def test_r2_tilde(self):
self.test_r1_tilde()
self.test_F_xy()
r2_integrand = Func(lambda t, t1: self.r1_tilde(t1) *
(funcs_1d.exp(self.F_xy(0, t1=t1, t2=t)) - 1))
self.r2_tilde = Func(lambda t: self.r1_tilde(t) * Functional(
r2_integrand(t=t), x0=0, x1=t, du=True)())
self.assert_mathcad_python_equal(
self.pth('2_r2_tilde'),
[1e3 * a for a in self.r2_tilde(self.Time)])
def test_f3(self):
self.test_R1()
self.test_R2()
self.test_f3_prime()
f3_integrand = Func(
lambda x, y, t, t2: self.R1(t2, x=x, y=y, t=t) * self.f3_prime(
t2, x=x, y=y, t=t) - self.R2(t2, x=x, y=y, t=t))
self.f3 = Func(lambda x, y, t, T: Functional(
f3_integrand(x=x, y=y, t=t), x0=t, x1=T, du=True)())
self.assert_mathcad_python_equal(self.pth('2_f3'), [
1e6 * a
for a in self.f3(x=self.x0, y=self.y0, t=self.t0)(self.Time)
])
def test_f2(self):
self.test_R1()
self.test_r1_tilde()
self.f2 = Func(lambda x, y, t, T: 0.5 * pow(
Functional(Func(lambda x, y, t, t1: self.R1(t1, x=x, y=y, t=t) -
self.r1_tilde(t1))(x=x, y=y, t=t),
x0=t,
x1=T,
du=True)(), 2))
self.assert_mathcad_python_equal(self.pth('2_f2'), [
1e3 * a
for a in self.f2(self.Time, x=self.x0, y=self.y0, t=self.t0)
])
def test_f1(self):
self.test_R1()
self.test_r1_tilde()
self.f1 = Func(lambda x, y, t, T: Functional(Func(
lambda x, y, t, t1: self.R1(t1, x=x, y=y, t=t) - self.r1_tilde(t1))
(x=x, y=y, t=t),
x0=t,
x1=T,
du=True)())
self.assert_mathcad_python_equal(
self.pth('2_f1'),
self.f1(self.Time, x=self.x0, y=self.y0, t=self.t0))
def test_f3_prime(self):
self.test_R1()
self.test_F_xy()
self.f3_prime = Func(lambda x, y, t, t2: Functional(Func(
lambda x, y, t, t1, t2: self.R1(t1, x=x, y=y, t=t) * (funcs_1d.exp(
self.F_xy(t1, t=t, t2=t2)) - 1))(x=x, y=y, t=t, t2=t2),
x0=t,
x1=t2,
du=True)())
self.assert_mathcad_python_equal(self.pth('2_f3_prime'), [
a * 1e3
for a in self.f3_prime(x=self.x0, y=self.y0, t=self.t0)(self.Time)
])
def test_sigma_xy(self):
self.sigma_xy = Func(
lambda t, v: ((self.rho * self.sigma_x * self.sigma_y) /
(self.alpha_x + self.alpha_y)) *
(1 - funcs_1d.exp(-(self.alpha_x + self.alpha_y) * (v - t))))
self.assert_mathcad_python_equal(self.pth('2_sigma_xy'),
self.sigma_xy(self.Time, t=self.t0))
def test_F1(self):
self.test_f1()
self.test_D()
self.F1 = Func(lambda x, y, t, T: self.D(t, v=T) *
(1 - self.f1(t, x=x, y=y, T=T)))
self.assert_mathcad_python_equal(
self.pth('2_FCapital1'),
self.F1(self.Time, x=self.x0, y=self.y0, t=self.t0))
def test_R2(self):
self.test_r2_tilde()
self.test_sigma_star()
self.test_phi_y()
self.test_phi_x()
self.R2 = Func(lambda x, y, t, t1: self.r2_tilde(t1) * funcs_1d.exp(
self.phi_x(t, v=t1) * x + self.phi_y(t, v=t1) * y - 0.5 * self.
sigma_star(t, u=t1)))
self.assert_mathcad_python_equal(
self.pth('2_R2'),
self.R2(self.Time, t=self.t0, x=self.x0, y=self.y0))
def test_sigma_star(self):
self.test_phi_x()
self.test_phi_y()
self.test_sigma_xx()
self.test_sigma_yy()
self.test_sigma_xy()
self.sigma_star = Func(
lambda t, u: pow(self.phi_x(t, v=u), 2) * self.sigma_xx(0, v=t) + 2
* self.phi_x(t, v=u) * self.phi_y(t, v=u) * self.sigma_xy(
0, v=t) + pow(self.phi_y(t, v=u), 2) * self.sigma_yy(0, v=t))
self.assert_mathcad_python_equal(self.pth('2_sigma_star'),
self.sigma_star(self.Time, t=self.t0))
def test_F_xy(self):
self.test_phi_x()
self.test_phi_y()
self.test_sigma_xx()
self.test_sigma_xy()
self.test_sigma_yy()
self.test_sigma_yy()
self.test_sigma_star()
self.F_xy = Func(
lambda t, t1, t2: self.phi_x(t1, v=t2) * self.sigma_xx(t, v=t1) +
(self.phi_x(t1, v=t2) + self.phi_y(t1, v=t2)) * self.sigma_xy(
t, v=t1) + self.phi_y(t1, v=t2) * self.sigma_yy(t, v=t1))
self.assert_mathcad_python_equal(
self.pth('2_Fxy'), self.F_xy(self.Time, t=self.t0, t2=1.5))
def test_sigma_yy(self):
self.sigma_yy = Func(lambda t, v: (pow(self.sigma_y, 2)) /
(2 * self.alpha_y) *
(1 - funcs_1d.exp(-2 * self.alpha_y * (v - t))))
self.assert_mathcad_python_equal(self.pth('2_sigma_yy'),
self.sigma_yy(self.Time, t=self.t0))
def test_phi_y(self):
self.phi_y = Func(lambda t, v: funcs_1d.exp(-self.alpha_y * (v - t)))
self.assert_mathcad_python_equal(self.pth('2_phi_y'),
self.phi_y(self.Time, t=self.t0))
def test_D(self):
self.test_delta()
self.D = Func(lambda t, v: funcs_1d.exp(-self.delta(t, v=v)))
self.assert_mathcad_python_equal(self.pth('2D0'),
self.D(self.Time, t=self.t0))
def test_delta(self):
self.delta = Func(
lambda t, v: Functional(self.r_bar, x0=t, x1=v, du=True)())
self.assert_mathcad_python_equal(self.pth('2delta_t_T'),
self.delta(self.Time, t=self.t0))
def test_r1_tilde(self):
self.r1_tilde = Func(lambda t: self.r_bar - self.s)
self.assert_mathcad_python_equal(self.pth('2_r1_tilde'),
self.r1_tilde(self.Time))