse
a_dscalar, b_dscalar = dscalars('a', 'b')
x_dmatrix, y_dmatrix = dmatrices('x', 'y')
z_switch_dmatrix = switch(lt(a_dscalar, b_dscalar), mean(x_dmatrix), mean(y_dmatrix))
z_ifelse_dmatrix = ifelse(lt(a_dscalar, b_dscalar), mean(x_dmatrix), mean(y_dmatrix))
# Both ops build a condition over symbolic variables. IfElse takes a boolean condition and two variables as inputs.
# Switch evaluates both output variables, ifelse is lazy and only evaluates one variable with respect to the condition.
# Unless linker='vm' or linker='cvm' are used, ifelse will compute both variables and take the same computation time as switch.
f_switch = function([a_dscalar, b_dscalar, x_dmatrix, y_dmatrix], z_switch_dmatrix, mode=Mode(linker='vm'))
f_ifelse = function([a_dscalar, b_dscalar, x_dmatrix, y_dmatrix], z_ifelse_dmatrix, mode=Mode(linker='vm'))
var1 = 0.
var2 = 1.
big_mat1 = ones((10000, 1000))
big_mat2 = ones((10000, 1000))
def get_compiled_Hkep_Hpert_full():
# resonance j and k
j,k = T.lscalars('jk')
s = (j-k) / k
# Planet masses: m1,m2
m1,m2 = T.dscalars(2)
Mstar = 1
eta0 = Mstar
eta1 = eta0+m1
eta2 =eta1+m2
mtilde1 = m1 * (eta0/eta1)
Mtilde1 = Mstar * (eta1/eta0)
mtilde2 = m2 * (eta1/eta2)
Mtilde2 = Mstar * (eta2/eta1)
eps = m1 * m2 / (mtilde1 + mtilde2) / Mstar
beta1 = mtilde1 / (mtilde1 + mtilde2)
beta2 = mtilde2 / (mtilde1 + mtilde2)
gamma = mtilde2/mtilde1
# Dynamical variables:
dyvars = T.vector()
Q,sigma1, sigma2, I1, I2, amd = [dyvars[i] for i in range(6)]
# Set lambda2=0
l2 = T.constant(0.)
l1 = -1 * k * Q
w1 = (1+s) * l2 - s * l1 - sigma1
w2 = (1+s) * l2 - s * l1 - sigma2
Gamma1 = I1
Gamma2 = I2
# Resonant semi-major axis ratio
alpha_res = ((j-k)/j)**(2/3) * ((Mstar + m1) / (Mstar+m2))**(1/3)
P0 = k * ( beta2 - beta1 * T.sqrt(alpha_res) ) / 2
P = P0 - k * (s+1/2) * amd
Ltot = beta1 * T.sqrt(alpha_res) + beta2 - amd
L1 = Ltot/2 - P / k - s * (I1 + I2)
L2 = Ltot/2 + P / k + (1 + s) * (I1 + I2)
a1 = (L1 / beta1 )**2 * eta0 / eta1
e1 = T.sqrt(1-(1-(Gamma1 / L1))**2)
a2 = (L2 / beta2 )**2 * eta1 / eta2
e2 = T.sqrt(1-(1-(Gamma2 / L2))**2)
Hkep = - eta1 * beta1 / (2 * a1) / eta0 - eta2 * beta2 / (2 * a2) / eta1
alpha = a1 / a2
ko = KeplerOp()
M1 = l1 - w1
M2 = l2 - w2
sinf1,cosf1 = ko( M1, e1 + T.zeros_like(M1) )
sinf2,cosf2 = ko( M2, e2 + T.zeros_like(M2) )
R = calc_DisturbingFunction_with_sinf_cosf(alpha,e1,e2,w1,w2,sinf1,cosf1,sinf2,cosf2)
Hpert = -eps * R / a2
omega_syn = T.sqrt(eta2/eta1)/a2**1.5 - T.sqrt(eta1/eta0) / a1**1.5
gradHpert = T.grad(Hpert,wrt=dyvars)
gradHkep = T.grad(Hkep,wrt=dyvars)
grad_omega_syn = T.grad(omega_syn,wrt=dyvars)
extra_ins = [m1,m2,j,k]
ins = [dyvars] + extra_ins
# Scalars
omega_syn_fn = theano.function(
inputs=ins,
outputs=omega_syn,
givens=None,
on_unused_input='ignore'
)
Hpert_fn = theano.function(
inputs=ins,
outputs=Hpert,
givens=None,
on_unused_input='ignore'
)
Hkep_fn = theano.function(
inputs=ins,
outputs=Hkep,
givens=None,
on_unused_input='ignore'
)
# gradients
grad_omega_syn_fn = theano.function(
inputs=ins,
outputs=grad_omega_syn,
givens=None,
on_unused_input='ignore'
)
gradHpert_fn = theano.function(
inputs=ins,
outputs=gradHpert,
givens=None,
on_unused_input='ignore'
)
gradHkep_fn = theano.function(
inputs=ins,
outputs=gradHkep,
givens=None,
on_unused_input='ignore'
)
return omega_syn_fn,Hkep_fn,Hpert_fn,grad_omega_syn_fn,gradHkep_fn,gradHpert_fn
'''
Executing multiple functions
'''
a,b = T.dmatrices('a','b')
diff = a-b
abs_diff = abs(a-b)
diff_sq = diff**2
mult = function([a,b],[diff,abs_diff,diff_sq])
print mult([[0,1],[1,2]],[[-1,2],[5,7]])
#print pp(diff)
#print pp(abs_diff)
'''
Setting a default value for an argument
So, if arg not give, take default value; else take the given value
'''
x, y = T.dscalars("x","y")
z = x+y
add = function([x,Param(y,default=1)],z)
print add(33.0)
print add(2,6)
'''
Setting names to parameters
'''
x,y,w = T.dscalars("x","y","w")
z = (x+y)*w
add_par = function([x,Param(y,default=1),Param(w,default=2,name="debalu")],z)
print add_par(33)
print add_par(33,6,debalu=5)
def _get_compiled_theano_functions(N_QUAD_PTS):
# Planet masses: m1,m2
m1, m2 = T.dscalars(2)
mstar = 1
mu1 = m1 * mstar / (mstar + m1)
mu2 = m2 * mstar / (mstar + m2)
Mstar1 = mstar + m1
Mstar2 = mstar + m2
beta1 = mu1 * T.sqrt(Mstar1 / mstar) / (mu1 + mu2)
beta2 = mu2 * T.sqrt(Mstar2 / mstar) / (mu1 + mu2)
j, k = T.lscalars('jk')
s = (j - k) / k
# Angle variable for averaging over
psi = T.dvector()
# Quadrature weights
quad_weights = T.dvector('w')
# Dynamical variables:
Ndof = 3
Nconst = 1
dyvars = T.vector()
y1, y2, y_inc, x1, x2, x_inc, amd = [
dyvars[i] for i in range(2 * Ndof + Nconst)
]
a20 = T.constant(1.)
a10 = ((j - k) / j)**(2 / 3) * (Mstar1 / Mstar2)**(1 / 3)
L10 = beta1 * T.sqrt(a10)
L20 = beta2 * T.sqrt(a20)
Ltot = L10 + L20
f = L10 / L20
L2res = (Ltot + amd) / (1 + f)
Psi = -k * (s * L2res + (1 + s) * f * L2res)
###
# actions
###
I1 = 0.5 * (x1 * x1 + y1 * y1)
I2 = 0.5 * (x2 * x2 + y2 * y2)
Phi = 0.5 * (x_inc * x_inc + y_inc * y_inc)
L1 = -s * Ltot - Psi / k - s * (I1 + I2 + Phi)
L2 = (1 + s) * Ltot + Psi / k + (1 + s) * (I1 + I2 + Phi)
# Set lambda2=0
l2 = T.constant(0.)
l1 = -1 * k * psi
theta_res = (1 + s) * l2 - s * l1
cos_theta_res = T.cos(theta_res)
sin_theta_res = T.sin(theta_res)
kappa1 = x1 * cos_theta_res + y1 * sin_theta_res
eta1 = y1 * cos_theta_res - x1 * sin_theta_res
kappa2 = x2 * cos_theta_res + y2 * sin_theta_res
eta2 = y2 * cos_theta_res - x2 * sin_theta_res
sigma = x_inc * cos_theta_res + y_inc * sin_theta_res
rho = y_inc * cos_theta_res - x_inc * sin_theta_res
# y = (sigma-i*rho)/sqrt(2)
# = sqrt(Phi) * exp[i (Omega1+Omega2) / 2]
# Malige+ 2002, Eqs 20 and 21
r2byr1 = (L2 - L1 - I2 + I1) / Ltot
sigma1 = rho * T.sqrt(1 + r2byr1) / T.sqrt(2)
sigma2 = -rho * T.sqrt(1 - r2byr1) / T.sqrt(2)
rho1 = -sigma * T.sqrt(1 + r2byr1) / T.sqrt(2)
rho2 = sigma * T.sqrt(1 - r2byr1) / T.sqrt(2)
Xre1 = kappa1 / T.sqrt(L1)
Xim1 = -eta1 / T.sqrt(L1)
Yre1 = 0.5 * sigma1 / T.sqrt(L1)
Yim1 = -0.5 * rho1 / T.sqrt(L1)
Xre2 = kappa2 / T.sqrt(L2)
Xim2 = -eta2 / T.sqrt(L2)
Yre2 = 0.5 * sigma2 / T.sqrt(L2)
Yim2 = -0.5 * rho2 / T.sqrt(L2)
absX1_sq = 2 * I1 / L1
absX2_sq = 2 * I2 / L2
X_to_z1 = T.sqrt(1 - absX1_sq / 4)
X_to_z2 = T.sqrt(1 - absX2_sq / 4)
Y_to_zeta1 = 1 / T.sqrt(1 - absX1_sq / 2)
Y_to_zeta2 = 1 / T.sqrt(1 - absX2_sq / 2)
a1 = (L1 / beta1)**2
k1 = Xre1 * X_to_z1
h1 = Xim1 * X_to_z1
q1 = Yre1 * Y_to_zeta1
p1 = Yim1 * Y_to_zeta1
e1 = T.sqrt(absX1_sq) * X_to_z1
inc1 = 2 * T.arcsin(T.sqrt(p1 * p1 + q1 * q1))
a2 = (L2 / beta2)**2
k2 = Xre2 * X_to_z2
h2 = Xim2 * X_to_z2
q2 = Yre2 * Y_to_zeta2
p2 = Yim2 * Y_to_zeta2
e2 = T.sqrt(absX2_sq) * X_to_z2
inc2 = 2 * T.arcsin(T.sqrt(p2 * p2 + q2 * q2))
beta1p = T.sqrt(Mstar1) * beta1
beta2p = T.sqrt(Mstar2) * beta2
Hkep = -0.5 * beta1p / a1 - 0.5 * beta2p / a2
Hdir, Hind = calc_Hint_components_spatial(a1, a2, l1, l2, h1, k1, h2, k2,
p1, q1, p2, q2, Mstar1, Mstar2)
eps = m1 * m2 / (mu1 + mu2) / T.sqrt(mstar)
Hpert = (Hdir + Hind / mstar)
Hpert_av = Hpert.dot(quad_weights)
Htot = Hkep + eps * Hpert_av
#####################################################
# Set parameters for compiling functions with Theano
#####################################################
# Get numerical quadrature nodes and weights
nodes, weights = np.polynomial.legendre.leggauss(N_QUAD_PTS)
# Rescale for integration interval from [-1,1] to [-pi,pi]
nodes = nodes * np.pi
weights = weights * 0.5
# 'givens' will fix some parameters of Theano functions compiled below
givens = [(psi, nodes), (quad_weights, weights)]
# 'ins' will set the inputs of Theano functions compiled below
# Note: 'extra_ins' will be passed as values of object attributes
# of the 'ResonanceEquations' class 'defined below
extra_ins = [m1, m2, j, k]
ins = [dyvars] + extra_ins
Stilde = Phi * (L2 - I2 - L1 + I1) / (Ltot)
Q1 = 0.5 * (Phi + Stilde)
Q2 = 0.5 * (Phi - Stilde)
inc1 = T.arccos(1 - Q1 / (L1 - I1))
inc2 = T.arccos(1 - Q2 / (L2 - I2))
orbels = [
a1, e1, inc1, k * T.arctan2(y1, x1), a2, e2, inc2,
k * T.arctan2(y2, x2),
T.arctan2(y_inc, x_inc)
]
orbels_dict = dict(
zip([
'a1', 'e1', 'inc1', 'theta1', 'a2', 'e2', 'inc2', 'theta2', 'phi'
], orbels))
actions = [L1, L2, I1, I2, Q1, Q2]
actions_dict = dict(
zip(['L1', 'L2', 'Gamma1', 'Gamma2', 'Q1', 'Q2'], actions))
# Conservative flow
gradHtot = T.grad(Htot, wrt=dyvars)
gradHpert = T.grad(Hpert_av, wrt=dyvars)
gradHkep = T.grad(Hkep, wrt=dyvars)
hessHtot = theano.gradient.hessian(Htot, wrt=dyvars)
hessHpert = theano.gradient.hessian(Hpert_av, wrt=dyvars)
hessHkep = theano.gradient.hessian(Hkep, wrt=dyvars)
Jtens = T.as_tensor(np.pad(getOmegaMatrix(Ndof), (0, Nconst), 'constant'))
H_flow_vec = Jtens.dot(gradHtot)
Hpert_flow_vec = Jtens.dot(gradHpert)
Hkep_flow_vec = Jtens.dot(gradHkep)
H_flow_jac = Jtens.dot(hessHtot)
Hpert_flow_jac = Jtens.dot(hessHpert)
Hkep_flow_jac = Jtens.dot(hessHkep)
##########################
# Compile Theano functions
##########################
func_dict = {
# Hamiltonians
'H': Htot,
#'Hpert':Hpert_av,
#'Hkep':Hkep,
## Hamiltonian flows
'H_flow': H_flow_vec,
#'Hpert_flow':Hpert_flow_vec,
#'Hkep_flow':Hkep_flow_vec,
## Hamiltonian flow Jacobians
'H_flow_jac': H_flow_jac,
#'Hpert_flow_jac':Hpert_flow_jac,
#'Hkep_flow_jac':Hkep_flow_jac,
## Extras
'orbital_elements': orbels_dict,
'actions': actions_dict
}
compiled_func_dict = dict()
with tqdm(func_dict.items()) as t:
for key, val in t:
t.set_description("Compiling '{}'".format(key))
if key is 'timescales':
inputs = extra_ins
else:
inputs = ins
cf = theano.function(inputs=inputs,
outputs=val,
givens=givens,
on_unused_input='ignore')
compiled_func_dict[key] = cf
return compiled_func_dict
def __init__(self):
# ------------------- #
# --- variables --- #
# ------------------- #
# focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p
focus = T.dscalar('focus') # focus length od camera
# variables of device state
xt, yt, zt = T.dscalars('xt', 'yt', 'zt') # position
ox, oy, oz = T.dscalars('ox', 'oy', 'oz') # orientation
# variables of landmark state
xi, yi, zi = T.dscalars('xi', 'yi',
'zi') # Device position at first observation
theta, phi = T.dscalars(
'theta', 'phi'
) # theta, phi (Azimuth & elevation of the ray at first observation)
p = T.dscalar(
'p'
) # d_inv (Inverse depth at first observation. 0.1 means depth is 10 meter.)
# ------------------- #
# --- observation --- #
# ------------------- #
# T.sin(ox)
# T.cos(ox)
# T.sin(oy)
# T.cos(oy)
# T.sin(oz)
# T.cos(oz)
# T.sin(theta)
# T.cos(theta)
# T.sin(phi)
# T.cos(phi)
# --- # h_ = [hx, hy, hz].T in the global coordinates --- #
h_x = p * (xi - xt) + T.cos(phi) * T.sin(theta)
h_y = p * (yi - yt) - T.sin(phi)
h_z = p * (zi - zt) + T.cos(phi) * T.cos(theta)
# ---- hx, hy, hz ---- #
hx = (T.cos(oy) * T.cos(oz)) * h_x + (T.cos(oy) * T.sin(oz)) * h_y + (
-T.sin(oy)) * h_z
hy = (-T.cos(ox) * T.sin(oz) + T.sin(ox) * T.sin(oy) * T.cos(oz)
) * h_x + (T.cos(ox) * T.cos(oz) + T.sin(ox) * T.sin(oy) *
T.sin(oz)) * h_y + (T.sin(ox) * T.cos(oy)) * h_z
hz = (T.sin(ox) * T.sin(oz) + T.cos(ox) * T.sin(oy) * T.cos(oz)
) * h_x + (-T.sin(ox) * T.cos(oz) + T.cos(ox) * T.sin(oy) *
T.sin(oz)) * h_y + (T.cos(ox) * T.cos(oy)) * h_z
# --- h1, h2 --- #
h1 = -(focus * hx / hz)
h2 = focus * hy / hz
self.fh1 = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=h1)
self.fh2 = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=h2)
# partial derivative
dh1xt = T.grad(cost=h1, wrt=xt)
dh1yt = T.grad(cost=h1, wrt=yt)
dh1zt = T.grad(cost=h1, wrt=zt)
dh1ox = T.grad(cost=h1, wrt=ox)
dh1oy = T.grad(cost=h1, wrt=oy)
dh1oz = T.grad(cost=h1, wrt=oz)
dh1xi = T.grad(cost=h1, wrt=xi)
dh1yi = T.grad(cost=h1, wrt=yi)
dh1zi = T.grad(cost=h1, wrt=zi)
dh1theta = T.grad(cost=h1, wrt=theta)
dh1phi = T.grad(cost=h1, wrt=phi)
dh1p = T.grad(cost=h1, wrt=p)
dh2xt = T.grad(cost=h2, wrt=xt)
dh2yt = T.grad(cost=h2, wrt=yt)
dh2zt = T.grad(cost=h2, wrt=zt)
dh2ox = T.grad(cost=h2, wrt=ox)
dh2oy = T.grad(cost=h2, wrt=oy)
dh2oz = T.grad(cost=h2, wrt=oz)
dh2xi = T.grad(cost=h2, wrt=xi)
dh2yi = T.grad(cost=h2, wrt=yi)
dh2zi = T.grad(cost=h2, wrt=zi)
dh2theta = T.grad(cost=h2, wrt=theta)
dh2phi = T.grad(cost=h2, wrt=phi)
dh2p = T.grad(cost=h2, wrt=p)
# function of partial derivative
self.fdh1xt = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1xt)
self.fdh1yt = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1yt)
self.fdh1zt = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1zt)
self.fdh1ox = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1ox)
self.fdh1oy = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1oy)
self.fdh1oz = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1oz)
self.fdh1xi = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1xi)
self.fdh1yi = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1yi)
self.fdh1zi = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1zi)
self.fdh1theta = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1theta)
self.fdh1phi = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1phi)
self.fdh1p = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh1p)
self.fdh2xt = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2xt)
self.fdh2yt = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2yt)
self.fdh2zt = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2zt)
self.fdh2ox = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2ox)
self.fdh2oy = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2oy)
self.fdh2oz = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2oz)
self.fdh2xi = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2xi)
self.fdh2yi = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2yi)
self.fdh2zi = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2zi)
self.fdh2theta = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2theta)
self.fdh2phi = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2phi)
self.fdh2p = theano.function(
inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p],
outputs=dh2p)
def test_1_examples_param_default():
x, y = T.dscalars('x', 'y')
f = theano.function([x, theano.Param(y, default=1)], x + y)
assert f(1, 2) == 3
assert f(1) == 2
ion_list = ['O3', 'S3', 'H1r', 'He1r']
emtt = sr.EmissionTensors(label_list, ion_list)
emis_ratio, cHbeta, flambda, abund, ftau = 0.352, 0.12, 0.2, 7.8, 0.0
params = dict(emis_ratio=emis_ratio,
cHbeta=cHbeta,
flambda=flambda,
abund=abund,
ftau=ftau)
flux_i = emtt.emFluxEqDict['O3_5007A'](emis_ratio, cHbeta, flambda, abund,
ftau, {})
print('Flux_i', flux_i)
print('\nFlux computation using theano graphs')
emis_ratio_t, cHbeta_t, flambda_t, abund_t, ftau_t = T.dscalars(
'emis_ratio_t', 'cHbeta_t', 'flambda_t', 'abund_t', 'ftau_t')
emGraph = sr.EmissionFluxModel(label_list, ion_list)
params = {
emis_ratio_t: 0.352,
cHbeta_t: 0.12,
flambda_t: 0.2,
abund_t: 7.8,
ftau_t: 0.0
}
flux_j = emGraph.emFluxEqDict['O3_5007A'](emis_ratio_t, cHbeta_t, flambda_t,
abund_t, ftau_t, {})
print('flux_j = ', flux_j.eval(params))
print('\nEmissivity interpolation')
def defaultValue():
x, y, z = T.dscalars('x', 'y', 'z')
return function([x, In(y, value=1), In(z, value=2, name='namedZ')], (x + y) * z)
def set_default_value():
x, y = T.dscalars('x','y')
z = x+y
f = theano.function([x, theano.Param(y, default=1)], z)
print f(33)
def get_compiled_theano_functions(N_QUAD_PTS):
# Planet masses: m1,m2
m1,m2 = T.dscalars(2)
mstar = 1
mu1 = m1 * mstar / (mstar + m1)
mu2 = m2 * mstar / (mstar + m2)
Mstar1 = mstar + m1
Mstar2 = mstar + m2
beta1 = mu1 * T.sqrt(Mstar1/mstar) / (mu1 + mu2)
beta2 = mu2 * T.sqrt(Mstar2/mstar) / (mu1 + mu2)
j,k = T.lscalars('jk')
s = (j-k) / k
# Angle variable for averaging over
psi = T.dvector()
# Dynamical variables:
Ndof = 2
Nconst = 1
dyvars = T.vector()
y1, y2, x1, x2, amd = [dyvars[i] for i in range(2*Ndof + Nconst)]
# Quadrature weights
quad_weights = T.dvector('w')
# Set lambda2=0
l2 = T.constant(0.)
l1 = -1 * k * psi
theta_res = (1+s) * l2 - s * l1
cos_theta_res = T.cos(theta_res)
sin_theta_res = T.sin(theta_res)
kappa1 = x1 * cos_theta_res + y1 * sin_theta_res
eta1 = y1 * cos_theta_res - x1 * sin_theta_res
kappa2 = x2 * cos_theta_res + y2 * sin_theta_res
eta2 = y2 * cos_theta_res - x2 * sin_theta_res
Gamma1 = (x1 * x1 + y1 * y1) / 2
Gamma2 = (x2 * x2 + y2 * y2) / 2
# Resonant semi-major axis ratio
alpha_res = ((j-k)/j)**(2/3) * (Mstar1 / Mstar2)**(1/3)
#P0 = k * ( beta2 - beta1 * T.sqrt(alpha_res) ) / 2
#P = P0 - k * (s+1/2) * amd
#Ltot = beta1 * T.sqrt(alpha_res) + beta2 - amd
a20 = 1
a10 = alpha_res * a20
Ltot = beta1 * T.sqrt(a10) + beta2 * np.sqrt(a20)
L1byL2res = beta1 * T.sqrt(a10) / beta2 * np.sqrt(a20)
L2res = (amd + Ltot) / (1 + L1byL2res)
P = 0.5 * L2res * (1 - L1byL2res) - (s+1/2) * amd
L1 = Ltot/2 - P / k - s * (Gamma1 + Gamma2)
L2 = Ltot/2 + P / k + (1 + s) * (Gamma1 + Gamma2)
Xre1 = kappa1 / T.sqrt(L1)
Xim1 = -eta1 / T.sqrt(L1)
Xre2 = kappa2 / T.sqrt(L2)
Xim2 = -eta2 / T.sqrt(L2)
absX1_sq = 2 * Gamma1 / L1
absX2_sq = 2 * Gamma2 / L2
X_to_z1 = T.sqrt(1 - absX1_sq / 4 )
X_to_z2 = T.sqrt(1 - absX2_sq / 4 )
a1 = (L1 / beta1 )**2
k1 = Xre1 * X_to_z1
h1 = Xim1 * X_to_z1
e1 = T.sqrt( absX1_sq ) * X_to_z1
a2 = (L2 / beta2 )**2
k2 = Xre2 * X_to_z2
h2 = Xim2 * X_to_z2
e2 = T.sqrt( absX2_sq ) * X_to_z2
beta1p = T.sqrt(Mstar1) * beta1
beta2p = T.sqrt(Mstar2) * beta2
Hkep = -0.5 * beta1p / a1 - 0.5 * beta2p / a2
Hdir,Hind = calc_Hint_components_planar(
a1,a2,l1,l2,h1,k1,h2,k2,Mstar1/mstar,Mstar2/mstar
)
eps = m1*m2/ (mu1 + mu2) / T.sqrt(mstar)
Hpert = (Hdir + Hind/mstar)
Hpert_av = Hpert.dot(quad_weights)
Htot = Hkep + eps * Hpert_av
######################
# Dissipative dynamics
######################
tau_alpha_0, K1, K2, p = T.dscalars(4)
y1dot_dis,y2dot_dis,x1dot_dis,x2dot_dis,amddot_dis = T.dscalars(5)
tau_m_inv = 1/tau_alpha_0
# Define timescales
tau_e1 = tau_alpha_0 / K1
tau_e2 = tau_alpha_0 / K2
tau_a1_0_inv = -beta2p * alpha_res * tau_m_inv / (beta1p + alpha_res * beta2p)
tau_a2_0_inv = beta1p * tau_m_inv / (beta1p + alpha_res * beta2p)
tau_a1 = 1 / (tau_a1_0_inv + 2 * p * e1*e1 / tau_e1 )
tau_a2 = 1 / (tau_a2_0_inv + 2 * p * e2*e2 / tau_e2 )
tau_L1 = 2 * tau_a1
tau_L2 = 2 * tau_a2
tau_Gamma1_inv = 1/tau_L1 + (Gamma1-2*L1) / (Gamma1-L1) / tau_e1
tau_Gamma2_inv = 1/tau_L2 + (Gamma2-2*L2) / (Gamma2-L2) / tau_e2
# Time derivatives of canonical variables
x1dot_dis = -0.5 * x1 * tau_Gamma1_inv
x2dot_dis = -0.5 * x2 * tau_Gamma2_inv
y1dot_dis = -0.5 * y1 * tau_Gamma1_inv
y2dot_dis = -0.5 * y2 * tau_Gamma2_inv
Pdot_dis = -0.5 * k * ( L2 / tau_L2 - L1 / tau_L1) + k * (s + 1/2) * (Gamma1 * tau_Gamma1_inv + Gamma2 * tau_Gamma2_inv)
amddot_dis = Pdot_dis / T.grad(P,amd)
#####################################################
# Set parameters for compiling functions with Theano
#####################################################
# Get numerical quadrature nodes and weight
nodes,weights = np.polynomial.legendre.leggauss(N_QUAD_PTS)
# Rescale for integration interval from [-1,1] to [-pi,pi]
nodes = nodes * np.pi
weights = weights * 0.5
# 'givens' will fix some parameters of Theano functions compiled below
givens = [(psi,nodes),(quad_weights,weights)]
# 'ins' will set the inputs of Theano functions compiled below
# Note: 'extra_ins' will be passed as values of object attributes
# of the 'ResonanceEquations' class defined below
extra_ins = [m1,m2,j,k,tau_alpha_0,K1,K2,p]
ins = [dyvars] + extra_ins
# Define flows and jacobians.
# Conservative flow
gradHtot = T.grad(Htot,wrt=dyvars)
gradHpert = T.grad(Hpert_av,wrt=dyvars)
gradHkep = T.grad(Hkep,wrt=dyvars)
hessHtot = theano.gradient.hessian(Htot,wrt=dyvars)
hessHpert = theano.gradient.hessian(Hpert_av,wrt=dyvars)
hessHkep = theano.gradient.hessian(Hkep,wrt=dyvars)
Jtens = T.as_tensor(np.pad(getOmegaMatrix(Ndof),(0,Nconst),'constant'))
H_flow_vec = Jtens.dot(gradHtot)
Hpert_flow_vec = Jtens.dot(gradHpert)
Hkep_flow_vec = Jtens.dot(gradHkep)
H_flow_jac = Jtens.dot(hessHtot)
Hpert_flow_jac = Jtens.dot(hessHpert)
Hkep_flow_jac = Jtens.dot(hessHkep)
# Dissipative flow
dis_flow_vec = T.stack(y1dot_dis,y2dot_dis,x1dot_dis,x2dot_dis,amddot_dis)
dis_flow_jac = theano.gradient.jacobian(dis_flow_vec,dyvars)
# Extras
sigma1 = T.arctan2(y1,x1)
sigma2 = T.arctan2(y2,x2)
orbels = [a1,e1,k*sigma1,a2,e2,k*sigma2]
dis_timescales = [1/tau_a1_0_inv,1/tau_a2_0_inv,tau_e1,tau_e2]
orbels_dict = dict(zip(
['a1','e1','theta1','a2','e2','theta2'],
orbels
)
)
actions = [L1,L2,Gamma1,Gamma2]
actions_dict = dict(
zip(
['L1','L2','Gamma1','Gamma2'],
actions
)
)
timescales_dict = dict(zip(
['tau_m1','tau_m2','tau_e1','tau_e2'],
dis_timescales
)
)
##########################
# Compile Theano functions
##########################
func_dict={
# Hamiltonians
'H':Htot,
'Hpert':Hpert_av,
'Hkep':Hkep,
# Hamiltonian flows
'H_flow':H_flow_vec,
'Hpert_flow':Hpert_flow_vec,
'Hkep_flow':Hkep_flow_vec,
# Hamiltonian flow Jacobians
'H_flow_jac':H_flow_jac,
'Hpert_flow_jac':Hpert_flow_jac,
'Hkep_flow_jac':Hkep_flow_jac,
# Dissipative flow and Jacobian
'dissipative_flow':dis_flow_vec,
'dissipative_flow_jac':dis_flow_jac,
# Extras
'orbital_elements':orbels_dict,
'actions':actions_dict,
'timescales':timescales_dict
}
compiled_func_dict=dict()
for key,val in func_dict.items():
if key is 'timescales':
inputs = extra_ins
else:
inputs = ins
cf = theano.function(
inputs=inputs,
outputs=val,
givens=givens,
on_unused_input='ignore'
)
compiled_func_dict[key]=cf
return compiled_func_dict
def create_spatialglimpse_function(img_h=480, img_w=640, fovH=64, fovW=64):
fovHalfH = fovH / 2
fovHalfW = fovW / 2
glimpseInpImg = T.dtensor3('glimpseInpImg')
glimpseInpLoc_y, glimpseInpLoc_x = T.dscalars('gilY', 'gilX') # each lies between -1 and 1
glimpseLocOnImg_y = T.cast(((glimpseInpLoc_y + 1) / 2.0) * img_h, 'int32')
glimpseLocOnImg_x = T.cast(((glimpseInpLoc_x + 1) / 2.0) * img_w, 'int32')
y1 = T.max((glimpseLocOnImg_y - fovHalfH, 0))
y2 = T.min((glimpseLocOnImg_y + fovHalfH, img_h))
x1 = T.max((glimpseLocOnImg_x - fovHalfW, 0))
x2 = T.min((glimpseLocOnImg_x + fovHalfW, img_w))
y3 = T.max((glimpseLocOnImg_y - fovH, 0))
y4 = T.min((glimpseLocOnImg_y + fovH, img_h))
x3 = T.max((glimpseLocOnImg_x - fovW, 0))
x4 = T.min((glimpseLocOnImg_x + fovW, img_w))
y5 = T.max((glimpseLocOnImg_y - 2*fovH, 0))
y6 = T.min((glimpseLocOnImg_y + 2*fovH, img_h))
x5 = T.max((glimpseLocOnImg_x - 2*fovW, 0))
x6 = T.min((glimpseLocOnImg_x + 2*fovW, img_w))
glimpse1= glimpseInpImg[:, y1:y2, x1:x2]
if T.lt(glimpse1.shape[1], fovH):
pad = T.zeros((glimpse1.shape[0], fovH - glimpse1.shape[1], glimpse1.shape[2]))
if T.eq(y1, 0):
glimpse1 = T.concatenate((pad, glimpse1), 1)
else:
glimpse1 = T.concatenate((glimpse1, pad), 1)
if T.lt(glimpse1.shape[2], fovW):
pad = T.zeros((glimpse1.shape[0], glimpse1.shape[1], fovW - glimpse1.shape[2]))
if T.eq(x1, 0):
glimpse1 = T.concatenate((pad, glimpse1), 2)
else:
glimpse1 = T.concatenate((glimpse1, pad), 2)
glimpse2 = glimpseInpImg[:, y3:y4, x3:x4]
if T.lt(glimpse2.shape[1], 2*fovH):
pad = T.zeros((glimpse2.shape[0], 2*fovH - glimpse2.shape[1], glimpse2.shape[2]))
if T.eq(y3, 0):
glimpse2 = T.concatenate((pad, glimpse2), 1)
else:
glimpse2 = T.concatenate((glimpse2, pad), 1)
if T.lt(glimpse2.shape[2], 2*fovW):
pad = T.zeros((glimpse2.shape[0], glimpse2.shape[1], 2*fovW - glimpse2.shape[2]))
if T.eq(x3, 0):
glimpse2 = T.concatenate((pad, glimpse2), 2)
else:
glimpse2 = T.concatenate((glimpse2, pad), 2)
glimpse2 = T.signal.pool.pool_2d(glimpse2, (2, 2), ignore_border=True, mode='average_exc_pad')
glimpse3 = glimpseInpImg[:, y5:y6, x5:x6]
if T.lt(glimpse3.shape[1], 4*fovH):
pad = T.zeros((glimpse3.shape[0], 4*fovH - glimpse3.shape[1], glimpse3.shape[2]))
if T.eq(y5, 0):
glimpse3 = T.concatenate((pad, glimpse3), 1)
else:
glimpse3 = T.concatenate((glimpse3, pad), 1)
if T.lt(glimpse3.shape[2], 4*fovW):
pad = T.zeros((glimpse3.shape[0], glimpse3.shape[1], 4*fovW - glimpse3.shape[2]))
if T.eq(x5, 0):
glimpse3 = T.concatenate((pad, glimpse3), 2)
else:
glimpse3 = T.concatenate((glimpse3, pad), 2)
glimpse3 = pool.pool_2d(glimpse3, (4, 4), ignore_border=True, mode='average_exc_pad')
glimpse1 = T.cast(glimpse1, 'uint8')
glimpse2 = T.cast(glimpse2, 'uint8')
glimpse3 = T.cast(glimpse3, 'uint8')
fun = theano.function([glimpseInpImg, glimpseInpLoc_y, glimpseInpLoc_x], [glimpse1, glimpse2, glimpse3])
return fun
'''
Created on Feb 24, 2016
@author: lqy
'''
import theano
import theano.tensor as T
from theano import In
from theano import function
x, y = T.dscalars("x", "y")
out = x + y
f = function([x, In(y, value=1)], out)
print f(2, 3)
def get_compiled_theano_functions(N_QUAD_PTS):
# resonance j and k
j, k = T.lscalars('jk')
# Planet masses: m1,m2
m1, m2 = T.dscalars(2)
# resonance f and g coefficients
f, g = T.dscalars(2)
# Planet and star mass variables
Mstar = 1
mu1 = m1 / (Mstar + m1)
mu2 = m2 / (Mstar + m2)
eps = m1 * mu2 / (mu1 + mu2) / Mstar
# Resonant semi-major axis ratio
alpha = ((j - k) / j)**(2 / 3) * ((Mstar + m1) / (Mstar + m2))**(1 / 3)
# Constants in Eq. (15)
fTilde = T.sqrt((mu1 + mu2) / (mu1 * T.sqrt(alpha))) * f
gTilde = T.sqrt((mu1 + mu2) / mu2) * g
# Constant in Eq. (8)
A = 1.5 * j * (mu1 + mu2) * (j / mu2 + (j - k) / mu1 / T.sqrt(alpha))
# Dynamical variables:
dyvars = T.vector()
theta, theta_star, J, J_star = [dyvars[i] for i in range(4)]
# Angle variable to average disturbing function over
kappa = T.dvector()
# Quadrature weights
quad_weights = T.dvector('w')
# Convert dynamical variables to eccentricities and angles:
# Note:
# Q is set to zero since it does not
# enter disturbing function except in combinations
# with z and w.
Q = T.as_tensor(0)
z = Q / k - theta
# See Eq. 20
Zsq = J * (fTilde * fTilde + gTilde * gTilde) / (f * f + g * g)
Z = T.sqrt(Zsq)
# Set W to zero
Wsinw, Wcosw = 0, 0
Zsinz, Zcosz = Z * T.sin(z), Z * T.cos(z)
# Convert Z and W to planet eccentricities
atan_f_g = T.arctan2(g, f)
c, s = T.cos(atan_f_g), T.sin(atan_f_g)
e1cos = c * Zcosz - s * Wcosw
e1sin = c * Zsinz - s * Wsinw
e2cos = s * Zcosz + c * Wcosw
e2sin = s * Zsinz + c * Wsinw
w1 = T.arctan2(e1sin, e1cos)
w2 = T.arctan2(e2sin, e2cos)
e1 = T.sqrt(e1sin * e1sin + e1cos * e1cos)
e2 = T.sqrt(e2sin * e2sin + e2cos * e2cos)
# Planets' mean longitudes
l1 = Q / k - j * kappa
l2 = Q / k + (k - j) * kappa
# Planets mean anomalies
M1 = l1 - w1
M2 = l2 - w2
# Convert mean to true anomalies using
# function 'exoplanet.theano_ops.kepler.KeplerOp'
ko = KeplerOp()
sinf1, cosf1 = ko(M1, e1 + T.zeros_like(M1))
sinf2, cosf2 = ko(M2, e2 + T.zeros_like(M2))
# Vector of distrubing function values with same dimension as kappa vector
DFfull = calc_DisturbingFunction_with_sinf_cosf(alpha, e1, e2, w1, w2,
sinf1, cosf1, sinf2, cosf2)
# Average distrubing function by weighting values with user-specified
# quadrature weights.
DFav = DFfull.dot(quad_weights)
# Hamiltonian
Hkep = -0.5 * A / k / k * (J - J_star) * (J - J_star)
Hres = -2 * eps * DFav
# ******************IMPORTANT NOTE*************************
# I have *NOT* subtraced off the secular component of
# the disturbing function. This means that the Hamiltonian
# differs slightly from the one defined in the paper.
# This is generally of little consequence to the resonant
# dynamics but should be borne in mind when exploring
# secular dynamics.
# *********************************************************
H = Hkep + Hres
# Gradient and hessian of Hamiltonian w.r.t. phase space variables
gradHtot = T.grad(H, wrt=dyvars)
hessHtot = theano.gradient.hessian(H, wrt=dyvars)
# Flow vector and Jacobian for equations of motion
OmegaTens = T.as_tensor(getOmegaMatrix(2))
H_flow_vec = OmegaTens.dot(gradHtot)
H_flow_jac = OmegaTens.dot(hessHtot)
#####################################################
# Set parameters for compiling functions with Theano
#####################################################
# Get numerical quadrature nodes and weights
nodes, weights = np.polynomial.legendre.leggauss(N_QUAD_PTS)
# Rescale for integration interval from [-1,1] to [-pi,pi]
nodes = nodes * np.pi
weights = weights * 0.5
# 'ins' will set the inputs of Theano functions compiled below
extra_ins = [m1, m2, j, k, f, g]
ins = [dyvars] + extra_ins
# 'givens' will fix some parameters of Theano functions compiled below
givens = [(kappa, nodes), (quad_weights, weights)]
##########################
# Compile Theano functions
##########################
if not DEBUG:
# Note that compiling can take a while
# so I've put a debugging switch here
# to skip evaluating these functions when
# desired.
H_fn = theano.function(inputs=ins, outputs=H, givens=givens)
H_flow_vec_fn = theano.function(inputs=ins,
outputs=H_flow_vec,
givens=givens)
H_flow_jac_fn = theano.function(inputs=ins,
outputs=H_flow_jac,
givens=givens)
else:
H_fn, H_flow_vec_fn, H_flow_jac_fn = [lambda x: x for _ in range(3)]
# Some convenience functions...
Zsq_to_J_Eq20 = (f * f + g * g) / (fTilde * fTilde + gTilde * gTilde)
dJ_to_Delta_Eq21 = 1.5 * (mu1 + mu2) * (j * mu1 * T.sqrt(alpha) +
(j - k) * mu2) / (
k * T.sqrt(alpha) * mu1 * mu2)
ecc_vars_fn = theano.function(inputs=ins,
outputs=[e1, w1, e2, w2],
on_unused_input='ignore')
Zsq_to_J_Eq20_fn = theano.function(inputs=extra_ins,
outputs=Zsq_to_J_Eq20,
on_unused_input='ignore')
dJ_to_Delta_Eq21_fn = theano.function(inputs=extra_ins,
outputs=dJ_to_Delta_Eq21,
on_unused_input='ignore')
return (H_fn, H_flow_vec_fn, H_flow_jac_fn, Zsq_to_J_Eq20_fn,
dJ_to_Delta_Eq21_fn, ecc_vars_fn)
#coding: utf-8
import theano
import theano.tensor as T
## まとめて宣言
x, y = T.dscalars("x", "y")
z = (x+2*y)**2
## zをxについて微分
gx = T.grad(z, x)
## zをyについて微分
gy = T.grad(z, y)
## まとめて
v1 = [x, y]
v2 = [x, y]
## 配列を足してもできる
v = v1+v2
# vの中の変数について順番に微分
grads = T.grad(z, v)
print grads
fgy = theano.function([x, y], grads[3])
fgx = theano.function([x, y], grads[2])
import theano, time from theano import tensor as T from theano import function from theano.ifelse import ifelse #tensor.gt (greater than), .ge (greater than or equal to) #Similarly there are lt, le, eq, ne #The evaluation of the above are all element-wise #time.clock() can be used to get the time at any point in the operation. # tic_1 = time.clock() # Operation #tic_2 = time.clock() #tic_2 - tic_1 gives the time taken to run Operation. a, b = T.dscalars(2) x, y = T.dvectors(2) z_switch = T.switch(T.le(a, b), T.mean(x), T.max(y)) z_ifelse = ifelse(T.gt(a, b), T.max(x), T.mean(y)) f_switch = function([a, b, x, y], z_switch, mode=theano.Mode(linker='vm')) f_ifelse = function([a, b, x, y], z_ifelse, mode=theano.Mode(linker='vm')) value1 = 2.3 value2 = 3.44 vector_1 = np.ones((4000, )) vector_2 = [2.3, 4.5, 5.6, 7.8, 9, 10, 11, 12, 13, 14, 576, 456, 32467, 43598] print f_switch(value1, value2, vector_1, vector_2)
'''
Executing multiple functions
'''
a, b = T.dmatrices('a', 'b')
diff = a - b
abs_diff = abs(a - b)
diff_sq = diff**2
mult = function([a, b], [diff, abs_diff, diff_sq])
print mult([[0, 1], [1, 2]], [[-1, 2], [5, 7]])
#print pp(diff)
#print pp(abs_diff)
'''
Setting a default value for an argument
So, if arg not give, take default value; else take the given value
'''
x, y = T.dscalars("x", "y")
z = x + y
add = function([x, Param(y, default=1)], z)
print add(33.0)
print add(2, 6)
'''
Setting names to parameters
'''
x, y, w = T.dscalars("x", "y", "w")
z = (x + y) * w
add_par = function(
[x, Param(y, default=1),
Param(w, default=2, name="debalu")], z)
print add_par(33)
print add_par(33, 6, debalu=5)
'''
Created on Jun 1, 2015
@author: xujian
'''
import theano
from theano import Param
import theano.tensor as T
from samba.dcerpc.atsvc import Third
a,b,c = T.dscalars('a','b','c')
z=(a+b)*c
f=theano.function([a,Param(b,default=0),Param(c,default=1,name="third_var")],z)
print f(1)
print f(1,2)
print f(1,third_var=2)
import numpy
import theano.tensor as T
from theano import function
from theano import In
x, y, w = T.dscalars('x', 'y', 'w')
z = (x + 2 * y) * w
f = function([In(x, value = 0), In(y, value = 0, name='y_name'), In(w, value = 1)], z)
print 'f(): ' + str(f())
print 'f(4): ' + str(f(4))
print 'f(y_name=3): ' + str(f(y_name=3))
print 'f(4, 3, 2): ' + str(f(4, 3, 2))
print 'f(4, 3): ' + str(f(4, 3))
print 'f(y_name=3, w = 4): ' + str(f(y_name=3, w = 4))
def tuto():
print "\nLogistic Function 1"
print "---------------------"
x = T.dmatrix('x')
s = 1 / (1 + T.exp(-x))
logistic = theano.function([x], s)
print logistic([[0, 1], [-1, -2]])
print "\nLogistic Function 2"
print "---------------------"
s2 = (1 + T.tanh(x / 2)) / 2
logistic2 = theano.function([x], s2)
print logistic2([[0, 1], [-1, -2]])
print "\nComputing More than one Thing at the Same Time"
print "------------------------------------------------"
a, b = T.dmatrices('a', 'b')
diff = a - b
abs_diff = abs(diff)
diff_squared = diff**2
f = theano.function([a, b], [diff, abs_diff, diff_squared])
print f([[1, 1], [1, 1]], [[0, 1], [2, 3]])
print "\nSetting a Default Value for an Argument"
print "---------------------------------------"
x, y = T.dscalars('x', 'y')
z = x + y
f = function([x, In(y, value=1)], z)
print f(33)
print f(33, 2)
print "A Real Example: Logistic Regression"
print "-----------------------------------"
rng = numpy.random
N = 400 # training sample size
feats = 784 # number of input variables
# generate a dataset: D = (input_values, target_class)
D = (rng.randn(N, feats), rng.randint(size=N, low=0, high=2))
training_steps = 10000
# Declare Theano symbolic variables
x = T.dmatrix("x")
y = T.dvector("y")
# initialize the weight vector w randomly
#
# this and the following bias variable b
# are shared so they keep their values
# between training iterations (updates)
w = theano.shared(rng.randn(feats), name="w")
# initialize the bias term
b = theano.shared(0., name="b")
print("Initial model:")
print(w.get_value())
print(b.get_value())
# Construct Theano expression graph
p_1 = 1 / (1 + T.exp(-T.dot(x, w) - b)) # Probability that target = 1
prediction = p_1 > 0.5 # The prediction thresholded
xent = -y * T.log(p_1) - (1-y) * T.log(1-p_1) # Cross-entropy loss function
cost = xent.mean() + 0.01 * (w ** 2).sum()# The cost to minimize
gw, gb = T.grad(cost, [w, b]) # Compute the gradient of the cost
# w.r.t weight vector w and
# bias term b
# (we shall return to this in a
# following section of this tutorial)
# Compile
train = theano.function(
inputs=[x,y],
outputs=[prediction, xent],
updates=((w, w - 0.1 * gw), (b, b - 0.1 * gb)))
predict = theano.function(inputs=[x], outputs=prediction)
# Train
for i in range(training_steps):
pred, err = train(D[0], D[1])
print("Final model:")
print(w.get_value())
print(b.get_value())
print("target values for D:")
print(D[1])
print("prediction on D:")
print(predict(D[0]))
import theano.tensor as T
from theano import *
# x and y are double precision scalars defined at once.
x, y = T.dscalars('x', 'y')
# define sum of those
z = x + y
# define default value for y with Param object.
f = function([x, Param(y, default=1)], z)
# works. should be 34
print f(33)
# override default value, should be 35
print f(33, 2)
# define three double precision scalars
x, y, w = T.dscalars('x', 'y', 'w')
# define an expression out of them
z = (x + y) * w
# attach default values and name for overriding keyword arg
f = function([x, Param(y, default=1),
Param(w, default=2, name='w_by_name')], z)
print f(33) # (33 + 1) * 2 = 68
print f(33, 2) # (33 + 2) * 2 = 70
print f(33, 0, 1) # (33 + 0) * 1 = 33
def plot_results(ens,params,mn,corr,lam_lst,figname,\
figsize=(7,7/1.618034333)):
''' plot data '''
dset = {'proton': 0, 'gA': 1, 'gV': 2}
di = dset[corr]
clrs = ['k', rgb(ens)]
lbl = ['SS', 'PS']
ylabel = {
'proton': r'$m_{eff}(t)$',
'gA': r'$g_A^{FH}(t)$',
'gV': r'$g_V^{FH}(t)$'
}
y, y_bs = get_data(ens, params, alldata=True)
nt = y[di].shape[0]
fig = plt.figure(figname)
ax = plt.axes([.15, .15, .8, .8])
for i in range(y[di].shape[-1]):
if corr == 'proton':
eff = np.log(y[di][:, i] / np.roll(y[di][:, i], -1))
eff_bs = np.log(y_bs[di][:, :, i] /
np.roll(y_bs[di][:, :, i], -1, axis=1))
else:
eff = y[di][:, i]
eff_bs = y_bs[di][:, :, i]
ax.errorbar(np.arange(nt),eff,yerr=eff_bs.std(axis=0),linestyle='None',\
color=clrs[i],marker='s',mfc='None',mec=clrs[i],label=lbl[i])
ax.axis(params[ens]['plt_range'][corr])
ax.set_xlabel(r'$t$', fontsize=20)
ax.set_ylabel(ylabel[corr], fontsize=20)
ax.legend(numpoints=1, fontsize=16, loc=2)
''' add Theano functions to plot fits '''
lam_all = mn.parameters
p_all = {k: mn.values[k] for k in lam_all}
l_ss, l_ps = lam_lst[0], lam_lst[1]
i_ss = [i for i, l in enumerate(lam_all) if l not in l_ss]
i_ps = [i for i, l in enumerate(lam_all) if l not in l_ps]
cov_param = np.array(mn.matrix(correlation=False))
cov_ss = np.delete(np.delete(cov_param, i_ss, axis=0), i_ss, axis=1)
cov_ps = np.delete(np.delete(cov_param, i_ps, axis=0), i_ps, axis=1)
t_p_i, t_p_f = params[ens]['t_min_max']['proton']
t_gA_i, t_gA_f = params[ens]['t_min_max']['gA']
t_gV_i, t_gV_f = params[ens]['t_min_max']['gV']
dt = 0.1
shift = int(params['tau'] / dt)
if corr == 'proton':
tp = np.arange(t_p_i, t_p_f + dt, dt)
elif corr == 'gA':
tp = np.arange(t_gA_i, t_gA_f + dt, dt)
elif corr == 'gV':
tp = np.arange(t_gV_i, t_gV_f + dt, dt)
''' define the theano scalars we need '''
t, tau, e0, zs0, zp0, de10, zs1, zp1 = Tn.dscalars('t', 'tau', 'e0', 'zs0',
'zp0', 'de10', 'zs1',
'zp1')
g00, g11, g10 = Tn.dscalars('g00', 'g11', 'g10')
ds0, dp0, ds1, dp1 = Tn.dscalars('ds0', 'dp0', 'ds1', 'dp1')
''' now construct the theano functions '''
parr_ss = dict()
for p in l_ss:
n = p.split('_')[-1]
if 'zs' in p:
parr_ss['src_' + n] = p_all[p]
parr_ss['snk_' + n] = p_all[p]
elif 'dA' in p or 'dV' in p:
parr_ss['d_' + n] = p_all[p]
elif 'gA' in p or 'gV' in p:
parr_ss['g_' + n] = p_all[p]
else:
parr_ss[p] = p_all[p]
parr_ps = dict()
for p in l_ps:
n = p.split('_')[-1]
if 'zs' in p:
parr_ps['src_' + n] = p_all[p]
elif 'zp' in p:
parr_ps['snk_' + n] = p_all[p]
elif 'dA' in p or 'dV' in p:
parr_ps['d_' + n] = p_all[p]
elif 'gA' in p or 'gV' in p:
parr_ps['g_' + n] = p_all[p]
else:
parr_ps[p] = p_all[p]
''' 2pt function '''
th_ss = zs0**2 * Tn.exp(-t * e0) + zs1**2 * Tn.exp(-t * (e0 + de10))
th_tau_ss = zs0**2 * Tn.exp(-(t + tau) * e0) + zs1**2 * Tn.exp(-(t + tau) *
(e0 + de10))
th_eff_ss = Tn.log(th_ss / th_tau_ss) / tau
d_th_eff_ss = Tn.grad(th_eff_ss, [e0, de10, zs0, zs1])
d_th_eff_ss_def = th.function([t, tau, e0, de10, zs0, zs1], d_th_eff_ss)
d_th_eff_ss_fun = lambda t,tau:\
d_th_eff_ss_def(t,tau,p_all['E_0'],p_all['dE_10'],\
p_all['zs_0'],p_all['zs_1'])
th_ps = zp0 * zs0 * Tn.exp(-t * e0) + zp1 * zs1 * Tn.exp(-t * (e0 + de10))
th_tau_ps = zp0 * zs0 * Tn.exp(-(t + tau) * e0) + zp1 * zs1 * Tn.exp(
-(t + tau) * (e0 + de10))
th_eff_ps = Tn.log(th_ps / th_tau_ps) / tau
d_th_eff_ps = Tn.grad(th_eff_ps, [e0, de10, zs0, zp0, zs1, zp1])
d_th_eff_ps_def = th.function([t, tau, e0, de10, zs0, zp0, zs1, zp1],
d_th_eff_ps)
d_th_eff_ps_fun = lambda t,tau:\
d_th_eff_ps_def(t,tau,p_all['E_0'],p_all['dE_10'],\
p_all['zs_0'],p_all['zp_0'],p_all['zs_1'],p_all['zp_1'])
''' FH gA function '''
g_00 = corr + '_00'
g_11 = corr + '_11'
g_10 = corr + '_10'
d_ss_0 = corr.replace('g', 'd') + 'ss_0'
d_ss_1 = corr.replace('g', 'd') + 'ss_1'
d_ps_0 = corr.replace('g', 'd') + 'ps_0'
d_ps_1 = corr.replace('g', 'd') + 'ps_1'
th_num_ss = (t - 1) * zs0**2 * Tn.exp(-t * e0) * g00
th_num_ss += (t - 1) * zs1**2 * Tn.exp(-t * (e0 + de10)) * g11
th_num_ss += ds0 * Tn.exp(-t * e0)
th_num_ss += ds1 * Tn.exp(-t * (e0 + de10))
th_num_ss += zs0*zs1*g10*(Tn.exp(-t*e0)*Tn.exp(-de10/2) - Tn.exp(-t*(e0+de10))*Tn.exp(de10/2))\
/ (Tn.exp(de10 / 2) - Tn.exp(-de10 / 2))
th_num_ss += zs1*zs0*g10*(Tn.exp(-t*(e0+de10))*Tn.exp(de10/2) - Tn.exp(-t*e0)*Tn.exp(-de10/2))\
/(Tn.exp(-de10 / 2) - Tn.exp(de10 / 2))
th_num_dt_ss = (t - 1 + tau) * zs0**2 * Tn.exp(-(t + tau) * e0) * g00
th_num_dt_ss += (t - 1 + tau) * zs1**2 * Tn.exp(-(t + tau) *
(e0 + de10)) * g11
th_num_dt_ss += ds0 * Tn.exp(-(t + tau) * e0)
th_num_dt_ss += ds1 * Tn.exp(-(t + tau) * (e0 + de10))
th_num_dt_ss += zs0*zs1*g10*\
(Tn.exp(-(t+tau)*e0)*Tn.exp(-de10/2) - Tn.exp(-(t+tau)*(e0+de10))*Tn.exp(de10/2))\
/ (Tn.exp(de10 / 2) - Tn.exp(-de10 / 2))
th_num_dt_ss += zs1*zs0*g10*\
(Tn.exp(-(t+tau)*(e0+de10))*Tn.exp(de10/2) - Tn.exp(-(t+tau)*e0)*Tn.exp(-de10/2))\
/(Tn.exp(-de10 / 2) - Tn.exp(de10 / 2))
th_fh_ss = (th_num_dt_ss / th_tau_ss - th_num_ss / th_ss) / tau
th_fh_grad_ss = Tn.grad(th_fh_ss,
[e0, de10, zs0, zs1, g00, g11, g10, ds0, ds1])
th_grad_ss_def = th.function(
[t, tau, e0, de10, zs0, zs1, g00, g11, g10, ds0, ds1], th_fh_grad_ss)
th_grad_ss_fun = lambda t,tau: \
th_grad_ss_def(t,tau,p_all['E_0'],p_all['dE_10'],p_all['zs_0'],p_all['zs_1'],\
p_all[g_00],p_all[g_11],p_all[g_10],\
p_all[d_ss_0],p_all[d_ss_1])
''' FH PS '''
th_num_ps = (t - 1) * zp0 * zs0 * Tn.exp(-t * e0) * g00
th_num_ps += (t - 1) * zp1 * zs1 * Tn.exp(-t * (e0 + de10)) * g11
th_num_ps += dp0 * Tn.exp(-t * e0)
th_num_ps += dp1 * Tn.exp(-t * (e0 + de10))
th_num_ps += zp0*zs1*g10*(Tn.exp(-t*e0)*Tn.exp(-de10/2) - Tn.exp(-t*(e0+de10))*Tn.exp(de10/2))\
/ (Tn.exp(de10 / 2) - Tn.exp(-de10 / 2))
th_num_ps += zp1*zs0*g10*(Tn.exp(-t*(e0+de10))*Tn.exp(de10/2) - Tn.exp(-t*e0)*Tn.exp(-de10/2))\
/(Tn.exp(-de10 / 2) - Tn.exp(de10 / 2))
th_num_dt_ps = (t - 1 + tau) * zp0 * zs0 * Tn.exp(-(t + tau) * e0) * g00
th_num_dt_ps += (t - 1 + tau) * zp1 * zs1 * Tn.exp(-(t + tau) *
(e0 + de10)) * g11
th_num_dt_ps += dp0 * Tn.exp(-(t + tau) * e0)
th_num_dt_ps += dp1 * Tn.exp(-(t + tau) * (e0 + de10))
th_num_dt_ps += zp0*zs1*g10*\
(Tn.exp(-(t+tau)*e0)*Tn.exp(-de10/2) - Tn.exp(-(t+tau)*(e0+de10))*Tn.exp(de10/2))\
/ (Tn.exp(de10 / 2) - Tn.exp(-de10 / 2))
th_num_dt_ps += zp1*zs0*g10*\
(Tn.exp(-(t+tau)*(e0+de10))*Tn.exp(de10/2) - Tn.exp(-(t+tau)*e0)*Tn.exp(-de10/2))\
/(Tn.exp(-de10 / 2) - Tn.exp(de10 / 2))
th_fh_ps = (th_num_dt_ps / th_tau_ps - th_num_ps / th_ps) / tau
th_fh_grad_ps = Tn.grad(
th_fh_ps, [e0, de10, zs0, zp0, zs1, zp1, g00, g11, g10, dp0, dp1])
th_grad_ps_def = th.function(
[t, tau, e0, de10, zs0, zp0, zs1, zp1, g00, g11, g10, dp0, dp1],
th_fh_grad_ps)
th_grad_ps_fun = lambda t,tau: \
th_grad_ps_def(t,tau,p_all['E_0'],p_all['dE_10'],\
p_all['zs_0'],p_all['zp_0'],p_all['zs_1'],p_all['zp_1'],\
p_all[g_00],p_all[g_11],p_all[g_10],\
p_all[d_ps_0],p_all[d_ps_1])
if corr == 'proton':
fit_ss = fit_fh.c2pt(tp, **parr_ss)
eff_ss = np.log(fit_ss / np.roll(fit_ss, -shift)) / (shift * dt)
eff_ss[-shift:] = eff_ss[-(shift + 1)]
fit_ps = fit_fh.c2pt(tp, **parr_ps)
eff_ps = np.log(fit_ps / np.roll(fit_ps, -shift)) / (shift * dt)
eff_ps[-shift:] = eff_ps[-(shift + 1)]
err_ss = np.zeros_like(tp)
err_ps = np.zeros_like(tp)
for i, t in enumerate(tp):
err_ss[i] = np.sqrt(np.dot(\
d_th_eff_ss_fun(t,dt),np.dot(cov_ss,d_th_eff_ss_fun(t,dt))))
err_ps[i] = np.sqrt(np.dot(\
d_th_eff_ps_fun(t,dt),np.dot(cov_ps,d_th_eff_ps_fun(t,dt))))
elif corr in ['gA', 'gV']:
fit_ss = fit_fh.fh_derivative(tp, shift * dt, **parr_ss)
eff_ss = fit_ss
eff_ss[-shift:] = eff_ss[-(shift + 1)]
fit_ps = fit_fh.fh_derivative(tp, shift * dt, **parr_ps)
eff_ps = fit_ps
eff_ps[-shift:] = eff_ps[-(shift + 1)]
err_ss = np.zeros_like(tp)
err_ps = np.zeros_like(tp)
for i, t in enumerate(tp):
err_ss[i] = np.sqrt(np.dot(\
th_grad_ss_fun(t,dt),np.dot(cov_ss,th_grad_ss_fun(t,dt))))
err_ps[i] = np.sqrt(np.dot(\
th_grad_ps_fun(t,dt),np.dot(cov_ps,th_grad_ps_fun(t,dt))))
ax.fill_between(tp,
eff_ss - err_ss,
eff_ss + err_ss,
color=clrs[0],
alpha=.3)
ax.fill_between(tp,
eff_ps - err_ps,
eff_ps + err_ps,
color=clrs[1],
alpha=.3)
def get_compiled_theano_functions(N_QUAD_PTS):
# resonance j and k
j,k = T.lscalars('jk')
s = (j-k) / k
# Planet masses: m1,m2
m1,m2 = T.dscalars(2)
Mstar = 1
eta0 = Mstar
eta1 = eta0+m1
eta2 =eta1+m2
mtilde1 = m1 * (eta0/eta1)
Mtilde1 = Mstar * (eta1/eta0)
mtilde2 = m2 * (eta1/eta2)
Mtilde2 = Mstar * (eta2/eta1)
eps = m1 * m2 / (mtilde1 + mtilde2) / Mstar
beta1 = mtilde1 / (mtilde1 + mtilde2)
beta2 = mtilde2 / (mtilde1 + mtilde2)
gamma = mtilde2/mtilde1
# Angle variable for averaging over
Q = T.dvector('Q')
# Dynamical variables:
dyvars = T.vector()
sigma1, sigma2, I1, I2, amd = [dyvars[i] for i in range(5)]
# Quadrature weights
quad_weights = T.dvector('w')
# Set lambda2=0
l2 = T.constant(0.)
l1 = -1 * k * Q
w1 = (1+s) * l2 - s * l1 - sigma1
w2 = (1+s) * l2 - s * l1 - sigma2
Gamma1 = I1
Gamma2 = I2
# Resonant semi-major axis ratio
alpha_res = ((j-k)/j)**(2/3) * ((Mstar + m1) / (Mstar+m2))**(1/3)
P0 = k * ( beta2 - beta1 * T.sqrt(alpha_res) ) / 2
P = P0 - k * (s+1/2) * amd
Ltot = beta1 * T.sqrt(alpha_res) + beta2 - amd
L1 = Ltot/2 - P / k - s * (I1 + I2)
L2 = Ltot/2 + P / k + (1 + s) * (I1 + I2)
a1 = (L1 / beta1 )**2 * eta0 / eta1
e1 = T.sqrt(1-(1-(Gamma1 / L1))**2)
a2 = (L2 / beta2 )**2 * eta1 / eta2
e2 = T.sqrt(1-(1-(Gamma2 / L2))**2)
Hkep = - eta1 * beta1 / (2 * a1) / eta0 - eta2 * beta2 / (2 * a2) / eta1
alpha = a1 / a2
ko = KeplerOp()
M1 = l1 - w1
M2 = l2 - w2
sinf1,cosf1 = ko( M1, e1 + T.zeros_like(M1) )
sinf2,cosf2 = ko( M2, e2 + T.zeros_like(M2) )
R = calc_DisturbingFunction_with_sinf_cosf(alpha,e1,e2,w1,w2,sinf1,cosf1,sinf2,cosf2)
Rav = R.dot(quad_weights)
Hpert = -eps * Rav / a2
Htot = Hkep + Hpert
######################
# Dissipative dynamics
######################
tau_alpha_0, K1, K2, p = T.dscalars(4)
sigma1dot_dis,sigma2dot_dis,I1dot_dis,I2dot_dis,amddot_dis = T.dscalars(5)
sigma1dot_dis,sigma2dot_dis = T.as_tensor(0.),T.as_tensor(0.)
# Define timescales
tau_e1 = tau_alpha_0 / K1
tau_e2 = tau_alpha_0 / K2
tau_a1_0 = -1 * tau_alpha_0 * (1+alpha_res * gamma)/ (alpha_res * gamma)
tau_a2_0 = -1 * alpha_res * gamma * tau_a1_0
tau_a1 = 1 / (1/tau_a1_0 + 2 * p * e1*e1 / tau_e1 )
tau_a2 = 1 / (1/tau_a2_0 + 2 * p * e2*e2 / tau_e2 )
# Time derivative of orbital elements
e1dot_dis = -1*e1 / tau_e1
e2dot_dis = -1*e2 / tau_e2
a1dot_dis = -1*a1 / tau_a1
a2dot_dis = -1*a2 / tau_a2
# Time derivatives of canonical variables
I1dot_dis = L1 * e1 * e1dot_dis / ( T.sqrt(1-e1*e1) ) - I1 / tau_a1 / 2
I2dot_dis = L2 * e2 * e2dot_dis / ( T.sqrt(1-e2*e2) ) - I2 / tau_a2 / 2
Pdot_dis = -1*k * ( L2 / tau_a2 - L1 / tau_a1) / 4 - k * (s + 1/2) * (I1dot_dis + I2dot_dis)
amddot_dis = Pdot_dis / T.grad(P,amd)
#####################################################
# Set parameters for compiling functions with Theano
#####################################################
# Get numerical quadrature nodes and weights
nodes,weights = np.polynomial.legendre.leggauss(N_QUAD_PTS)
# Rescale for integration interval from [-1,1] to [-pi,pi]
nodes = nodes * np.pi
weights = weights * 0.5
# 'givens' will fix some parameters of Theano functions compiled below
givens = [(Q,nodes),(quad_weights,weights)]
# 'ins' will set the inputs of Theano functions compiled below
# Note: 'extra_ins' will be passed as values of object attributes
# of the 'ResonanceEquations' class 'defined below
extra_ins = [m1,m2,j,k,tau_alpha_0,K1,K2,p]
ins = [dyvars] + extra_ins
# Define flows and jacobians.
# Conservative flow
gradHtot = T.grad(Htot,wrt=dyvars)
hessHtot = theano.gradient.hessian(Htot,wrt=dyvars)
Jtens = T.as_tensor(np.pad(getOmegaMatrix(2),(0,1),'constant'))
H_flow_vec = Jtens.dot(gradHtot)
H_flow_jac = Jtens.dot(hessHtot)
# Dissipative flow
dis_flow_vec = T.stack(sigma1dot_dis,sigma2dot_dis,I1dot_dis,I2dot_dis,amddot_dis)
dis_flow_jac = theano.gradient.jacobian(dis_flow_vec,dyvars)
# Extras
dis_timescales = [tau_a1_0,tau_a2_0,tau_e1,tau_e2]
orbels = [a1,e1,sigma1*k,a2,e2,sigma2*k]
##########################
# Compile Theano functions
##########################
if not DEBUG:
# Note that compiling can take a while
# so I've put a debugging switch here
# to skip evaluating these functions when
# desired.
Rav_fn = theano.function(
inputs=ins,
outputs=Rav,
givens=givens,
on_unused_input='ignore'
)
Hpert_av_fn = theano.function(
inputs=ins,
outputs=Hpert,
givens=givens,
on_unused_input='ignore'
)
Htot_fn = theano.function(
inputs=ins,
outputs=Htot,
givens=givens,
on_unused_input='ignore'
)
H_flow_vec_fn = theano.function(
inputs=ins,
outputs=H_flow_vec,
givens=givens,
on_unused_input='ignore'
)
H_flow_jac_fn = theano.function(
inputs=ins,
outputs=H_flow_jac,
givens=givens,
on_unused_input='ignore'
)
dis_flow_vec_fn = theano.function(
inputs=ins,
outputs=dis_flow_vec,
givens=givens,
on_unused_input='ignore'
)
dis_flow_jac_fn = theano.function(
inputs=ins,
outputs=dis_flow_jac,
givens=givens,
on_unused_input='ignore'
)
dis_timescales_fn =theano.function(
inputs=extra_ins,
outputs=dis_timescales,
givens=givens,
on_unused_input='ignore'
)
orbels_fn = theano.function(
inputs=ins,
outputs=orbels,
givens=givens,
on_unused_input='ignore'
)
else:
return [lambda x: x for _ in range(8)]
return Rav_fn,Hpert_av_fn,Htot_fn,H_flow_vec_fn,H_flow_jac_fn,dis_flow_vec_fn,dis_flow_jac_fn,dis_timescales_fn,orbels_fn
Q22 = matrix[y1, x1]
den12 = (x0-x1) / (y0-y1)
den21 = (x0-x1) / (y1-y0)
a0 = Q11 * x1*y1 / den12 + Q12 * x1*y0 / den21 + Q21 * x0*y1 / den21 + Q22 * x0*y0 / den12
a1 = Q11 * y1 / den21 + Q12 * y0 / den12 + Q21 * y1 / den12 + Q22 * y0 / den21
a2 = Q11 * x1 / den21 + Q12 * x1 / den12 + Q21 * x0 / den12 + Q22 * x0 / den21
a3 = Q11 / den12 + Q12 / den21 + Q21 / den21 + Q22 / den12
return a0, a1, a2, a3
# Theano operations
temp_vector, den_vector = tt.dvectors('temp_vector', 'den_vector')
temp_scalar, den_scalar = tt.dscalars('temp_scalar', 'den_scalar')
indexing_Qxx_ttfunction = function(inputs=[temp_vector, temp_scalar, den_vector, den_scalar],
outputs=indexing_Qxx_tt(temp_vector, temp_scalar, den_vector, den_scalar))
x, y = tt.dscalars('x', 'y')
x0_limit, y0_limit, x1_limit, y1_limit = tt.dscalars('x0_limit', 'y0_limit', 'x1_limit', 'y1_limit')
matrixGrid = tt.dmatrix('matrixGrid')
bilinearInterpolationttfunction = function(inputs=[x, y, matrixGrid, x0_limit, y0_limit, x1_limit, y1_limit],
outputs=biLinearInterpolation_v2_tt(x, y, matrixGrid, x0_limit, y0_limit, x1_limit, y1_limit))
biLinearInterpolation_CoeffsFunction_tt = function(inputs=[x, y, matrixGrid, x0_limit, y0_limit, x1_limit, y1_limit],
outputs=biLinearInterpolation_Coeffs_tt(x, y, matrixGrid, x0_limit, y0_limit, x1_limit, y1_limit))
# Numpy steps
idx_temp, idx_den = indexing_Qxx(temp_range, temp_true, den_range, den_true)
def _get_compiled_theano_functions():
# Planet masses: m1,m2
m1, m2 = T.dscalars(2)
mstar = 1
mu1 = m1 * mstar / (mstar + m1)
mu2 = m2 * mstar / (mstar + m2)
eta1 = mstar + m1
eta2 = mstar + m2
beta1 = mu1 * T.sqrt(eta1 / mstar) / (mu1 + mu2)
beta2 = mu2 * T.sqrt(eta2 / mstar) / (mu1 + mu2)
# Dynamical variables:
dyvars = T.vector()
l1, l2, y1, y2, Omega, L1, L2, x1, x2, Rtilde = [
dyvars[i] for i in range(10)
]
Gamma1 = 0.5 * (x1 * x1 + y1 * y1)
Gamma2 = 0.5 * (x2 * x2 + y2 * y2)
gamma1 = T.arctan2(y1, x1)
gamma2 = T.arctan2(y2, x2)
Cz = -1 * Rtilde
R1 = Gamma1
R2 = Gamma2
R = L1 + L2 - R1 - R2 - Cz
G1 = L1 - Gamma1
G2 = L2 - Gamma2
r2_by_r1 = (L2 - L1 - R2 + R1) / (L1 + L2 - R1 - R2 - R)
rho1 = 0.5 * R * (1 + r2_by_r1)
rho2 = 0.5 * R * (1 - r2_by_r1)
a1 = (L1 / beta1)**2
e1 = T.sqrt(1 - (1 - (Gamma1 / L1))**2)
a2 = (L2 / beta2)**2
e2 = T.sqrt(1 - (1 - (Gamma2 / L2))**2)
cos_inc1 = 1 - rho1 / G1
cos_inc2 = 1 - rho2 / G2
inc1 = T.arccos(cos_inc1)
inc2 = T.arccos(cos_inc2)
l1_r = l1 - Omega
l2_r = l2 - Omega
Omega1_r = T.constant(np.pi / 2) - Omega
Omega2_r = Omega1_r - T.constant(np.pi)
pomega1 = -1 * gamma1
pomega2 = -1 * gamma2
pomega1_r = pomega1 - Omega
pomega2_r = pomega2 - Omega
omega1 = pomega1_r - Omega1_r
omega2 = pomega2_r - Omega2_r
Hkep = -0.5 * T.sqrt(eta1) * beta1 / a1 - 0.5 * T.sqrt(eta2) * beta2 / a2
ko = KeplerOp()
M1 = l1_r - pomega1_r
M2 = l2_r - pomega2_r
sinf1, cosf1 = ko(M1, e1 + T.zeros_like(M1))
sinf2, cosf2 = ko(M2, e2 + T.zeros_like(M2))
#
n1 = T.sqrt(eta1 / mstar) * a1**(-3 / 2)
n2 = T.sqrt(eta2 / mstar) * a2**(-3 / 2)
Hint_dir, Hint_ind, r1, r2, v1, v2 = calc_Hint_components_sinf_cosf(
a1, a2, e1, e2, inc1, inc2, omega1, omega2, Omega1_r, Omega2_r, n1, n2,
sinf1, cosf1, sinf2, cosf2)
eps = m1 * m2 / (mu1 + mu2) / T.sqrt(mstar)
Hpert = (Hint_dir + Hint_ind / mstar)
Htot = Hkep + eps * Hpert
#####################################################
# Set parameters for compiling functions with Theano
#####################################################
# 'ins' will set the inputs of Theano functions compiled below
# Note: 'extra_ins' will be passed as values of object attributes
# of the 'ResonanceEquations' class 'defined below
extra_ins = [m1, m2]
givens = []
ins = [dyvars] + extra_ins
orbels = [
a1, e1, inc1, l1_r, pomega1_r, Omega1_r, a2, e2, inc2, l2_r, pomega2_r,
Omega2_r
]
orbels_dict = dict(
zip([
'a1', 'e1', 'inc1', 'l1', 'pomega1', 'Omega1', 'a2', 'e2', 'inc2',
'l2', 'pomega2', 'Omega2'
], orbels))
actions = [L1, L2, Gamma1, Gamma2, rho1, rho2]
actions_dict = dict(
zip(['L1', 'L2', 'Gamma1', 'Gamma2', 'Q1', 'Q2'], actions))
# Conservative flow
gradHtot = T.grad(Htot, wrt=dyvars)
hessHtot = theano.gradient.hessian(Htot, wrt=dyvars)
Jtens = T.as_tensor(_get_Omega_matrix(5))
H_flow_vec = Jtens.dot(gradHtot)
H_flow_jac = Jtens.dot(hessHtot)
##########################
# Compile Theano functions
##########################
orbels_fn = theano.function(inputs=ins,
outputs=orbels_dict,
givens=givens,
on_unused_input='ignore')
actions_fn = theano.function(inputs=ins,
outputs=actions_dict,
givens=givens,
on_unused_input='ignore')
rv1_fn = theano.function(inputs=ins,
outputs=r1 + v1,
givens=givens,
on_unused_input='ignore')
rv2_fn = theano.function(inputs=ins,
outputs=r2 + v2,
givens=givens,
on_unused_input='ignore')
Htot_fn = theano.function(inputs=ins,
outputs=Htot,
givens=givens,
on_unused_input='ignore')
Hpert_fn = theano.function(inputs=ins,
outputs=Hpert,
givens=givens,
on_unused_input='ignore')
Hpert_components_fn = theano.function(inputs=ins,
outputs=[Hint_dir, Hint_ind],
givens=givens,
on_unused_input='ignore')
H_flow_vec_fn = theano.function(inputs=ins,
outputs=H_flow_vec,
givens=givens,
on_unused_input='ignore')
H_flow_jac_fn = theano.function(inputs=ins,
outputs=H_flow_jac,
givens=givens,
on_unused_input='ignore')
return dict({
'orbital_elements': orbels_fn,
'actions': actions_fn,
'Hamiltonian': Htot_fn,
'Hpert': Hpert_fn,
'Hpert_components': Hpert_components_fn,
'Hamiltonian_flow': H_flow_vec_fn,
'Hamiltonian_flow_jacobian': H_flow_jac_fn,
'positions_and_velocities1': rv1_fn,
'positions_and_velocities2': rv2_fn
})
#!/usr/bin/env python
from theano import function
import theano.tensor as T
from theano.tensor import shared_randomstreams
import numpy as np
import numpy.random
from scipy.special import gammaincinv
from numpy.linalg import norm
# tensor stand-in for np.random.RandomState
rngT = shared_randomstreams.RandomStreams()
rng = numpy.random.RandomState()
# {{{ Fastfood Params }}}
n, d = T.dscalars('n', 'd')
# transform dimensions to be a power of 2
d0, n0 = d, n
l = T.ceil(T.log2(d)) # TODO cast to int
d = 2**l
k = T.ceil(n / d) # TODO cast to int
n = d * k
# generate parameter 'matrices'
B = rng.choice([-1, 1], size=(k, d))
G = rng.normal(size=(k, d), dtype=np.float64)
PI = np.array([rng.permutation(d) for _ in xrange(k)]).T
S = np.empty((k * d, 1), dtype=np.float64)
# generate scaling matrix, S
for i in xrange(k):
for j in xrange(d):
p1 = rng.uniform(size=d)
p2 = d / 2
"""
2016-07-04-15:52:19
arhik
"""
"""
The aim of this script is to show you how to set the default values of an
Argument
"""
import theano.tensor as T
from theano import In, function
x, y = T.dscalars('x', 'y')
z = x + y
f = function([x, In(y, value=1)], z)
print(f(23))
Computing multiple things
"""
# shorthand definition of vars
a, b = T.dmatrices('a', 'b')
diff = a - b
# NOTE: we do not need to use a, b again - diff is already a formed expression
abs_diff = abs(diff)
diff_squared = diff ** 2
f = theano.function([a, b], [diff, abs_diff, diff_squared])
print(f([[1, 1], [1, 1],], [[0, 1], [2, 3]])) # has 3 outputs
"""
Default values
"""
from theano import In
x, y = T.dscalars('x', 'y')
z = x + y
# NOTE: you can do even more complex stuff with In(), not only default values
# NOTE: default values always come AFTER the other inputs with no defaults
f = theano.function([x, In(y, value=1)], z)
print(f(33)) # 34
print(f(33, 2)) # 35
w = T.dscalar('w')
z2 = (x + y)*w
f2 = theano.function([x, In(y, value=1), In(w, value=2, name='w_by_name')], z2)
print(f2(33)) # 68
print(f2(33, 2)) # 70
print(f2(33, 0, 1)) # 33
# NOTE: the above w_by_name allows us to specify w's value at another position
# than that of the original w (just like in regular languages). w_by_name overrides
#!/usr/bin/env python
from theano import function
import theano.tensor as T
from theano.tensor import shared_randomstreams
import numpy as np
import numpy.random
from scipy.special import gammaincinv
from numpy.linalg import norm
# tensor stand-in for np.random.RandomState
rngT = shared_randomstreams.RandomStreams()
rng = numpy.random.RandomState()
# {{{ Fastfood Params }}}
n, d = T.dscalars('n', 'd')
# transform dimensions to be a power of 2
d0, n0 = d, n
l = T.ceil(T.log2(d)) # TODO cast to int
d = 2**l
k = T.ceil(n/d) # TODO cast to int
n = d*k
# generate parameter 'matrices'
B = rng.choice([-1, 1], size=(k, d))
G = rng.normal(size=(k, d), dtype=np.float64)
PI = np.array([rng.permutation(d) for _ in xrange(k)]).T
S = np.empty((k*d, 1), dtype=np.float64)
# generate scaling matrix, S
for i in xrange(k):
for j in xrange(d):
p1 = rng.uniform(size=d)
p2 = d/2
import numpy as np
from scipy import optimize
import theano
import theano.tensor as tt
# Read xlsx file
workbook = xlrd.open_workbook('../Data/Dataset.xlsx')
sheet = workbook.sheet_by_name('daily_average')
species = 'Pm_RN_S'#'Pm_RN_S' 'Am_RN_S' 'Nd_RN_S' 'Qc_RN_S' 'Qg_SN_S'
# Get data
keys = np.asarray(list(sheet.row_values(0)), dtype='str')
get_data = lambda lab: np.asarray(sheet.col_values(np.where(keys == lab)[0][0])[1:])
''' Priors '''
alpha, bs, c, g1, kxmax, p50, s0, Z = tt.dscalars('alpha', 'bs', 'c', 'g1', 'kxmax', 'p50', 's0', 'Z')
''' Data '''
Tod = get_data('T')
Iod = get_data('I')
Rfod = get_data('Rf')
Dod = get_data('D')
vnod = get_data(species)
''' Other parameters '''
ca = 400
Kc = 460
q = 0.3
R = 8.314
Jmax = 80
Vcmax = 30
def __init__(self):
# ------------------- #
# --- variables --- #
# ------------------- #
# focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p
focus = T.dscalar('focus') # focus length od camera
# variables of device state
xt, yt, zt = T.dscalars('xt', 'yt', 'zt') # position
ox, oy, oz = T.dscalars('ox', 'oy', 'oz') # orientation
# variables of landmark state
xi, yi, zi = T.dscalars('xi', 'yi', 'zi') # Device position at first observation
theta, phi = T.dscalars('theta', 'phi') # theta, phi (Azimuth & elevation of the ray at first observation)
p = T.dscalar('p') # d_inv (Inverse depth at first observation. 0.1 means depth is 10 meter.)
# ------------------- #
# --- observation --- #
# ------------------- #
# T.sin(ox)
# T.cos(ox)
# T.sin(oy)
# T.cos(oy)
# T.sin(oz)
# T.cos(oz)
# T.sin(theta)
# T.cos(theta)
# T.sin(phi)
# T.cos(phi)
# --- # h_ = [hx, hy, hz].T in the global coordinates --- #
h_x = p*(xi - xt) + T.cos(phi)*T.sin(theta)
h_y = p*(yi - yt) - T.sin(phi)
h_z = p*(zi - zt) + T.cos(phi)*T.cos(theta)
# ---- hx, hy, hz ---- #
hx = (T.cos(oy)*T.cos(oz)) * h_x + (T.cos(oy)*T.sin(oz)) * h_y + (-T.sin(oy)) * h_z
hy = (-T.cos(ox)*T.sin(oz)+T.sin(ox)*T.sin(oy)*T.cos(oz)) * h_x + (T.cos(ox)*T.cos(oz)+T.sin(ox)*T.sin(oy)*T.sin(oz)) * h_y + (T.sin(ox)*T.cos(oy)) * h_z
hz = (T.sin(ox)*T.sin(oz)+T.cos(ox)*T.sin(oy)*T.cos(oz)) * h_x + (-T.sin(ox)*T.cos(oz) + T.cos(ox)*T.sin(oy)*T.sin(oz)) * h_y + (T.cos(ox)*T.cos(oy)) * h_z
# --- h1, h2 --- #
h1 = - (focus * hx / hz)
h2 = focus * hy / hz
self.fh1 = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=h1)
self.fh2 = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=h2)
# partial derivative
dh1xt = T.grad(cost=h1, wrt=xt)
dh1yt = T.grad(cost=h1, wrt=yt)
dh1zt = T.grad(cost=h1, wrt=zt)
dh1ox = T.grad(cost=h1, wrt=ox)
dh1oy = T.grad(cost=h1, wrt=oy)
dh1oz = T.grad(cost=h1, wrt=oz)
dh1xi = T.grad(cost=h1, wrt=xi)
dh1yi = T.grad(cost=h1, wrt=yi)
dh1zi = T.grad(cost=h1, wrt=zi)
dh1theta = T.grad(cost=h1, wrt=theta)
dh1phi = T.grad(cost=h1, wrt=phi)
dh1p = T.grad(cost=h1, wrt=p)
dh2xt = T.grad(cost=h2, wrt=xt)
dh2yt = T.grad(cost=h2, wrt=yt)
dh2zt = T.grad(cost=h2, wrt=zt)
dh2ox = T.grad(cost=h2, wrt=ox)
dh2oy = T.grad(cost=h2, wrt=oy)
dh2oz = T.grad(cost=h2, wrt=oz)
dh2xi = T.grad(cost=h2, wrt=xi)
dh2yi = T.grad(cost=h2, wrt=yi)
dh2zi = T.grad(cost=h2, wrt=zi)
dh2theta = T.grad(cost=h2, wrt=theta)
dh2phi = T.grad(cost=h2, wrt=phi)
dh2p = T.grad(cost=h2, wrt=p)
# function of partial derivative
self.fdh1xt = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1xt)
self.fdh1yt = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1yt)
self.fdh1zt = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1zt)
self.fdh1ox = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1ox)
self.fdh1oy = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1oy)
self.fdh1oz = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1oz)
self.fdh1xi = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1xi)
self.fdh1yi = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1yi)
self.fdh1zi = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1zi)
self.fdh1theta = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1theta)
self.fdh1phi = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1phi)
self.fdh1p = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh1p)
self.fdh2xt = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2xt)
self.fdh2yt = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2yt)
self.fdh2zt = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2zt)
self.fdh2ox = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2ox)
self.fdh2oy = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2oy)
self.fdh2oz = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2oz)
self.fdh2xi = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2xi)
self.fdh2yi = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2yi)
self.fdh2zi = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2zi)
self.fdh2theta = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2theta)
self.fdh2phi = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2phi)
self.fdh2p = theano.function(inputs=[focus, xt, yt, zt, ox, oy, oz, xi, yi, zi, theta, phi, p], outputs=dh2p)
def __init__(self):
# Dictionary to store the functions for the fitting
self.emFlux_ttMethods = dict(H1r=self.H1_emisTensor,
He1r=self.He1_emisTensor,
He2r=self.He2_emisTensor,
metals=self.metal_emisTensor,
O2_7319A_b=self.corO2_7319_emisTensor)
# All input values scalars
emisRatio, cHbeta, flambda, abund, ftau, continuum, O2_abund, O3_abund, Te_high = tt.dscalars(
'emisRatio', 'cHbeta', 'flambda', 'abund', 'ftau', 'continuum',
'O2_abund', 'O3_abund', 'Te_high')
# Dictionary to store the compiled functions for the fitting
self.emFluxTensors = dict(
H1r=function(
inputs=[emisRatio, cHbeta, flambda, abund, ftau, continuum],
outputs=self.emFlux_ttMethods['H1r'](emisRatio, cHbeta,
flambda, abund, ftau,
continuum),
on_unused_input='ignore'),
He1r=function(
inputs=[emisRatio, cHbeta, flambda, abund, ftau, continuum],
outputs=self.emFlux_ttMethods['He1r'](emisRatio, cHbeta,
flambda, abund, ftau,
continuum),
on_unused_input='ignore'),
He2r=function(
inputs=[emisRatio, cHbeta, flambda, abund, ftau, continuum],
outputs=self.emFlux_ttMethods['He2r'](emisRatio, cHbeta,
flambda, abund, ftau,
continuum),
on_unused_input='ignore'),
metals=function(
inputs=[emisRatio, cHbeta, flambda, abund, ftau, continuum],
outputs=self.emFlux_ttMethods['metals'](emisRatio, cHbeta,
flambda, abund, ftau,
continuum),
on_unused_input='ignore'),
O2_7319A_b=function(inputs=[
emisRatio, cHbeta, flambda, O2_abund, O3_abund, Te_high
],
outputs=self.emFlux_ttMethods['O2_7319A_b'](
emisRatio, cHbeta, flambda, O2_abund,
O3_abund, Te_high),
on_unused_input='ignore'))