def test_integralKernelMinus(self):
n = 10
m = 10
listn = np.zeros(n, dtype=object)
vals = np.zeros((n, m), dtype=object)
for i in range(n):
Plus0 = np.array(CFS_Action.integralKernelMinus(i + 1)).reshape(
2, 2)
print(Plus0)
#Plus1 = np.array(CFS_Action.integralKernelMinus(i +1), dtype = object).reshape(2,2)
listn[i] = si.lambdify(r[0], [
sy.simplify(-2 * si.cos(r[0] / 2) * CFS_Action.prefactor(i) *
JacPol(si.Rational(1, 2), si.Rational(3, 2), i) +
Plus0[0, 0] + Plus0[1, 1])
],
real=False)
#print( sy.simplify(JacPol(1/2,3/2, i)),'=?=', sy.jacobi(i, 1/2,3/2, r[0]))
#listn[i] =si.lambdify(r[0], [sy.simplify(JacPol(1/2,3/2, i)) - sy.jacobi(i, 1/2,3/2, r[0])])
for i in range(n):
for j in range(m):
vals[i, j] = listn[i](j)
print(vals)
np.testing.assert_almost_equal(vals, np.zeros((n, m)), 10)
def test_integralKernelPlus(self):
'''
The idea in this test is to use the fact, that i know that if i
add the diagonal terms, the imaginary parts cancel each other out and
the real terms add up. That's the idea for this and the following 3 tests.
Also this test is the most updated version. Here i do not use lambdify,
because of simplify, the terms really cancel to zero. Befor that i didn't
use simplify, so i had to use lambdify. I'm keeping the other tests the
way they are, so that i just can check how i did this. There were some
problems, i had to figure out and in future i maybe need to look it up.:)
'''
n = 10
m = 10
listn = np.zeros(n, dtype=object)
vals = np.zeros((n, m), dtype=object)
for i in range(n):
Plus0 = np.array(CFS_Action.integralKernelPlus(
i + 1)) #, dtype = object).reshape(2,2)
print(Plus0)
listn[i] = sy.simplify(
-2 * si.cos(r[0] / 2) * CFS_Action.prefactor(i) *
JacPol(si.Rational(1, 2), si.Rational(3, 2), i) + Plus0[0, 0] +
Plus0[1, 1])
for i in range(n):
vals[i] = listn[i]
print(vals)
np.testing.assert_array_equal(listn, np.zeros(n), 10)
def integralKernelMinus(self, n):
n = n - 1
lala1 = sy.jacobi(n, si.Rational(1, 2), si.Rational(3, 2), r[0])
lala2 = sy.jacobi(n, si.Rational(3, 2), si.Rational(1, 2), r[0])
return self.prefactor(n) * (si.cos(r[0] / 2) * lala1 * ident +
I * si.sin(r[0] / 2) * lala2 * sigma3)
def test_Lagrangian(self):
"""
This Test only works for N = 1, Rho=1.
"""
n = 10
LagVals = np.zeros(n)
for i in range(n):
KK = si.Rational(i, 1)
CFS_Action.K_Liste[0] = KK
Lag = CFS_Action.lagrangian_without_bound_constr()
delta = 1 - KK**2 + (1 + KK**2) * sy.cos(r[0])
Res = si.pi**(-8) * 8 * (1 + KK**2) * si.cos(r[0] / 2)**2 * delta
LagVals[i] = sy.simplify(Res - Lag)
np.testing.assert_array_equal(LagVals, np.zeros(n))
Taking everything together, our code is:
.. literalinclude:: ../examples/noisy_lorenz.py
:dedent: 1
:lines: 75-100
"""
if __name__ == "__main__":
from jitcsde import y, jitcsde
import numpy
import symengine
ρ = 28
σ = 10
β = symengine.Rational(8, 3)
p = 0.1
f = [σ * (y(1) - y(0)), y(0) * (ρ - y(2)) - y(1), y(0) * y(1) - β * y(2)]
g = [p * y(i) for i in range(3)]
SDE = jitcsde(f, g)
initial_state = numpy.random.random(3)
SDE.set_initial_value(initial_state, 0.0)
data = []
for time in numpy.arange(0.0, 100.0, 0.01):
data.append(SDE.integrate(time))
numpy.savetxt("timeseries.dat", data)
def lagrangian_without_bound_constr(self):
sub1 = self.closedChain()
return np.trace(np.dot(
sub1, sub1)) - si.Rational(1, 4) * np.trace(sub1) * np.trace(sub1)